On the Connexion of the Physical Sciences (part 2 of 4)

Introduction

SCIENCE, regarded as the pursuit of truth, must ever afford occupation of consummate interest, and subject of elevated meditation. The contemplation of the works of creation elevates the mind to the admiration of whatever is great and noble; accomplishing the object of all study, which, in the eloquent language of Sir James Mackintosh, “is to inspire the love of truth, of wisdom, of beauty—especially of goodness, the highest beauty—and of that supreme and eternal Mind, which contains all truth and wisdom, all beauty and goodness. By the love or delightful contemplation and pursuit of these transcendent aims, for their own sake only, the mind of man is raised from low and perishable objects, and prepared for those high destinies which are appointed for all those who are capable of them.”

Astronomy affords the most extensive example of the connection of the physical sciences. In it are combined the sciences of number and quantity, of rest and motion. In it we perceive the operation of a force which is mixed up with everything that exists in the heavens or on earth; which pervades every atom, rules the motions of animate and inanimate beings, and is as sensible in the descent of a rain-drop as in the falls of Niagara; in the weight of the air, as in the periods of the moon. Gravitation not only binds satellites to their planet, and planets to the sun, but it connects sun with sun throughout the wide extent of creation, and is the cause of the disturbances, as well as of the order of nature; since every tremor it excites in any one planet is immediately transmitted to the farthest limits of the system, in oscillations which correspond in their periods with the cause producing them, like sympathetic notes in music, or vibrations from the deep tones of an organ.

The heavens afford the most sublime subject of study which can be derived from science. The magnitude and splendour of the objects, the inconceivable rapidity with which they move, and the enormous distances between them, impress the mind with some notion of the energy that maintains them in their motions, with a durability to which we can see no limit. Equally conspicuous is the goodness of the great First Cause, in having endowed man with faculties, by which he can not only appreciate the magnificence of His works, but trace, with precision, the operation of His laws, use the globe he inhabits as a base wherewith to measure the magnitude and distance of the sun and planets, and make the diameter (Note 1) of the earth’s orbit the first step of a scale by which he may ascend to the starry firmament. Such pursuits, while they ennoble the mind, at the same time inculcate humility, by showing that there is a barrier which no energy, mental or physical, can ever enable us to pass: that, however profoundly we may penetrate the depths of space, there still remain innumerable systems, compared with which, those apparently so vast must dwindle into insignificance, or even become invisible; and that not only man, but the globe he inhabits—nay, the whole system of which it forms so small a part—might be annihilated, and its extinction be unperceived in the immensity of creation.

A complete acquaintance with physical astronomy can be attained by those only who are well versed in the higher branches of mathematical and mechanical science (N. 2), and they alone can appreciate the extreme beauty of the results, and of the means by which these results are obtained. It is nevertheless true, that a sufficient skill in analysis (N. 3) to follow the general outline—to see the mutual dependence of the different parts of the system, and to comprehend by what means the most extraordinary conclusions have been arrived at,—is within the reach of many who shrink from the task, appalled by difficulties, not more formidable than those incident to the study of the elements of every branch of knowledge. There is a wide distinction between the degree of mathematical acquirement necessary for making discoveries, and that which is requisite for understanding what others have done.

Our knowledge of external objects is founded upon experience, which furnishes facts; the comparison of these facts establishes relations, from which the belief that like causes will produce like effects leads to general laws. Thus, experience teaches that bodies fall at the surface of the earth with an accelerated velocity, and with a force proportional to their masses. By comparison, Newton proved that the force which occasions the fall of bodies at the earth’s surface is identical with that which retains the moon in her orbit; and he concluded, that, as the moon is kept in her orbit by the attraction of the earth, so the planets might be retained in their orbits by the attraction of the sun. By such steps he was led to the discovery of one of those powers with which the Creator has ordained that matter should reciprocally act upon matter.

Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens: and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations (N. 4) of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter experience—changes which require millions of years for their accomplishment.

The accumulated efforts of astronomers, from the earliest dawn of civilization, have been necessary to establish the mechanical theory of astronomy. The courses of the planets have been observed for ages, with a degree of perseverance that is astonishing, if we consider the imperfection and even the want of instruments. The real motions of the earth have been separated from the apparent motions of the planets; the laws of the planetary revolutions have been discovered; and the discovery of these laws has led to the knowledge of the gravitation (N. 5) of matter. On the other hand, descending from the principle of gravitation, every motion in the solar system has been so completely explained, that the laws of any astronomical phenomena that may hereafter occur are already determined.

SECTION I.

Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation retains the Moon in her Orbit—The Heavenly Bodies move in Conic Sections—Gravitation Proportional to Mass—Gravitation of the Particles of Matter—Figure of the Planets—How it affects the Motions of their Satellites—Rotation and Translation impressed by the same Impulse—Motion of the Sun and Solar System.

IT has been proved by Newton, that a particle of matter (N. 6) placed without the surface of a hollow sphere (N. 7) is attracted by it in the same manner as if the mass of the hollow sphere, or the whole matter it contains, were collected into one dense particle in its centre. The same is therefore true of a solid sphere, which may be supposed to consist of an infinite number of concentric hollow spheres (N. 8). This, however, is not the case with a spheroid (N. 9); but the celestial bodies are so nearly spherical, and at such remote distances from one another, that they attract and are attracted as if each were condensed into a single particle situate in its centre of gravity (N. 10)—a circumstance which greatly facilitates the investigation of their motions.

Newton has shown that the force which retains the moon in her orbit is the same with that which causes heavy substances to fall at the surface of the earth. If the earth were a sphere, and at rest, a body would be equally attracted, that is, it would have the same weight at every point of its surface, because the surface of a sphere is everywhere equally distant from its centre. But, as our planet is flattened at the poles (N. 11), and bulges at the equator, the weight of the same body gradually decreases from the poles, where it is greatest, to the equator, where it is least. There is, however, a certain mean (N. 12) latitude (N. 13), or part of the earth intermediate between the pole and the equator, where the attraction of the earth on bodies at its surface is the same as if it were a sphere; and experience shows that bodies there fall through 16·0697 feet in a second. The mean distance (N. 14) of the moon from the earth is about sixty times the mean radius (N. 15) of the earth. When the number 16·0697 is diminished in the ratio (N. 16) of 1 to 3600, which is the square of the moon’s distance (N. 17) from the earth’s centre, estimated in terrestrial radii, it is found to be exactly the space the moon would fall through in the first second of her descent to the earth, were she not prevented by the centrifugal force (N. 18) arising from the velocity with which she moves in her orbit. The moon is thus retained in her orbit by a force having the same origin, and regulated by the same law, with that which causes a stone to fall at the earth’s surface. The earth may, therefore, be regarded as the centre of a force which extends to the moon; and, as experience shows that the action and reaction of matter are equal and contrary (N. 19), the moon must attract the earth with an equal and contrary force.

Newton also ascertained that a body projected (N. 20) in space (N. 21) will move in a conic section (N. 22), if attracted by a force proceeding from a fixed point, with an intensity inversely as the square of the distance (N. 23); but that any deviation from that law will cause it to move in a curve of a different nature. Kepler found, by direct observation, that the planets describe ellipses (N. 24), or oval paths, round the sun. Later observations show that comets also move in conic sections. It consequently follows that the sun attracts all the planets and comets inversely as the square of their distances from its centre; the sun, therefore, is the centre of a force extending indefinitely in space, and including all the bodies of the system in its action.

Kepler also deduced from observation that the squares of the periodic times (N. 25) of the planets, or the times of their revolutions round the sun, are proportional to the cubes of their mean distances from its centre (N. 26). Hence the intensity of gravitation of all the bodies towards the sun is the same at equal distances. Consequently, gravitation is proportional to the masses (N. 27); for, if the planets and comets were at equal distances from the sun, and left to the effects of gravity, they would arrive at his surface at the same time (N. 28). The satellites also gravitate to their primaries (N. 29) according to the same law that their primaries do to the sun. Thus, by the law of action and reaction, each body is itself the centre of an attractive force extending indefinitely in space, causing all the mutual disturbances which render the celestial motions so complicated, and their investigation so difficult.

The gravitation of matter directed to a centre, and attracting directly as the mass and inversely as the square of the distance, does not belong to it when considered in mass only; particle acts on particle according to the same law when at sensible distances from each other. If the sun acted on the centre of the earth, without attracting each of its particles, the tides would be very much greater than they now are, and would also, in other respects, be very different. The gravitation of the earth to the sun results from the gravitation of all its particles, which, in their turn, attract the sun in the ratio of their respective masses. There is a reciprocal action likewise between the earth and every particle at its surface. The earth and a feather mutually attract each other in the proportion of the mass of the earth to the mass of the feather. Were this not the case, and were any portion of the earth, however small, to attract another portion, and not be itself attracted, the centre of gravity of the earth would be moved in space by this action, which is impossible.

The forms of the planets result from the reciprocal attraction of their component particles. A detached fluid mass, if at rest, would assume the form of a sphere, from the reciprocal attraction of its particles. But if the mass revolve about an axis, it becomes flattened at the poles and bulges at the equator (N. 11), in consequence of the centrifugal force arising from the velocity of rotation (N. 30); for the centrifugal force diminishes the gravity of the particles at the equator, and equilibrium can only exist where these two forces are balanced by an increase of gravity. Therefore, as the attractive force is the same on all particles at equal distances from the centre of a sphere, the equatorial particles would recede from the centre, till their increase in number balance the centrifugal force by their attraction. Consequently, the sphere would become an oblate or flattened spheroid, and a fluid, partially or entirely covering a solid, as the ocean and atmosphere cover the earth, must assume that form in order to remain in equilibrio. The surface of the sea is, therefore, spheroidal, and the surface of the earth only deviates from that figure where it rises above or sinks below the level of the sea. But the deviation is so small, that it is unimportant when compared with the magnitude of the earth; for the mighty chain of the Andes, and the yet more lofty Himalaya, bear about the same proportion to the earth that a grain of sand does to a globe three feet in diameter. Such is the form of the earth and planets. The compression (N. 31) or flattening at their poles is, however, so small, that even Jupiter, whose rotation is the most rapid, and therefore the most elliptical of the planets, may, from his great distance, be regarded as spherical. Although the planets attract each other as if they were spheres, on account of their distances, yet the satellites (N. 32) are near enough to be sensibly affected in their motions by the forms of their primaries. The moon, for example, is so near the earth, that the reciprocal attraction between each of her particles, and each of the particles in the prominent mass at the terrestrial equator, occasions considerable disturbances in the motions of both bodies; for the action of the moon on the matter at the earth’s equator produces a nutation (N. 33) in the axis (N. 34) of rotation, and the reaction of that matter on the moon is the cause of a corresponding nutation in the lunar orbit (N. 35).

If a sphere at rest in space receive an impulse passing through its centre of gravity, all its parts will move with an equal velocity in a straight line; but, if the impulse does not pass through the centre of gravity, its particles, having unequal velocities, will have a rotatory or revolving motion, at the same time that it is translated (N. 36) in space. These motions are independent of one another; so that a contrary impulse, passing through its centre of gravity, will impede its progress, without interfering with its rotation. The sun rotates about an axis, and modern observations show that an impulse in a contrary direction has not been given to his centre of gravity, for he moves in space, accompanied by all those bodies which compose the solar system—a circumstance which in no way interferes with their relative motions; for, in consequence of the principle that force is proportional to velocity (N. 37), the reciprocal attractions of a system remain the same whether its centre of gravity be at rest, or moving uniformly in space. It is computed that, had the earth received its motion from a single impulse, that impulse must have passed through a point about twenty-five miles from its centre.

Since the motions of rotation and translation of the planets are independent of each other, though probably communicated by the same impulse, they form separate subjects of investigation.

SECTION II.

Elliptical Motion—Mean and True Motion—Equinoctial—Ecliptic—Equinoxes—Mean and True Longitude—Equation of Centre—Inclination of the Orbits of Planets—Celestial Latitude—Nodes—Elements of an Orbit—Undisturbed or Elliptical Orbits—Great Inclination of the Orbits of the New Planets—Universal Gravitation the Cause of Perturbations in the Motions of the Heavenly Bodies—Problem of the Three Bodies—Stability of Solar System depends upon the Primitive Momentum of the Bodies.

A PLANET moves in its elliptical orbit with a velocity varying every instant, in consequence of two forces, one tending to the centre of the sun, and the other in the direction of a tangent (N. 38) to its orbit, arising from the primitive impulse given at the time when it was launched into space. Should the force in the tangent cease, the planet would fall to the sun by its gravity. Were the sun not to attract it, the planet would fly off in the tangent. Thus, when the planet is at the point of its orbit farthest from the sun, his action overcomes the planet’s velocity, and brings it towards him with such an accelerated motion, that at last it overcomes the sun’s attraction, and, shooting past him, gradually decreases in velocity until it arrives at the most distant point, where the sun’s attraction again prevails (N. 39). In this motion the radii vectores (N. 40), or imaginary lines joining the centres of the sun and the planets, pass over equal areas or spaces in equal times (N. 41).

The mean distance of a planet from the sun is equal to half the major axis (N. 42) of its orbit: if, therefore, the planet described a circle (N. 43) round the sun at its mean distance, the motion would be uniform, and the periodic time unaltered, because the planet would arrive at the extremities of the major axis at the same instant, and would have the same velocity, whether it moved in the circular or elliptical orbit, since the curves coincide in these points. But in every other part the elliptical, or true motion (N. 44), would either be faster or slower than the circular or mean motion (N. 45). As it is necessary to have some fixed point in the heavens from whence to estimate these motions, the vernal equinox (N. 46) at a given epoch has been chosen. The equinoctial, which is a great circle traced in the starry heavens by the imaginary extension of the plane of the terrestrial equator, is intersected by the ecliptic, or apparent path of the sun, in two points diametrically opposite to one another, called the vernal and autumnal equinoxes. The vernal equinox is the point through which the sun passes in going from the southern to the northern hemisphere; and the autumnal, that in which he crosses from the northern to the southern. The mean or circular motion of a body, estimated from the vernal equinox, is its mean longitude; and its elliptical, or true motion, reckoned from that point, is its true longitude (N. 47): both being estimated from west to east, the direction in which the bodies move. The difference between the two is called the equation of the centre (N. 48); which consequently vanishes at the apsides (N. 49), or extremities of the major axis, and is at its maximum ninety degrees (N. 50) distant from these points, or in quadratures (N. 51), where it measures the excentricity (N. 52) of the orbit; so that the place of the planet in its elliptical orbit is obtained by adding or subtracting the equation of the centre to or from its mean longitude.

The orbits of the principal planets have a very small obliquity or inclination (N. 53) to the plane of the ecliptic in which the earth moves; and, on that account, astronomers refer their motions to this plane at a given epoch as a known and fixed position. The angular distance of a planet from the plane of the ecliptic is its latitude (N. 54), which is south or north according as the planet is south or north of that plane. When the planet is in the plane of the ecliptic, its latitude is zero; it is then said to be in its nodes (N. 55). The ascending node is that point in the ecliptic through which the planet passes in going from the southern to the northern hemisphere. The descending node is a corresponding point in the plane of the ecliptic diametrically opposite to the other, through which the planet descends in going from the northern to the southern hemisphere. The longitude and latitude of a planet cannot be obtained by direct observation, but are deduced from observations made at the surface of the earth by a very simple computation. These two quantities, however, will not give the place of a planet in space. Its distance from the sun (N. 56) must also be known; and, for the complete determination of its elliptical motion, the nature and position of its orbit must be ascertained by observation. This depends upon seven quantities, called the elements of the orbit (N. 57). These are, the length of the major axis, and the excentricity, which determine the form of the orbit; the longitude of the planet when at its least distance from the sun, called the longitude of the perihelion; the inclination of the orbit to the plane of the ecliptic, and the longitude of its ascending node: these give the position of the orbit in space; but the periodic time, and the longitude of the planet at a given instant, called the longitude of the epoch, are necessary for finding the place of the body in its orbit at all times. A perfect knowledge of these seven elements is requisite for ascertaining all the circumstances of undisturbed elliptical motion. By such means it is found that the paths of the planets, when their mutual disturbances are omitted, are ellipses nearly approaching to circles, whose planes, slightly inclined to the ecliptic, cut it in straight lines, passing through the centre of the sun (N. 58). The orbits of the recently-discovered planets deviate more from the ecliptic than those of the ancient planets: that of Pallas, for instance, has an inclination of 34° 42ʹ 29·8ʺ to it; on which account it is more difficult to determine their motions.

Were the planets attracted by the sun only, they would always move in ellipses, invariable in form and position; and because his action is proportional to his mass, which is much larger than that of all the planets put together, the elliptical is the nearest approximation to their true motions. The true motions of the planets are extremely complicated, in consequence of their mutual attraction, so that they do not move in any known or symmetrical curve, but in paths now approaching to, now receding from, the elliptical form; and their radii vectores do not describe areas or spaces exactly proportional to the time, so that the areas become a test of disturbing forces.

To determine the motion of each body, when disturbed by all the rest, is beyond the power of analysis. It is therefore necessary to estimate the disturbing action of one planet at a time, whence the celebrated problem of the three bodies, originally applied to the moon, the earth, and the sun—namely, the masses being given of three bodies projected from three given points, with velocities given both in quantity and direction; and supposing the bodies to gravitate to one another with forces that are directly as their masses, and inversely as the squares of the distances, to find the lines described by these bodies, and their positions at any given instant; or, in other words, to determine the path of a celestial body when attracted by a second body, and disturbed in its motion round the second body by a third—a problem equally applicable to planets, satellites, and comets.

By this problem the motions of translation of the celestial bodies are determined. It is an extremely difficult one, and would be infinitely more so if the disturbing action were not very small when compared with the central force; that is, if the action of the planets on one another were not very small when compared with that of the sun. As the disturbing influence of each body may be found separately, it is assumed that the action of the whole system, in disturbing any one planet, is equal to the sum of all the particular disturbances it experiences, on the general mechanical principle, that the sum of any number of small oscillations is nearly equal to their simultaneous and joint effect.

On account of the reciprocal action of matter, the stability of the system depends upon the intensity of the primitive momentum (N. 59) of the planets, and the ratio of their masses to that of the sun; for the nature of the conic sections in which the celestial bodies move depends upon the velocity with which they were first propelled in space. Had that velocity been such as to make the planets move in orbits of unstable equilibrium (N. 60), their mutual attractions might have changed them into parabolas, or even hyperbolas (N. 22); so that the earth and planets might, ages ago, have been sweeping far from our sun through the abyss of space. But as the orbits differ very little from circles, the momentum of the planets, when projected, must have been exactly sufficient to ensure the permanency and stability of the system. Besides, the mass of the sun is vastly greater than that of any planet; and as their inequalities bear the same ratio to their elliptical motions that their masses do to that of the sun, their mutual disturbances only increase or diminish the excentricities of their orbits by very minute quantities; consequently the magnitude of the sun’s mass is the principal cause of the stability of the system. There is not in the physical world a more splendid example of the adaptation of means to the accomplishment of an end than is exhibited in the nice adjustment of these forces, at once the cause of the variety and of the order of Nature.

SECTION III.

Perturbations, Periodic and Secular—Disturbing Action equivalent to three Partial Forces—Tangential Force the cause of the Periodic Inequalities in Longitude, and Secular Inequalities in the Form and Position of the Orbit in its own Plane—Radial Force the cause of Variations in the Planet’s Distance from the Sun—It combines with the Tangential Force to produce the Secular Variations in the Form and Position of the Orbit in its own Plane—Perpendicular Force the cause of Periodic Perturbations in Latitude, and Secular Variations in the Position of the Orbit with regard to the Plane of the Ecliptic—Mean Motion and Major Axis Invariable—Stability of System—Effects of a Resisting Medium—Invariable Plane of the Solar System and of the Universe—Great Inequality of Jupiter and Saturn.

THE planets are subject to disturbances of two kinds, both resulting from the constant operation of their reciprocal attraction: one kind, depending upon their positions with regard to each other, begins from zero, increases to a maximum, decreases, and becomes zero again, when the planets return to the same relative positions. In consequence of these, the disturbed planet is sometimes drawn away from the sun, sometimes brought nearer to him: sometimes it is accelerated in its motion, and sometimes retarded. At one time it is drawn above the plane of its orbit, at another time below it, according to the position of the disturbing body. All such changes, being accomplished in short periods, some in a few months, others in years, or in hundreds of years, are denominated periodic inequalities. The inequalities of the other kind, though occasioned likewise by the disturbing energy of the planets, are entirely independent of their relative positions. They depend upon the relative positions of the orbits alone, whose forms and places in space are altered by very minute quantities, in immense periods of time, and are therefore called secular inequalities.

The periodical perturbations are compensated when the bodies return to the same relative positions with regard to one another and to the sun: the secular inequalities are compensated when the orbits return to the same positions relatively to one another and to the plane of the ecliptic.

Planetary motion, including both these kinds of disturbance, may be represented by a body revolving in an ellipse, and making small and transient deviations, now on one side of its path, and now on the other, whilst the ellipse itself is slowly, but perpetually, changing both in form and position.

The periodic inequalities are merely transient deviations of a planet from its path, the most remarkable of which only lasts about 918 years; but, in consequence of the secular disturbances, the apsides, or extremities of the major axes of all the orbits, have a direct but variable motion in space, excepting those of the orbit of Venus, which are retrograde (N. 61), and the lines of the nodes move with a variable velocity in a contrary direction. Besides these, the inclination and excentricity of every orbit are in a state of perpetual but slow change. These effects result from the disturbing action of all the planets on each. But, as it is only necessary to estimate the disturbing influence of one body at a time, what follows may convey some idea of the manner in which one planet disturbs the elliptical motion of another.

Suppose two planets moving in ellipses round the sun; if one of them attracted the other and the sun with equal intensity, and in parallel directions (N. 62), it would have no effect in disturbing the elliptical motion. The inequality of this attraction is the sole cause of perturbation, and the difference between the disturbing planet’s action on the sun and on the disturbed planet constitutes the disturbing force, which consequently varies in intensity and direction with every change in the relative positions of the three bodies. Although both the sun and planet are under the influence of the disturbing force, the motion of the disturbed planet is referred to the centre of the sun as a fixed point, for convenience. The whole force (N. 63) which disturbs a planet is equivalent to three partial forces. One of these acts on the disturbed planet, in the direction of a tangent to its orbit, and is called the tangential force: it occasions secular inequalities in the form and position of the orbit in its own plane, and is the sole cause of the periodical perturbations in the planet’s longitude. Another acts upon the same body in the direction of its radius vector, that is, in the line joining the centres of the sun and planet, and is called the radial force: it produces periodical changes in the distance of the planet from the sun, and affects the form and position of the orbit in its own plane. The third, which may be called the perpendicular force, acts at right angles to the plane of the orbit, occasions the periodic inequalities in the planet’s latitude, and affects the position of the orbit with regard to the plane of the ecliptic.

It has been observed, that the radius vector of a planet, moving in a perfectly elliptical orbit, passes over equal spaces or areas in equal times; a circumstance which is independent of the law of the force, and would be the same whether it varied inversely as the square of the distance, or not, provided only that it be directed to the centre of the sun. Hence the tangential force, not being directed to the centre, occasions an unequable description of areas, or, what is the same thing, it disturbs the motion of the planet in longitude. The tangential force sometimes accelerates the planet’s motion, sometimes retards it, and occasionally has no effect at all. Were the orbits of both planets circular, a complete compensation would take place at each revolution of the two planets, because the arcs in which the accelerations and retardations take place would be symmetrical on each side of the disturbing force. For it is clear, that if the motion be accelerated through a certain space, and then retarded through as much, the motion at the end of the time will be the same as if no change had taken place. But, as the orbits of the planets are ellipses, this symmetry does not hold: for, as the planet moves unequably in its orbit, it is in some positions more directly, and for a longer time, under the influence of the disturbing force than in others. And, although multitudes of variations do compensate each other in short periods, there are others, depending on peculiar relations among the periodic times of the planets, which do not compensate each other till after one, or even till after many revolutions of both bodies. A periodical inequality of this kind in the motions of Jupiter and Saturn has a period of no less than 918 years.

The radial force, or that part of the disturbing force which acts in the direction of the line joining the centres of the sun and disturbed planet, has no effect on the areas, but is the cause of periodical changes of small extent in the distance of the planet from the sun. It has already been shown, that the force producing perfectly elliptical motion varies inversely as the square of the distance, and that a force following any other law would cause the body to move in a curve of a very different kind. Now, the radial disturbing force varies directly as the distance; and, as it sometimes combines with and increases the intensity of the sun’s attraction for the disturbed body, and at other times opposes and consequently diminishes it, in both cases it causes the sun’s attraction to deviate from the exact law of gravity, and the whole action of this compound central force on the disturbed body is either greater or less than what is requisite for perfectly elliptical motion. When greater, the curvature of the disturbed planet’s path, on leaving its perihelion (N. 64), or point nearest the sun, is greater than it would be in the ellipse, which brings the planet to its aphelion (N. 65), or point farthest from the sun, before it has passed through 180°, as it would do if undisturbed. So that in this case the apsides, or extremities of the major axis, advance in space. When the central force is less than the law of gravity requires, the curvature of the planet’s path is less than the curvature of the ellipse. So that the planet, on leaving its perihelion, would pass through more than 180° before arriving at its aphelion, which causes the apsides to recede in space (N. 66). Cases both of advance and recess occur during a revolution of the two planets; but those in which the apsides advance preponderate. This, however, is not the full amount of the motion of the apsides; part arises also from the tangential force (N. 63), which alternately accelerates and retards the velocity of the disturbed planet. An increase in the planet’s tangential velocity diminishes the curvature of its orbit, and is equivalent to a decrease of central force. On the contrary, a decrease of the tangential velocity, which increases the curvature of the orbit, is equivalent to an increase of central force. These fluctuations, owing to the tangential force, occasion an alternate recess and advance of the apsides, after the manner already explained (N. 66). An uncompensated portion of the direct motion, arising from this cause, conspires with that already impressed by the radial force, and in some cases even nearly doubles the direct motion of these points. The motion of the apsides may be represented by supposing a planet to move in an ellipse, while the ellipse itself is slowly revolving about the sun in the same plane (N. 67). This motion of the major axis, which is direct in all the orbits except that of the planet Venus, is irregular, and so slow that it requires more than 109,830 years for the major axis of the earth’s orbit to accomplish a sidereal revolution (N. 68), that is, to return to the same stars; and 20,984 years to complete its tropical revolution (N. 69), or to return to the same equinox. The difference between these two periods arises from a retrograde motion in the equinoctial point, which meets the advancing axis before it has completed its revolution with regard to the stars. The major axis of Jupiter’s orbit requires no less than 200,610 years to perform its sidereal revolution, and 22,748 years to accomplish its tropical revolution from the disturbing action of Saturn alone.

A variation in the excentricity of the disturbed planet’s orbit is an immediate consequence of the deviation from elliptical curvature, caused by the action of the disturbing force. When the path of the body, in proceeding from its perihelion to its aphelion, is more curved than it ought to be from the effect of the disturbing forces, it falls within the elliptical orbit, the excentricity is diminished, and the orbit becomes more nearly circular; when that curvature is less than it ought to be, the path of the planet falls without its elliptical orbit (N. 66), and the excentricity is increased; during these changes, the length of the major axis is not altered, the orbit only bulges out, or becomes more flat (N. 70). Thus the variation in the excentricity arises from the same cause that occasions the motion of the apsides (N. 67). There is an inseparable connection between these two elements: they vary simultaneously, and have the same period; so that, whilst the major axis revolves in an immense period of time, the excentricity increases and decreases by very small quantities, and at length returns to its original magnitude at each revolution of the apsides. The terrestrial excentricity is decreasing at the rate of about 40 miles annually; and, if it were to decrease equably, it would be 39,861 years before the earth’s orbit became a circle. The mutual action of Jupiter and Saturn occasions variations in the excentricity of both orbits, the greatest excentricity of Jupiter’s orbit corresponding to the least of Saturn’s. The period in which these vicissitudes are accomplished is 70,414 years, estimating the action of these two planets alone; but, if the action of all the planets were estimated, the cycle would extend to millions of years.

That part of the disturbing force is now to be considered which acts perpendicularly to the plane of the orbit, causing periodic perturbations in latitude, secular variations in the inclination of the orbit, and a retrograde motion to its nodes on the true plane of the ecliptic (N. 71). This force tends to pull the disturbed body above, or push (N. 72) it below, the plane of its orbit, according to the relative positions of the two planets with regard to the sun, considered to be fixed. By this action, it sometimes makes the plane of the orbit of the disturbed body tend to coincide with the plane of the ecliptic, and sometimes increases its inclination to that plane. In consequence of which, its nodes alternately recede or advance on the ecliptic (N. 73). When the disturbing planet is in the line of the disturbed planet’s nodes (N. 74), it neither affects these points, the latitude, nor the inclination, because both planets are then in the same plane. When it is at right angles to the line of the nodes, and the orbit symmetrical on each side of the disturbing force, the average motion of these points, after a revolution of the disturbed body, is retrograde, and comparatively rapid: but, when the disturbing planet is so situated that the orbit of the disturbed planet is not symmetrical on each side of the disturbing force, which is most frequently the case, every possible variety of action takes place. Consequently, the nodes are perpetually advancing or receding with unequal velocity; but, as a compensation is not effected, their motion is, on the whole, retrograde.

With regard to the variations in the inclination, it is clear, that, when the orbit is symmetrical on each side of the disturbing force, all its variations are compensated after a revolution of the disturbed body, and are merely periodical perturbations in the planet’s latitude; and no secular change is induced in the inclination of the orbit. When, on the contrary, that orbit is not symmetrical on each side of the disturbing force, although many of the variations in latitude are transient or periodical, still, after a complete revolution of the disturbed body, a portion remains uncompensated, which forms a secular change in the inclination of the orbit to the plane of the ecliptic. It is true, part of this secular change in the inclination is compensated by the revolution of the disturbing body, whose motion has not hitherto been taken into the account, so that perturbation compensates perturbation; but still a comparatively permanent change is effected in the inclination, which is not compensated till the nodes have accomplished a complete revolution.

The changes in the inclination are extremely minute (N. 75), compared with the motion of the nodes, and there is the same kind of inseparable connection between their secular changes that there is between the variation of the excentricity and the motion of the major axis. The nodes and inclinations vary simultaneously; their periods are the same, and very great. The nodes of Jupiter’s orbit, from the action of Saturn alone, require 36,261 years to accomplish even a tropical revolution. In what precedes, the influence of only one disturbing body has been considered; but, when the action and reaction of the whole system are taken into account, every planet is acted upon, and does itself act, in this manner, on all the others; and the joint effect keeps the inclinations and excentricities in a state of perpetual variation. It makes the major axes of all the orbits continually revolve, and causes, on an average, a retrograde motion of the nodes of each orbit upon every other. The ecliptic (N. 71) itself is in motion from the mutual action of the earth and planets, so that the whole is a compound phenomenon of great complexity, extending through unknown ages. At the present time the inclinations of all the orbits are decreasing, but so slowly, that the inclination of Jupiter’s orbit is only about six minutes less than it was in the age of Ptolemy.

But, in the midst of all these vicissitudes, the length of the major axes and the mean motions of the planets remain permanently independent of secular changes. They are so connected by Kepler’s law, of the squares of the periodic times being proportional to the cubes of the mean distances of the planets from the sun, that one cannot vary without affecting the other. And it is proved, that any variations which do take place are transient, and depend only on the relative positions of the bodies.

It is true that, according to theory, the radial disturbing force should permanently alter the dimensions of all the orbits, and the periodic times of all the planets, to a certain degree. For example, the masses of all the planets revolving within the orbit of any one, such as Mars, by adding to the interior mass, increase the attracting force of the sun, which, therefore, must contract the dimensions of the orbit of that planet, and diminish its periodic time; whilst the planets exterior to Mars’s orbit must have the contrary effect. But the mass of the whole of the planets and satellites taken together is so small, when compared with that of the sun, that these effects are quite insensible, and could only have been discovered by theory. And, as it is certain that the length of the major axes and the mean motions are not permanently changed by any other power whatever, it may be concluded that they are invariable.

With the exception of these two elements, it appears that all the bodies are in motion, and every orbit in a state of perpetual change. Minute as these changes are, they might be supposed to accumulate in the course of ages, sufficiently to derange the whole order of nature, to alter the relative positions of the planets, to put an end to the vicissitudes of the seasons, and to bring about collisions which would involve our whole system, now so harmonious, in chaotic confusion. It is natural to inquire, what proof exists that nature will be preserved from such a catastrophe? Nothing can be known from observation, since the existence of the human race has occupied comparatively but a point in duration, while these vicissitudes embrace myriads of ages. The proof is simple and conclusive. All the variations of the solar system, secular as well as periodic, are expressed analytically by the sines and cosines of circular arcs (N. 76), which increase with the time; and, as a sine or cosine can never exceed the radius, but must oscillate between zero and unity, however much the time may increase, it follows that when the variations have accumulated to a maximum by slow changes, in however long a time, they decrease, by the same slow degrees, till they arrive at their smallest value, again to begin a new course; thus for ever oscillating about a mean value. This circumstance, however, would be insufficient, were it not for the small excentricities of the planetary orbits, their minute inclinations to the plane of the ecliptic, and the revolutions of all the bodies, as well planets as satellites, in the same direction. These secure the perpetual stability of the solar system (N. 77). However, at the time that the stability was proved by La Grange and La Place, the telescopic planets between Mars and Jupiter had not been discovered; but La Grange, having investigated the subject under a very general point of view, showed that, if a planetary system be composed of very unequal masses, the whole of the larger would maintain an unalterable stability with regard to the form and position of their orbits, while the orbits of the lesser might undergo unlimited changes. M. Le Verrier has applied this to the solar system, and has found that the orbits of all the larger planets will for ever maintain an unalterable stability in form and position; for, though liable to mutations of very long periods, they return again exactly to what they originally were, oscillating between very narrow limits; but he found a zone of instability between the orbit of Mars, and twice the mean distance of the earth from the sun,[1] or between 1·5 and 2·00; therefore the position and form of the orbits of such of the telescopic planets as revolve within that zone will be subject to unlimited variations. But the orbits of those more remote from the sun than Flora, or beyond 2·20, will be stable, so that their excentricities and inclinations must always have been, and will always remain, very great, since they must have depended upon the primitive conditions that prevailed when these planetary atoms were launched into space. The 51st of these small bodies, which was discovered, and the elements of its orbit determined, by M. Valz, at Nimes, has a mean distance of 1·88; so it revolves within the zone of instability. It has a shorter periodic time than any of those previously discovered, and a greater excentricity, with the exception of Nysa. Its orbit cuts that of Mars, and comes nearer to the earth than the orbits of either Mars or Venus, a circumstance which would be favourable for correcting the parallax of the sun, or confirming its accuracy. The telescopic planets, numerous as they are, have no influence on the motions of the larger planets, for Jupiter has a diameter of 90,734 miles, while that of Pallas, his nearest neighbour, is only 97 miles, little more than the distance from London to Bath. The diameter of Mars, on the other side of the small planets, is 4546 miles, and that of the earth 7925-1/2 miles, so that the telescopic group are too minute to disturb the others. M. Le Verrier found another zone of instability between Venus and the sun, on the border of which Mercury is revolving, the inclination of whose orbit to the plane of the ecliptic is about 7°, which is more than that of any of the large planets. Neptune’s orbit is, no doubt, as stable as that of any other of the large planets, as the inclination is very small, but he will have periodical variations of very long duration from the reciprocal attraction between him and Uranus, one especially of an enormous duration, similar to those of Jupiter and Saturn, and, like them, depending on the time of his revolution round the sun, being nearly twice as long as that of Saturn. Mr. Adams has computed that Neptune produces a periodical perturbation in the motion of Uranus, whose duration is about 6800 years.

The equilibrium of the system, however, would be deranged if the planets moved in a resisting medium (N. 78) sufficiently dense to diminish their tangential velocity, for then both the excentricities and the major axes of the orbits would vary with the time, so that the stability of the system would be ultimately destroyed. The existence of an ethereal medium is now proved; and, although it is so extremely rare that hitherto its effects on the motions of the planets have been altogether insensible, there can be no doubt that, in the immensity of time, it will modify the forms of the planetary orbits, and may at last even cause the destruction of our system, which in itself contains no principle of decay, unless a rotatory motion from west to east has been given to this medium by the bodies of the solar system, which have all been revolving about the sun in that direction for unknown ages. This rotation, which seems to be highly probable, may even have been coeval with its creation. Such a vortex would have no effect on bodies moving with it, but it would influence the motions of those revolving in a contrary direction. It is possible that the disturbances experienced by comets, which have already revealed the existence of this medium, may also, in time, disclose its rotatory motion.

The form and position of the planetary orbits, and the motion of the bodies in the same direction, together with the periodicity of the terms in which the inequalities are expressed, assure us that the variations of the system are confined within very narrow limits, and that, although we do not know the extent of the limits, nor the period of that grand cycle which probably embraces millions of years, yet they never will exceed what is requisite for the stability and harmony of the whole; for the preservation of which every circumstance is so beautifully and wonderfully adapted.

The plane of the ecliptic itself, though assumed to be fixed at a given epoch for the convenience of astronomical computation, is subject to a minute secular variation of 45ʺ·7, occasioned by the reciprocal action of the planets. But, as this is also periodical, and cannot exceed 2° 42ʹ, the terrestrial equator, which is inclined to it at an angle[2] of 23° 27ʹ 28ʺ·29, will never coincide with the plane of the ecliptic: so there never can be perpetual spring (N. 79). The rotation of the earth is uniform; therefore day and night, summer and winter, will continue their vicissitudes while the system endures, or is undisturbed by foreign causes.

Yonder starry sphere Of planets and of fix’d, in all her wheels, Resembles nearest mazes intricate, Eccentric, intervolved, yet regular, Then most, when most irregular they seem.

The stability of our system was established by La Grange: “a discovery,” says Professor Playfair, “that must render the name for ever memorable in science, and revered by those who delight in the contemplation of whatever is excellent and sublime.” After Newton’s discovery of the mechanical laws of the elliptical orbits of the planets, that of their periodical inequalities, by La Grange, is, without doubt, the noblest truth in the mechanism of the heavens; and, in respect of the doctrine of final causes, it may be regarded as the greatest of all.

Notwithstanding the permanency of our system, the secular variations in the planetary orbits would have been extremely embarrassing to astronomers when it became necessary to compare observations separated by long periods. The difficulty was in part obviated, and the principle for accomplishing it established, by La Place, and has since been extended by M. Poinsot. It appears that there exists an invariable plane (N. 80), passing through the centre of gravity of the system, about which the whole oscillates within very narrow limits, and that this plane will always remain parallel to itself, whatever changes time may induce in the orbits of the planets, in the plane of the ecliptic, or even in the law of gravitation; provided only that our system remains unconnected with any other. The position of the plane is determined by this property—that, if each particle in the system be multiplied by the area described upon this plane in a given time, by the projection of its radius vector about the common centre of gravity of the whole, the sum of all these products will be a maximum (N. 81). La Place found that the plane in question is inclined to the ecliptic at an angle of nearly 1° 34ʹ 15ʺ, and that, in passing through the sun, and about midway between the orbits of Jupiter and Saturn, it may be regarded as the equator of the solar system, dividing it into two parts, which balance one another in all their motions. This plane of greatest inertia, by no means peculiar to the solar system, but existing in every system of bodies submitted to their mutual attractions only, always maintains a fixed position, whence the oscillations of the system may be estimated through unlimited time. Future astronomers will know, from its immutability or variation, whether the sun and his attendants are connected or not with the other systems of the universe. Should there be no link between them, it may be inferred, from the rotation of the sun, that the centre of gravity (N. 82) of the system situate within his mass describes a straight line in this invariable plane or great equator of the solar system, which, unaffected by the changes of time, will maintain its stability through endless ages. But, if the fixed stars, comets, or any unknown and unseen bodies, affect our sun and planets, the nodes of this plane will slowly recede on the plane of that immense orbit which the sun may describe about some most distant centre, in a period which it transcends the power of man to determine. There is every reason to believe that this is the case; for it is more than probable that, remote as the fixed stars are, they in some degree influence our system, and that even the invariability of this plane is relative, only appearing fixed to creatures incapable of estimating its minute and slow changes during the small extent of time and space granted to the human race. “The development of such changes,” as M. Poinsot justly observes, “is similar to an enormous curve, of which we see so small an arc that we imagine it to be a straight line.” If we raise our views to the whole extent of the universe, and consider the stars, together with the sun, to be wandering bodies, revolving about the common centre of creation, we may then recognise in the equatorial plane passing through the centre of gravity of the universe the only instance of absolute and eternal repose.

All the periodic and secular inequalities deduced from the law of gravitation are so perfectly confirmed by observation, that analysis has become one of the most certain means of discovering the planetary irregularities, either when they are too small, or too long in their periods, to be detected by other methods. Jupiter and Saturn, however, exhibit inequalities which for a long time seemed discordant with that law. All observations, from those of the Chinese and Arabs down to the present day, prove that for ages the mean motions of Jupiter and Saturn have been affected by a great inequality of a very long period, forming an apparent anomaly in the theory of the planets. It was long known by observation that five times the mean motion of Saturn is nearly equal to twice that of Jupiter; a relation which the sagacity of La Place perceived to be the cause of a periodic irregularity in the mean motion of each of these planets, which completes its period in nearly 918 years, the one being retarded while the other is accelerated; but both the magnitude and period of these quantities vary, in consequence of the secular variations in the elements of the orbits. Suppose the two planets to be on the same side of the sun, and all three in the same straight line, they are then said to be in conjunction (N. 83). Now, if they begin to move at the same time, one making exactly five revolutions in its orbit while the other only accomplishes two, it is clear that Saturn, the slow-moving body, will only have got through a part of its orbit during the time that Jupiter has made one whole revolution and part of another, before they be again in conjunction. It is found that during this time their mutual action is such as to produce a great many perturbations which compensate each other, but that there still remains a portion outstanding, owing to the length of time during which the forces act in the same manner; and, if the conjunction always happened in the same point of the orbit, this uncompensated inequality in the mean motion would go on increasing till the periodic times and forms of the orbits were completely and permanently changed: a case that would actually take place if Jupiter accomplished exactly five revolutions in the time Saturn performed two. These revolutions are, however, not exactly commensurable; the points in which the conjunctions take place are in advance each time as much as 8°·37; so that the conjunctions do not happen exactly in the same points of the orbits till after a period of 850 years; and, in consequence of this small advance, the planets are brought into such relative positions, that the inequality, which seemed to threaten the stability of the system, is completely compensated, and the bodies, having returned to the same relative positions with regard to one another and the sun, begin a new course. The secular variations in the elements of the orbit increase the period of the inequality to 918 years (N. 84). As any perturbation which affects the mean motion affects also the major axis, the disturbing forces tend to diminish the major axis of Jupiter’s orbit, and increase that of Saturn’s, during one half of the period, and the contrary during the other half. This inequality is strictly periodical, since it depends upon the configuration (N. 85) of the two planets; and theory is confirmed by observation, which shows that, in the course of twenty centuries, Jupiter’s mean motion has been accelerated by about 3° 23ʹ, and Saturn’s retarded by 5° 13ʹ. Several instances of perturbations of this kind occur in the solar system. One, in the mean motions of the Earth and Venus, only amounting to a few seconds, has been recently worked out with immense labour by Professor Airy. It accomplishes its changes in 240 years, and arises from the circumstance of thirteen times the periodic time of Venus being nearly equal to eight times that of the Earth. Small as it is, it is sensible in the motions of the Earth.

It might be imagined that the reciprocal action of such planets as have satellites would be different from the influence of those that have none. But the distances of the satellites from their primaries are incomparably less than the distances of the planets from the sun, and from one another. So that the system of a planet and its satellites moves nearly as if all these bodies were united in their common centre of gravity. The action of the sun, however, in some degree disturbs the motion of the satellites about their primary.

SECTION IV.

Theory of Jupiter’s Satellites—Effects of the Figure of Jupiter upon his Satellites—Position of their Orbits—Singular Laws among the Motions of the first Three Satellites—Eclipses of the Satellites—Velocity of Light—Aberration—Ethereal Medium—Satellites of Saturn and Uranus.

THE changes which take place in the planetary system are exhibited on a smaller scale by Jupiter and his satellites; and, as the period requisite for the development of the inequalities of these moons only extends to a few centuries, it may be regarded as an epitome of that grand cycle which will not be accomplished by the planets in myriads of ages. The revolutions of the satellites about Jupiter are precisely similar to those of the planets about the sun; it is true they are disturbed by the sun, but his distance is so great, that their motions are nearly the same as if they were not under his influence. The satellites, like the planets, were probably projected in elliptical orbits: but, as the masses of the satellites are nearly 100,000 times less than that of Jupiter; and as the compression of Jupiter’s spheroid is so great, in consequence of his rapid rotation, that his equatorial diameter exceeds his polar diameter by no less than 6000 miles; the immense quantity of prominent matter at his equator must soon have given the circular form observed in the orbits of the first and second satellites, which its superior attraction will always maintain. The third and fourth satellites, being farther removed from its influence, revolve in orbits with a very small excentricity. And, although the first two sensibly move in circles, their orbits acquire a small ellipticity, from the disturbances they experience (N. 86).

It has been stated, that the attraction of a sphere on an exterior body is the same as if its mass were united in one particle in its centre of gravity, and therefore inversely as the square of the distance. In a spheroid, however, there is an additional force arising from the bulging mass at its equator, which, not following the exact law of gravity, acts as a disturbing force. One effect of this disturbing force in the spheroid of Jupiter is to occasion a direct motion in the greater axes of the orbits of all his satellites, which is more rapid the nearer the satellite is to the planet, and very much greater than that part of their motion which arises from the disturbing action of the sun. The same cause occasions the orbits of the satellites to remain nearly in the plane of Jupiter’s equator (N. 87), on account of which the satellites are always seen nearly in the same line (N. 88); and the powerful action of that quantity of prominent matter is the reason why the motions of the nodes of these small bodies are so much more rapid than those of the planet. The nodes of the fourth satellite accomplish a tropical revolution in 531 years, while those of Jupiter’s orbit require no less than 36,261 years;—a proof of the reciprocal attraction between each particle of Jupiter’s equator and of the satellites. In fact, if the satellites moved exactly in the plane of Jupiter’s equator, they would not be pulled out of that plane, because his attraction would be equal on both sides of it. But, as their orbits have a small inclination to the plane of the planet’s equator, there is a want of symmetry, and the action of the protuberant matter tends to make the nodes regress by pulling the satellites above or below the planes of their orbits; an action which is so great on the interior satellites, that the motions of their nodes are nearly the same as if no other disturbing force existed.

The orbits of the satellites do not retain a permanent inclination, either to the plane of Jupiter’s equator, or to that of his orbit, but to certain planes passing between the two, and through their intersection. These have a greater inclination to his equator the farther the satellite is removed, owing to the influence of Jupiter’s compression; and they have a slow motion corresponding to secular variations in the planes of Jupiter’s orbit and equator.

The satellites are not only subject to periodic and secular inequalities from their mutual attraction, similar to those which affect the motions and orbits of the planets, but also to others peculiar to themselves. Of the periodic inequalities arising from their mutual attraction the most remarkable take place in the angular motions (N. 89) of the three nearest to Jupiter, the second of which receives from the first a perturbation similar to that which it produces in the third; and it experiences from the third a perturbation similar to that which it communicates to the first. In the eclipses these two inequalities are combined into one, whose period is 437·659 days. The variations peculiar to the satellites arise from the secular inequalities occasioned by the action of the planets in the form and position of Jupiter’s orbit, and from the displacement of his equator. It is obvious that whatever alters the relative positions of the sun, Jupiter, and his satellites, must occasion a change in the directions and intensities of the forces, which will affect the motions and orbits of the satellites. For this reason the secular variations in the excentricity of Jupiter’s orbit occasion secular inequalities in the mean motions of the satellites, and in the motions of the nodes and apsides of their orbits. The displacement of the orbit of Jupiter, and the variation in the position of his equator, also affect these small bodies (N. 90). The plane of Jupiter’s equator is inclined to the plane of his orbit at an angle of 3° 5ʹ 30ʺ, so that the action of the sun and of the satellites themselves produces a nutation and precession (N. 91) in his equator, precisely similar to that which takes place in the rotation of the earth, from the action of the sun and moon. Hence the protuberant matter at Jupiter’s equator is continually changing its position with regard to the satellites, and produces corresponding mutations in their motions. And, as the cause must be proportional to the effect, these inequalities afford the means, not only of ascertaining the compression of Jupiter’s spheroid, but they prove that his mass is not homogeneous. Although the apparent diameters of the satellites are too small to be measured, yet their perturbations give the values of their masses with considerable accuracy—a striking proof of the power of analysis.

A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean motion of the first satellite, plus twice that of the third, is equal to three times that of the second; and that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles. It is proved by theory, that, if these relations had only been approximate when the satellites were first launched into space, their mutual attractions would have established and maintained them, notwithstanding the secular inequalities to which they are liable. They extend to the synodic motions (N. 92) of the satellites; consequently they affect their eclipses, and have a very great influence on their whole theory. The satellites move so nearly in the plane of Jupiter’s equator, which has a very small inclination to his orbit, that the first three are eclipsed at each revolution by the shadow of the planet, which is much larger than the shadow of the moon: the fourth satellite is not eclipsed so frequently as the others. The eclipses take place close to the disc of Jupiter when he is near opposition (N. 93); but at times his shadow is so projected with regard to the earth, that the third and fourth satellites vanish and reappear on the same side of the disc (N. 94). These eclipses are in all respects similar to those of the moon: but, occasionally, the satellites eclipse Jupiter, sometimes passing like obscure spots across his surface, resembling annular eclipses of the sun, and sometimes like a bright spot traversing one of his dark belts. Before opposition, the shadow of the satellite, like a round black spot, precedes its passage over the disc of the planet; and, after opposition, the shadow follows the satellite.

In consequence of the relations already mentioned in the mean motions and mean longitudes of the first three satellites, they never can be all eclipsed at the same time: for, when the second and third are in one direction, the first is in the opposite direction; consequently, when the first is eclipsed, the other two must be between the sun and Jupiter. The instant of the beginning or end of an eclipse of a satellite marks the same instant of absolute time to all the inhabitants of the earth; therefore, the time of these eclipses observed by a traveller, when compared with the time of the eclipse computed for Greenwich, or any other fixed meridian (N. 95), gives the difference of the meridians in time, and, consequently, the longitude of the place of observation. The longitude is determined with extreme precision whenever it is possible to convey the time instantaneously by means of electricity from one place to another, since it obviates the errors of clocks and chronometers. The eclipses of Jupiter’s satellites have been the means of a discovery which, though not so immediately applicable to the wants of man, unfolds one of the properties of light—that medium without whose cheering influence all the beauties of the creation would have been to us a blank. It is observed, that those eclipses of the first satellite which happen when Jupiter is near conjunction (N. 96), are later by 16ʹ 26ʺ·6 than those which take place when the planet is in opposition. As Jupiter is nearer to us when in opposition by the whole breadth of the earth’s orbit than when in conjunction, this circumstance is to be attributed to the time employed by the rays of light in crossing the earth’s orbit, a distance of about 190,000,000 of miles; whence it is estimated that light travels at the rate of 192,000 miles in one second. Such is its velocity, that the earth, moving at the rate of nineteen miles in a second, would take two months to pass through a distance which a ray of light would dart over in eight minutes. The subsequent discovery of the aberration of light has fully confirmed this astonishing result.

Objects appear to be situate in the direction of the rays which proceed from them. Were light propagated instantaneously, every object, whether at rest or in motion, would appear in the direction of these rays; but, as light takes some time to travel, we see Jupiter in conjunction, by means of rays that left him 16^m 26^s·6 before; but, during that time, we have changed our position, in consequence of the motion of the earth in its orbit: we therefore refer Jupiter to a place in which he is not. His true position is in the diagonal (N. 97) of the parallelogram, whose sides are in the ratio of the velocity of light to the velocity of the earth in its orbit, which is as 192,000 to 19, or nearly as 10,000 to 1. In consequence of the aberration of light, the heavenly bodies seem to be in places in which they are not. In fact, if the earth were at rest, rays from a star would pass along the axis of a telescope directed to it; but, if the earth were to begin to move in its orbit with its usual velocity, these rays would strike against the side of the tube; it would, therefore, be necessary to incline the telescope a little, in order to see the star. The angle contained between the axis of the telescope and a line drawn to the true place of the star is its aberration, which varies in quantity and direction in different parts of the earth’s orbit; but, as it is only 20ʺ·481, it is insensible in ordinary cases (N. 98).

The velocity of light deduced from the observed aberration of the fixed stars perfectly corresponds with that given by the eclipses of the first satellite. The same result, obtained from sources so different, leaves not a doubt of its truth. Many such beautiful coincidences, derived from circumstances apparently the most unpromising and dissimilar, occur in physical astronomy, and prove connections which we might otherwise be unable to trace. The identity of the velocity of light, at the distance of Jupiter, and on the earth’s surface, shows that its velocity is uniform; and as light consists in the vibrations of an elastic medium or ether filling space, the uniformity of its velocity shows that the density of the medium throughout the whole extent of the solar system must be proportional to its elasticity (N. 99). Among the fortunate conjectures which have been confirmed by subsequent experience, that of Bacon is not the least remarkable, “It produces in me,” says the restorer of true philosophy, “a doubt whether the face of the serene and starry heavens be seen at the instant it really exists, or not till some time later: and whether there be not, with respect to the heavenly bodies, a true time and an apparent time, no less than a true place and an apparent place, as astronomers say, on account of parallax. For it seems incredible that the species or rays of the celestial bodies can pass through the immense interval between them and us in an instant, or that they do not even require some considerable portion of time.”

Great discoveries generally lead to a variety of conclusions: the aberration of light affords a direct proof of the motion of the earth in its orbit; and its rotation is proved by the theory of falling bodies, since the centrifugal force it induces retards the oscillations of the pendulum (N. 100) in going from the pole to the equator. Thus a high degree of scientific knowledge has been requisite to dispel the errors of the senses (N. 237).

The little that is known of the theories of the satellites of Saturn and Uranus is, in all respects, similar to that of Jupiter. Saturn is accompanied by eight satellites. The seventh is about the size of Mars, and the eighth was simultaneously discovered by Mr. Bond in America, and that distinguished astronomer Mr. Lassell, of Liverpool. The orbits of the two last have a sensible inclination to the plane of the ring; but the great compression of Saturn occasions the other satellites to move nearly in the plane of his equator. So many circumstances must concur to render the two interior satellites visible, that they have very rarely been seen. They move exactly at the edge of the ring, and their orbits never deviate from its plane. In 1789 Sir William Herschel saw them like beads, threading the slender line of light which the ring is reduced to when seen edgewise from the earth. And for a short time he perceived them advancing off it at each end, when turning round in their orbits. The eclipses of the exterior satellites only take place when the ring is in this position. Mr. Lassell, with a powerful telescope, made by himself, has seen Iapetus, the nearest of the two, on several occasions, even when the opening of the ring was very wide, which made it extremely difficult to see so minute an object. Of the situation of the equator of Uranus we know nothing, nor of his compression; but the orbits of his satellites are nearly perpendicular to the plane of the ecliptic; and, by analogy, they ought to be in the plane of his equator. Uranus is so remote that he has more the appearance of a planetary nebula than a planet, which renders it extremely difficult to distinguish the satellites at all; and quite hopeless without such a telescope as is rarely to be met with even in observatories. Sir William Herschel discovered the two that are farthest from the planet, and ascertained their approximate periods, which his son afterwards determined to be 13^d 11^h 7^m 12^s·6 and 8^d 16^h 56^m 28^s·6 respectively. The orbits of both seem to have an inclination of about 101°·2 to the plane of the ecliptic. The two interior satellites are so faint and small, and so near the edge of the planet, that they can with difficulty be seen even under the most favourable circumstances: however, Mr. Lassell has ascertained that the more distant of the two revolves about Uranus in 4 days, and that nearest to the planet in 2-1/2 days, and from a long and minute examination he is convinced that the system only consists of four satellites. Soon after Neptune was seen Mr. Lassell discovered the only satellite known to belong to that planet. The satellites of Uranus and Neptune, the two planets on the remotest verge of the solar system, offer the singular and only instance of a revolution from east to west, while all the planets and all the other satellites revolve from west to east. Retrograde motion is occasionally met with in the comets and double stars.

SECTION V.

Lunar Theory—Periodic Perturbations of the Moon—Equation of Centre—Evection—Variation—Annual Equation—Direct and Indirect Action of Planets—The Moon’s Action on the Earth disturbs her own Motion—Excentricity and Inclination of Lunar Orbit invariable—Acceleration—Secular Variation in Nodes and Perigee—Motion of Nodes and Perigee inseparably connected with the Acceleration—Nutation of Lunar Orbit—Form and Internal Structure of the Earth determined from it—Lunar, Solar, and Planetary Eclipses—Occultations and Lunar Distances—Mean Distance of the Sun from the Earth obtained from Lunar Theory—Absolute Distances of the Planets, how found.

OUR constant companion, the moon, next claims our attention. Several circumstances concur to render her motions the most interesting, and at the same time the most difficult to investigate, of all the bodies of our system. In the solar system, planet troubles planet; but, in the lunar theory, the sun is the great disturbing cause, his vast distance being compensated by his enormous magnitude, so that the motions of the moon are more irregular than those of the planets; and, on account of the great ellipticity of her orbit, and the size of the sun, the approximations to her motions are tedious and difficult, beyond what those unaccustomed to such investigations could imagine. The average distance of the moon from the centre of the earth is only 238,793 miles, so that her motion among the stars is perceptible in a few hours. She completes a circuit of the heavens in 27^d 7^h 43^m 11^s·5, moving in an orbit whose excentricity is about 12,985 miles. The moon is about four hundred times nearer to the earth than the sun. The proximity of the moon to the earth keeps them together. For so great is the attraction of the sun, that, if the moon were farther from the earth, she would leave it altogether, and would revolve as an independent planet about the sun.

The disturbing action (N. 101) of the sun on the moon is equivalent to three forces. The first, acting in the direction of the line joining the moon and earth, increases or diminishes her gravity to the earth. The second, acting in the direction of a tangent to her orbit, disturbs her motion in longitude. And the third, acting perpendicularly to the plane of her orbit, disturbs her motion in latitude; that is, it brings her nearer to, or removes her farther from, the plane of the ecliptic than she would otherwise be. The periodic perturbations in the moon, arising from these forces, are perfectly similar to the periodic perturbations of the planets. But they are much greater and more numerous; because the sun is so large, that many inequalities which are quite insensible in the motions of the planets, are of great magnitude in those of the moon. Among the innumerable periodic inequalities to which the moon’s motion in longitude is liable, the most remarkable are, the Equation of the Centre, which is the difference between the moon’s mean and true longitude, the Evection, the Variation, and the Annual Equation. The disturbing force which acts in the line joining the moon and earth produces the Evection: it diminishes the excentricity of the lunar orbit in conjunction and opposition, thereby making it more circular, and augments it in quadrature, which consequently renders it more elliptical. The period of this inequality is less than thirty-two days. Were the increase and diminution always the same, the Evection would only depend upon the distance of the moon from the sun; but its absolute value also varies with her distance from the perigee (N. 102) of her orbit. Ancient astronomers, who observed the moon solely with a view to the prediction of eclipses, which can only happen in conjunction and opposition, where the excentricity is diminished by the Evection, assigned too small a value to the ellipticity of her orbit (N. 103). The Evection was discovered by Ptolemy from observation, about A.D. 140. The Variation produced by the tangential disturbing force, which is at its maximum when the moon is 45° distant from the sun, vanishes when that distance amounts to a quadrant, and also when the moon is in conjunction and opposition; consequently, that inequality never could have been discovered from the eclipses: its period is half a lunar month (N. 104). The Annual Equation depends upon the sun’s distance from the earth: it arises from the moon’s motion being accelerated when that of the earth is retarded, and vice versâ—for, when the earth is in its perihelion, the lunar orbit is enlarged by the action of the sun; therefore, the moon requires more time to perform her revolution. But, as the earth approaches its aphelion, the moon’s orbit contracts, and less time is necessary to accomplish her motion—its period, consequently, depends upon the time of the year. In the eclipses the Annual Equation combines with the Equation of the Centre of the terrestrial orbit, so that ancient astronomers imagined the earth’s orbit to have a greater excentricity than modern astronomers assign to it.

The planets disturb the motion of the moon both directly and indirectly; their action on the earth alters its relative position with regard to the sun and moon, and occasions inequalities in the moon’s motion, which are more considerable than those arising from their direct action; for the same reason the moon, by disturbing the earth, indirectly disturbs her own motion. Neither the excentricity of the lunar orbit, nor its mean inclination to the plane of the ecliptic, have experienced any changes from secular inequalities; for, although the mean action of the sun on the moon depends upon the inclination of the lunar orbit to the ecliptic, and the position of the ecliptic is subject to a secular inequality, yet analysis shows that it does not occasion a secular variation in the inclination of the lunar orbit, because the action of the sun constantly brings the moon’s orbit to the same inclination to the ecliptic. The mean motion, the nodes, and the perigee, however, are subject to very remarkable variations.

From the eclipse observed at Babylon, on the 19th of March, seven hundred and twenty-one years before the Christian era, the place of the moon is known from that of the sun at the instant of opposition (N. 83), whence her mean longitude may be found. But the comparison of this mean longitude with another mean longitude, computed back for the instant of the eclipse from modern observations, shows that the moon performs her revolution round the earth more rapidly and in a shorter time now than she did formerly, and that the acceleration in her mean motion has been increasing from age to age as the square of the time (N. 105). All ancient and intermediate eclipses confirm this result. As the mean motions of the planets have no secular inequalities, this seemed to be an unaccountable anomaly. It was at one time attributed to the resistance of an ethereal medium pervading space, and at another to the successive transmission of the gravitating force. But, as La Place proved that neither of these causes, even if they exist, have any influence on the motions of the lunar perigee (N. 102) or nodes, they could not affect the mean motion; a variation in the mean motion from such causes being inseparably connected with variations in the motions of the perigee and nodes. That great mathematician, in studying the theory of Jupiter’s satellites, perceived that the secular variation in the elements of Jupiter’s orbit, from the action of the planets, occasions corresponding changes in the motions of the satellites, which led him to suspect that the acceleration in the mean motion of the moon might be connected with the secular variation in the excentricity of the terrestrial orbit. Analysis has shown that he assigned the true cause of the acceleration.

It is proved that the greater the excentricity of the terrestrial orbit, the greater is the disturbing action of the sun on the moon. Now, as the excentricity has been decreasing for ages, the effect of the sun in disturbing the moon has been diminishing during that time. Consequently the attraction of the earth has had a more and more powerful effect on the moon, and has been continually diminishing the size of the lunar orbit. So that the moon’s velocity has been gradually augmenting for many centuries to balance the increase of the earth’s attraction. This secular increase in the moon’s velocity is called the Acceleration, a name peculiarly appropriate at present, and which will continue to be so for a vast number of ages; because, as long as the earth’s excentricity diminishes, the moon’s mean motion will be accelerated; but when the excentricity has passed its minimum, and begins to increase, the mean motion will be retarded from age to age. The secular acceleration is now about 11ʺ·9, but its effect on the moon’s place increases as the square of the time (N. 106). It is remarkable that the action of the planets, thus reflected by the sun to the moon, is much more sensible than their direct action either on the earth or moon. The secular diminution in the excentricity, which has not altered the equation of the centre of the sun by eight minutes since the earliest recorded eclipses, has produced a variation of about 1° 48ʹ in the moon’s longitude, and of 7° 12ʹ in her mean anomaly (N. 107).

The action of the sun occasions a rapid but variable motion in the nodes and perigee of the lunar orbit. Though the nodes recede during the greater part of the moon’s revolution, and advance during the smaller, they perform their sidereal revolution in 6793^d 9^h 23^m 9^s·3, or about 18-6/10 years; and the perigee accomplishes a revolution, called of the moon’s apsides, in 3232^d 13^h 48^m 29^s·6, or a little more than nine years, notwithstanding its motion is sometimes retrograde and sometimes direct: but such is the difference between the disturbing energy of the sun and that of all the planets put together, that it requires no less than 109,830 years for the greater axis of the terrestrial orbit to do the same, moving at the rate of 11ʺ·8 annually. The form of the earth has no sensible effect either on the lunar nodes or apsides. It is evident that the same secular variation which changes the sun’s distance from the earth, and occasions the acceleration in the moon’s mean motion, must affect the nodes and perigee. It consequently appears, from theory as well as observation, that both these elements are subject to a secular inequality, arising from the variation in the excentricity of the earth’s orbit, which connects them with the Acceleration, so that both are retarded when the mean motion is anticipated. The secular variations in these three elements are in the ratio of the numbers 3, 0·735, and 1; whence the three motions of the moon, with regard to the sun, to her perigee, and to her nodes, are continually accelerated, and their secular equations are as the numbers 1, 4·702, and 0·612. A comparison of ancient eclipses observed by the Arabs, Greeks, and Chaldeans, imperfect as they are, with modern observations, confirms these results of analysis. Future ages will develop these great inequalities, which at some most distant period will amount to many circumferences (N. 108). They are, indeed, periodic; but who shall tell their period? Millions of years must elapse before that great cycle is accomplished.

The moon is so near, that the excess of matter at the earth’s equator occasions periodic variations in her longitude, and also that remarkable inequality in her latitude, already mentioned as a nutation in the lunar orbit, which diminishes its inclination to the ecliptic when the moon’s ascending node coincides with the equinox of spring, and augments it when that node coincides with the equinox of autumn. As the cause must be proportional to the effect, a comparison of these inequalities, computed from theory, with the same given by observation, shows that the compression of the terrestrial spheroid, or the ratio of the difference between the polar and the equatorial diameters, to the diameter of the equator, is 1/305·05. It is proved analytically, that, if a fluid mass of homogeneous matter, whose particles attract each other inversely as the squares of the distance, were to revolve about an axis as the earth does, it would assume the form of a spheroid whose compression is 1/230. Since that is not the case, the earth cannot be homogeneous, but must decrease in density from its centre to its circumference. Thus the moon’s eclipses show the earth to be round; and her inequalities not only determine the form, but even the internal structure of our planet; results of analysis which could not have been anticipated. Similar inequalities in the motions of Jupiter’s satellites prove that his mass is not homogeneous, and that his compression is 1/13·8. His equatorial diameter exceeds his polar diameter by about 6000 miles.

The phases (N. 109) of the moon, which vary from a slender silvery crescent soon after conjunction, to a complete circular disc of light in opposition, decrease by the same degrees till the moon is again enveloped in the morning beams of the sun. These changes regulate the returns of the eclipses. Those of the sun can only happen in conjunction, when the moon, coming between the earth and the sun, intercepts his light. Those of the moon are occasioned by the earth intervening between the sun and moon when in opposition. As the earth is opaque and nearly spherical, it throws a conical shadow on the side of the moon opposite to the sun, the axis of which passes through the centres of the sun and earth (N. 110). The length of the shadow terminates at the point where the apparent diameters (N. 111) of the sun and earth would be the same. When the moon is in opposition, and at her mean distance, the diameter of the sun would be seen from her centre under an angle of 1918ʺ·1. That of the earth would appear under an angle of 6908ʺ·3. So that the length of the shadow is at least three times and a half greater than the distance of the moon from the earth, and the breadth of the shadow, where it is traversed by the moon, is about eight-thirds of the lunar diameter. Hence the moon would be eclipsed every time she is in opposition, were it not for the inclination of her orbit to the plane of the ecliptic, in consequence of which the moon, when in opposition, is either above or below the cone of the earth’s shadow, except when in or near her nodes. Her position with regard to them occasions all the varieties in the lunar eclipses. Every point of the moon’s surface successively loses the light of different parts of the sun’s disc before being eclipsed. Her brightness therefore gradually diminishes before she plunges into the earth’s shadow. The breadth of the space occupied by the penumbra (N. 112) is equal to the apparent diameter of the sun, as seen from the centre of the moon. The mean duration of a revolution of the sun, with regard to the node of the lunar orbit, is to the duration of a synodic revolution (N. 113) of the moon as 223 to 19. So that, after a period of 223 lunar months, the sun and moon would return to the same relative position with regard to the node of the moon’s orbit, and therefore the eclipses would recur in the same order were not the periods altered by irregularities in the motions of the sun and moon. In lunar eclipses, our atmosphere bends the sun’s rays which pass through it all round into the cone of the earth’s shadow. And as the horizontal refraction (N. 114) or bending of the rays surpasses half the sum of the semidiameters of the sun and moon, divided by their mutual distance, the centre of the lunar disc, supposed to be in the axis of the shadow, would receive the rays from the same point of the sun, round all sides of the earth; so that it would be more illuminated than in full moon, if the greater portion of the light were not stopped or absorbed by the atmosphere. Instances are recorded where this feeble light has been entirely absorbed, so that the moon has altogether disappeared in her eclipses.

The sun is eclipsed when the moon intercepts his rays (N. 115). The moon, though incomparably smaller than the sun, is so much nearer the earth, that her apparent diameter differs but little from his, but both are liable to such variations that they alternately surpass one another. Were the eye of a spectator in the same straight line with the centres of the sun and moon, he would see the sun eclipsed. If the apparent diameter of the moon surpassed that of the sun, the eclipse would be total. If it were less, the observer would see a ring of light round the disc of the moon, and the eclipse would be annular, as it was on the 17th of May, 1836, and on the 15th of March, 1858. If the centre of the moon should not be in the straight line joining the centres of the sun and the eye of the observer, the moon might only eclipse a part of the sun. The variation, therefore, in the distances of the sun and moon from the centre of the earth, and of the moon from her node at the instant of conjunction, occasions great varieties in the solar eclipses. Besides, the height of the moon above the horizon changes her apparent diameter, and may augment or diminish the apparent distances of the centres of the sun and moon, so that an eclipse of the sun may occur to the inhabitants of one country, and not to those of another. In this respect the solar eclipses differ from the lunar, which are the same for every part of the earth where the moon is above the horizon. In solar eclipses, the light reflected by the atmosphere diminishes the obscurity they produce. Even in total eclipses the higher part of the atmosphere is enlightened by a part of the sun’s disc, and reflects its rays to the earth. The whole disc of the new moon is frequently visible from atmospheric reflection. During the eclipse of the 19th of March, 1849, the spots on the lunar disc were distinctly visible, and during that of 1856 the moon was like a beautiful rose-coloured ball floating in the ether: the colour is owing to the refraction of the sun’s light passing through the earth’s atmosphere.

In total solar eclipses the slender luminous arc that is visible for a few seconds before the sun vanishes and also before he reappears, resembles a string of pearls surrounding the dark edge of the moon; it is occasioned by the sun’s rays passing between the tops of the lunar mountains: it occurs likewise in annular eclipses.

A phenomenon altogether unprecedented was seen during the total eclipse of the sun which happened on the 8th of July, 1842. The moon was like a black patch on the sky surrounded by a faint whitish light or corona about the eighth of the moon’s diameter in breadth, which is supposed to be the solar atmosphere rendered visible by the intervention of the moon. In this whitish corona there appeared three rose-coloured flames like the teeth of a saw. Similar flames were also seen in the white corona of the total eclipse which took place in 1851, and a long rose-coloured chain of what appeared to be jagged mountains or sierras united at the base by a red band seemed to be raised into the corona by mirage; but there is no doubt that the corona and red phenomena belong to the sun. This red chain was so bright that Mr. Airy saw it illuminate the northern horizon through an azimuth of 90° with red light. M. Faye attributes the rose-coloured protuberances to the constitution of the sun, which, like Sir William Herschel, he conceives to be an incandescent globe, consisting of two concentric parts of very unequal density, the internal part being a dark spherical mass, the external a very extensive atmosphere, at a certain height in which there is a stratum of luminous clouds which constitutes the photosphere of the sun; above this rises his real atmosphere, so rare as to be only visible as a white aureola or corona during total and annular eclipses. M. Faye conceives that from the central mass gaseous eruptions issue, which form the spots by dissipating and partly extinguishing the luminous clouds, and then rising into the rare atmosphere above that they appear as rose-coloured protuberances during annular eclipses. He estimates that the volume of these vapours sometimes surpasses that of the earth a thousand or even two thousand times. Sir William Herschel attributed the spots to occasional openings in the luminous coating, which seems to be always in motion; but whatever the cause of the spots may be, it is certainly periodical. The white corona and beads were seen during the eclipse of the 15th March, 1858, but there were no rose-coloured appearances, in England at least; but the sky was clouded, so that the eclipse was only visible at intervals.

Planets sometimes eclipse one another. On the 17th of May, 1737, Mercury was eclipsed by Venus near their inferior conjunction; Mars passed over Jupiter on the 9th of January, 1591; and on the 30th of October, 1825, the moon eclipsed Saturn. These phenomena, however, happen very seldom, because all the planets, or even a part of them, are very rarely seen in conjunction at once; that is, in the same part of the heavens at the same time. More than 2500 years before our era the five great planets were in conjunction. On the 15th of September, 1186, a similar assemblage took place between the constellations of Virgo and Libra; and in 1801 the Moon, Jupiter, Saturn, and Venus were united in the heart of the Lion. These conjunctions are so rare, that Lalande has computed that more than seventeen millions of millions of years separate the epochs of the contemporaneous conjunctions of the six great planets.

The motions of the moon have now become of more importance to the navigator and geographer than those of any other heavenly body, from the precision with which terrestrial longitude is determined by occultations of stars, and by lunar distances. In consequence of the retrograde motion of the nodes of the lunar orbit, at the rate of 3ʹ 10ʺ·64 daily, these points make a tour of the heavens in a little more than eighteen years and a half. This causes the moon to move round the earth in a kind of spiral, so that her disc at different times passes over every point in a zone of the heavens extending rather more than 5° 9ʹ on each side of the ecliptic. It is therefore evident that at one time or other she must eclipse every star and planet she meets with in this space. Therefore the occultation of a star by the moon is a phenomenon of frequent occurrence. The moon seems to pass over the star, which almost instantaneously vanishes at one side of her disc, and after a short time as suddenly reappears on the other. A lunar distance is the observed distance of the moon from the sun, or from a particular star or planet, at any instant. The lunar theory is brought to such perfection, that the times of these phenomena, observed under any meridian, when compared with those computed for that of Greenwich, and given in the Nautical Almanac, furnish the longitude of the observer within a few miles (N. 95.)

From the lunar theory, the mean distance of the sun from the earth, and thence the whole dimensions of the solar system, are known; for the forces which retain the earth and moon in their orbits are respectively proportional to the radii vectores of the earth and moon, each being divided by the square of its periodic time. And, as the lunar theory gives the ratio of the forces, the ratio of the distances of the sun and moon from the earth is obtained. Hence it appears that the sun’s mean distance from the earth is 399·7 or nearly 400 times greater than that of the moon. The method of finding the absolute distances of the celestial bodies, in miles, is in fact the same with that employed in measuring the distances of terrestrial objects. From the extremities of a known base (N. 116), the angles which the visual rays from the object form with it are measured; their sum subtracted from two right angles gives the angle opposite the base; therefore, by trigonometry, all the angles and sides of the triangle may be computed—consequently the distance of the object is found. The angle under which the base of the triangle is seen from the object is the parallax of that object. It evidently increases and decreases with the distance. Therefore the base must be very great indeed to be visible from the celestial bodies. The globe itself, whose dimensions are obtained by actual admeasurement, furnishes a standard of measures with which we compare the distances, masses, densities, and volumes of the sun and planets.

SECTION VI.

Form of the Earth and Planets—Figure of a Homogeneous Spheroid in Rotation—Figure of a Spheroid of variable Density—Figure of the Earth, supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree of the Meridian—Compression and Size of the Earth from Degrees of Meridian—Figure of Earth from the Pendulum.

THE theoretical investigation of the figure of the earth and planets is so complicated, that neither the geometry of Newton, nor the refined analysis of La Place, has attained more than an approximation. The solution of that difficult problem has been accomplished by our distinguished countryman Mr. Ivory. The investigation has been conducted by successive steps, beginning with a simple case, and then proceeding to the more difficult. But, in all, the forces which occasion the revolutions of the earth and planets are omitted, because, by acting equally upon all the particles, they do not disturb their mutual relations. A fluid mass of uniform density, whose particles mutually gravitate to each other, will assume the form of a sphere when at rest. But, if the sphere begins to revolve, every particle will describe a circle (N. 117), having its centre in the axis of revolution. The planes of all these circles will be parallel to one another and perpendicular to the axis, and the particles will have a tendency to fly from that axis in consequence of the centrifugal force arising from the velocity of rotation. The force of gravity is everywhere perpendicular to the surface (N. 118), and tends to the interior of the fluid mass; whereas the centrifugal force acts perpendicularly to the axis of rotation, and is directed to the exterior. And, as its intensity diminishes with the distance from the axis of rotation, it decreases from the equator to the poles, where it ceases. Now it is clear that these two forces are in direct opposition to each other in the equator alone, and that gravity is there diminished by the whole effect of the centrifugal force, whereas, in every other part of the fluid, the centrifugal force is resolved into two parts, one of which, being perpendicular to the surface, diminishes the force of gravity; but the other, being at a tangent to the surface, urges the particles towards the equator, where they accumulate till their numbers compensate the diminution of gravity, which makes the mass bulge at the equator, and become flattened at the poles. It appears, then, that the influence of the centrifugal force is most powerful at the equator, not only because it is actually greater there than elsewhere, but because its whole effect is employed in diminishing gravity, whereas, in every other point of the fluid mass, it is only a part that is so employed. For both these reasons, it gradually decreases towards the poles, where it ceases. On the contrary, gravity is least at the equator, because the particles are farther from the centre of the mass, and increases towards the poles, where it is greatest. It is evident, therefore, that, as the centrifugal force is much less than the force of gravity—gravitation, which is the difference between the two, is least at the equator, and continually increases towards the poles, where it is a maximum. On these principles Sir Isaac Newton proved that a homogeneous fluid (N. 119) mass in rotation assumes the form of an ellipsoid of revolution (N. 120), whose compression is 1/230. Such, however, cannot be the form of the earth, because the strata increase in density towards the centre. The lunar inequalities also prove the earth to be so constructed; it was requisite, therefore, to consider the fluid mass to be of variable density. Including this condition, it has been found that the mass, when in rotation, would still assume the form of an ellipsoid of revolution (N. 120); that the particles of equal density would arrange themselves in concentric elliptical strata (N. 121), the most dense being in the centre; but that the compression or flattening would be less than in the case of the homogeneous fluid. The compression is still less when the mass is considered to be, as it actually is, a solid nucleus, decreasing regularly in density from the centre to the surface, and partially covered by the ocean, because the solid parts, by their cohesion, nearly destroy that part of the centrifugal force which gives the particles a tendency to accumulate at the equator, though not altogether; otherwise the sea, by the superior mobility of its particles, would flow towards the equator and leave the poles dry. Besides, it is well known that the continents at the equator are more elevated than they are in higher latitudes. It is also necessary for the equilibrium of the ocean that its density should be less than the mean density of the earth, otherwise the continents would be perpetually liable to inundations from storms and other causes. On the whole, it appears from theory, that a horizontal line passing round the earth through both poles must be nearly an ellipse, having its major axis in the plane of the equator, and its minor axis coincident with the axis of the earth’s rotation (N. 122). It is easy to show, in a spheroid whose strata are elliptical, that the increase in the length of the radii (N. 123), the decrease of gravitation, and the increase in the length of the arcs of the meridian, corresponding to angles of one degree, from the poles to the equator, are all proportional to the square of the cosine of the latitude (N. 124). These quantities are so connected with the ellipticity of the spheroid, that the total increase in the length of the radii is equal to the compression or flattening, and the total diminution in the length of the arcs is equal to the compression, multiplied by three times the length of an arc of one degree at the equator. Hence, by measuring the meridian curvature of the earth, the compression, and consequently its figure, become known. This, indeed, is assuming the earth to be an ellipsoid of revolution; but the actual measurement of the globe will show how far it corresponds with that solid in figure and constitution.

The courses of the great rivers, which are in general navigable to a considerable extent, prove that the curvature of the land differs but little from that of the ocean; and, as the heights of the mountains and continents are inconsiderable when compared with the magnitude of the earth, its figure is understood to be determined by a surface at every point perpendicular to the direction of gravitation, or of the plumb-line, and is the same which the sea would have if it were continued all round the earth beneath the continents. Such is the figure that has been measured in the following manner:—

A terrestrial meridian is a line passing through both poles, all the points of which have their noon contemporaneously. Were the lengths and curvatures of different meridians known, the figure of the earth might be determined. But the length of one degree is sufficient to give the figure of the earth, if it be measured on different meridians, and in a variety of latitudes. For, if the earth were a sphere, all degrees would be of the same length; but, if not, the lengths of the degrees would be greater, exactly in proportion as the curvature is less. A comparison of the length of a degree in different parts of the earth’s surface will therefore determine its size and form.

An arc of the meridian may be measured by determining the latitude of its extreme points by astronomical observations (N. 125), and then measuring the distance between them in feet or fathoms. The distance thus determined on the surface of the earth, divided by the degrees and parts of a degree contained in the difference of the latitudes, will give the exact length of one degree, the difference of the latitudes being the angle contained between the verticals at the extremities of the arc. This would be easily accomplished were the distance unobstructed and on a level with the sea. But, on account of the innumerable obstacles on the surface of the earth, it is necessary to connect the extreme points of the arc by a series of triangles (N. 126), the sides and angles of which are either measured or computed, so that the length of the arc is ascertained with much laborious calculation. In consequence of the irregularities of the surface each triangle is in a different plane. They must therefore be reduced by computation to what they would have been had they been measured on the surface of the sea. And, as the earth may in this case be esteemed spherical, they require a correction to reduce them to spherical triangles. The officers who conducted the trigonometrical survey, in measuring 500 feet of a base in Ireland twice over, found that the difference in the two measurements did not amount to the 800th part of an inch; and in the General Survey of Great Britain, five bases were measured from 5 to 7 miles long, and some of them 400 miles apart, yet, when connected by series of triangles, the measured and computed lengths did not differ by more than 3 inches, an unparalleled degree of accuracy; but such is the accuracy with which these operations are conducted.

Arcs of the meridian have been measured in a variety of latitudes in both hemispheres, as well as arcs perpendicular to the meridian. From these measurements it appears that the length of the degrees increases from the equator to the poles, nearly in proportion to the square of the sine of the latitude (N. 127). Consequently, the convexity of the earth diminishes from the equator to the poles.

Were the earth an ellipsoid of revolution, the meridians would be ellipses whose lesser axes would coincide with the axis of rotation, and all the degrees measured between the pole and the equator would give the same compression when combined two and two. That, however, is far from being the case. Scarcely any of the measurements give exactly the same results, chiefly on account of local attractions, which cause the plumb-line to deviate from the vertical. The vicinity of mountains produces that effect. One of the most remarkable anomalies of this kind has been observed in certain localities of northern Italy, where the action of some dense subterraneous matter causes the plumb-line to deviate seven or eight times more than it did from the attraction of Chimborazo, in the observations of Bouguer, while measuring a degree of the meridian at the equator. In consequence of this local attraction, the degrees of the meridian in that part of Italy seem to increase towards the equator through a small space, instead of decreasing, as if the earth was drawn out at the poles, instead of being flattened.

Many other discrepancies occur, but from the mean of the five principal measurements of arcs in Peru, India, France, England, and Lapland, Mr. Ivory has deduced that the figure which most nearly follows this law is an ellipsoid of revolution whose equatorial radius is 3962·824 miles, and the polar radius 3949·585 miles. The difference, or 13·239 miles, divided by the equatorial radius, is 1/299 nearly[3] (N. 128). This fraction is called the compression of the earth, and does not differ much from that given by the lunar inequalities. Since the preceding quantities were determined, arcs of the meridian have been measured in various parts of the globe, of which the most extensive are the Russian arc of 25° 20ʹ between the Glacial Sea and the Danube, conducted under the superintendence of M. Struve, and the Indian arc extended to 21° 21ʹ, by Colonel Everest. The compression deduced by Bessel from the sum of ten arcs is 298-3/4, the equatorial radius 3962·802, and the polar 3949·554 miles, whilst Mr. Airy arrives at an almost identical result (3962·824, 3949·585, and 298-83/100) from a consideration of all the arcs, measured up to 1831, including the great Indian and Russian ones. If we assume the earth to be a sphere, the length of a degree of the meridian is 69-14/100 English miles. Therefore 360 degrees, or the whole equatorial circumference of the globe, is 24,899 English miles. Eratosthenes, who died 194 years before the Christian era, was the first to give an approximate value of the earth’s circumference, by the measurement of an arc between Alexandria and Syene.

There is another method of finding the figure of the earth, totally different from the preceding, solely depending upon the increase of gravitation from the equator to the poles. The force of gravitation at any place is measured by the descent of a heavy body during the first second of its fall. And the intensity of the centrifugal force is measured by the deflection of any point from the tangent in a second. For, since the centrifugal force balances the attraction of the earth, it is an exact measure of the gravitating force. Were the attraction to cease, a body on the surface of the earth would fly off in the tangent by the centrifugal force, instead of bending round in the circle of rotation. Therefore, the deflection of the circle from the tangent in a second measures the intensity of the earth’s attraction, and is equal to the versed sine of the arc described during that time, a quantity easily determined from the known velocity of the earth’s rotation. Whence it has been found that at the equator the centrifugal force is equal to the 289th part of gravity. Now, it is proved by analysis that, whatever the constitution of the earth and planets may be, if the intensity of gravitation at the equator be taken equal to unity, the sum of the compression of the ellipsoid, and the whole increase of gravitation from the equator to the pole, is equal to five halves of the ratio of the centrifugal force to gravitation at the equator. This quantity with regard to the earth is 5/2 of 1/289 or 1/115·2. Consequently, the compression of the earth is equal to 1/115·2 diminished by the whole increase of gravitation. So that its form will be known, if the whole increase of gravitation from the equator to the pole can be determined by experiment. This has been accomplished by a method founded upon the following considerations:—If the earth were a homogeneous sphere without rotation, its attraction on bodies at its surface would be everywhere the same. If it be elliptical and of variable density, the force of gravity, theoretically, ought to increase from the equator to the pole, as unity plus a constant quantity multiplied into the square of the sine of the latitude (N. 127). But for a spheroid in rotation the centrifugal force varies, by the laws of mechanics, as the square of the sine of the latitude, from the equator, where it is greatest, to the pole, where it vanishes. And, as it tends to make bodies fly off the surface, it diminishes the force of gravity by a small quantity. Hence, by gravitation, which is the difference of these two forces, the fall of bodies ought to be accelerated from the equator to the poles proportionably to the square of the sine of the latitude; and the weight of the same body ought to increase in that ratio. This is directly proved by the oscillations of the pendulum (N. 129), which, in fact, is a falling body; for, if the fall of bodies be accelerated, the oscillations will be more rapid: in order, therefore, that they may always be performed in the same time, the length of the pendulum must be altered. By numerous and careful experiments it is proved that a pendulum, which oscillates 86,400 times in a mean day at the equator, will do the same at every point of the earth’s surface, if its length be increased progressively to the pole, as the square of the sine of the latitude.

From the mean of these it appears that the whole decrease of gravitation from the poles to the equator is 0·0051449, which, subtracted from 1/115·2, shows that the compression of the terrestrial spheroid is about 1/285·26. This value has been deduced by the late Mr. Baily, president of the Astronomical Society, who devoted much attention to this subject; at the same time, it may be observed that no two sets of pendulum experiments give the same result, probably from local attractions. The compression obtained by this method does not differ much from that given by the lunar inequalities, nor from the arcs in the direction of the meridian, and those perpendicular to it. The near coincidence of these three values, deduced by methods so entirely independent of each other, shows that the mutual tendencies of the centres of the celestial bodies to one another, and the attraction of the earth for bodies at its surface, result from the reciprocal attraction of all their particles. Another proof may be added. The nutation of the earth’s axis and the precession of the equinoxes (N. 146) are occasioned by the action of the sun and moon on the protuberant matter at the earth’s equator. And, although these inequalities do not give the absolute value of the terrestrial compression, they show that the fraction expressing it is comprised between the limits 1/279 and 1/573.

It might be expected that the same compression should result from each, if the different methods of observation could be made without error. This, however, is not the case; for after allowance has been made for every cause of error, such discrepancies are found, both in the degrees of the meridian and in the length of the pendulum, as show that the figure of the earth is very complicated. But they are so small, when compared with the general results, that they may be disregarded. The compression deduced from the mean of the whole appears not to differ much from 1/300; that given by the lunar theory has the advantage of being independent of the irregularities of the earth’s surface and of local attractions. The regularity with which the observed variation in the length of the pendulum follows the law of the square of the sine of the latitude proves the strata to be elliptical, and symmetrically disposed round the centre of gravity of the earth, which affords a strong presumption in favour of its original fluidity. It is remarkable how little influence the sea has on the variation of the lengths of the arcs of the meridian, or on gravitation; neither does it much affect the lunar inequalities, from its density being only about a fifth of the mean density of the earth. For, if the earth were to become fluid, after being stripped of the ocean, it would assume the form of an ellipsoid of revolution whose compression is 1/304·8, which differs very little from that determined by observation, and proves, not only that the density of the ocean is inconsiderable, but that its mean depth is very small. There are profound cavities in the bottom of the sea, but its mean depth probably does not much exceed the mean height of the continents and islands above its level. On this account, immense tracts of land may be deserted or overwhelmed by the ocean, as appears really to have been the case, without any great change in the form of the terrestrial spheroid. The variation in the length of the pendulum was first remarked by Richter in 1672, while observing transits of the fixed stars across the meridian at Cayenne, about five degrees north of the equator. He found that his clock lost at the rate of 2^m 28^s daily, which induced him to determine the length of a pendulum beating seconds in that latitude; and, repeating the experiments on his return to Europe, he found the seconds’ pendulum at Paris to be more than the twelfth of an inch longer than that at Cayenne. The form and size of the earth being determined, a standard of measure is furnished with which the dimensions of the solar system may be compared.

SECTION VII.

Parallax—Lunar Parallax found from Direct Observation—Solar Parallax deduced from the Transit of Venus—Distance of the Sun from the Earth—Annual Parallax—Distance of the Fixed Stars.

THE parallax of a celestial body is the angle under which the radius of the earth would be seen if viewed from the centre of that body; it affords the means of ascertaining the distances of the sun, moon, and planets (N. 130). When the moon is in the horizon at the instant of rising or setting, suppose lines to be drawn from her centre to the spectator and to the centre of the earth: these would form a right-angled triangle with the terrestrial radius, which is of a known length; and, as the parallax or angle at the moon can be measured, all the angles and one side are given; whence the distance of the moon from the centre of the earth may be computed. The parallax of an object may be found, if two observers under the same meridian, but at a very great distance from one another, observe its zenith distances on the same day at the time of its passage over the meridian. By such contemporaneous observations at the Cape of Good Hope and at Berlin, the mean horizontal parallax of the moon was found to be 3459ʺ, whence the mean distance of the moon is about sixty times the greatest terrestrial radius, or 237,608 miles nearly.[4] Since the parallax is equal to the radius of the earth divided by the distance of the moon, it varies with the distance of the moon from the earth under the same parallel of latitude, and proves the ellipticity of the lunar orbit. When the moon is at her mean distance, it varies with the terrestrial radii, thus showing that the earth is not a sphere (N. 131).

Although the method described is sufficiently accurate for finding the parallax of an object as near as the moon, it will not answer for the sun, which is so remote that the smallest error in observation would lead to a false result. But that difficulty is obviated by the transits of Venus. When that planet is in her nodes (N. 132), or within 1-1/4° of them, that is, in, or nearly in, the plane of the ecliptic, she is occasionally seen to pass over the sun like a black spot. If we could imagine that the sun and Venus had no parallax, the line described by the planet on his disc, and the duration of the transit, would be the same to all the inhabitants of the earth. But, as the semi-diameter of the earth has a sensible magnitude when viewed from the centre of the sun, the line described by the planet in its passage over his disc appears to be nearer to his centre, or farther from it, according to the position of the observer; so that the duration of the transit varies with the different points of the earth’s surface at which it is observed (N. 133). This difference of time, being entirely the effect of parallax, furnishes the means of computing it from the known motions of the earth and Venus, by the same method as for the eclipses of the sun. In fact, the ratio of the distances of Venus and the sun from the earth at the time of the transit is known from the theory of their elliptical motion. Consequently the ratio of the parallaxes of these two bodies, being inversely as their distances, is given; and as the transit gives the difference of the parallaxes, that of the sun is obtained. In 1769 the parallax of the sun was determined by observations of a transit of Venus made at Wardhus in Lapland, and at Tahiti in the South Sea. The latter observation was the object of Cook’s first voyage. The transit lasted about six hours at Tahiti, and the difference in duration at these two stations was eight minutes; whence the sun’s horizontal parallax was found to be 8ʺ·72. But by other considerations it has been reduced by Professor Encke to 8ʺ·5776; from which the mean distance of the sun appears to be about ninety-five millions of miles. This is confirmed by an inequality in the motion of the moon, which depends upon the parallax of the sun, and which, when compared with observation, gives 8ʺ·6 for the sun’s parallax. The transits of Venus in 1874 and 1882 will be unfavourable for ascertaining the accuracy of the solar parallax, and no other transit of that planet will take place till the twenty-first century; but in the mean time recourse may be had to the oppositions of Mars.

The parallax of Venus is determined by her transits; that of Mars by direct observation, and it is found to be nearly double that of the sun, when the planet is in opposition. The distance of these two planets from the earth is therefore known in terrestrial radii, consequently their mean distances from the sun may be computed; and as the ratios of the distances of the planets from the sun are known by Kepler’s law, of the squares of the periodic times of any two planets being as the cubes of their mean distances from the sun, their absolute distances in miles are easily found (N. 134). This law is very remarkable, in thus uniting all the bodies of the system, and extending to the satellites as well as the planets.

Far as the earth seems to be from the sun, Uranus is no less than nineteen, and Neptune thirty times farther. Situate on the verge of the system, the sun must appear from Uranus not much larger than Venus does to us, and from Neptune as a star of the fifth magnitude. The earth cannot even be visible as a telescopic object to a body so remote as either Uranus or Neptune. Yet man, the inhabitant of the earth, soars beyond the vast dimensions of the system to which his planet belongs, and assumes the diameter of its orbit as the base of a triangle whose apex extends to the stars.

Sublime as the idea is, this assumption proves ineffectual, except in a very few cases; for the apparent places of the fixed stars are not sensibly changed by the earth’s annual revolution. With the aid derived from the refinements of modern astronomy, and of the most perfect instruments, a sensible parallax has been detected only in a very few of these remote suns. α Centauri has a parallax of one second of space, therefore it is the nearest known star, and yet it is more than two hundred thousand times farther from us than the sun is. At such a distance not only the terrestrial orbit shrinks to a point, but the whole solar system, seen in the focus of the most powerful telescope, might be eclipsed by the thickness of a spider’s thread. Light, flying at the rate of 190,000 miles in a second, would take more than three years to travel over that space. One of the nearest stars may therefore have been kindled or extinguished more than three years before we could have been aware of so mighty an event. But this distance must be small when compared with that of the most remote of the bodies which are visible in the heavens. The fixed stars are undoubtedly luminous like the sun: it is therefore probable that they are not nearer to one another than the sun is to the nearest of them. In the milky way and the other starry nebulæ, some of the stars that seem to us to be close to others may be far behind them in the boundless depth of space; nay, may be rationally supposed to be situate many thousand times farther off. Light would therefore require thousands of years to come to the earth from those myriads of suns of which our own is but “the remote companion.”

SECTION VIII.

Masses of Planets that have no Satellites determined from their Perturbations—Masses of the others obtained from the Motions of their Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial System—Mass of the Moon—Real Diameters of Planets, how obtained—Size of Sun, Densities of the Heavenly Bodies—Formation of Astronomical Tables—Requisite Data and Means of obtaining them.

THE masses of such planets as have no satellites are known by comparing the inequalities they produce in the motions of the earth and of each other, determined theoretically, with the same inequalities given by observation; for the disturbing cause must necessarily be proportional to the effect it produces. The masses of the satellites themselves may also be compared with that of the sun by their perturbations. Thus, it is found, from the comparison of a vast number of observations with La Place’s theory of Jupiter’s satellites, that the mass of the sun is no less than 65,000,000 times greater than the least of these moons. But, as the quantities of matter in any two primary planets are directly as the cubes of the mean distances at which their satellites revolve, and inversely as the squares of their periodic times (N. 135), the mass of the sun and of any planets which have satellites may be compared with the mass of the earth. In this manner it is computed that the mass of the sun is 354,936 times that of the earth; whence the great perturbations of the moon, and the rapid motion of the perigee and nodes of her orbit (N. 136). Even Jupiter, the largest of the planets, has been found by Professor Airy to be 1047·871 times less than the sun; and, indeed, the mass of the whole Jovial system is not more than the 1054·4th part of that of the sun. So that the mass of the satellites bears a very small proportion to that of their primary. The mass of the moon is determined from several sources—from her action on the terrestrial equator, which occasions the nutation in the axis of rotation; from her horizontal parallax; from an inequality she produces in the sun’s longitude; and from her action on the tides. The three first quantities, computed from theory and compared with their observed values, give her mass respectively equal to the 1/71, 1/74·2, and 1/69·2, part of that of the earth, which do not differ much from each other. Dr. Brinkley has found it to be 1/80 from the constant of lunar nutation: but, from the moon’s action in raising the tides, her mass appears to be about the 1/75 part of that of the earth—a value that cannot differ much from the truth.

The apparent diameters of the sun, moon, and planets are determined by measurement; therefore their real diameters may be compared with that of the earth; for the real diameter of a planet is to the real diameter of the earth, or 7926 miles, as the apparent diameter of the planet to the apparent diameter of the earth as seen from the planet, that is, to twice the parallax of the planet. According to Bessel, the mean apparent diameter of the sun is 1923ʺ·64, and with the solar parallax 8ʺ·5776, it will be found that the diameter of the sun is about 886,877 miles. Therefore, if the centre of the sun were to coincide with the centre of the earth, his volume would not only include the orbit of the moon, but would extend nearly as far again; for the moon’s mean distance from the earth is about sixty times the earth’s equatorial radius, or 238,793 miles: so that twice the distance of the moon is 477,586 miles, which differs but little from the solar radius; his equatorial radius is probably not much less than the major axis of the lunar orbit. The diameter of the moon is only 2160 miles; and Jupiter’s diameter of 88,200 miles is very much less than that of the sun; the diameter of Pallas does not much exceed 79 miles, so that an inhabitant of that planet, in one of our steam carriages, might go round his world in a few hours. The diameters of Lutetia and Atalanta are only 8 and 4 miles respectively; but the whole of the 55 telescopic planets are so small, that their united mass is probably not more than the fifth or sixth part of that of the moon.

The densities of bodies are proportional to their masses, divided by their volumes. Hence, if the sun and planets be assumed to be spheres, their volumes will be as the cubes of their diameters. Now, the apparent diameters of the sun and earth, at their mean distance, are 1923ʺ·6 and 17ʺ·1552, and the mass of the earth is the 354,936th part of that of the sun taken as the unit. It follows, therefore, that the earth is four times as dense as the sun. But the sun is so large that his attractive force would cause bodies to fall through about 334·65 feet in a second. Consequently, if he were habitable by human beings, they would be unable to move, since their weight would be thirty times as great as it is here. A man of moderate size would weigh about two tons at the surface of the sun; whereas at the surface of some of the new planets he would be so light that it would be impossible to stand steady, since he would only weigh a few pounds. The mean density of the earth has been determined by the following method. Since a comparison of the action of two planets upon a third gives the ratio of the masses of these two planets, it is clear that, if we can compare the effect of the whole earth with the effect of any part of it, a comparison may be instituted between the mass of the whole earth and the mass of that part of it. Now a leaden ball was weighed against the earth by comparing the effects of each upon a pendulum; the nearness of the smaller mass making it produce a sensible effect as compared with that of the larger: for by the laws of attraction the whole earth must be considered as collected in its centre. By this method it has been found that the mean density of the earth is 5·660 times greater than that of water at the temperature of 62° of Fahrenheit’s thermometer. The late Mr. Baily, whose accuracy as an experimental philosopher is acknowledged, was unremittingly occupied nearly four years in accomplishing this very important object. In order to ascertain the mean density of the earth still more perfectly, Mr. Airy made a series of experiments to compare the simultaneous oscillations of two pendulums, one at the bottom of the Harton coal-pit, 1260 feet deep, in Northumberland, and the other on the surface of the earth immediately above it. The oscillations of the pendulums were compared with an astronomical clock at each station, and the time was instantaneously transmitted from one to the other by a telegraphic wire. The oscillations were observed for more than 100 hours continuously, when it was found that the lower pendulum made 2-1/2 oscillations more in 24 hours than the upper one. The experiment was repeated for the same length of time with the same result; but on this occasion the upper pendulum was taken to the bottom of the mine and the lower brought to the surface. From the difference between the oscillations at the two stations it appears that gravitation at the bottom of the mine exceeds that at the surface by the 1/19190 part, and that the mean density of the earth is 6·565, which is greater than that obtained by Mr. Baily by ·89. While employed on the trigonometrical survey of Scotland, Colonel James determined the mean density of the earth to be 5·316, from a deviation of the plumb-line amounting to 2ʺ, caused by the attraction of Arthur’s Seat and the heights east of Edinburgh: it agrees more nearly with the density found by Mr. Baily than with that deduced from Mr. Airy’s experiments. All the planets and satellites appear to be of less density than the earth. The motions of Jupiter’s satellites show that his density increases towards his centre. Were his mass homogeneous, his equatorial and polar axes would be in the ratio of 41 to 36, whereas they are observed to be only as 41 to 38. The singular irregularities in the form of Saturn, and the great compression of Mars, prove the internal structure of these two planets to be very far from uniform.

Before entering on the theory of rotation, it may not be foreign to the subject to give some idea of the methods of computing the places of the planets, and of forming astronomical tables. Astronomy is now divided into the three distinct departments of theory, observation, and computation. Since the problem of the three bodies can only be solved by approximation, the analytical astronomer determines the position of a planet in space by a series of corrections. Its place in its circular orbit is first found, then the addition or subtraction of the equation of the centre (N. 48) to or from its mean place gives its position in the ellipse. This again is corrected by the application of the principal periodic inequalities. But, as these are determined for some particular position of the three bodies, they require to be corrected to suit other relative positions. This process is continued till the corrections become less than the errors of observation, when it is obviously unnecessary to carry the approximation further. The true latitude and distance of the planet from the sun are obtained by methods similar to those employed for the longitude.

As the earth revolves equably about its axis in 24 hours, at the rate of 15° in an hour, time becomes a measure of angular motion, and the principal element in astronomy, where the object is to determine the exact state of the heavens and the successive changes it undergoes in all ages, past, present, and to come. Now, the longitude, latitude, and distance of a planet from the sun are given in terms of the time, by general analytical formulæ. These formulæ will consequently give the exact place of the body in the heavens, for any time assumed at pleasure, provided they can be reduced to numbers. But before the calculator begins his task the observer must furnish the necessary data, which are, obviously, the forms of the orbits, and their positions with regard to the plane of the ecliptic (N. 57). It is therefore necessary to determine by observation, for each planet, the length of the major axis of its orbit, the excentricity, the inclination of the orbit to the plane of the ecliptic, the longitudes of its perihelion and ascending node at a given time, the periodic time of the planet, and its longitude at any instant arbitrarily assumed, as an origin from whence all its subsequent and antecedent longitudes are estimated. Each of these quantities is determined from that position of the planet on which it has most influence. For example, the sum of the greatest and least distances of the planet from the sun is equal to the major axis of the orbit, and their difference is equal to twice the excentricity. The longitude of the planet, when at its least distance from the sun, is the same with the longitude of the perihelion; the greatest latitude of the planet is equal to the inclination of the orbit: the longitude of the planet, when in the plane of the ecliptic in passing towards the north, is the longitude of the ascending node, and the periodic time is the interval between two consecutive passages of the planet through the same node, a small correction being made for the precession of the node during the revolution of the planet (N. 137). Notwithstanding the excellence of instruments and the accuracy of modern observers, unavoidable errors of observation can only be compensated by finding the value of each element from the mean of a thousand, or even many thousands of observations. For as it is probable that the errors are not all in one direction, but that some are in excess and others in defect, they will compensate each other when combined.

However, the values of the elements determined separately can only be regarded as approximate, because they are so connected that the estimation of any one independently will induce errors in the others. The excentricity depends upon the longitude of the perihelion, the mean motion depends upon the major axis, the longitude of the node upon the inclination of the orbit, and vice versâ. Consequently, the place of a planet computed with the approximate data will differ from its observed place. Then the difficulty is to ascertain what elements are most in fault, since the difference in question is the error of all; that is obviated by finding the errors of some thousands of observations, and combining them, so as to correct the elements simultaneously, and to make the sum of the squares of the errors a minimum with regard to each element (N. 138). The method of accomplishing this depends upon the Theory of Probabilities; a subject fertile in most important results in the various departments of science and of civil life, and quite indispensable in the determination of astronomical data. A series of observations continued for some years will give approximate values of the secular and periodic inequalities, which must be corrected from time to time, till theory and observation agree. And these again will give values of the masses of the bodies forming the solar system, which are important data in computing their motions. The periodic inequalities derived from a great number of observations are employed for the determination of the values of the masses till such time as the secular inequalities shall be perfectly known, which will then give them with all the necessary precision. When all these quantities are determined in numbers, the longitude, latitude, and distance of the planet from the sun are computed for stated intervals, and formed into tables, arranged according to the time estimated from a given epoch, so that the place of the body may be determined from them by inspection alone, at any instant for perhaps a thousand years before and after that epoch. By this tedious process, tables have been computed for all the great planets, and several of the small, besides the moon and the satellites of Jupiter. In the present state of astronomy the masses and elements of the orbits are pretty well known, so that the tables only require to be corrected from time to time as observations become more accurate. Those containing the motions of Jupiter, Saturn, and Uranus have already been twice constructed within the last thirty years, and the tables of Jupiter and Saturn agree almost perfectly with modern observation. The following prediction will be found in the sixth edition of this book, published in the year 1842: “Those of Uranus, however, are already defective, probably because the discovery of that planet in 1781 is too recent to admit of much precision in the determination of its motions, or that possibly it may be subject to disturbances from some unseen planet revolving about the sun beyond the present boundaries of our system. If, after a lapse of years, the tables formed from a combination of numerous observations should be still inadequate to represent the motions of Uranus, the discrepancies may reveal the existence, nay, even the mass and orbit, of a body placed for ever beyond the sphere of vision.”[5]

That prediction has been fulfilled since the seventh edition of this book was published. Not only the existence of Neptune, revolving at the distance of three thousand millions of miles from the sun, has been discovered from his disturbing action on Uranus, but his mass, the form and position of his orbit in space, and his periodic time had been determined before the planet had been seen, and the planet itself was discovered in the very point of the heavens which had been assigned to it. It had been noticed for years that the perturbation of Uranus had increased in an unaccountable manner (N. 139). After the disturbing action of all the known planets had been determined, it was found that, between the years 1833 and 1837, the observed and computed distance of Uranus from the sun differed by 240,000 miles, which is about the mean distance of the moon from the earth, while, in 1841, the error in the geocentric longitude of the planet amounted to 96ʺ. These discrepancies were therefore attributed to the attraction of some unseen and unknown planet, consequently they gave rise to a case altogether unprecedented in the history of astronomy. Heretofore it was required to determine the disturbing action of one known planet upon another. Whereas the inverse problem had now to be solved, in which it was required to find the place of an unknown body in the heavens, at a given time, together with its mass, and the form and position of its orbit, from the disturbance it produced on the motions of another. The difficulty was extreme, because all the elements of the orbit of Uranus were erroneous from the action of Neptune, and those of Neptune’s orbit were unknown. In this dilemma it was necessary to form some hypothesis with regard to the unknown planet; it was therefore assumed, according to Bode’s empirical law on the mean distances of the planets, that it was revolving at twice the distance of Uranus from the sun. In fact, the periodic time of Uranus is about 84 years, and, as the discrepancies in his motions increased slowly and regularly, it was evident that it would require a planet with a much longer periodic time to produce them—moreover, it was clear that the new planet must be exterior to Uranus, otherwise it would have disturbed the motions of Saturn.

Another circumstance tended to lessen the difficulty; the latitude of Uranus was not much affected, therefore it was concluded that the inclination of the orbit of the unknown body must be very small, and, as that of the orbit of Uranus is only 46ʹ 28ʺ·4, both planets were assumed to be moving in the plane of the ecliptic, and thus the elements of the orbit of the unknown planet were reduced from six to four. Having thus assumed that the unknown body was revolving in a circle in the plane of the ecliptic, the analytical expression of its action on the motion of Uranus, when in numerous points of its orbit, was compared with the observed longitude of Uranus, through a regular series of years, by means of which the faulty elements of the orbit of Uranus were eliminated, or got rid of, and there only remained a relation between the mass of the new planet and three of the elements of its orbit; and it then was necessary to assume such a value for two of them as would suit the rest. That was accomplished so dexterously, that the perturbations of Uranus were perfectly conformable to the motions of Neptune, moving in the orbit thus found, and the place of the new planet exactly agreed with observation. Subsequently its orbit and motions have been determined more accurately.

The honour of this admirable effort of genius is shared by Mr. Adams and M. Le Verrier, who, independently of each other, arrived at these wonderful results. Mr. Adams had determined the mass and apparent diameter of Neptune, with all the circumstances of its motion, eight months before M. Le Verrier had terminated his results, and had also pointed out the exact spot where the planet would be found; but the English observers neglected to look for it till M. Le Verrier made known his researches, and communicated its position to Dr. Galle, at Berlin, who found it the very first night he looked for it, and then it was evident that it would have been seen in the place Mr. Adams had assigned to it eight months before had it been looked for. So closely did the results of these two great mathematicians agree.

Neptune has a diameter of 39,793 miles, consequently he is nearly 200 times larger than the earth, and may be seen with a telescope of moderate power. His motion is retrograde at present, and six times slower than that of the earth. At so great a distance from the sun it can only have the 1/1300th part of the light and heat the earth receives; but having a satellite, the deficiency of light may in some measure be supplied.

The prediction may now be transferred from Uranus to Neptune, whose perturbations may reveal the existence of a planet still further removed, which may for ever remain beyond the reach of telescopic vision—yet its mass, the form and position of its orbit, and all the circumstances of its motion may become known, and the limits of the solar system may still be extended hundreds of millions of miles.

The mean distance of Neptune from the sun has subsequently proved to be only 2893 millions of miles, and the period of his revolution 166 years, so that Baron Bode’s law, of the interval between the orbits of any two planets being twice as great as the inferior interval and half of the superior, fails in the case of Neptune, though it was useful on the first approximation to his motions; and since Bode’s time it has led to the discovery of fifty-five telescopic planets revolving between the orbits of Mars and Jupiter, some by chance, others by a systematic search on the faith that these minute planets are fragments of a larger body that has exploded, because their distances from the sun are nearly the same; the lines of the nodes of some of their orbits terminate in the same points of the heavens, and the inclinations of their orbits are such as might have taken place from their mutual disturbances at the time of the explosion, and while yet they were near enough for their forms to affect their motions. The orbits of the more recently discovered asteroids show that this hypothesis is untenable.

The tables of Mars, Venus, and even those of the sun, have been greatly improved, and still engage the attention of our Astronomer Royal, Mr. Airy, and other eminent astronomers. We are chiefly indebted to the German astronomers for tables of the four older telescopic planets, Vesta, Juno, Ceres, and Pallas; the others have only been discovered since the year 1845.

The determination of the path of a planet when disturbed by all the others, a problem which has employed the talents of the greatest astronomers, from Newton to the present day, is only successfully accomplished with regard to the older planets, which revolve in nearly circular orbits, but little inclined to the plane of the ecliptic. When the excentricity and inclination of the orbits are great, their analysis fails, because the series expressing the co-ordinates of the bodies become extremely complicated, and do not converge when applied to comets and the telescopic planets. This difficulty has been overcome by Sir John Lubbock, and other mathematicians, who have the honour of having completed the theory of planetary motion, which becomes every day of more importance, from the new planets that have been discovered, and also with regard to comets, many of which return to the sun at regular intervals, and from whose perturbations the masses of the planets will be more accurately determined, and the retarding influence of the ethereal medium better known.

SECTION IX.

Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation of the Moon and other Satellites equal to the Periods of their Revolutions—Form of Lunar Spheroid—Libration, Aspect, and Constitution of the Moon—Rotation of Jupiter’s Satellites.

THE oblate form of several of the planets indicates rotatory motion. This has been confirmed in most cases by tracing spots on their surface, by which their poles and times of rotation have been determined. The rotation of Mercury is unknown, on account of his proximity to the sun; that of the new planets has not yet been ascertained. The sun revolves in twenty-five days and ten hours about an axis which is directed towards a point half-way between the pole-star and α of Lyra, the plane of rotation being inclined by 7° 30ʹ, or a little more than seven degrees, to the plane of the ecliptic: it may therefore be concluded that the sun’s mass is a spheroid, flattened at the poles. From the rotation of the sun, there was every reason to believe that he has a progressive motion in space, a circumstance which is confirmed by observation. But, in consequence of the reaction of the planets, he describes a small irregular orbit about the centre of gravity of the system, never deviating from his position by more than twice his own diameter, or a little more than seven times the distance of the moon from the earth. The sun and all his attendants rotate from west to east, on axes that remain nearly parallel to themselves (N. 140) in every point of their orbit, and with angular velocities that are sensibly uniform (N. 141). Although the uniformity in the direction of their rotation is a circumstance hitherto unaccounted for in the economy of nature, yet, from the design and adaptation of every other part to the perfection of the whole, a coincidence so remarkable cannot be accidental. And, as the revolutions of the planets and satellites are also from west to east, it is evident that both must have arisen from the primitive cause which determined the planetary motions.[6] Indeed, La Place has computed the probability to be as four millions to one that all the motions of the planets, both of rotation and revolution, were at once imparted by an original common cause, but of which we know neither the nature nor the epoch.

The larger planets rotate in shorter periods than the smaller planets and the earth. Their compression is consequently greater, and the action of the sun and of their satellites occasions a nutation in their axes and a precession of their equinoxes (N. 147) similar to that which obtains in the terrestrial spheroid, from the attraction of the sun and moon on the prominent matter at the equator. Jupiter revolves in less than ten hours round an axis at right angles to certain dark belts or bands, which always cross his equator. (See Plate 1.) This rapid rotation occasions a very great compression in his form. His equatorial axis exceeds his polar axis by 6000 miles, whereas the difference in the axes of the earth is only about twenty-six and a half. It is an evident consequence of Kepler’s law of the squares of the periodic times of the planets being as the cubes of the major axes of their orbits, that the heavenly bodies move slower the farther they are from the sun. In comparing the periods of the revolutions of Jupiter and Saturn with the times of their rotation, it appears that a year of Jupiter contains nearly ten thousand of his days, and that of Saturn about thirty thousand Saturnian days.

The appearance of Saturn is unparalleled in the system of the world. He is a spheroid nearly 1000 times larger than the earth, surrounded by a ring even brighter than himself, which always remains suspended in the plane of his equator: and, viewed with a very good telescope, it is found to consist of two concentric rings, divided by a dark band. The exterior ring, as seen through Mr. Lassell’s great equatorial at Malta, has a dark-striped band through the centre, and is altogether less bright than the interior ring, one half of which is extremely brilliant; while the interior half is shaded in rings like the seats in an amphitheatre. Mr. Lassell made the remarkable discovery of a dark transparent ring, whose edge coincides with the inner edge of the interior ring, and which occupies about half the space between it and Saturn. He compares it to a band of dark-coloured crape drawn across a portion of the disc of the planet, and the part projected upon the blue sky is also transparent. At the time these observations were made at Malta, Captain Jacob discovered the transparent ring at Madras. It is conjectured to be fluid; even the luminous rings cannot be very dense, since the density of Saturn himself is known to be less than the eighth part of that of the earth. A transit of the ring across a star might reveal something concerning this wonderful object. The ball of Saturn is striped by belts of different colours. At the time of these observations the part above the ring was bright white; at his equator there was a ruddy belt divided in two, above which were belts of a bluish green alternately dark and light, while at the pole there was a circular space of a pale colour. (See Plate 2.) The mean distance of the interior part of the double ring from the surface of the planet is about 22,240 miles, it is no less than 33,360 miles broad, but, by the estimation of Sir John Herschel, its thickness does not much exceed 100 miles, so that it appears like a plane. By the laws of mechanics, it is impossible that this body can retain its position by the adhesion of its particles alone. It must necessarily revolve with a velocity that will generate a centrifugal force sufficient to balance the attraction of Saturn. Observation confirms the truth of these principles, showing that the rings rotate from west to east about the planet in ten hours and a half, which is nearly the time a satellite would take to revolve about Saturn at the same distance. Their plane is inclined to the ecliptic, at an angle of 28° 10ʹ 44ʺ·5; in consequence of this obliquity of position, they always appear elliptical to us, but with an excentricity so variable as even to be occasionally like a straight line drawn across the planet. In the beginning of October, 1832, the plane of the rings passed through the centre of the earth; in that position they are only visible with very superior instruments, and appear like a fine line across the disc of Saturn. About the middle of December, in the same year, the rings became invisible, with ordinary instruments, on account of their plane passing through the sun. In the end of April, 1833, the rings vanished a second time, and reappeared in June of that year. Similar phenomena will occur as often as Saturn has the same longitude with either node of his rings. Each side of these rings has alternately fifteen years of sunshine and fifteen years of darkness.

It is a singular result of theory, that the rings could not maintain their stability of rotation if they were everywhere of uniform thickness; for the smallest disturbance would destroy the equilibrium, which would become more and more deranged, till, at last, they would be precipitated on the surface of the planet. The rings of Saturn must therefore be irregular solids, of unequal breadth in different parts of the circumference, so that their centres of gravity do not coincide with the centres of their figures. Professor Struve has also discovered that the centre of the rings is not concentric with the centre of Saturn. The interval between the outer edge of the globe of the planet and the outer edge of the rings on one side is 11ʺ·272, and, on the other side, the interval is 11ʺ·390, consequently there is an excentricity of the globe in the rings of 0ʺ·215. If the rings obeyed different forces, they would not remain in the same plane, but the powerful attraction of Saturn always maintains them and his satellites in the plane of his equator. The rings, by their mutual action, and that of the sun and satellites, must oscillate about the centre of Saturn, and produce phenomena of light and shadow whose periods extend to many years. According to M. Bessel the mass of Saturn’s ring is equal to the 1/118 part of that of the planet.

The periods of rotation of the moon and the other satellites are equal to the times of their revolutions, consequently these bodies always turn the same face to their primaries. However, as the mean motion of the moon is subject to a secular inequality, which will ultimately amount to many circumferences (N. 108), if the rotation of the moon were perfectly uniform and not affected by the same inequalities, it would cease exactly to counterbalance the motion of revolution; and the moon, in the course of ages, would successively and gradually discover every point of her surface to the earth. But theory proves that this never can happen; for the rotation of the moon, though it does not partake of the periodic inequalities of her revolution, is affected by the same secular variations, so that her motions of rotation and revolution round the earth will always balance each other, and remain equal. This circumstance arises from the form of the lunar spheroid, which has three principal axes of different lengths at right angles to each other.

The moon is flattened at her poles from her centrifugal force, therefore her polar axis is the least. The other two are in the plane of her equator, but that directed towards the earth is the greatest (N. 142). The attraction of the earth, as if it had drawn out that part of the moon’s equator, constantly brings the greatest axis, and consequently the same hemisphere, towards us, which makes her rotation participate in the secular variations of her mean motion of revolution. Even if the angular velocities of rotation and revolution had not been nicely balanced in the beginning of the moon’s motion, the attraction of the earth would have recalled the greatest axis to the direction of the line joining the centres of the moon and earth; so that it would have vibrated on each side of that line in the same manner as a pendulum oscillates on each side of the vertical from the influence of gravitation. No such libration is perceptible; and, as the smallest disturbance would make it evident, it is clear that, if the moon has ever been touched by a comet, the mass of the latter must have been extremely small. If it had been only the hundred thousandth part of that of the earth, it would have rendered the libration sensible. According to analysis, a similar libration exists in the motions of Jupiter’s satellites, which still remains insensible to observation, and yet the comet of 1770 passed twice through the midst of them.

The moon, it is true, is liable to librations depending upon the position of the spectator. At her rising, part of the western edge of her disc is visible, which is invisible at her setting, and the contrary takes place with regard to her eastern edge. There are also librations arising from the relative positions of the earth and moon in their respective orbits; but, as they are only optical appearances, one hemisphere will be eternally concealed from the earth. For the same reason the earth, which must be so splendid an object to one lunar hemisphere, will be for ever veiled from the other. On account of these circumstances, the remoter hemisphere of the moon has its day a fortnight long, and a night of the same duration, not even enlightened by a moon, while the favoured side is illuminated by the reflection of the earth during its long night. A planet exhibiting a surface thirteen times larger than that of the moon, with all the varieties of clouds, land, and water, coming successively into view, must be a splendid object to a lunar traveller in a journey to his antipodes. The great height of the lunar mountains probably has a considerable influence on the phenomena of her motion, the more so as her compression is small, and her mass considerable. In the curve passing through the poles, and that diameter of the moon which always points to the earth, nature has furnished a permanent meridian, to which the different spots on her surface have been referred, and their positions are determined with as much accuracy as those of many of the most remarkable places on the surface of our globe. According to the observations of Professor Secchi at Rome, the mountains of the moon are mostly volcanic and of three kinds. The first and oldest have their borders obliterated, so that they look like deep wells; the second, which are of an intermediate class, have elevated, and, for the most part, regular unbroken edges, with the ground around them raised to a prodigious extent in proportion to the size of the volcano, with generally an insulated rock in the centre of the crater. The third, and most recent class, are very small, and seem to be the last effort of the expiring volcanic force, which is probably now extinct.

The distance and minuteness of Jupiter’s satellites render it extremely difficult to ascertain their rotation. It was, however, accomplished by Sir William Herschel from their relative brightness. He observed that they alternately exceed each other in brilliancy, and, by comparing the maxima and minima of their illumination with their positions relatively to the sun and to their primary, he found that, like the moon, the time of their rotation is equal to the period of their revolution about Jupiter. Miraldi was led to the same conclusion with regard to the fourth satellite, from the motion of a spot on its surface.

SECTION X.

Rotation of the Earth invariable—Decrease in the Earth’s mean Temperature—Earth originally in a state of Fusion—Length of Day constant—Decrease of Temperature ascribed by Sir John Herschel to the variation in the Excentricity of the Terrestrial Orbit—Difference in the Temperature of the two Hemispheres erroneously ascribed to the Excess in the Length of Spring and Summer in the Southern Hemisphere; attributed by Sir Charles Lyell to the Operation of existing Causes—Three principal Axes of Rotation—Position of the Axis of Rotation on the Surface of the Earth invariable—Ocean not sufficient to restore the Equilibrium of the Earth if deranged—Its Density and mean Depth—Internal Structure of the Earth.

The rotation of the earth, which determines the length of the day, may be regarded as one of the most important elements in the system of the world. It serves as a measure of time, and forms the standard of comparison for the revolutions of the celestial bodies, which, by their proportional increase or decrease, would soon disclose any changes it might sustain. Theory and observation concur in proving that, among the innumerable vicissitudes which prevail throughout creation, the period of the earth’s diurnal rotation is immutable. The water of rivers, falling from a higher to a lower level, carries with it the velocity due to its revolution with the earth at a greater distance from the centre; it will therefore accelerate, although to an almost infinitesimal extent, the earth’s daily rotation. The sum of all these increments of velocity, arising from the descent of all the rivers on the earth’s surface, would in time become perceptible, did not nature, by the process of evaporation, raise the waters back to their sources, and thus, by again removing matter to a greater distance from the centre, destroy the velocity generated by its previous approach; so that the descent of rivers does not affect the earth’s rotation. Enormous masses projected by volcanoes from the equator to the poles, and the contrary, would indeed affect it, but there is no evidence of such convulsions. The disturbing action of the moon and planets, which has so powerful an effect on the revolution of the earth, in no way influences its rotation. The constant friction of the trade winds on the mountains and continents between the tropics does not impede its velocity, which theory even proves to be the same as if the sea, together with the earth, formed one solid mass. But, although these circumstances be insufficient, a variation in the mean temperature would certainly occasion a corresponding change in the velocity of rotation. In the science of dynamics it is a principle in a system of bodies or of particles revolving about a fixed centre, that the momentum or sum of the products of the mass of each into its angular velocity and distance from the centre is a constant quantity, if the system be not deranged by a foreign cause. Now, since the number of particles in the system is the same whatever its temperature may be, when their distances from the centre are diminished, their angular velocity must be increased, in order that the preceding quantity may still remain constant. It follows, then, that, as the primitive momentum of rotation with which the earth was projected into space must necessarily remain the same, the smallest decrease in heat, by contracting the terrestrial spheroid, would accelerate its rotation, and consequently diminish the length of the day. Notwithstanding the constant accession of heat from the sun’s rays, geologists have been induced to believe, from the fossil remains, that the mean temperature of the globe is decreasing.

The high temperature of mines, hot springs, and above all the internal fires which have produced, and do still occasion, such devastation on our planet, indicate an augmentation of heat towards its centre. The increase of density corresponding to the depth and the form of the spheroid, being what theory assigns to a fluid mass in rotation, concurs to induce the idea that the temperature of the earth was originally so high as to reduce all the substances of which it is composed to a state of fusion or of vapour, and that in the course of ages it has cooled down to its present state; that it is still becoming colder; and that it will continue to do so till the whole mass arrives at the temperature of the medium in which it is placed, or rather at a state of equilibrium between this temperature, the cooling power of its own radiation, and the heating effect of the sun’s rays.

Previous to the formation of ice at the poles, the ancient lands of northern latitudes might, no doubt, have been capable of producing those tropical plants preserved in the coal-measures, if indeed such plants could flourish without the intense light of a tropical sun. But, even if the decreasing temperature of the earth be sufficient to produce the observed effects, it must be extremely slow in its operation; for, in consequence of the rotation of the earth being a measure of the periods of the celestial motions, it has been proved that, if the length of the day had decreased by the three-thousandth part of a second since the observations of Hipparchus two thousand years ago, it would have diminished the secular equation of the moon by 44ʺ·4. It is, therefore, beyond a doubt that the mean temperature of the earth cannot have sensibly varied during that time. If, then, the appearances exhibited by the strata are really owing to a decrease of internal temperature, it either shows the immense periods requisite to produce geological changes, to which two thousand years are as nothing, or that the mean temperature of the earth had arrived at a state of equilibrium before these observations.

However strong the indications of the primitive fluidity of the earth, as there is no direct proof of it, the hypothesis can only be regarded as very probable. But one of the most profound philosophers and elegant writers of modern times has found in the secular variation of the excentricity of the terrestrial orbit an evident cause of decreasing temperature. That accomplished author, in pointing out the mutual dependencies of phenomena, says, “It is evident that the mean temperature of the whole surface of the globe, in so far as it is maintained by the action of the sun at a higher degree than it would have were the sun extinguished, must depend on the mean quantity of the sun’s rays which it receives, or—which comes to the same thing—on the total quantity received in a given invariable time; and, the length of the year being unchangeable in all the fluctuations of the planetary system, it follows that the total amount of solar radiation will determine, cæteris paribus, the general climate of the earth. Now, it is not difficult to show that this amount is inversely proportional to the minor axis of the ellipse described by the earth about the sun (N. 143), regarded as slowly variable; and that, therefore, the major axis remaining, as we know it to be, constant, and the orbit being actually in a state of approach to a circle, and consequently the minor axis being on the increase, the mean annual amount of solar radiation received by the whole earth must be actually on the decrease. We have, therefore, an evident real cause to account for the phenomenon.” The limits of the variation in the excentricity of the earth’s orbit are unknown. But, if its ellipticity has ever been as great as that of the orbit of Mercury or Pallas, the mean temperature of the earth must have been sensibly higher than it is at present. Whether it was great enough to render our northern climates fit for the production of tropical plants, and for the residence of the elephant and other animals now inhabitants of the torrid zone, it is impossible to say.

Of the decrease in temperature of the northern hemisphere there is abundant evidence in the fossil plants discovered in very high latitudes, which could only have existed in a tropical climate, and which must have grown near the spot where they are found, from the delicacy of their structure and the perfect state of their preservation. This change of temperature has been erroneously ascribed to an excess in the duration of spring and summer in the northern hemisphere, in consequence of the excentricity of the solar ellipse. The length of the seasons varies with the position of the perihelion (N. 64) of the earth’s orbit for two reasons. On account of the excentricity, small as it is, any line passing through the centre of the sun divides the terrestrial ellipse into two unequal parts, and by the laws of elliptical motion the earth moves through these two portions with unequal velocities. The perihelion always lies in the smaller portion, and there the earth’s motion is the most rapid. In the present position of the perihelion, spring and summer north of the equator exceed by about eight days the duration of the same seasons south of it. And 10,492 years ago the southern hemisphere enjoyed the advantage we now possess from the secular variation of the perihelion. Yet Sir John Herschel has shown that by this alternation neither hemisphere acquires any excess of light or heat above the other; for, although the earth is nearer to the sun while moving through that part of its orbit in which the perihelion lies than in the other part, and consequently receives a greater quantity of light and heat, yet as it moves faster it is exposed to the heat for a shorter time. In the other part of the orbit, on the contrary, the earth, being farther from the sun, receives fewer of his rays; but because its motion is slower, it is exposed to them for a longer time; and, as in both cases the quantity of heat and the angular velocity vary exactly in the same proportion, a perfect compensation takes place (N. 144). So that the excentricity of the earth’s orbit has little or no effect on the temperature corresponding to the difference of the seasons.

Sir Charles Lyell, in his excellent works on Geology, refers the increased cold of the northern hemisphere to the operation of existing causes with more probability than most theories that have been advanced in solution of this difficult subject. The loftiest mountains would be represented by a grain of sand on a globe six feet in diameter, and the depth of the ocean by a scratch on its surface. Consequently the gradual elevation of a continent or chain of mountains above the surface of the ocean, or their depression below it, is no very great event compared with the magnitude of the earth, and the energy of its subterranean fires, if the same periods of time be admitted in the progress of geological as in astronomical phenomena, which the successive and various races of extinct beings show to have been immense. Climate is always more intense in the interior of continents than in islands or sea-coasts. An increase of land within the tropics would therefore augment the general heat, and an increase in the temperate and frigid zones would render the cold more severe. Now it appears that most of the European, North Asiatic, and North American continents and islands were raised from the deep after the coal-measures were formed in which the fossil tropical plants are found; and a variety of geological facts indicate the existence of an ancient and extensive archipelago throughout the greater part of the northern hemisphere. Sir Charles Lyell is therefore of opinion that the climate of these islands must have been sufficiently mild, in consequence of the surrounding ocean, to clothe them with tropical plants, and render them a fit abode for the huge animals whose fossil remains are so often found; that the arborescent ferns and the palms of these regions, carried by streams to the bottom of the ocean, were imbedded in the strata which were by degrees heaved up by the subterranean fires during a long succession of ages, till the greater part of the northern hemisphere became dry land as it now is, and that the consequence has been a continual decrease of temperature.

It is evident, from the marine shells found on the tops of the highest mountains and in almost every part of the globe, that immense continents have been elevated above the ocean which must have engulfed others. Such a catastrophe would be occasioned by a variation in the position of the axis of rotation on the surface of the earth; for the seas tending to a new equator would leave some portions of the globe and overwhelm others. Now, it is found by the laws of mechanics that in every body, be its form or density what it may, there are at least three axes at right angles to each other, round any one of which, if the solid begins to rotate, it will continue to revolve for ever, provided it be not disturbed by a foreign cause, but that the rotation about any other axis will only be for an instant, and consequently the poles or extremities of the instantaneous axis of rotation would perpetually change their position on the surface of the body. In an ellipsoid of revolution the polar diameter and every diameter in the plane of the equator are the only permanent axes of rotation (N. 145). Hence, if the ellipsoid were to begin to revolve about any diameter between the pole and the equator, the motion would be so unstable that the axis of rotation and the position of the poles would change every instant. Therefore, as the earth does not differ much from this figure, if it did not turn round one of its principal axes, the position of the poles would change daily; the equator, which is 90° distant, would undergo corresponding variations; and the geographical latitudes of all places, being estimated from the equator, assumed to be fixed, would be perpetually changing. A displacement in the position of the poles of only two hundred miles would be sufficient to produce these effects, and would immediately be detected. But, as the latitudes are found to be invariable, it may be concluded that the terrestrial spheroid must have revolved about the same axis for ages. The earth and planets differ so little from ellipsoids of revolution, that in all probability any libration from one axis to another, produced by the primitive impulse which put them in motion, must have ceased soon after their creation from the friction of the fluids at their surface.

Theory also proves that neither nutation, precession, nor any of the disturbing forces that affect the system, have the smallest influence on the axis of rotation, which maintains a permanent position on the surface, if the earth be not disturbed in its rotation by a foreign cause, as the collision of a comet, which might have happened in the immensity of time. But, had that been the case, its effects would still have been perceptible in the variations of the geographical latitudes. If we suppose that such an event had taken place, and that the disturbance had been very great, equilibrium could then only have been restored with regard to a new axis of rotation by the rushing of the seas to the new equator, which they must have continued to do till the surface was everywhere perpendicular to the direction of gravity. But it is probable that such an accumulation of the waters would not be sufficient to restore equilibrium if the derangement had been great, for the mean density of the sea is only about a fifth part of the mean density of the earth, and the mean depth of the Pacific Ocean is supposed not to be more than four or five miles, whereas the equatorial diameter of the earth exceeds the polar diameter by about 26-1/2 miles. Consequently the influence of the sea on the direction of gravity is very small. And, as it thus appears that a great change in the position of the axis is incompatible with the law of equilibrium, the geological phenomena in question must be ascribed to an internal cause. Indeed it is now demonstrated that the strata containing marine diluvia, which are in lofty situations, must have been formed at the bottom of the ocean, and afterwards upheaved by the action of subterraneous fires. Besides, it is clear, from the mensuration of the arcs of the meridian and the length of the seconds’ pendulum, as well as from the lunar theory, that the internal strata and also the external outline of the globe are elliptical, their centres being coincident and their axes identical with that of the surface—a state of things which, according to the distinguished author lately quoted, is incompatible with a subsequent accommodation of the surface to a new and different state of rotation from that which determined the original distribution of the component matter. Thus, amidst the mighty revolutions which have swept innumerable races of organized beings from the earth, which have elevated plains and buried mountains in the ocean, the rotation of the earth and the position of the axes on its surface have undergone but slight variations.

The strata of the terrestrial spheroid are not only concentric and elliptical, but the lunar inequalities show that they increase in density from the surface of the earth to its centre. This would certainly have happened if the earth had originally been fluid, for the denser parts must have subsided towards the centre as it approached a state of equilibrium. But the enormous pressure of the superincumbent mass is a sufficient cause for the phenomenon. Professor Leslie observes that air compressed into the fiftieth part of its volume has its elasticity fifty times augmented. If it continues to contract at that rate, it would, from its own incumbent weight, acquire the density of water at the depth of thirty-four miles. But water itself would have its density doubled at the depth of ninety-three miles, and would even attain the density of quicksilver at a depth of 362 miles. Descending therefore towards the centre through nearly 4000 miles, the condensation of ordinary substances would surpass the utmost powers of conception. Dr. Young says that steel would be compressed into one-fourth and stone into one-eighth of its bulk at the earth’s centre. However, we are yet ignorant of the laws of compression of solid bodies beyond a certain limit; from the experiments of Mr. Perkins they appear to be capable of a greater degree of compression than has generally been imagined.

But a density so extreme is not borne out by astronomical observation. It might seem to follow therefore that our planet must have a widely cavernous structure, and that we tread on a crust or shell whose thickness bears a very small proportion to the diameter of its sphere. Possibly, too, this great condensation at the central regions may be counterbalanced by the increased elasticity due to a very elevated temperature.

SECTION XI.

Precession and Nutation—Their Effects on the Apparent Places of the Fixed Stars.

IT has been shown that the axis of rotation is invariable on the surface of the earth; and observation as well as theory prove that, were it not for the action of the sun and moon on the matter at the equator, it would remain exactly parallel to itself in every point of its orbit.

The attraction of an external body not only draws a spheroid towards it, but, as the force varies inversely as the square of the distance, it gives it a motion about its centre of gravity, unless when the attracting body is situated in the prolongation of one of the axes of the spheroid. The plane of the equator is inclined to the plane of the ecliptic at an angle of 23° 27ʹ 28ʺ·29; and the inclination of the lunar orbit to the same is 5° 8ʹ 47ʺ·9. Consequently, from the oblate figure of the earth, the sun and moon, acting obliquely and unequally on the different parts of the terrestrial spheroid, urge the plane of the equator from its direction, and force it to move from east to west, so that the equinoctial points have a slow retrograde motion on the plane of the ecliptic of 50ʺ·41 annually. The direct tendency of this action is to make the planes of the equator and ecliptic coincide, but it is balanced by the tendency of the earth to return to stable rotation about the polar diameter, which is one of its principal axes of rotation. Therefore the inclination of the two planes remains constant, as a top spinning preserves the same inclination to the plane of the horizon. Were the earth spherical, this effect would not be produced, and the equinoxes would always correspond with the same points of the ecliptic, at least as far as this kind of motion is concerned. But another and totally different cause which operates on this motion has already been mentioned. The action of the planets on one another and on the sun occasions a very slow variation in the position of the plane of the ecliptic, which affects its inclination to the plane of the equator, and gives the equinoctial points a slow but direct motion on the ecliptic of 0ʺ·31 annually, which is entirely independent of the figure of the earth, and would be the same if it were a sphere. Thus the sun and moon by moving the plane of the equator cause the equinoctial points to retrograde on the ecliptic: and the planets by moving the plane of the ecliptic give them a direct motion, though much less than the former. Consequently the difference of the two is the mean precession, which is proved both by theory and observation to be about 50ʺ·1 annually (N. 146).

As the longitudes of all the fixed stars are increased by this quantity, the effects of precession are soon detected. It was accordingly discovered by Hipparchus in the year 128 before Christ, from a comparison of his own observations with those of Timocharis 155 years before. In the time of Hipparchus the entrance of the sun into the constellation Aries was the beginning of spring; but since that time the equinoctial points have receded 30°, so that the constellations called the signs of the zodiac are now at a considerable distance from those divisions of the ecliptic which bear their names. Moving at the rate of 50ʺ·1 annually, the equinoctial points will accomplish a revolution in 25,868 years. But, as the precession varies in different centuries, the extent of this period will be slightly modified. Since the motion of the sun is direct, and that of the equinoctial points retrograde, he takes a shorter time to return to the equator than to arrive at the same stars; so that the tropical year of 365^d 5^h 48^m 49^s·7 must be increased by the time he takes to move through an arc of 50ʺ·1, in order to have the length of the sidereal year. The time required is 20^m 19^s·6, so that the sidereal year contains 365^d 6^h 9^m 9^s·6 mean solar days.

The mean annual precession is subject to a secular variation; for, although the change in the plane of the ecliptic in which the orbit of the sun lies be independent of the form of the earth, yet, by bringing the sun, moon, and earth into different relative positions from age to age, it alters the direct action of the two first on the prominent matter at the equator: on this account the motion of the equinox is greater by 0ʺ·455 now than it was in the time of Hipparchus. Consequently the actual length of the tropical year is about 4^s·21 shorter than it was at that time. The utmost change that it can experience from this cause amounts to 43 seconds.

Such is the secular motion of the equinoxes. But it is sometimes increased and sometimes diminished by periodic variations, whose periods depend upon the relative positions of the sun and moon with regard to the earth, and which are occasioned by the direct action of these bodies on the equator. Dr. Bradley discovered that by this action the moon causes the pole of the equator to describe a small ellipse in the heavens, the axes of which are 18ʺ·5 and 13ʺ·674, the longer being directed towards the pole of the ecliptic. The period of this inequality is about 19 years, the time employed by the nodes of the lunar orbit to accomplish a revolution. The sun causes a small variation in the description of this ellipse; it runs through its period in half a year. Since the whole earth obeys these motions, they affect the position of its axis of rotation with regard to the starry heavens, though not with regard to the surface of the earth; for in consequence of precession alone the pole of the equator moves in a circle round the pole of the ecliptic in 25,868 years, and by nutation alone it describes a small ellipse in the heavens every 19 years, on each side of which it deviates every half-year from the action of the sun. The real curve traced in the starry heavens by the imaginary prolongation of the earth’s axis is compounded of these three motions (N. 147). This nutation in the earth’s axis affects both the precession and obliquity with small periodic variations. But in consequence of the secular variation in the position of the terrestrial orbit, which is chiefly owing to the disturbing energy of Jupiter on the earth, the obliquity of the ecliptic is annually diminished, according to M. Bessel, by 0ʺ·457. This variation in the course of ages may amount to 10 or 11 degrees; but the obliquity of the ecliptic to the equator can never vary more than 2° 42ʹ or 3°, since the equator will follow in some measure the motion of the ecliptic.

It is evident that the places of all the celestial bodies are affected by precession and nutation. Their longitudes estimated from the equinox are augmented by precession; but, as it affects all the bodies equally, it makes no change in their relative positions. Both the celestial latitudes and longitudes are altered to a small degree by nutation; hence all observations must be corrected for these inequalities. In consequence of this real motion in the earth’s axis, the pole-star, forming part of the constellation of the Little Bear, which was formerly 12° from the celestial pole, is now within 1° 24ʹ of it, and will continue to approach it till it is within 1/2°, after which it will retreat from the pole for ages; and 12,934 years hence the star α Lyræ will come within 5° of the celestial pole, and become the polar star of the northern hemisphere.

SECTION XII.

Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—Equation of Time—English and French Subdivisions of Time—Leap Year—Christian Era—Equinoctial Time—Remarkable Eras depending upon the Position of the Solar Perigee—Inequality of the Lengths of the Seasons in the two Hemispheres—Application of Astronomy to Chronology—English and French Standards of Weights and Measures.

ASTRONOMY has been of immediate and essential use in affording invariable standards for measuring duration, distance, magnitude, and velocity. The mean sidereal day measured by the time elapsed between two consecutive transits of any star at the same meridian (N. 148), and the mean sidereal year which is the time included between two consecutive returns of the sun to the same star, are immutable units with which all great periods of time are compared; the oscillations of the isochronous pendulum measure its smaller portions. By these invariable standards alone we can judge of the slow changes that other elements of the system may have undergone. Apparent sidereal time, which is measured by the transit of the equinoctial point at the meridian of any place, is a variable quantity, from the effects of precession and nutation. Clocks showing apparent sidereal time are employed for observation, and are so regulated that they indicate 0^h 0^m 0^s at the instant the equinoctial point passes the meridian of the observatory. And as time is a measure of angular motion, the clock gives the distances of the heavenly bodies from the equinox by observing the instant at which each passes the meridian, and converting the interval into arcs at the rate of 15° to an hour.

The returns of the sun to the meridian and to the same equinox or solstice have been universally adopted as the measure of our civil days and years. The solar or astronomical day is the time that elapses between two consecutive noons or midnights. It is consequently longer than the sidereal day, on account of the proper motion of the sun during a revolution of the celestial sphere. But, as the sun moves with greater rapidity at the winter than at the summer solstice, the astronomical day is more nearly equal to the sidereal day in summer than in winter. The obliquity of the ecliptic also affects its duration; for near the equinoxes the arc of the equator is less than the corresponding arc of the ecliptic, and in the solstices it is greater (N. 149). The astronomical day is therefore diminished in the first case, and increased in the second. If the sun moved uniformly in the equator at the rate of 59ʹ 8ʺ·33 every day, the solar days would be all equal. The time therefore which is reckoned by the arrival of an imaginary sun at the meridian, or of one which is supposed to move uniformly in the equator, is denominated mean solar time, and is given by clocks and watches in common life. When it is reckoned by the arrival of the real sun at the meridian, it is true or apparent time, and is given by dials. The difference between the time shown by a clock and a dial is the equation of time given in the Nautical Almanac, sometimes amounting to as much as sixteen minutes. The apparent and mean time coincide four times in the year; when the sun’s daily motion in right ascension is equal to 59ʹ 8ʺ·33 in a mean solar day, which happens about the 16th of April, the 16th of June, the 1st of September, and the 25th of December.

The astronomical day begins at noon, but in common reckoning the day begins at midnight. In England it is divided into twenty-four hours, which are counted by twelve and twelve; but in France astronomers, adopting the decimal division, divide the day into ten hours, the hour into one hundred minutes, and the minute into a hundred seconds, because of the facility in computation, and in conformity with their decimal system of weights and measures. This subdivision is not now used in common life, nor has it been adopted in any other country; and although some scientific writers in France still employ that division of time, the custom is beginning to wear out. At one period during the French Revolution, the clock in the gardens of the Tuileries was regulated to show decimal time. The mean length of the day, though accurately determined, is not sufficient for the purposes either of astronomy or civil life. The tropical or civil year of 365^d 5^h 48^m 49^s·7, which is the time elapsed between the consecutive returns of the sun to the mean equinoxes or solstices, including all the changes of the seasons, is a natural cycle peculiarly suited for a measure of duration. It is estimated from the winter solstice, the middle of the long annual night under the north pole. But although the length of the civil year is pointed out by nature as a measure of long periods, the incommensurability that exists between the length of the day and the revolution of the sun renders it difficult to adjust the estimation of both in whole numbers. If the revolution of the sun were accomplished in 365 days, all the years would be of precisely the same number of days, and would begin and end with the sun at the same point of the ecliptic. But as the sun’s revolution includes the fraction of a day, a civil year and a revolution of the sun have not the same duration. Since the fraction is nearly the fourth of a day, in four years it is nearly equal to a revolution of the sun, so that the addition of a supernumerary day every fourth year nearly compensates the difference. But in process of time further correction will be necessary, because the fraction is less than the fourth of a day. In fact, if a bissextile be suppressed at the end of three out of four centuries, the year so determined will only exceed the true year by an extremely small fraction of a day; and if in addition to this a bissextile be suppressed every 4000 years, the length of the year will be nearly equal to that given by observation. Were the fraction neglected, the beginning of the year would precede that of the tropical year, so that it would retrograde through the different seasons in a period of about 1507 years. The Egyptian year began with the heliacal rising of Sirius (N. 150), and contained only 365 days, by which they lost one year in every 1461 years, their Sothaic period, or that cycle in which the heliacal rising of Sirius passes through the whole year and takes place again on the same day. The division of the year into months is very old and almost universal. But the period of seven days, by far the most permanent division of time, and the most ancient monument of astronomical knowledge, was used by the Brahmins in India with the same denominations employed by us, and was alike found in the calendars of the Jews, Egyptians, Arabs, and Assyrians. It has survived the fall of empires, and has existed among all successive generations, a proof of their common origin.

The day of the new moon immediately following the winter solstice in the 707th year of Rome was made the 1st of January of the first year of Julius Cæsar. The 25th of December of his forty-fifth year is considered as the date of Christ’s nativity; and the forty-sixth year of the Julian Calendar is assumed to be the first of our era. The preceding year is called the first year before Christ by chronologists, but by astronomers it is called the year 0. The astronomical year begins on the 31st of December at noon; and the date of an observation expresses the days and hours which have actually elapsed since that time.

Since solar and sidereal time are estimated from the passage of the sun and the equinoctial point across the meridian of each place, the hours are different at different places: while it is one o’clock at one place, it is two at another, three at another, &c.; for it is obvious that it is noon at one part of the globe at the same moment that it is midnight at another diametrically opposite to it: consequently an event which happens at one and the same instant of absolute time is recorded at different places as having happened at different times. Therefore, when observations made at different places are to be compared, they must be reduced by computation to what they would have been had they been made under the same meridian. To obviate this it was proposed by Sir John Herschel to employ mean equinoctial time, which is the same for all the world, and independent alike of local circumstances and inequalities in the sun’s motion. It is the time elapsed from the instant the mean sun enters the mean vernal equinox, and is reckoned in mean solar days and parts of a day.

Some remarkable astronomical eras are determined by the position of the major axis of the solar ellipse, which depends upon the direct motion of the perigee (N. 102) and the precession of the equinoxes conjointly, the annual motion of the one being 11ʺ·8, and that of the other 50ʺ·1. Hence the axis, moving at the rate of 61ʺ·9 annually, accomplishes a tropical revolution in 209·84 years. It coincided with the line of the equinoxes 4000 or 4089 years before the Christian era, much about the time chronologists assign for the creation of man. In 6483 the major axis will again coincide with the line of the equinoxes; but then the solar perigee will coincide with the equinox of autumn, whereas at the creation of man it coincided with the vernal equinox. In the year 1246 the major axis was perpendicular to the line of the equinoxes; then the solar perigee coincided with the solstice of summer, and the apogee with the solstice of winter. According to La Place, who computed these periods from different data, the last coincidence happened in the year 1250 of our era, which induced him to propose that year as a universal epoch, the vernal equinox of the year 1250 to be the first day of the first year. These eras can only be regarded as approximate, since ancient observations are too inaccurate, and modern observations too recent, to afford data for their precise determination.

The variation in the position of the solar ellipse occasions corresponding changes in the length of the seasons. In its present position spring is shorter than summer, and autumn longer than winter; and while the solar perigee continues as it now is, between the solstice of winter and the equinox of spring, the period including spring and summer will be longer than that including autumn and winter. In this century the difference is between seven and eight days. The intervals will be equal towards the year 6483, when the perigee will coincide with the equinox of spring; but, when it passes that point, the spring and summer taken together will be shorter than the period including the autumn and winter (N. 151). These changes will be accomplished in a tropical revolution of the major axis of the earth’s orbit, which includes an interval of 20,984 years. Were the orbit circular, the seasons would be equal; their difference arises from the excentricity of the orbit, small as it is; but the changes are so trifling as to be imperceptible in the short span of human life.

No circumstance in the whole science of astronomy excites a deeper interest than its application to chronology. “Whole nations,” says La Place, “have been swept from the earth, with their languages, arts, and sciences, leaving but confused masses of ruins to mark the place where mighty cities stood; their history, with the exception of a few doubtful traditions, has perished; but the perfection of their astronomical observations marks their high antiquity, fixes the periods of their existence, and proves that, even at that early time, they must have made considerable progress in science.” The ancient state of the heavens may now be computed with great accuracy; and, by comparing the results of calculation with ancient observations, the exact period at which they were made may be verified if true, or, if false, their error may be detected. If the date be accurate and the observation good, it will verify the accuracy of modern tables, and will show to how many centuries they may be extended without the fear of error. A few examples will show the importance of the subject.

At the solstices the sun is at his greatest distance from the equator; consequently his declination at these times is equal to the obliquity of the ecliptic (N. 152), which was formerly determined from the meridian length of the shadow of the stile of a dial on the day of a solstice. The lengths of the meridian shadow at the summer and winter solstices are recorded to have been observed at the city of Layang, in China, 1100 years before the Christian era. From these the distances of the sun from the zenith (N. 153) of the city of Layang are known. Half the sum of these zenith distances determines the latitude, and half their difference gives the obliquity of the ecliptic at the period of the observation; and, as the law of the variation of the obliquity is known, both the time and place of the observations have been verified by computations from modern tables. Thus the Chinese had made some advances in the science of astronomy at that early period. Their whole chronology is founded on the observations of eclipses, which prove the existence of that empire for more than 4700 years. The epoch of the lunar tables of the Indians, supposed by Bailly to be 3000 years before the Christian era, was proved by La Place, from the acceleration of the moon, not to be more ancient than the time of Ptolemy, who lived in the second century after it. The great inequality of Jupiter and Saturn, whose cycle embraces 918 years, is peculiarly fitted for marking the civilization of a people. The Indians had determined the mean motions of these two planets in that part of their periods when the apparent mean motion of Saturn was at the slowest, and that of Jupiter the most rapid. The periods in which that happened were 3102 years before the Christian era, and the year 1491 after it. The returns of comets to their perihelia may possibly mark the present state of astronomy to future ages.

The places of the fixed stars are affected by the precession of the equinoxes; and, as the law of that variation is known, their positions at any time may be computed. Now Eudoxus, a contemporary of Plato, mentions a star situate in the pole of the equator, and it appears from computation that χ Draconis was not very far from that place about 3000 years ago; but, as it is only about 2150 years since Eudoxus lived, he must have described an anterior state of the heavens, supposed to be the same that was mentioned by Chiron about the time of the siege of Troy. Thus every circumstance concurs in showing that astronomy was cultivated in the highest ages of antiquity.

It is possible that a knowledge of astronomy may lead to the interpretation of hieroglyphical characters. Astronomical signs are often found on the ancient Egyptian monuments, probably employed by the priests to record dates. The author had occasion to witness an instance of this most interesting application of astronomy, in ascertaining the date of a papyrus, sent from Egypt by Mr. Salt, in the hieroglyphical researches of the late Dr. Thomas Young, whose profound and varied acquirements do honour to his country, and to the age in which he lived. The manuscript was found in a mummy case; it proved to be a horoscope of the age of Ptolemy, and its date was determined from the configuration of the heavens at the time of its construction.

The form of the earth furnishes a standard of weights and measures for the ordinary purposes of life, as well as for the determination of the masses and distances of the heavenly bodies. The length of the pendulum vibrating seconds of mean solar time, in the latitude of London, forms the standard of the British measure of extension. Its approximate length oscillating in vacuo at the temperature of 62° of Fahrenheit, and reduced to the level of the sea (N. 154), was determined by Captain Kater to be 39·1393 inches. The weight of a cubic inch of water at the temperature of 62° of Fahrenheit, barometer 30 inches, was also determined in parts of the imperial troy pound, whence a standard both of weight and capacity was deduced. The French have adopted the mètre, equal to 3·2808992 English feet, for their unit of linear measure, which is the ten-millionth part of the arc of the meridian which extends from the equator to the pole, as deduced from the measures of the separate arc extending from Formentera, the most southern of the Balearic Islands, to Dunkirk. Should the national standards of the two countries ever be lost, both may be recovered, since they are derived from natural and invariable ones. The length of the measure deduced from that of the pendulum would be found again with more facility than the mètre. But, as no measure is mathematically exact, an error in the original standard may at length become sensible in measuring a great extent, whereas the error that must necessarily arise in measuring the quadrant of the meridian (N. 155) is rendered totally insensible by subdivision in taking its ten-millionth part. The French have adopted the decimal division, not only in time, but also in their degrees, weights, and measures, on account of the very great facility it affords in computation. It has not been adopted by any other country, though nothing is more desirable than that all nations should concur in using the same standards, not only on account of convenience, but as affording a more definite idea of quantity. It is singular that the decimal division of the day, of space, weights, and measures, was employed in China 4000 years ago; and that at the time Ibn Junis made his observations at Cairo, about the year 1000 of the Christian era, the Arabs were in the habit of employing the vibrations of the pendulum in their astronomical observations as a measure of time.

SECTION XIII.

Tides—Forces that produce them—Origin and Course of Tidal Wave—Its Speed—Three kinds of Oscillations in the Ocean—The Semidiurnal Tides—Equinoctial Tides—Effects of the Declination of the Sun and Moon—Theory insufficient without Observation—Direction of the Tidal Wave—Height of Tides—Mass of Moon obtained from her Action on the Tides—Interference of Undulations—Impossibility of a Universal Inundation—Currents.

ONE of the most immediate and remarkable effects of a gravitating force external to the earth is the alternate rise and fall of the surface of the sea twice in the course of a lunar day, or 24^h 50^m 28^s of mean solar time. As it depends upon the action of the sun and moon, it is classed among astronomical problems, of which it is by far the most difficult and its explanation the least satisfactory. The form of the surface of the ocean in equilibrio, when revolving with the earth round its axis, is an ellipsoid flattened at the poles; but the action of the sun and moon, especially of the moon, disturbs the equilibrium of the ocean. If the moon attracted the centre of gravity of the earth and all its particles with equal and parallel forces, the whole system of the earth and the waters that cover it would yield to these forces with a common motion, and the equilibrium of the seas would remain undisturbed. The difference of the forces and the inequality of their directions alone disturb the equilibrium.

The particles of water under the moon are more attracted than the centre of gravity of the earth, in the inverse ratio of the square of the distance. Hence they have a tendency to leave the earth, but are retained by their gravitation, which is diminished by this tendency. On the contrary, the moon attracts the centre of the earth more powerfully than she attracts the particles of water in the hemisphere opposite to her; so that the earth has a tendency to leave the waters, but is retained by gravitation, which is again diminished by this tendency. Thus the waters immediately under the moon are drawn from the earth, at the same time that the earth is drawn from those which are diametrically opposite to her, in both instances producing an elevation of the ocean of nearly the same height above the surface of equilibrium; for the diminution of the gravitation of the particles in each position is almost the same, on account of the distance of the moon being great in comparison of the radius of the earth. Were the earth entirely covered by the sea, the waters thus attracted by the moon would assume the form of an oblong spheroid whose greater axis would point towards the moon; since the columns of water under the moon, and in the direction diametrically opposite to her, are rendered lighter in consequence of the diminution of their gravitation; and, in order to preserve the equilibrium, the axes 90° distant would be shortened. The elevation, on account of the smaller space to which it is confined, is twice as great as the depression, because the contents of the spheroid always remain the same. If the waters were capable of assuming the form of equilibrium instantaneously, that is, the form of the spheroid, its summit would always point to the moon notwithstanding the earth’s rotation. But, on account of their resistance, the rapid motion produced in them by rotation prevents them from assuming at every instant the form which the equilibrium of the forces acting upon them requires. Hence, on account of the inertia of the waters, if the tides be considered relatively to the whole earth and open seas, there is a meridian about 30° eastward of the moon, where it is always high water both in the hemisphere where the moon is and in that which is opposite. On the west side of this circle the tide is flowing, on the east it is ebbing, and on every part of the meridian at 90° distant it is low water. This great wave, which follows all the motions of the moon as far as the rotation of the earth will permit, is modified by the action of the sun, the effects of whose attraction are in every respect like those produced by the moon, though greatly less in degree. Consequently a similar wave, but much smaller, raised by the sun, tends to follow his motions, which at times combines with the lunar wave, and at others opposes it, according to the relative positions of the two luminaries; but as the lunar wave is only modified a little by the solar, the tides must necessarily happen twice in a day, since the rotation of the earth brings the same point twice under the meridian of the moon in that time, once under the superior and once under the inferior meridian.

The periodic motions of the waters of the ocean, on the hypothesis of an ellipsoid of revolution, entirely covered by the sea, are, however, very far from according with observation. This arises from the great irregularities in the surface of the earth, which is but partially covered by the sea, from the variety in the depths of the ocean, the manner in which it is spread out on the earth, the position and inclination of the shores, the currents, and the resistance which the waters meet with: causes impossible to estimate generally, but which modify the oscillations of the great mass of the ocean. However, amidst all these irregularities, the ebb and flow of the sea maintain a ratio to the forces producing them sufficient to indicate their nature, and to verify the law of the attraction of the sun and moon on the sea. La Place observes, that the investigation of such relations between cause and effect is no less useful in natural philosophy than the direct solution of problems, either to prove the existence of the causes or to trace the laws of their effects. Like the theory of probabilities, it is a happy supplement to the ignorance and weakness of the human mind.

Since the disturbing action of the sun and moon can only become sensible in a very great extent of deep water, the Antarctic Ocean is the origin and birthplace of our tides. A succession of tidal waves from that source follow one another in a north-westerly direction down the Pacific and Atlantic Oceans, modified as they proceed by the depth of the water and the form of the coasts. For when the sun and moon are in the same meridian, and pass over the mass of waters lying east from Van Diemen’s Land, New Zealand, and the South Pole, the resulting force of their combined attraction, penetrating to the abyss of the deep and boundless circuit of the Southern Ocean, raises a vast wave or ridge of water, which tends to follow the luminaries to the north and west, and continues to flow in that direction long after the bodies cease to act upon it; but it is so retarded by the rotation of the earth and by the inertia of the water, that it does not arrive at the different parts of the coasts till after the moon’s southing (N. 156). When this tidal wave leaves the Antarctic Ocean and enters the Pacific, it rushes along the western coast of America to its farthest end, but it is so much obstructed by the number of islands in the middle of that ocean that it is hardly perceptible among them; while on the east it enters the Indian Ocean, strikes with violence on the coasts of Hindostan and the shores at the mouths of the Ganges, and causes the terrific bore in the Hoogly. The part of this tidal wave that enters the Atlantic passes impetuously along the coasts of Africa and America, arriving later and later at each place. It is modified, however, by a tide raised in the Atlantic, which is deep and free from islands; and this combined tidal wave, still coming northward, pours its surge into the Gulf of Fundy to the height of fifty feet; then being deflected by the coast of America at right angles, it rushes eastward, bringing high water to the western coasts of Ireland and England. It then goes round Scotland, brings high water to Aberdeen and the opposite coasts of Norway and Denmark, and, continuing its course to the south, arrives at the mouth of the Thames and fills the channels of that river on the morning of the third day after leaving the Antarctic Ocean.

Thus the tides in our ports are owing to an impulse from the waters of the Antarctic seas raised by the action of the sun and moon. No doubt a similar action raised that tide in the North Polar Ocean which Dr. Kane saw rolling on the northern coast of Greenland in 82° N. latitude, but which, in the present state of the globe, is imprisoned by bars of ice and ice-bound lands.

The tidal wave extends to the bottom of the ocean, and moves uniformly and with great speed in very deep water, variably and slow in shallow water; the time of propagation depends upon the depth of the sea, as well as on the nature and form of the coasts. It varies inversely as the square of the depth—a law which theoretically affords the means of ascertaining the proportionate depth of the sea in different parts. It is one of the great constants of nature, and is to fluids what the pendulum is to solids—a connecting link between time and force.

For example: the tidal wave moves across the Southern Ocean with the velocity of 1000 miles an hour, and in the Atlantic it is scarcely less on account of the deep trough which runs through the centre of that ocean; but the sea is so shallow on the British coast that it takes more time to come from Aberdeen to London than to travel over an arc of 120°, between 60° S. lat. and 60° N. lat.

In deep water the tidal wave is merely a rise and fall of the surface; the water does not advance, though the wave does. Indeed, if so heavy a body as water were to move at the rate of 1000 miles an hour, it would cause universal destruction, since in the most violent hurricanes the velocity of the wind is little more than 100 miles an hour. Besides, it is evident that no ship could either sail or steam against it. When the water is shallow, however, there is a motion of translation in the water along with the tide.

In the deep ocean the undulating motion consists of two distinct things—an advancing form and a molecular movement. The motion of each particle of water is in an ellipse lying wholly in the vertical plane; so that, after the momentary displacement during the passage of the wave, they return to their places again. The resistance of the sea-bed is insensible in deep water; but when the tidal wave, which extends to the very bottom of the ocean, comes into shallow water with diminished velocity, the particles of water moving in vertical ellipses strike the bottom, and by reaction the wave rises higher; and that being continually repeated, as the form moves on the wave rises higher and higher, bends more and more forward, till at last it loses its equilibrium, and then both form and water roll to the shore, and the elliptical trajectories of the particles, which in deep water were vertical, incline more and more, till at length they become horizontal. The distance from the shore at which the water begins to be translated depends upon the depth, the nature of the coast, and the form of the shore. Mr. Scott Russell has demonstrated that in shallow water the velocity of the wave is equal to that which a heavy body falling freely by its gravity would acquire in descending through half the depth of the fluid.

It is proved by daily experience, as well as by strict mathematical reasoning, that, if a number of waves or oscillations be excited in a fluid by different forces, each pursues its course and has its effect independently of the rest. Now, in the tides there are three kinds of oscillations, depending on different causes, and producing their effects independently of each other, which may therefore be estimated separately. The oscillations of the first kind, which are very small, are independent of the rotation of the earth, and, as they depend upon the motion of the disturbing body in its orbit, they are of long periods. The second kind of oscillations depend upon the rotation of the earth, therefore their period is nearly a day. The oscillations of the third kind vary with an angle equal to twice the angular rotation of the earth, and consequently happen twice in twenty-four hours (N. 157). The first afford no particular interest, and are extremely small; but the difference of two consecutive tides depends upon the second. At the time of the solstices this difference, which ought to be very great according to Newton’s theory, is hardly sensible on our shores. La Place has shown that the discrepancy arises from the depth of the sea, and that if the depth were uniform there would be no difference in the consecutive tides but that which is occasioned by local circumstances. It follows, therefore, that, as this difference is extremely small, the sea, considered in a large extent, must be nearly of uniform depth, that is to say, there is a certain mean depth from which the deviation is not great. The mean depth of the Pacific Ocean is supposed to be about four or five miles, that of the Atlantic only three or four, which, however, is mere conjecture. Possibly the great extent and uniformly small depth of the Atlantic over the telegraphic platform may prevent the difference of the oscillations in question from being perceptible on our shores. From the formulæ which determine the difference of these consecutive tides it is proved that the precession of the equinoxes and the nutation of the earth’s axis are the same as if the sea formed one solid mass with the earth.

The oscillations of the third kind are the semi-diurnal tides so remarkable on our coasts. In these there are two phenomena particularly to be distinguished, one occurring twice in a month, the other twice in a year.

The first phenomenon is, that the tides are much increased in the syzygies (N. 158), or at the time of new and full moon: in both cases the sun and moon are in the same meridian; for when the moon is new they are in conjunction, and when she is full they are in opposition. In each of these positions their action is combined to produce the highest or spring tides under that meridian, and the lowest in those points that are 90° distant. It is observed that the higher the sea rises in full tide, the lower it is in the ebb. The neap tides take place when the moon is in quadrature. They neither rise so high nor sink so low as the spring tides. It is evident that the spring tides must happen twice in a month, since in that time the moon is once new and once full. Theory proves that each partial tide increases as the cube of the parallax or apparent diameter of the body producing it, for the greater the apparent diameter the nearer the body and the more intense its action upon the sea; hence the spring tides are much increased when the moon is in perigee, for then she is nearest to the earth.

The second phenomenon in the tides is the augmentation occurring at the time of the equinoxes, when the sun’s declination is zero (N. 159), which happens twice in every year. The spring tides which take place at that time are often much increased by the equinoctial gales, and, on the hypothesis of the whole earth covered by the ocean, would be the greatest possible if the line of the moon’s nodes coincided with that of her perigee, for then the whole action of the luminaries would be in the plane of the equator. But since the Antarctic Ocean is the source of the tides, it is evident that the spring tide must be greatest when the moon is in perigee, and when both luminaries have their highest southern declination, for then they act most directly upon the great circuit of the south polar seas.

The sun and moon are continually making the circuit of the heavens at different distances from the plane of the equator, on account of the obliquity of the ecliptic and the inclination of the lunar orbit. The moon takes about 29-1/2 days to vary through all her declinations, which sometimes extend 28-3/4° on each side of the equator, while the sun requires nearly 365-1/4 days to accomplish his motions through 23-1/2° on each side of the same plane, so that their combined action causes great variations in the tides. Both the height and time of high water are perpetually changing, and, although the problem does not admit of a general solution, it is necessary to analyse the phenomena which ought to arise from the attraction of the sun and moon, but the result must be corrected in each particular case for local circumstances, so that the theory of the tides in each port becomes really a matter of experiment, and can only be determined by means of a vast number of observations, including many revolutions of the moon’s nodes.

The mean height of the tides will be increased by a very small quantity for ages to come, in consequence of the decrease in the mean distance of the moon from the earth; the contrary effect will take place after that period has elapsed, and the moon’s mean distance begins to increase again, which it will continue to do for many ages. Thus the mean distance of the moon and the consequent minute increase in the height of the tides will oscillate between fixed limits for ever.

The height to which the tides rise is much greater in narrow channels than in the open sea, on account of the obstructions they meet with. The sea is so pent up in the British Channel that the tides sometimes rise as much as fifty feet at St. Malo, on the coast of France; whereas on the shores of some of the South Sea islands, near the centre of the Pacific, they do not exceed one or two feet. The winds have great influence on the height of the tides, according as they conspire with or oppose them. But the actual effect of the wind in exciting the waves of the ocean extends very little below the surface. Even in the most violent storms the water is probably calm at the depth of ninety or a hundred fathoms. The tidal wave of the ocean does not reach the Mediterranean nor the Baltic, partly from their position and partly from the narrowness of the Straits of Gibraltar and of the Categat, but it is very perceptible in the Red Sea and in Hudson’s Bay. The ebb and flow of the sea are perceptible in rivers to a very great distance from their estuaries. In the Narrows of Pauxis, in the river of the Amazons, more than five hundred miles from the sea, the tides are evident. It requires so many days for the tide to ascend this mighty stream, that the returning tides meet a succession of those which are coming up; so that every possible variety occurs at some part or other of its shores, both as to magnitude and time. It requires a very wide expanse of water to accumulate the impulse of the sun and moon, so as to render their influence sensible; on that account the tides in the Mediterranean and Black Sea are scarcely perceptible.

These perpetual commotions in the waters are occasioned by forces that bear a very small proportion to terrestrial gravitation: the sun’s action in raising the ocean is only the 1/38448000 of gravitation at the earth’s surface, and the action of the moon is little more than twice as much; these forces being in the ratio of 1 to 2.35333, when the sun and moon are at their mean distances from the earth. From this ratio the mass of the moon is found to be only the 1/75 part of that of the earth. Had the action of the sun on the ocean been exactly equal to that of the moon, there would have been no neap tides, and the spring tides would have been of twice the height which the action of either the sun or moon would have produced separately—a phenomenon depending upon the interference of the waves or undulations.

A stone plunged into a pool of still water occasions a series of waves to advance along the surface, though the water itself is not carried forward, but only rises into heights and sinks into hollows, each portion of the surface being elevated and depressed in its turn. Another stone of the same size, thrown into the water near the first, will occasion a similar set of undulations. Then, if an equal and similar wave from each stone arrive at the same spot at the same time, so that the elevation of the one exactly coincides with the elevation of the other, their united effect will produce a wave twice the size of either. But, if one wave precede the other by exactly half an undulation, the elevation of the one will coincide with the hollow of the other, and the hollow of the one with the elevation of the other; and the waves will so entirely obliterate one another, that the surface of the water will remain smooth and level. Hence, if the length of each wave be represented by 1, they will destroy one another at intervals of 1/2, 3/2, 5/2, &c., and will combine their effects at the intervals 1, 2, 3, &c. It will be found according to this principle, when still water is disturbed by the fall of two equal stones, that there are certain lines on its surface of a hyperbolic form, where the water is smooth in consequence of the waves obliterating each other, and that the elevation of the water in the adjacent parts corresponds to both the waves united (N. 160). Now, in the spring and neap tides arising from the combination of the simple solilunar waves, the spring tide is the joint result of the combination when they coincide in time and place; and the neap tide happens when they succeed each other by half an interval, so as to leave only the effect of their difference sensible. It is, therefore, evident that, if the solar and lunar tides were of the same height, there would be no difference, consequently no neap tides, and the spring tides would be twice as high as either separately. In the port of Batsha, in Tonquin, where the tides arrive by two channels of lengths corresponding to half an interval, there is neither high nor low water on account of the interference of the waves.

The initial state of the ocean has no influence on the tides; for, whatever its primitive conditions may have been, they must soon have vanished by the friction and mobility of the fluid. One of the most remarkable circumstances in the theory of the tides is the assurance that, in consequence of the density of the sea being only one-fifth of the mean density of the earth, and the earth itself increasing in density towards the centre, the stability of the equilibrium of the ocean never can be subverted by any physical cause. A general inundation arising from the mere instability of the ocean is therefore impossible. A variety of circumstances, however, tend to produce partial variations in the equilibrium of the seas, which is restored by means of currents. Winds and the periodical melting of the ice at the poles occasion temporary watercourses; but by far the most important causes are the centrifugal force induced by the velocity of the earth’s rotation, and variations in the density of the sea.

The centrifugal force may be resolved into two forces—one perpendicular, and another tangent to the earth’s surface (N. 161). The tangential force, though small, is sufficient to make the fluid particles within the polar circles tend towards the equator, and the tendency is much increased by the immense evaporation in the equatorial regions from the heat of the sun, which disturbs the equilibrium of the ocean. To this may also be added the superior density of the waters near the poles, from their low temperature. In consequence of the combination of all these circumstances, two great currents perpetually set from each pole towards the equator. But, as they come from latitudes where the rotatory motion of the surface of the earth is very much less than it is between the tropics, on account of their inertia, they do not immediately acquire the velocity with which the solid part of the earth’s surface is revolving at the equatorial regions; from whence it follows that, within twenty-five or thirty degrees on each side of the line, the ocean has a general motion from east to west, which is much increased by the action of the trade winds. Both in the Pacific and Atlantic currents of enormous magnitude are deflected by the continents and islands to the north and south from this mighty mass of rushing waters, which convey the warmth of the equator to temper the severity of the polar regions, while to maintain the equilibrium of the seas counter currents of cold water are poured from the polar oceans to mingle with the warm waters at the line, so that a perpetual circulation is maintained.

Icebergs are sometimes drifted as far as the Azores from the Polar seas, and from the south pole they have come even to the Cape of Good Hope. But the ice which encircles the south pole extends to lower latitudes by 10° than that which surrounds the north. In consequence of the polar current Sir Edward Parry was obliged to give up his attempt to reach the north pole in the year 1827, because the fields of ice were drifting to the south faster than his party could travel over them to the north.

Kotzebue and Sir James Ross found a stratum of constant temperature in the ocean at a depth depending upon the latitude: at the equator it is at the depth of 7200 feet, from whence it gradually rises till it comes to the surface in both hemispheres about the latitude of 56° 26ʹ, where the water has the same temperature at all depths; it then descends to 4500 feet below the surface about the 70th parallel both in the Arctic and Antarctic Seas. The temperature of that aqueous zone is about 39°·5 of Fahrenheit.[7] It divides the surface of the ocean into five great zones of temperature, namely, a medial region, in which the highest mean temperature is 82° Fahr., two temperate zones each of 39°·5 Fahr., and two polar basins at the freezing point of salt water.

SECTION XIV.

Molecular Forces—Permanency of the ultimate Particles of Matter—Interstices—Mossotti’s Theory—Rankin’s Theory of Molecular Vortices—Gases reduced to Liquids by Pressure—Gravitation of Particles—Cohesion—Crystallization—Cleavage—Isomorphism—Minuteness of the Particles—Height of Atmosphere—Chemical Affinity—Definite Proportions and Relative Weights of Atoms—Faraday’s Discovery with regard to Affinity—Capillary Attraction.

THE oscillations of the atmosphere, and its action upon the rays of light coming from the heavenly bodies, connect the science of astronomy with the equilibrium and movements of fluids and the laws of molecular attraction. Hitherto that force has been under consideration which acts upon masses of matter at sensible distances; but now the effects of such forces are to be considered as act at inappreciable distances upon the ultimate molecules of material bodies.

All substances consist of an assemblage of material particles, or molecules, which are far too small to be visible by any means human ingenuity has yet been able to devise, and which are much beyond the limits of our perceptions. They neither can be created nor destroyed; bodies may be burned, but their particles are not consumed—they are merely liberated from one combination to enter into another, nor are their peculiar properties ever changed; whatever combinations they may enter into, they are ever and invariably the same.

Since every known substance may be reduced in bulk by pressure, it follows that the particles of matter are not in actual contact, but are separated by interstices; and it is evident that the smaller the interstitial spaces the greater the density. These spaces appear to be filled with air in some cases, as may be inferred from certain semi-opaque minerals and other substances becoming transparent when plunged into water. Sometimes they may possibly contain some unknown and highly elastic fluid, such as Sir David Brewster has discovered in the minute cavities of various minerals, which occasionally causes them to explode under the hands of the lapidary; but as it is inconceivable that the particles of matter should act upon one another without some means of communication, it is presumed that the interstices of material substances contain a portion of the ethereal medium with which the regions of space are filled.

The various hypotheses that have been formed as to the nature and action of the forces which unite the particles of matter, have been successively given up as science advanced, and now nothing decisive has been attained, although Professor Mossotti, of Pisa, by a very able analysis, has endeavoured to prove the identity of the cohesive force with gravitation. As the particles of material bodies are not in actual contact, he supposes that each is surrounded by an atmosphere of the ethereal medium, which he conceives to be electricity; moreover he assumes that the atoms of the medium repel one another, that the particles of matter also repel one another, but with less intensity, and that there is a mutual attraction between the particles of matter and the atoms of the medium, forces which are assumed to vary inversely as the square of the distance.

Hence, when the material molecules of a body are inappreciably near to one another, they mutually repel each other with a force which diminishes rapidly as the infinitely small distance between the material molecules augments, and at last vanishes. When the molecules are still farther apart, the force becomes attractive. At that particular point where the change takes place the forces of repulsion and attraction balance each other, so that the molecules of a body are neither disposed to approach nor recede, but remain in equilibrio. If we try to press them nearer, the repulsive force resists the attempt; and if we endeavour to break the body so as to tear the particles asunder, the attractive force predominates and keeps them together. This is what constitutes the cohesive force, or force of aggregation, by which the molecules of all substances are united. The limits of the distance at which the negative action becomes positive vary according to the temperature and nature of the molecules, and determine whether the body which they form be solid, liquid, or aëriform.

Beyond this neutral point the attractive force increases as the distance between the molecules augments till it attains a maximum; when the particles are more apart, it diminishes; and, as soon as they are separated by finite or sensible distances, it varies directly as their mass and inversely as the square of the distance, which is precisely the law of universal gravitation.

Thus, on the hypothesis that the mutual repulsion between the electric atoms is a little more powerful than the mutual repulsion between the particles of matter, the ether and the matter attract each other with unequal intensities, which leaves an excess of attractive force constituting gravitation. As the gravitating force is in operation wherever there is matter, the ethereal electric medium must encompass all the bodies in the universe; and, as it is utterly incomprehensible that the celestial bodies should exert a reciprocal attraction through a void, the Professor concludes that the ethereal electrical medium fills all space.

It is true that this connexion between the molecular forces and gravitation depends upon hypothesis; but in the greater number of physical investigations some hypothesis is requisite in the first instance to aid the imperfection of our senses; and when the phenomena of nature accord with the assumption, we are justified in believing it to be a general law.

Mr. Rankin’s theory of molecular vortices, or the molecular structure of matter, is independent of electricity. According to his hypothesis, each atom of matter consists of an inappreciably small nucleus, encompassed by an elastic ethereal atmosphere which is retained in its position by attractive forces directed towards the molecule, whilst the molecules attract each other in the direction of straight lines joining their centres. The nuclei may either be solid, or a high condensation of the atmospheres which surround each with decreasing density. When the attraction between the molecules is such that the elasticity of the atmospheres is insensible, the body is a perfect solid, the rigidity of which bears a certain definite proportion to the elasticity of the volume. When the atmospheres are less condensed and the attraction of the molecules merely produces a cohesive force sufficient to balance the atomic elasticity of the atmosphere, the body is a perfect liquid; and when the attraction of the molecules is very small compared with the elasticity of their ethereal atmospheres, the body is a perfect gas. These atmospheres are supposed to be portions of the ethereal medium which penetrates into the interstices of every substance, and their elasticity to be due to the heat generated by the centrifugal force or oscillations among their atoms, for motion is the cause of heat, the force producing the motions varying simply as the density of the ether.

In aëriform fluids, although the particles are more remote from each other than in liquids and solids, yet the pressure may be so great as to reduce an aëriform fluid to a liquid, and a liquid to a solid. Dr. Faraday has reduced some of the gases to a liquid state by very great compression; but although atmospheric air is capable of a diminution of volume to which we do not know a limit, it has hitherto always retained its gaseous qualities, and resumes its primitive volume the instant the pressure is removed. Substances are said to be more or less elastic, according to the facility with which they regain their bulk or volume when the pressure is removed; thus liquids resist compression on account of their elasticity, and in solids the resistance is much greater but variable, and the effort required to break a substance is a measure of the cohesive force exerted by its particles. In stone, iron, steel, and all brittle and hard substances, the cohesion of the particles is powerful but of small extent; in elastic bodies, on the contrary, its action is weak, but more extensive. An infinite variety of conditions may be observed in the fusion of metals and other substances passing from hardness to toughness, viscidity, and through all the other stages to perfect fluidity and even to vapour. Since all bodies expand by heat, the cohesive force is weakened by increase of temperature. The cohesion of matter or the strength of substances forms an important branch of study in engineering.

Every particle of matter, whether it forms a constituent part of a solid, liquid, or aëriform fluid, is subject to the law of gravitation. The weight of the atmosphere, of gases and vapour, shows that they consist of gravitating particles. In liquids the cohesive force is not sufficiently powerful to resist the action of gravitation. Therefore, although their component particles still maintain their connexion, the liquid is scattered by their weight, unless when it is confined in a vessel or has already descended to the lowest point possible, and assumed a level surface from the mobility of its particles and the influence of the gravitating forces, as in the ocean, or a lake. Solids would also fall to pieces by the weight of their particles, if the force of cohesion were not powerful enough to resist the efforts of gravitation.

The phenomena arising from the force of cohesion are innumerable. The spherical form of rain-drops; the difficulty of detaching a plate of glass from the surface of water; the force with which two plane surfaces adhere when pressed together; the drops that cling to the window-glass in a shower of rain—are all effects of cohesion entirely independent of atmospheric pressure, and are included in the same analytical formula (N. 162) which expresses all the circumstances accurately, although the laws according to which the forces of cohesion and repulsion vary are unknown. It is more than probable that the spherical form of the sun and planets is due to the force of cohesion, as they have every appearance of having been at one period in a state of fusion.

A very remarkable instance has occasionally been observed in plate-glass manufactories. After the large plates of glass of which mirrors are to be made have received their last polish, they are carefully wiped and laid on their edges with their surfaces resting on one another. In the course of time the cohesion has sometimes been so powerful, that they could not be separated without breaking. Instances have occurred where two or three have been so perfectly united, that they have been cut and their edges polished as if they had been fused together; and so great was the force required to make the surfaces slide that one tore off a portion of the surface of the other.

In liquids and gases the forms of the particles have no influence, they are so far apart; but the structure of solids varies according to the sides which the particles present to one another during their aggregation. Nothing is known of their form further than the dissimilarity of their different sides in certain cases, which appears from their reciprocal attractions during crystallisation being more or less powerful according to the sides they present to one another. Crystallisation is an effect of molecular attraction regulated by certain laws, according to which atoms of the same kind of matter unite in regular forms—a fact easily proved by dissolving a piece of alum in pure water. The mutual attraction of the particles is destroyed by the water; but, if it be evaporated, they unite, and form in uniting eight-sided figures called octahedrons (N. 163). These however are not all the same. Some have their angles cut off, others their edges, and some both, while the remainder take the regular form. It is quite clear that the same circumstances which cause the aggregation of a few particles would, if continued, cause the addition of more; and the process would go on as long as any particles remain free round the primitive nucleus, which would increase in size, but would remain unchanged in form, the figure of the particles being such as to maintain the regularity and smoothness of the surfaces of the solid and their mutual inclinations. A broken crystal will by degrees resume its regular figure when put back again into the solution of alum, which shows that the internal and external particles are similar, and have a similar attraction for the particles held in solution. The original conditions of aggregation which make the molecules of the same substance unite in different forms must be very numerous, since of carbonate of lime alone there are many hundred varieties; and certain it is, from the motion of polarised light through rock crystal, that a very different arrangement of particles is requisite to produce an extremely small change in external form. A variety of substances in crystallising combine chemically with a certain portion of water which in a dry state forms an essential part of their crystals, and, according to the experiments of MM. Haidinger and Mitscherlich, seems in some cases to give the peculiar determination to their constituent molecules. These gentlemen have observed that the same substance crystallising at different temperatures unites with different quantities of water and assumes a corresponding variety of forms. Seleniate of zinc, for example, unites with three different portions of water, and assumes three different forms, according as its temperature in the act of crystallising is hot, lukewarm, or cold. Sulphate of soda also, which crystallises at 90° of Fahrenheit without water of crystallisation, combines with water at the ordinary temperature, and takes a different form. Heat appears to have a great influence on the phenomena of crystallisation, not only when the particles of matter are free, but even when firmly united, for it dissolves their union, and gives them another determination. Professor Mitscherlich found that prismatic crystals of sulphate of nickel (N. 164), exposed to a summer’s sun in a close vessel, had their internal structure so completely altered without any exterior change, that when broken open they were composed internally of octahedrons with square bases. The original aggregation of the internal particles had been dissolved, and a disposition given to arrange themselves in a crystalline form. Crystals of sulphate of magnesia and of sulphate of zinc, gradually heated in alcohol till it boils, lose their transparency by degrees, and when opened are found to consist of innumerable minute crystals totally different in form from the whole crystals; and prismatic crystals of zinc (N. 165) are changed in a few seconds into octahedrons by the heat of the sun: other instances might be given of the influence of even moderate degrees of temperature on molecular attraction in the interior of substances. It must be observed that these experiments give entirely new views with regard to the constitution of solid bodies. We are led from the mobility of fluids to expect great changes in the relative positions of their molecules, which must be in perpetual motion even in the stillest water or calmest air; but we were not prepared to find motion to such an extent in the interior of solids. That their particles are brought nearer by cold and pressure, or removed farther from one another by heat, might be expected; but it could not have been anticipated that their relative positions could be so entirely changed as to alter their mode of aggregation. It follows, from the low temperature at which these changes are effected, that there is probably no portion of inorganic matter that is not in a state of relative motion.

Professor Mitscherlich’s discoveries with regard to the forms of crystallised substances, as connected with their chemical character, have thrown additional light on the constitution of material bodies. There is a certain set of crystalline forms which are not susceptible of variation, as the die or cube (N. 166), which may be small or large, but is invariably a solid bounded by six square surfaces or planes. Such also is the tetrahedron (N. 167) or four-sided solid contained by four equal-sided triangles. Several other solids belong to this class, which is called the Tessular system of crystallisation. There are other crystals which, though bounded by the same number of sides, and having the same form, are yet susceptible of variation; for instance, the eight-sided figure with a square base, called an octahedron (N. 168), which is sometimes flat and low, and sometimes acute and high. It was formerly believed that identity of form in all crystals not belonging to the Tessular system indicated identity of chemical composition. Professor Mitscherlich, however, has shown that substances differing to a certain degree in chemical composition have the property of assuming the same crystalline form. For example, the neutral phosphate of soda and the arseniate of soda crystallise in the very same form, contain the same quantities of acid, alkali, and water of crystallisation; yet they differ so far, that one contains arsenic and the other an equivalent quantity of phosphorus. Substances having such properties are said to be isomorphous, that is, equal in form. Of these there are many groups, each group having the same form, and similarity though not identity of chemical composition. For instance, one of the isomorphous groups is that consisting of certain chemical substances called the protoxides of iron, copper, zinc, nickel, and manganese, all of which are identical in form and contain the same quantity of oxygen, but differ in the respective metals they contain, which are, however, nearly in the same proportion in each. All these circumstances tend to prove that substances having the same crystalline form must consist of ultimate atoms having the same figure and arranged in the very same order; so that the form of crystals is dependent on their atomic constitution.

All crystallised bodies have joints called cleavages, at which they split more easily than in other directions; on this property the whole art of cutting diamonds depends. Each substance splits in a manner and in forms peculiar to itself. For example, all the hundreds of forms of carbonate of lime split into six-sided figures, called rhombohedrons (N. 169), whose alternate angles measure 105·55° and 75·05°, however far the division may be carried; therefore the ultimate particle of carbonate of lime is presumed to have that form. However this may be, it is certain that all the various crystals of that mineral may be formed by building up six-sided solids of the form described, in the same manner as children build houses with miniature bricks. It may be imagined that a wide difference may exist between the particles of an unformed mass and a crystal of the same substance—between the common shapeless limestone and the pure and limpid crystal of Iceland spar; yet chemical analysis detects none; their ultimate atoms are identical, and crystallisation shows that the difference arises only from the mode of aggregation. Besides, all substances either crystallise naturally, or may be made to do so by art. Liquids crystallise in freezing, vapours by sublimation (N. 170); and hard bodies, when fused, crystallise in cooling. Hence it may be inferred that all substances are composed of atoms, on whose magnitude, density, and form, their nature and qualities depend; and, as these qualities are unchangeable, the ultimate particles of matter must be incapable of wear—the same now as when created.

The size of the ultimate particles of matter must be small in the extreme. Organised beings, possessing life and all its functions, have been discovered so small, that a million of them would occupy less space than a grain of sand. The malleability of gold, the perfume of musk, the odour of flowers, and many other instances might be given of the excessive minuteness of the atoms of matter. Supposing the density of the air at the surface of the earth to be represented by unity, Sir John Herschel has shown that, under any hypothesis as to its atoms, it would require a fraction having at least 1370 figures in its denominator to express its tenuity in the interplanetary space; yet the definite proportions of chemical compounds afford a proof that divisibility of matter has a limit. The cohesive force, which has been the subject of the preceding considerations, only unites particles of the same kind of matter; whereas affinity, which is the cause of chemical compounds, is the mutual attraction between particles of different kinds of matter, generally producing a compound which has no sensible property in common with its component parts except that of their combined gravity, as, for example, water, which is a compound of oxygen and hydrogen gases. It is merely a result of the electrical state of the particles, chemical affinity and electricity being only forms of the same power. In most cases it produces electricity, as in the oxidation of metals and combustion, and in every case without exception heat is evolved by bodies while combining chemically; and as heat is an expansive force, chemical action is changed into mechanical expansion, but it is not known in this case why heat is produced, nor the manner in which the particles act.

It is a permanent and universal law in vast numbers of unorganised bodies that their composition is definite and invariable, the same compound always consisting of the same elements united together in the same proportions. Two substances may indeed be mixed; but they will not combine to form a third substance different from both, unless their component particles unite in definite proportions; that is to say, one part by weight of one of the substances will unite with one part by weight of the other, or with two parts, or three, or four, &c., so as to form a new substance; but in any other proportions they will only be mechanically mixed. For example, one part by weight of hydrogen gas will combine with eight parts by weight of oxygen gas, and form water; or it will unite with sixteen parts by weight of oxygen, and form a substance called deutoxide of hydrogen; but, added to any other weight of oxygen, it will produce one or both of these compounds mingled with the portion of oxygen or hydrogen in excess. The law of definite proportion established by Dr. Dalton, on the principle that every compound body consists of a combination of the atoms of its constituent parts, is of universal application, and is in fact one of the most important discoveries in physical science, furnishing information previously unhoped for with regard to the most secret and minute operations of nature, in disclosing the relative weights of the ultimate atoms of matter. Thus an atom of oxygen uniting with an atom of hydrogen forms the compound water; but, as every drop of water however small consists of eight parts by weight of oxygen and one part by weight of hydrogen, it follows that an atom of oxygen is eight times heavier than an atom of hydrogen. In the same manner sulphuretted hydrogen gas consists of sixteen parts by weight of sulphur and one of hydrogen; therefore an atom of sulphur is sixteen times heavier than an atom of hydrogen. Also carbonic oxide is constituted of six parts by weight of carbon and eight of oxygen; and, as an atom of oxygen has eight times the weight of an atom of hydrogen, it follows that an atom of carbon is six times heavier than one of hydrogen. Since the same definite proportion holds in the composition of a vast number of substances that have been examined, it has been concluded that there are great differences in the weights of the ultimate particles of matter. Although Dalton’s law is fully established, yet instances have occurred from which it appears that the atomic theory deduced from it is not always maintained. M. Gay Lussac discovered that gases unite together by their bulk or volumes, in such simple and definite proportions as one to one, one to two, one to three, &c. For example, one volume or measure of oxygen unites with two volumes or measures of hydrogen in the formation of water.

Dr. Faraday has proved, by experiments on bodies both in solution and fusion, that chemical affinity is merely a result of the electrical state of the particles of matter. Now it must be observed that the composition of bodies, as well as their decomposition, may be accomplished by means of electricity; and Dr. Faraday has found that this chemical composition and decomposition, by a given current of electricity, is always accomplished according to the laws of definite proportions; and that the quantity of electricity requisite for the decomposition of a substance is exactly the quantity necessary for its composition. Thus the quantity of electricity which can decompose a grain weight of water is exactly equal to the quantity of electricity which unites the elements of that grain of water together, and is equivalent to the quantity of atmospheric electricity which is active in a very powerful flash of lightning. This law is universal, and of that high and general order which characterises all great discoveries. Chemical force is extremely powerful. A pound of the best coal gives when burnt sufficient heat to raise the temperature of 8086 pounds of water one Centigrade degree, whence Professor Helmholtz of Bonn has computed that the magnitude of the chemical force of attraction between the particles of a pound of coal and the quantity of oxygen that corresponds to it, is capable of lifting a weight of 100 pounds to the height of 20 miles.

Dr. Faraday has given a singular instance of cohesive force inducing chemical combination, by the following experiment, which seems to be nearly allied to the discovery made by M. Dœbereiner, in 1823, of the spontaneous combustion of spongy platinum (N. 171) exposed to a stream of hydrogen gas mixed with common air. A plate of platinum with extremely clean surfaces, when plunged into oxygen and hydrogen gas mixed in the proportions which are found in the constitution of water, causes the gases to combine and water to be formed, the platinum to become red-hot, and at last an explosion to take place; the only conditions necessary for this curious experiment being excessive purity in the gases and in the surface of the plate. A sufficiently pure metallic surface can only be obtained by immersing the platinum in very strong hot sulphuric acid and then washing it in distilled water, or by making it the positive pole of a galvanic pile in dilute sulphuric acid. It appears that the force of cohesion, as well as the force of affinity, exerted by particles of matter, extends to all the particles within a very minute distance. Hence the platinum, while drawing the particles of the two gases towards its surface by its great cohesive attraction, brings them so near to one another that they come within the sphere of their mutual affinity, and a chemical combination takes place. Dr. Faraday attributes the effect in part also to a diminution in the elasticity of the gaseous particles on their sides adjacent to the platinum, and to their perfect mixture or association, as well as to the positive action of the metal in condensing them against its surface by its attractive force. The particles when chemically united run off the surface of the metal in the form of water by their gravitation, or pass away as aqueous vapour and make way for others.

The oscillations of the atmosphere, and the changes in its temperature, are measured by variations in the heights of the barometer and thermometer. But the actual length of the liquid columns depends not only upon the force of gravitation, but upon the cohesive force or reciprocal attraction between the molecules of the liquid and those of the tube containing it. This peculiar action of the cohesive force is called capillary attraction or capillarity. If a glass tube of extremely fine bore, such as a small thermometer tube, be plunged into a cup of water or spirit of wine, the liquid will immediately rise in the tube above the level of that in the cup; and the surface of the little column thus suspended will be a hollow hemisphere, whose diameter is the interior diameter of the tube. If the same tube be plunged into a cupful of mercury, the liquid will also rise in the tube, but it will never attain the level of that in the cup, and its surface will be a hemisphere whose diameter is also the diameter of the tube (N. 172). The elevation or depression of the same liquid in different tubes of the same matter is in the inverse ratio of their internal diameters (N. 173), and altogether independent of their thickness; whence it follows that the molecular action is insensible at sensible distances, and that it is only the thinnest possible film of the interior surface of the tubes that exerts a sensible action on the liquid. So much indeed is this the case, that, when tubes of the same bore are completely wetted with water throughout their whole extent, mercury will rise to the same height in all of them, whatever be their thickness or density, because the minute coating of moisture is sufficient to remove the internal column of mercury beyond the sphere of attraction of the tube, and to supply the place of a tube by its own capillary attraction. The forces which produce the capillary phenomena are the reciprocal attraction of the tube and the liquid, and of the liquid particles on one another; and, in order that the capillary column may be in equilibrio, the weight of that part of it which rises above or sinks below the level of the liquid in the cup must balance these forces.

The estimation of the action of the liquid is a difficult part of this problem. La Place, Dr. Young, and other mathematicians, have considered the liquid within the tube to be of uniform density; but M. Poisson, in one of those masterly productions in which he elucidates the most abstruse subjects, has proved that the phenomena of capillary attraction depend upon a rapid decrease in the density of the liquid column throughout an extremely small space at its surface. Every indefinitely thin layer of a liquid is compressed by the liquid above it, and supported by that below. Its degree of condensation depends upon the magnitude of the compressive force; and, as this force decreases rapidly towards the surface, where it vanishes the density of the liquid decreases also. M. Poisson has shown that, when this force is omitted, the capillary surface becomes plane, and that the liquid in the tube will neither rise above nor sink below the level of that in the cup. In estimating the forces, it is also necessary to include the variation in the density of the capillary surface round the edges from the attraction of the tube.

The direction of the resulting force determines the curvature of the surface of the capillary column. In order that a liquid may be in equilibrio, the force resulting from all the forces acting upon it must be perpendicular to the surface. Now it appears that, as glass is more dense than water or alcohol, the resulting force will be inclined towards the interior side of the tube; therefore the surface of the liquid must be more elevated at the sides of the tube than in the centre in order to be perpendicular to it, so that it will be concave as in the thermometer. But, as glass is less dense than mercury, the resulting force will be inclined from the interior side of the tube (N. 174), so that the surface of the capillary column must be more depressed at the sides of the tube than in the centre, in order to be perpendicular to the resulting force, and is consequently convex, as may be perceived in the mercury of the barometer when rising. The absorption of moisture by sponges, sugar, salt, &c., are familiar examples of capillary attraction. Indeed the pores of sugar are so minute, that there seems to be no limit to the ascent of the liquid. Wine is drawn up in a curve on the interior surface of a glass; tea rises above its level on the side of a cup; but, if the glass or cup be too full, the edges attract the liquid downwards, and give it a rounded form. A column of liquid will rise above or sink below its level between two plane parallel surfaces when near to one another, according to the relative densities of the plates and the liquid (N. 175); and the phenomena will be exactly the same as in a cylindrical tube whose diameter is double the distance of the plates from each other. If the two surfaces be very near to one another, and touch each other at one of their upright edges, the liquid will rise highest at the edges that are in contact, and will gradually diminish in height as the surfaces become more separated. The whole outline of the liquid column will have the form of a hyperbola. Indeed, so universal is the action of capillarity, that solids and liquids cannot touch one another without producing a change in the form of the surface of the liquid.

The attractions and repulsions arising from capillarity present many curious phenomena. If two plates of glass or metal, both of which are either dry or wet, be partly immersed in a liquid parallel to one another, the liquid will be raised or depressed close to their surfaces, but will maintain its level through the rest of the space that separates them. At such a distance they neither attract nor repel one another; but the instant they are brought so near as to make the level part of the liquid disappear, and the two curved parts of it meet, the two plates will rush towards each other and remain pressed together (N. 176). If one of the surfaces be wet and the other dry, they will repel one another when so near as to have a curved surface of liquid between them; but, if forced to approach a little nearer, the repulsion will be overcome, and they will attract each other as if they were both wet or both dry. Two balls of pith or wood floating in water, or two balls of tin floating in mercury, attract one another as soon as they are so near that the surface of the liquid is curved between them. Two ships in the ocean may be brought into collision by this principle. But two balls, one of which is wet and the other dry, repel one another as soon as the liquid which separates them is curved at its surface. A bit of tea-leaf is attracted by the edge of the cup if wet, and repelled when dry, provided it be not too far from the edge and the cup moderately full; if too full, the contrary takes place. It is probable that the rise of the sap in vegetables is in some degree owing to capillarity.

SECTION XV.

Analysis of the Atmosphere—Its Pressure—Law of Decrease in Density—Law of Decrease in Temperature—Measurement of Heights by the Barometer—Extent of the Atmosphere—Barometrical Variations—Oscillations—Trade-Winds—Cloud-Ring—Monsoons—Rotation of Winds—Laws of Hurricanes.

THE atmosphere is not homogeneous. It appears from analysis that, of 100 parts, 99·5 consist of nitrogen and oxygen gases mixed in the proportions of 79 to 21 of volume, the remainder consists of 0·05 parts of carbonic acid and on an average 0·45 of aqueous vapour. These proportions are found to be the same at all heights hitherto attained by man. The air is an elastic fluid, resisting pressure in every direction, and is subject to the law of gravitation. As the space in the top of the tube of a barometer is a vacuum, the column of mercury suspended by the pressure of the atmosphere on the surface of that in the cistern is a measure of its weight. Consequently every variation in the density occasions a corresponding rise or fall in the barometrical column. At the level of the sea in latitude 42°, and at the temperature of melting ice, the mean height of the barometer is 29·922 or 30 inches nearly. The pressure of the atmosphere is about fifteen pounds on every square inch; so that the surface of the whole globe sustains a weight of 11,671,000,000 hundreds of millions of pounds. Shell-fish, which have the power of producing a vacuum, adhere to the rocks by a pressure of fifteen pounds upon every square inch of contact.

The atmosphere when in equilibrio is an ellipsoid flattened at the poles from its rotation with the earth. In that state its strata are of uniform density at equal heights above the level of the sea; but since the air is both heavy and elastic, its density necessarily diminishes in ascending above the surface of the earth; for each stratum of air is compressed only by the weight above it. Therefore the upper strata are less dense because they are less compressed than those below them. Whence it is easy to show, supposing the temperature to be constant, that if the heights above the earth be taken in increasing arithmetical progression, that is, if they increase by equal quantities, as by a foot or a mile, the densities of the strata of air, or the heights of the barometer which are proportionate to them, will decrease in geometrical progression. For example, at the level of the sea if the mean height of the barometer be 29·922 inches, at the height of 18,000 feet it will be 14·961 inches, or one half as great; at the height of 36,000 feet it will be one-fourth as great; at 54,000 feet it will be one-eighth, and so on. Sir John Herschel has shown that the actual decrease is much more rapid, and that, in any hypothesis that has been formed with regard to the divisibility of the aërial atoms, a vacuum exists at the height of 80 or 90 miles above the earth’s surface, inconceivably more perfect than any that can be produced in the best air-pumps. Indeed the decrease in density is so rapid that three-fourths of all the air contained in the atmosphere is within four miles of the earth; and, as its superficial extent is 200 millions of square miles, its relative thickness is less than that of a sheet of paper when compared with its breadth. The air even on mountain tops is sufficiently rare to diminish the intensity of sound, to affect respiration, and to occasion a loss of muscular strength. The blood burst from the lips and ears of M. de Humboldt as he ascended the Andes; and he experienced the same difficulty in kindling and maintaining a fire at great heights which Marco Polo, the Venetian, felt on the mountains of Central Asia. M. Gay-Lussac ascended in a balloon to the height of 4·36 miles, and he suffered greatly from the rarity of the air. It is true that at the height of thirty-seven miles the atmosphere is still dense enough to reflect the rays of the sun when 18° below the horizon; but the tails of comets show that extremely attenuated matter is capable of reflecting light. And although, at the height of fifty miles, the bursting of the meteor of 1783 was heard on earth like the report of a cannon, it only proves the immensity of the explosion of a mass half a mile in diameter, which could produce a sound capable of penetrating air three thousand times more rare than that we breathe. But even these heights are extremely small when compared with the radius of the earth.

The density of the air is modified by various circumstances, chiefly by changes of temperature, because heat dilates the air and cold contracts it, varying 1/480 of the whole bulk when at 32° for every degree of Fahrenheit’s thermometer. Experience shows that the heat of the air decreases as the height above the surface of the earth increases. It appears that the mean temperature of space is 226° below the zero point of Fahrenheit by the theories of Fourier and Pouillet, but Sir John Herschel has computed it to be -239° Fahr. from observations made during the ascent in balloons. Such would probably be the temperature of the surface of the earth also, were it not for the non-conducting power of the air, whence it is enabled to retain the heat of the sun’s rays, which the earth imbibes and radiates in all directions. The decrease in heat is very irregular; each authority gives a different estimate, because it varies with latitude and local circumstances, but from the mean of five different statements it seems to be about one degree for every 334 feet; the mean of observations made in balloons is 400 feet, which is probably nearer the truth. This is the cause of the severe cold and perpetual snow on the summits of the alpine chains. In the year 1852 four ascents in a balloon took place from the meteorological observatory at Kew, in which the greatest height attained was 22,370 feet. The observations then made by Mr. Welsh furnished Sir John Herschel with data for computing that the temperature of space is minus 239°, that is 239° below the zero point of Fahrenheit, that the limiting temperature of the atmosphere is probably 77-1/2 degrees below that point at the equator, and 119-1/2 below it at the poles, with a range of temperature from the surface of 161-1/2° in the former case, and 119-1/2° in the latter. During these ascents it was found that the temperature of the air decreases uniformly up to a certain point, where it is arrested and remains constant, or increases through a depth of 2000 or 3000 feet, after which it decreases again according to the same law as before. Throughout this zone of constant temperature it either rains, or there is a great fall in the dew point; in short, it is the region of clouds, and the increase of temperature is owing to the latent or absorbed heat set free by the condensation of the aqueous vapour. In the latitude of Kew the cloud region begins at altitudes varying between 2000 and 6500 feet, according to the state of the weather.

Were it not for the effects of temperature on the density of the air, the heights of mountains might be determined by the barometer alone; but as the thermometer must also be consulted, the determination becomes more complicated. Mr. Ivory’s method of computing heights from barometrical measurements has the advantage of combining accuracy with the greatest simplicity. Indeed the accuracy with which the heights of mountains can be obtained by this method is very remarkable. Admiral Smyth, R.N., and Sir John Herschel measured the height of Etna by the barometer, without any communication and in different years; Admiral Smyth made it 10,874 feet, and Sir John Herschel 10,873, the difference being only one foot. In consequence of the diminished pressure of the atmosphere water boils at a lower temperature on mountain tops than in the valleys, which induced Fahrenheit to propose this mode of observation as a method of ascertaining their heights. It is very simple, as Professor Forbes ascertained that the temperature of the boiling point varies in arithmetical proportion with the height, or 5495 feet for every degree of Fahrenheit, so that the calculation of height becomes one of arithmetic only, without the use of any table.

The mean pressure of the atmosphere is not the same all over the globe. It is less by 0·24 of an inch at the equator than at the tropics or in the higher latitudes, in consequence of the ascent of heated air and vapour from the surface of the ocean. It is less also on the shores of the Baltic Sea than it is in France, and it was observed by Sir James C. Ross that throughout the whole of the Antarctic Ocean, from 68° to 74° S. latitude, and from 8° to 7° W. longitude, there is a depression of the barometer amounting to an inch and upwards, which is equivalent to an elevation above the sea level of 800 feet. A similar depression was observed by M. Erman in the sea of Ochotzk, and in the adjacent continent of eastern Siberia. Sir John Herschel assigns as the cause of these singular anomalies the great system of circulation of the trade and antetrade winds, in both hemispheres, reacting upon the general mass of the continents as obstacles in their path, which is modified by the configuration of the land.

There are various periodic oscillations in the atmosphere, which, rising and falling like waves in the sea, occasion corresponding changes in the height of the barometer, but they differ as much from the trade-winds, monsoons, and other currents, as the tides of the sea do from the Gulf-stream and other oceanic rivers. The sun and moon disturb the equilibrium of the atmosphere by their attraction, and produce annual undulations which have their maximum altitudes at the equinoxes, and their minima at the solstices. There are also lunar tides, which ebb and flow twice in the course of a lunation. The diurnal tides, which accomplish their rise and fall in six hours, are greatly modified by the heat of the sun. Between the tropics the barometer attains its maximum height about nine in the morning, then sinks till three or four in the afternoon; it again rises and attains a second maximum about nine in the evening, and then it begins to fall, and reaches a second minimum at three in the morning, again to pursue the same course. According to M. Bouvard, the amount of the oscillations at the equator is proportional to the temperature, and in other parallels it varies as the temperature and the square of the cosine of the latitude conjointly; consequently it decreases from the equator to the poles, but it is somewhat greater in the day than in the night.

Besides these small undulations, there are vast waves perpetually moving over the continents and oceans in separate and independent systems, being confined to local, yet very extensive districts, probably occasioned by long-continued rains or dry weather over large tracts of country. By numerous barometrical observations made simultaneously in both hemispheres, the courses of several have been traced, some of which occupy twenty-four, and others thirty-six, hours to accomplish their rise and fall. One especially of these vast barometric waves, many hundreds of miles in breadth, has been traced over the greater part of Europe; and not its breadth only, but also the direction of its front and its velocity, have been clearly ascertained. Although, like all other waves, these are but moving forms, yet winds arise dependent on them like tide streams in the ocean. Mr. Birt has determined the periods of other waves of still greater extent and duration, two of which required seventeen days to rise and fall; and another which takes fourteen days to complete its undulation, called by Mr. Birt the November wave, passes annually over the British Islands, probably over the whole of Europe and the seas on its northern coasts. Its crest, which appears to be 6000 miles in extent, moves from N.W. to S.E. at the rate of about 19 miles an hour; while the extent of its barometrical elevation from its trough to its crest is seldom less than an inch, sometimes double that quantity. The great crest is preceded and followed at about five days’ interval by two lower ones, and the beginning and end are marked by deep depressions. The researches of M. Leverrier leave no doubt that the great Crimean storm of the 14th November, 1854, was part of this phenomenon,[8] for even a very small difference of atmospheric pressure is sufficient to raise a considerable wind. Since each oscillation has its perfect effect independently of the others, each one is marked by a change in the barometer, and this is beautifully illustrated by curves constructed from a series of observations. The general form of the curve shows the course of the principal wave, while small undulations in its outline mark the maxima and minima of the minor oscillations.

The trade-winds, which are the principal currents in the atmosphere, are only a particular case of those very general laws which regulate the motion of the winds depending on the rarefaction of the air combined with the rotation of the earth on its axis. They are permanent currents of wind between the tropics, blowing to the N.E. on the N. side of the equator, and to the S.E. on the S. side.

If currents of air come from the poles, it is clear that equilibrium must be restored by counter-currents from the equator; moreover, winds coming from the poles, where there is no rotation, to the equator, which revolves from W. to E. at the rate of 1000 miles an hour, must of necessity move in a direction resulting from their own progressive motion and that of rotation; hence, in blowing towards the equator the bias is to the E., and in blowing from it the bias is to the W. Thus as N. and S. winds from the poles blow along the surface from the tropics to the equator, in consequence of this composition of motions that from the N. becomes the N.E. trade-wind, and that from the S. the S.E. trade-wind. Now these winds being in contrary directions cross at the equator, balance each other through about 6 degrees of latitude, and produce a belt of calms of that breadth encircling the globe, known as the calms of the equator, or the Variables of seamen. The heat of the sun rarefies the air so much, that the trade-winds, after crossing at the equator, ascend into the higher regions of the atmosphere, where that from the N. goes to the tropic of Capricorn, and that from the S. to the tropic of Cancer. But while travelling in these lofty regions they become cold and heavy, and, sinking to the surface at the tropics, each proceeds to the opposite pole from which it set out. Now, however, they have a greater rotatory motion than the places they successively arrive at, so the bias is to the W., and they become the N.W. and S.W. extra-tropical winds.

If on arriving at the poles the air were to accumulate there, the circulation of the winds would cease; but currents rise into the upper regions, and flow back again to the tropics, where they sink down to fill the vacuum caused by the great precipitation of vapour in these regions, and then flow to the equator as trade-winds (N. 177). So the currents of air cross again at the tropics and produce two belts of calms which surround the globe, named by Lieutenant Maury the Calms of Cancer and the Calms of Capricorn, but generally known to sailors as the Doldrums. Thus the winds go from pole to pole and back again, alternately as under and upper currents. In their circuits the winds cross each other five times, producing regions of calms at the poles, the tropics, and equator. The trade-winds generally extend for about 28° on each side of the equator, but, on account of the greater quantity of land in the northern hemisphere, the N.E. trade-wind is narrower than the S.E.

The sun is perpetually raising enormous quantities of vapour from the ocean which the trade-winds carry to the equator: it is condensed when it rises with the air into the higher strata, and forms a ring of clouds along the southern side of the belt of equatorial calms that surrounds the earth, which, during the day, is perpetually pouring down torrents of rain, while the sun continually beating upon its upper surface dissolves the clouds into invisible vapour which is carried by the winds and condensed into rain on the extra-tropical regions. The whole system of trade-winds, equatorial and tropical calms, with the cloud ring, follow the sun in declination; consequently in its journeys back and forwards it annually travels over 1000 miles of latitude, and regulates the dry and rainy season in the tropical parts of the earth.

The monsoons, which are periodic winds in the Indian Ocean, in part depend upon this movement. For when the sun is in the northern hemisphere the trade-winds come northward with him; and when his intense heat expands the air over the Great Gobi and other arid Asiatic deserts, it ascends; the N.E. trade-wind is drawn in to fill the vacuum and ascends with it; then the S.E. trade-wind, being no longer met and balanced by the N.E. trade, passes into the northern hemisphere, and as it proceeds northward from the equator it is deflected to the west by the rotation of the earth, combined with the indraught over the heated deserts, and becomes the S.W. monsoon, which blows while the sun is north of the equator, but as soon as he goes south, and no longer rarefies the air over the Indian deserts, the S.E. trade-wind resumes its usual course, and is then known as the S.E. monsoon. The influence of the heated deserts is perceptible to the distance of 1000 miles from the shore; the monsoons prevail with great steadiness over the Arabian Gulf, the Indian Ocean, and part of the China Sea. At the change, torrents of rain and violent thunderstorms accompany the conflict between the contending winds.

The Sahara desert in North Africa, and those of Utah, Texas, and New Mexico, occasion the monsoons which prevail in the North Atlantic and on both sides of Central America, and the monsoons which blow to the north of Australia show the sterility of the interior, even if other proofs were wanting. From the powerful effect of the land in drawing off the winds from their course, it may be seen why the N.E. trade-winds are narrower than the S.E. trades.

In the extra-tropical winds in the North Atlantic, which blow from the 40th parallel to the pole, the north-westerly are to the easterly as 2 to 1: hence there would be an accumulation of air at the pole at the expense of the equator, did not a current rise at the pole and return to the equator through the high regions of the atmosphere, which confirms the theory of the rotation of the wind.

There are many proofs of the existence of the counter-currents above the trade-winds. On the Peak of Teneriffe the prevailing winds are from the west. Light clouds have frequently been seen moving rapidly from west to east at a very great height above the trade-winds, which were sweeping along the surface of the ocean in a contrary direction. Rains, clouds, and nearly all the other atmospheric phenomena, occur below the height of 18,000 feet, and generally much nearer to the surface of the earth. They are owing to currents of air running upon each other in horizontal strata, differing in their electric state, in temperature and moisture, as well as in velocity and direction.

When north and south winds blow alternately, the wind at any place will veer in one uniform direction through every point of the compass, provided the one begins before the other has ceased. In the northern hemisphere a north wind sets out with a smaller degree of rotatory motion than the places have at which it successively arrives, consequently it passes through all the points of the compass from N. to N.E. and E. A current from the south, on the contrary, sets out with a greater rotatory velocity than the places have at which it successively arrives, so by the rotation of the earth it is deflected from S. to S.W. and W. Now, if the vane at any place should have veered from the N. through N.E. to E., and a south wind should spring up, it would combine its motion with the former and cause the vane to turn successively from the E. to S.E. and S. But by the earth’s rotation this south wind will veer to the S.W. and W., and, if a north wind should now arise, it would combine its motion with that of the west, and cause it to veer to the N.W. and N. Thus two alternations of north and south wind will cause the vane at any place to go completely round the compass, from N. to E., S., W., and N. again. At the Royal Observatory at Greenwich the wind accomplishes five circuits in that direction in the course of a year. When circumstances combine to produce alternate north and south winds in the southern hemisphere, the gyration is in the contrary direction. Although the general tendency of the wind may be rotatory, and is so in many instances, at least for part of the year, yet it is so often counteracted by local circumstances, that the winds are in general very irregular, every disturbance in atmospheric equilibrium from heat or any other cause producing a corresponding wind. The most prevalent winds in Europe are the N.E. and S.W.; the former arises from the north polar current, and the latter from causes already mentioned. The law of the wind’s rotation was first described by Dr. Dalton, but has been developed by Professor Dove, of Berlin.

Hurricanes are those storms of wind in which the portion of the atmosphere that forms them revolves in a horizontal circuit round a vertical or somewhat inclined axis of rotation, while the axis itself, and consequently the whole storm, is carried forward along the surface of the globe, so that the direction in which the storm is advancing is quite different from the direction in which the rotatory current may be blowing at any point. In the West Indies, where hurricanes are frequent and destructive, they generally originate in the tropical regions near the inner boundary of the trade-winds, and are caused by the vertical ascent of a column of rarefied air, whose place is supplied by a rush of wind from the surrounding regions, set into gyration by the rotation of the earth. By far the greater number of Atlantic hurricanes have begun eastward of the lesser Antilles or Caribbean Islands.

In every case the axis of the storm moves in an elliptical or parabolic curve, having its vertex in or near the tropic of Cancer, which marks the external limit of the trade-winds north of the equator. As the motion before it reaches the tropic is in a straight line from S.E. to N.W., and after it has passed it from S.W. to N.E., the bend of the curve is turned towards Florida and the Carolinas. In the southern hemisphere the body of the storm moves in exactly the opposite direction. The hurricanes which originate south of the equator, and whose initial path is from N.E. to S.W., bend round at the tropic of Capricorn, and then move from N.W. to S.E.

The extent and velocity of these storms are great; for instance, the hurricane that took place on the 12th of August, 1830, was traced from eastward of the Caribbee Islands, along the Gulf Stream, to the bank of Newfoundland, a distance of more than 3000 miles, which it passed over in six days. Although the hurricane of the 1st of September, 1821, was not so extensive, its velocity was greater, as it moved at the rate of 30 miles an hour: small storms are generally more rapid than those of greater dimensions.

The action of these storms seems to be at first confined to the stratum of air nearest the earth, and then they seldom appear to be more than a mile high, though sometimes they are raised higher; or even divided by a mountain into two separate storms, each of which continues its new path and gyrations with increased violence. This occurred in the gale of the 25th of December, 1821, in the Mediterranean, when the Spanish mountains and the Maritime Alps became new centres of motion.

By the friction of the earth the axis of the storm bends a little forward. This causes a continual intermixture of the lower and warmer strata of air with those that are higher and colder, producing torrents of rain and violent electric explosions.

The breadth of the whirlwind is greatly augmented when the path of the storm changes on crossing the tropic. The vortex of a storm has covered an extent of the surface of the globe 500 miles in diameter.

The revolving motion accounts for the sudden and violent changes observed during hurricanes. In consequence of the rotation of the air, the wind blows in opposite directions on each side of the axis of the storm, and the violence of the blast increases from the circumference towards the centre of gyration, but in the centre itself the air is in repose: hence, when the body of the storm passes over a place, the wind begins to blow moderately, and increases to a hurricane as the centre of the whirlwind approaches; then, in a moment, a dead and awful calm succeeds, suddenly followed by a renewal of the storm in all its violence, but now blowing in a direction diametrically opposite to its former course. This happened at the Island of St. Thomas on the 2nd of August, 1837, where the hurricane increased in violence till half-past seven in the morning, when perfect stillness took place for forty minutes, after which the storm recommenced in a contrary direction.

The sudden fall of the mercury in the barometer in the regions habitually visited by hurricanes is a certain indication of a coming tempest. In consequence of the centrifugal force of these rotatory storms the air becomes rarefied, and, as the atmosphere is disturbed to some distance beyond the actual circle of gyration or limits of the storm, the barometer often sinks some hours before its arrival, from the original cause of the rotatory disturbance. It continues sinking under the first half of the hurricane, is at a maximum sometimes of two inches in the centre of gyration, and again rises during the passage of the latter half, though it does not attain its greatest height till the storm is over. The diminution of atmospheric pressure is greater and extends over a wider area in the temperate zones than in the torrid, on account of the sudden expansion of the circle of rotation when the gale crosses the tropic.

As the fall of the barometer gives warning of the approach of a hurricane, so the laws of the storm’s motion afford the seaman knowledge to guide him in avoiding it. In the northern temperate zone, if the gale begins from the S.E. and veers by S. to W., the ship should steer to the S.E.; but, if the gale begins from the N.E., and changes through N. to N.W., the vessel should go to the N.W. In the northern part of the torrid zone, if the storm begin from the N.E., and veer through E. to S.E., the ship should steer to the N.E.; but, if it begin from the N.W., and veer by W. to S.W., the ship should steer to the S.W., because she is in the south-western side of the storm. Since the laws of storms are reversed in the southern hemisphere, the rules for steering vessels are necessarily reversed also. A heavy swell is peculiarly characteristic of these storms. In the open sea the swell often extends many leagues beyond the range of the gale which produced it.

Waterspouts are occasioned by small whirlwinds, which always have their origin at a great distance from that part of the sea from which the spout begins to rise, where it is generally calm. The whirl is produced by two currents of air, which, running in opposite directions, compress one another by their impetus, so that they rise in spiral eddies to the clouds. They move slowly along the surface of the sea, sometimes in vertical, and sometimes in twisted spirals, putting the sea into violent agitation as they pass, and carrying the water aloft by the force of gyration. Occasionally the eddies begin in the clouds and dip down to the sea.

SECTION XVI.

Sound—Propagation of Sound illustrated by a Field of Standing Corn—Nature of Waves—Propagation of Sound through the Atmosphere—Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of the Obstruction of Sound—Law of its Intensity—Reflection of Sound—Echoes—Thunder—Refraction of Sound—Interference of Sounds.

ONE of the most important uses of the atmosphere is the conveyance of sound. Without the air, deathlike silence would prevail through nature, for in common with all substances it has a tendency to impart vibrations to bodies in contact with it. Therefore undulations received by the air, whether it be from a sudden impulse, such as an explosion or the vibrations of a musical chord, are propagated in every direction, and produce the sensation of sound upon the auditory nerves. A bell rung under the exhausted receiver of an air-pump is inaudible, which shows that the atmosphere is really the medium of sound. In the small undulations of deep water in a calm, the vibrations of the liquid particles are made in the vertical plane, that is, up and down, or at right angles to the direction of the transmission of the waves. But the vibrations of the particles of air which produce sound differ from these, being performed in the same direction in which the waves of sound travel. The propagation of sound has been illustrated by a field of corn agitated by the wind. However irregular the motion of the corn may seem on a superficial view, it will be found, if the velocity of the wind be constant, that the waves are all precisely similar and equal, and that all are separated by equal intervals and move in equal times.

A sudden blast depresses each ear equally and successively in the direction of the wind, but, in consequence of the elasticity of the stalks and the force of the impulse, each ear not only rises again as soon as the pressure is removed, but bends back nearly as much in the contrary direction, and then continues to oscillate backwards and forwards in equal times, like a pendulum, to a less and less extent, till the resistance of the air puts a stop to the motion. These vibrations are the same for every individual ear of corn. Yet, as their oscillations do not all commence at the same time, but successively, the ears will have a variety of positions at any one instant. Some of the advancing ears will meet others in their returning vibrations, and, as the times of oscillation are equal for all, they will be crowded together at regular intervals. Between these there will occur equal spaces where the ears will be few, in consequence of being bent in opposite directions; and at other equal intervals they will be in their natural upright positions. So that over the whole field there will be a regular series of condensations and rarefactions among the ears of corn, separated by equal intervals, where they will be in their natural state of density. In consequence of these changes the field will be marked by an alternation of bright and dark bands. Thus the successive waves which fly over the corn with the speed of the wind are totally distinct from, and entirely independent of the extent of the oscillations of each individual ear, though both take place in the same direction. The length of a wave is equal to the space between two ears precisely in the same state of motion, or which are moving similarly, and the time of the vibration of each ear is equal to that which elapses between the arrival of two successive waves at the same point. The only difference between the undulations of a corn-field and those of the air which produce sound is, that each ear of corn is set in motion by an external cause, and is uninfluenced by the motion of the rest; whereas in air, which is a compressible and elastic fluid, when one particle begins to oscillate, it communicates its vibrations to the surrounding particles, which transmit them to those adjacent, and so on continually. Hence from the successive vibrations of the particles of air the same regular condensations and rarefactions take place as in the field of corn, producing waves throughout the whole mass of air, though each molecule like each individual ear of corn never moves far from its state of rest. The small waves of a liquid, and the undulations of the air, like waves in the corn, are evidently not real masses moving in the direction in which they are advancing, but merely outlines, motions, or forms passing along, and comprehending all the particles of an undulating fluid which are at once in a vibratory state. It is thus that an impulse given to any one point of the atmosphere is successively propagated in all directions, in a wave diverging as from the centre of a sphere to greater and greater distances, but with decreasing intensity, in consequence of the increasing number of particles of inert matter which the force has to move; like the waves formed in still water by a falling stone, which are propagated circularly all around the centre of disturbance (N. 160).

The intensity of sound depends upon the violence and extent of the initial vibrations of air; but, whatever they may be, each undulation when once formed can only be transmitted straight forwards, and never returns back again unless when reflected by an opposing obstacle. The vibrations of the aërial molecules are always extremely small, whereas the waves of sound vary from a few inches to several feet. The various musical instruments, the human voice and that of animals, the singing of birds, the hum of insects, the roar of the cataract, the whistling of the wind, and the other nameless peculiarities of sound, show at once an infinite variety in the modes of aërial vibration, and the astonishing acuteness and delicacy of the ear, thus capable of appreciating the minutest differences in the laws of molecular oscillation.

All mere noises are occasioned by irregular impulses communicated to the ear; and, if they be short, sudden, and repeated beyond a certain degree of quickness, the ear loses the intervals of silence, and the sound appears continuous. Still such sounds will be mere noise: in order to produce a musical sound, the impulses, and consequently the undulations of the air, must be all exactly similar in duration and intensity, and must recur after exactly equal intervals of time. If a blow be given to the nearest of a series of broad, flat, and equidistant palisades, set edgewise in a line direct from the ear, each palisade will repeat or echo the sound; and these echoes, returning to the ear at successive equal intervals of time, will produce a musical note. The quality of a musical note depends upon the abruptness, and its intensity upon the violence and extent of the original impulse. In the theory of harmony the only property of sound taken into consideration is the pitch, which varies with the rapidity of the vibrations. The grave or low tones are produced by very slow vibrations, which increase in frequency as the note becomes more acute. The lowest man’s voice makes 396 vibrations in a second, whilst the highest woman’s voice makes 2112. Very deep tones are not heard by all alike, and Dr. Wollaston, who made a variety of experiments on the sense of hearing, found that many people, though not at all deaf, are quite insensible to the cry of the bat or the cricket, while to others it is painfully shrill. From his experiments he concluded that human hearing is limited to about nine octaves, extending from the lowest note of the organ to the highest known cry of insects; and he observes with his usual originality that, “as there is nothing in the nature of the atmosphere to prevent the existence of vibrations incomparably more frequent than any of which we are conscious, we may imagine that animals like the Grylli, whose powers appear to commence nearly where ours terminate, may have the faculty of hearing still sharper sounds which we do not know to exist, and that there may be other insects hearing nothing in common with us, but endowed with a power of exciting, and a sense which perceives vibrations, of the same nature indeed as those which constitute our ordinary sounds, but so remote that the animals which perceive them may be said to possess another sense, agreeing with our own solely in the medium by which it is excited.”

M. Savart, so well known for the number and beauty of his researches in acoustics, has proved that a high note of a given intensity, being heard by some ears and not by others, must not be attributed to its pitch, but to its feebleness. His experiments, and those more recently made by Professor Wheatstone, show that, if the pulses could be rendered sufficiently powerful, it would be difficult to fix a limit to human hearing at either end of the scale. M. Savart had a wheel made about nine inches in diameter with 360 teeth set at equal distances round its rim, so that while in motion each tooth successively hit on a piece of card. The tone increased in pitch with the rapidity of the rotation, and was very pure when the number of strokes did not exceed three or four thousand in a second, but beyond that it became feeble and indistinct. With a wheel of a larger size a much higher tone could be obtained, because, the teeth being wider apart, the blows were more intense and more separated from one another. With 720 teeth on a wheel thirty-two inches in diameter, the sound produced by 12,000 strokes in a second was audible, which corresponds to 24,000 vibrations of a musical chord. So that the human ear can appreciate a sound which only lasts the 24,000th part of a second. This note was distinctly heard by M. Savart and by several people who were present, which convinced him that with another apparatus still more acute sounds might be rendered audible.

For the deep tones M. Savart employed a bar of iron, two feet eight inches long, about two inches broad, and half an inch in thickness, which revolved about its centre as if its arms were the spokes of a wheel. When such a machine rotates, it impresses a motion on the air similar to its own, and, when a thin board or card is brought close to its extremities, the current of air is momentarily interrupted at the instant each arm of the bar passes before the card; it is compressed above the card and dilated below; but the instant the spoke has passed a rush of air to restore equilibrium makes a kind of explosion, and, when these succeed each other rapidly, a musical note is produced of a pitch proportional to the velocity of the revolution. When M. Savart turned this bar slowly, a succession of single beats was heard; as the velocity became greater, the sound was only a rattle; but, as soon as it was sufficient to give eight beats in a second, a very deep musical note was distinctly audible corresponding to sixteen single vibrations in a second, which is the lowest that has hitherto been produced. When the velocity of the bar was much increased, the intensity of the sound was hardly bearable. The spokes of a revolving wheel produce the sensation of sound, on the very same principle that a burning stick whirled round gives the impression of a luminous circle. The vibrations excited in the organ of hearing by one beat have not ceased before another impulse is given. Indeed it is indispensable that the impressions made upon the auditory nerves should encroach upon each other in order to produce a full and continued note. On the whole, M. Savart has come to the conclusion, that the most acute sounds would be heard with as much ease as those of a lower pitch, if the duration of the sensation produced by each pulse could be diminished proportionally to the augmentation of the number of pulses in a given time: and on the contrary, if the duration of the sensation produced by each pulse could be increased in proportion to their number in a given time, that the deepest tones would be as audible as any of the others.

The velocity of sound is uniform and independent of the nature, extent, and intensity of the primitive disturbance. Consequently sounds of every quality and pitch travel with equal speed. The smallest difference in their velocity is incompatible either with harmony or melody, for notes of different pitches and intensities, sounded together at a little distance, would arrive at the ear in different times. A rapid succession of notes would in this case produce confusion and discord. But, as the rapidity with which sound is transmitted depends upon the elasticity of the medium through which it has to pass, whatever tends to increase the elasticity of the air must also accelerate the motion of sound. On that account its velocity is greater in warm than in cold weather, supposing the pressure of the atmosphere constant. In dry air, at the freezing temperature, sound travels at the rate of 1090 feet in a second, and for any higher temperature one foot must be added for every degree of the thermometer above 32°: hence at 62° of Fahrenheit its speed in a second is 1120 feet, or 765 miles an hour, which is about three-fourths of the diurnal velocity of the earth’s equator. Since all the phenomena of the transmission of sound are simple consequences of the physical properties of the air, they have been predicted and computed rigorously by the laws of mechanics. It was found, however, that the velocity of sound, determined by observation, exceeded what it ought to have been theoretically by 173 feet, or about one-sixth of the whole amount. La Place suggested that this discrepancy might arise from the increased elasticity of the air in consequence of a development of latent or absorbed heat (N. 178) during the undulations of sound, and calculation confirmed the accuracy of his views. The aërial molecules being suddenly compressed give out their absorbed heat; and, as air is too bad a conductor to carry it rapidly off, it occasions a momentary and local rise of temperature, which, increasing the elasticity of the air without at the same time increasing its inertia, causes the movement to be propagated more rapidly. Analysis gives the true velocity of sound in terms of the elevation of temperature that a mass of air is capable of communicating to itself, by the disengagement of its own absorbed heat when suddenly compressed in a given ratio. This change of temperature however could not be obtained directly by any experiments which had been made at that epoch; but by inverting the problem, and assuming the velocity of sound as given by experiment, it was computed that the temperature of a mass of air is raised nine-tenths of a degree when the compression is equal to 1/116 of its volume.

Probably all liquids are elastic, though considerable force is required to compress them. Water suffers a condensation of nearly 0·0000496 for every atmosphere of pressure, and is consequently capable of conveying sound even more rapidly than air, the velocity in the former being 4708 feet in a second. A person under water hears sounds made in air feebly, but those produced in water very distinctly. According to the experiments of M. Colladon, the sound of a bell was conveyed under water through the Lake of Geneva to the distance of about nine miles. He also perceived that the progress of sound through water is greatly impeded by the interposition of any object, such as a projecting wall; consequently sound under water resembles light in having a distinct shadow. It has much less in air, being transmitted all round buildings or other obstacles, so as to be heard in every direction, though often with a considerable diminution of intensity, as when a carriage turns the corner of a street.

The velocity of sound in passing through solids is in proportion to their hardness, and is much greater than in air or water. A sound which takes some time in travelling through the air passes almost instantaneously along a wire six hundred feet long; consequently it is heard twice—first as communicated by the wire, and afterwards through the medium of the air. The facility with which the vibrations of sound are transmitted along the grain of a log of wood is well known. Indeed they pass through iron, glass, and some kinds of wood, at the rate of 18,530 feet in a second. The velocity of sound is obstructed by a variety of circumstances, such as falling snow, fog, rain, or any other cause which disturbs the homogeneity of the medium through which it has to pass. M. de Humboldt says that it is on account of the greater homogeneity of the atmosphere during the night that sounds are then better heard than during the day, when its density is perpetually changing from partial variations of temperature. His attention was called to this subject on the plain surrounding the Mission of the Apures by the rushing noise of the great cataracts of the Orinoco, which seemed to be three times as loud by night as by day. This he illustrated by experiment. A tall glass half full of champagne cannot be made to ring as long as the effervescence lasts. In order to produce a musical note, the glass together with the liquid it contains must vibrate in unison as a system, which it cannot do in consequence of the fixed air rising through the wine and disturbing its homogeneity, because, the vibrations of the gas being much slower than those of the liquid, the velocity of the sound is perpetually interrupted. For the same reason the transmission of sound as well as light is impeded in passing through an atmosphere of variable density. Sir John Herschel, in his admirable Treatise on Sound, thus explains the phenomenon:—“It is obvious,” he says, “that sound as well as light must be obstructed, stifled, and dissipated from its original direction by the mixture of air of different temperatures, and consequently elasticities; and thus the same cause which produces that extreme transparency of the air at night, which astronomers alone fully appreciate, renders it also more favourable to sound. There is no doubt, however, that the universal and dead silence generally prevalent at night renders our auditory nerves sensible to impressions which would otherwise escape notice. The analogy between sound and light is perfect in this as in so many other respects. In the general light of day the stars disappear. In the continual hum of voices, which is always going on by day, and which reach us from all quarters, and never leave the ear time to attain complete tranquillity, those feeble sounds which catch our attention at night make no impression. The ear, like the eye, requires long and perfect repose to attain its utmost sensibility.”

Many instances may be brought in proof of the strength and clearness with which sound passes over the surface of water or ice. Lieutenant Forster was able to carry on a conversation across Port Bowen Harbour, when frozen, a distance of a mile and a half.

The intensity of sound depends upon the extent of the excursions of the fluid molecules, on the energy of the transient condensations and dilatations, and on the greater or less number of particles which experience these effects. We estimate that intensity by the impetus of these fluid molecules on our organs, which is consequently as the square of the velocity, and not by their inertia, which is as the simple velocity. Were the latter the case, there would be no sound, because the inertia of the receding waves of air would destroy the equal and opposite inertia of those advancing; whence it may be concluded that the intensity of sound diminishes inversely as the square of the distance from its origin. In a tube, however, the force of sound does not decay as in open air, unless perhaps by friction against the sides. M. Biot found, from a number of highly-interesting experiments made on the pipes of the aqueducts in Paris, that a continued conversation could be carried on in the lowest possible whisper through a cylindrical tube about 3120 feet long, the time of transmission through that space being 2·79 seconds. In most cases sound diverges in all directions so as to occupy at any one time a spherical surface; but Dr. Young has shown that there are exceptions, as, for example, when a flat surface vibrates only in one direction. The sound is then most intense when the ear is at right angles to the surface, whereas it is scarcely audible in a direction precisely perpendicular to its edge. In this case it is impossible that the whole of the surrounding air can be affected in the same manner, since the particles behind the sounding surface must be moving towards it whenever the particles before it are retreating. Hence in one half of the surrounding sphere of air its motions are retrograde, while in the other half they are direct; consequently, at the edges where these two portions meet, the motions of the air will neither be retrograde nor direct, and therefore it must be at rest.

It appears, from theory as well as daily experience, that sound is capable of reflection from surfaces (N. 179) according to the same laws as light. Indeed any one who has observed the reflection of the waves from a wall on the side of a river, after the passage of a steam-boat, will have a perfect idea of the reflection of sound and of light. As every substance in nature is more or less elastic, it may be agitated according to its own law by the impulse of a mass of undulating air; and reciprocally the surface by its reaction will communicate its undulations back again into the air. Such reflections produce echoes; and as a series of them may take place between two or more obstacles, each will cause an echo of the original sound, growing fainter and fainter till it dies away; because sound, like light, is weakened by reflection. Should the reflecting surface be concave towards a person, the sound will converge towards him with increased intensity, which will be greater still if the surface be spherical and concentric with him. Undulations of sound diverging from one focus of an elliptical shell (N. 180) converge in the other after reflection. Consequently a sound from the one will be heard in the other as if it were close to the ear. The rolling noise of thunder has been attributed to reverberation between different clouds, which may possibly be the case to a certain extent. Sir John Herschel is of opinion that an intensely prolonged peal is probably owing to a combination of sounds, because, the velocity of electricity being incomparably greater than that of sound, the thunder may be regarded as originating in every point of a flash of lightning at the same instant. The sound from the nearest point will arrive first; and if the flash run in a direct line from a person, the noise will come later and later from the remote points of its path in a continued roar. Should the direction of the flash be inclined, the succession of sounds will be more rapid and intense: and if the lightning describe a circular curve round a person, the sound will arrive from every point at the same instant with a stunning crash. In like manner the subterranean noises heard during earthquakes like distant thunder may arise from the consecutive arrival at the ear of undulations propagated at the same instant from nearer and more remote points; or if they originate in the same point, the sound may come by different routes through strata of different densities.

Sounds under water are heard very distinctly in the air immediately above; but the intensity decays with great rapidity as the observer goes farther off, and is altogether inaudible at the distance of two or three hundred yards. So that waves of sound, like those of light, in passing from a dense to a rare medium, are not only refracted, but suffer total reflection at very oblique incidences (N. 189).

The laws of interference extend also to sound. It is clear that two equal and similar musical strings will be in unison if they communicate the same number of vibrations to the air in the same time. But if two such strings be so nearly in unison that one performs a hundred vibrations in a second, and the other a hundred and one in the same period—during the first few vibrations the two resulting sounds will combine to form one of double the intensity of either, because the aërial waves will sensibly coincide in time and place; but one will gradually gain on the other till at the fiftieth vibration it will be half an oscillation in advance. Then the waves of air which produce the sound being sensibly equal, but the receding part of the one coinciding with the advancing part of the other, they will destroy one another, and occasion an instant of silence. The sound will be renewed immediately after, and will gradually increase till the hundredth vibration, when the two waves will combine to produce a sound double the intensity of either. These intervals of silence and greatest intensity, called beats, will recur every second; but if the notes differ much from one another, the alternations will resemble a rattle; and if the strings be in perfect unison, there will be no beats, since there will be no interference. Thus by interference is meant the co-existence of two undulations in which the lengths of the waves are the same. And as the magnitude of an undulation may be diminished by the addition of another transmitted in the same direction, it follows that one undulation may be absolutely destroyed by another when waves of the same length are transmitted in the same direction, provided that the maxima of the undulations are equal, and that one follows the other by half the length of a wave. A tuning-fork affords a good example of interference. When that instrument vibrates, its two branches alternately recede from and approach one another; each communicates its vibrations to the air, and a musical note is the consequence. If the fork be held upright about a foot from the ear, and turned round its axis while vibrating, at every quarter revolution the sound will scarcely be heard, while at the intermediate points it will be strong and clear. This phenomenon arises from the interference of the undulations of air coming from the two branches of the fork. When the two branches coincide, or when they are at equal distances from the ear, the waves of air combine to reinforce each other; but at the quadrants, where the two branches are at unequal distances from the ear, the lengths of the waves differ by half an undulation, and consequently destroy one another.

SECTION XVII.

Vibration of Musical Strings—Harmonic Sounds—Nodes—Vibration of Air in Wind-Instruments—Vibration of Solids—Vibrating Plates—Bells—Harmony—Sounding Boards—Forced Vibrations—Resonance—Speaking Machines.

WHEN the particles of elastic bodies are suddenly disturbed by an impulse, they return to their natural position by a series of isochronous vibrations, whose rapidity, force, and permanency depend upon the elasticity, the form, and the mode of aggregation which unites the particles of the body. These oscillations are communicated to the air, and on account of its elasticity they excite alternate condensations and dilatations in the strata of the fluid nearest to the vibrating body; from thence they are propagated to a distance. A string or wire stretched between two pins, when drawn aside and suddenly let go, will vibrate till its own rigidity and the resistance of the air reduce it to rest. These oscillations may be rotatory, in every plane, or confined to one plane according as the motion is communicated. In the piano-forte, where the strings are struck by a hammer at one extremity, the vibrations probably consist of a bulge running to and fro from end to end. Different modes of vibration may be obtained from the same sonorous body. Suppose a vibrating string to give the lowest C of the pianoforte which is the fundamental note of the string; if it be lightly touched exactly in the middle, so as to retain that point at rest, each half will then vibrate twice as fast as the whole, but in opposite directions; the ventral or bulging segments will be alternately above and below the natural position of the string, and the resulting note will be the octave above C. When a point at a third of the length of the string is kept at rest, the vibrations will be three times as fast as those of the whole string, and will give the twelfth above C. When the point of rest is one-fourth of the whole, the oscillations will be four times as fast as those of the fundamental note, and will give the double octave; and so on. These acute sounds are called the harmonics of the fundamental note. It is clear, from what has been stated, that the string thus vibrating could not give these harmonics spontaneously unless it divided itself at its aliquot parts into two, three, four, or more segments in opposite states of vibration separated by points actually at rest. In proof of this, pieces of paper placed on the string at the half, third, fourth, or other aliquot points, according to the corresponding harmonic sound, will remain on it during its vibration, but will instantly fly off from any of the intermediate points. The points of rest, called the nodal points of the string, are a mere consequence of the law of interferences; for, if a rope fastened at one end be moved to and fro at the other extremity so as to transmit a succession of equal waves along it, they will be successively reflected when they arrive at the other end of the rope by the fixed point, and in returning they will occasionally interfere with the advancing waves; and, as these opposite undulations will at certain points destroy one another, the point of the rope in which this happens will remain at rest. Thus a series of nodes and ventral segments will be produced whose number will depend upon the tension and the frequency of the alternate motions communicated to the moveable end. So, when a string fixed at both ends is put in motion by a sudden blow at any point of it, the primitive impulse divides itself into two pulses running opposite ways, which are each totally reflected at the extremities, and, running back again along the whole length, are again reflected at the other ends. And thus they will continue to run backwards and forwards, crossing one another at each traverse, and occasionally interfering, so as to produce nodes; so that the motion of a string fastened at both ends consists of a wave or pulse continually doubled back on itself by reflection at the fixed extremities.

Harmonics generally co-exist with the fundamental sound in the same vibrating body. If one of the lowest strings of the pianoforte be struck, an attentive ear will not only hear the fundamental note, but will detect all the others sounding along with it, though with less and less intensity as their pitch becomes higher. According to the law of co-existing undulations, the whole string and each of its aliquot parts are in different and independent states of vibration at the same time; and as all the resulting notes are heard simultaneously, not only the air, but the ear also, vibrates in unison with each at the same instant (N. 181).

Harmony consists in an agreeable combination of sounds. When two chords perform their vibrations in the same time, they are in unison; but, when their vibrations are so related as to have a common period, after a few oscillations they produce concord. Thus, when the vibrations of two strings bear a very simple relation to each other, as where one of them makes two, three, four, &c., vibrations in the time the other makes one; or, if it accomplishes three, four, &c., vibrations while the other makes two, the result is a concord which is the more perfect the shorter the common period. In discords, on the contrary, the beats are distinctly audible, which produces a disagreeable and harsh effect, because the vibrations do not bear a simple relation to one another, as where one of two strings makes eight vibrations while the other accomplishes fifteen. The pleasure afforded by harmony is attributed by Dr. Young to the love of order, and to a predilection for a regular repetition of sensations natural to the human mind, which is gratified by the perfect regularity and rapid recurrence of the vibrations. The love of poetry and dancing he conceives to arise in some degree from the rhythm of the one and the regularity of the motions in the other.

A blast of air passing over the open end of a tube, as over the reeds in Pan’s pipes; over a hole in one side, as in the flute; or through the aperture called a reed, with a flexible tongue, as in the clarinet, puts the internal column of air into longitudinal vibrations by the alternate condensations and rarefactions of its particles. At the same time the column spontaneously divides itself into nodes, between which the air also vibrates longitudinally, but with a rapidity inversely proportional to the length of the divisions, giving the fundamental note or one of its harmonics. The nodes are produced on the principle of interferences by the reflection of the longitudinal undulations of the air at the ends of the pipe, as in the musical string, only that in one case the undulations are longitudinal, and in the other transverse.

A pipe, either open or shut at both ends, when sounded, vibrates entire, or divides itself spontaneously into two, three, four, &c., segments separated by nodes. The whole column gives the fundamental note by waves or vibrations of the same length with the pipe. The first harmonic is produced by waves half as long as the tube, the second harmonic by waves a third as long, and so on. The harmonic segments in an open and shut pipe are the same in number, but differently placed. In a shut pipe the two ends are nodes, but in an open pipe there is half a segment at each extremity, because the air at these points is neither rarefied nor condensed, being in contact with that which is external. If one of the ends of the open pipe be closed, its fundamental note will be an octave lower: the air will now divide itself into three, five, seven, &c., segments; and the wave producing its fundamental note will be twice as long as the pipe, so that it will be doubled back (N. 182). All these notes may be produced separately by varying the intensity of the blast. Blowing steadily and gently, the fundamental note will sound; when the force of the blast is increased the note will all at once start up an octave; when the intensity of the wind is augmented the twelfth will be heard; and, by continuing to increase the force of the blast, the other harmonics may be obtained, but no force of wind will produce a note intermediate between these. The harmonics of a flute may be obtained in this manner, from the lowest C or D upwards, without altering the fingering, merely by increasing the intensity of the blast and altering the form of the lips. Pipes of the same dimensions, whether of lead, glass, or wood, give the same tone as to pitch under the same circumstances, which shows that the air alone produces the sound.

Metal springs fastened at one end, when forcibly bent, endeavour to return to rest by a series of vibrations, which give very pleasing tones, as in musical boxes. Various musical instruments have been constructed, consisting of metallic springs thrown into vibration by a current of air. Among the most perfect of these are Mr. Wheatstone’s Symphonion, Concertina, and Æolian Organ, instruments of different effects and capabilities, but all possessing considerable execution and expression.

The Syren is an ingenious instrument, devised by M. Cagniard de la Tour, for ascertaining the number of pulsations in a second, corresponding to each pitch: the notes are produced by jets of air passing through small apertures, arranged at regular distances in a circle on the side of a box, before which a disc revolves pierced with the same number of holes. During a revolution of the disc the currents are alternately intercepted and allowed to pass as many times as there are apertures in it, and a sound is produced whose pitch depends on the velocity of rotation.

A glass or metallic rod, when struck at one end, or rubbed in the direction of its length with a wet finger, vibrates longitudinally, like a column of air, by the alternate condensation and expansion of its constituent particles, producing a clear and beautiful musical note of a high pitch, on account of the rapidity with which these substances transmit sound. Rods, surfaces, and, in general, all undulating bodies, resolve themselves into nodes. But in surfaces the parts which remain at rest during their vibrations are lines which are curved or plane according to the substance, its form, and the mode of vibration. If a little fine dry sand be strewed over the surface of a plate of glass or metal, and if undulations be excited by drawing the bow of a violin across its edge, it will emit a musical sound, and the sand will immediately arrange itself in the nodal lines, where alone it will accumulate and remain at rest, because the segments of the surface on each side will be in different states of vibration, the one being elevated while the other is depressed; and, as these two motions meet in the nodal lines, they neutralise one another. These lines vary in form and position with the part where the bow is drawn across, and the point by which the plate is held. The motion of the sand shows in what direction the vibrations take place. If they be perpendicular to the surface, the sand will be violently tossed up and down till it finds the points of rest. If they be tangential, the sand will only creep along the surface to the nodal lines. Sometimes the undulations are oblique, or compounded of both the preceding. If a bow be drawn across one of the angles of a square plate of glass or metal held firmly by the centre, the sand will arrange itself in two straight lines parallel to the sides of the plate, and crossing in the centre so as to divide it into four equal squares, whose motions will be contrary to each other. Two of the diagonal squares will make their excursions on one side of the plate, while the other two make their vibrations on the other side of it. This mode of vibration produces the lowest tone of the plate (N. 183). If the plate be still held by the centre, and the bow applied to the middle of one of the sides, the vibrations will be more rapid, and the tone will be a fifth higher than in the preceding case: now the sand will arrange itself from corner to corner, and will divide the plate into four equal triangles, each pair of which will make their excursions on opposite sides of the plate. The nodal lines and pitch vary not only with the point where the bow is applied, but with the point by which the plate is held, which being at rest necessarily determines the direction of one of the quiescent lines. The forms assumed by the sand in square plates are very numerous, corresponding to all the various modes of vibration. The lines in circular plates are even more remarkable for their symmetry, and upon them the forms assumed by the sand may be classed in three systems. The first is the diametrical system, in which the figures consist of diameters dividing the circumference of the plate into equal parts, each of which is in a different state of vibration from those adjacent. Two diameters, for example, crossing at right angles, divide the circumference into four equal parts; three diameters divide it into six equal parts; four divide it into eight, and so on. In a metallic plate, these divisions may amount to thirty-six or forty. The next is the concentric system, where the sand arranges itself in circles, having the same centre with the plate; and the third is the compound system, where the figures assumed by the sand are compounded of the other two, producing very complicated and beautiful forms. Galileo seems to have been the first to notice the points of rest and motion in the sounding-board of a musical instrument; but to Chladni is due the whole discovery of the symmetrical forms of the nodal lines in vibrating plates (N. 184). Professor Wheatstone has shown, in a paper read before the Royal Society in 1833, that all Chladni’s figures, and indeed all the nodal figures of vibrating surfaces, result from very simple modes of vibration oscillating isochronously, and superposed upon each other; the resulting figure varying with the component modes of vibration, the number of the superpositions, and the angles at which they are superposed. For example, if a square plate be vibrating so as to make the sand arrange itself in straight lines parallel to one side of the plate, and if, in addition to this, such vibrations be excited as would have caused the sand to form in lines perpendicular to the first had the plate been at rest, the combined vibrations will make the sand form in lines from corner to corner (N. 185).

M. Savart’s experiments on the vibrations of flat glass rulers are highly interesting. Let a lamina of glass 27^{in}·56 long, 0·59 of an inch broad, and 0·06 of an inch in thickness, be held by the edges in the middle, with its flat surface horizontal. If this surface be strewed with sand, and set in longitudinal vibration by rubbing its under surface with a wet cloth, the sand on the upper surface will arrange itself in lines parallel to the ends of the lamina, always in one or other of two systems (N. 186). Although the same one of the two systems will always be produced by the same plate of glass, yet among different plates of the preceding dimensions, even though cut from the same sheet side by side, one will invariably exhibit one system, and the other the other, without any visible reason for the difference. Now, if the positions of these quiescent lines be marked on the upper surface, and if the plate be turned so that the lower surface becomes the upper one, the sand being strewed, and vibrations excited as before, the nodal lines will still be parallel to the ends of the lamina, but their positions will be intermediate between those of the upper surface (N. 187). Thus it appears that all the motions of one half of the thickness of the lamina, or ruler, are exactly contrary to those of the corresponding points of the other half. If the thickness of the lamina be increased, the other dimensions remaining the same, the sound will not vary, but the number of nodal lines will be less. When the breadth of the lamina exceeds the 0·6 of an inch, the nodal lines become curved, and are different on the two surfaces. A great variety of forms are produced by increasing the breadth and changing the form of the surface; but in all it appears that the motions in one half of the thickness are opposed to those in the other half.

M. Savart also found, by placing small paper rings round a cylindrical tube or rod, so as to rest upon it at one point only, that, when the tube or rod is continually turned on its axis in the same direction, the rings slide along during the vibrations, till they come to a quiescent point, where they rest. By tracing these nodal lines he discovered that they twist in a spiral or corkscrew round rods and cylinders, making one or more turns according to the length; but at certain points, varying in number according to the mode of vibration of the rod, the screw stops, and recommences on the other side, though it is turned in a contrary direction; that is, on one side it is a right-handed screw, on the other a left (N. 188). The nodal lines in the interior surface of the tube are perfectly similar to those in the exterior, but they occupy intermediate positions. If a small ivory ball be put within the tube, it will follow these nodal lines when the tube is made to revolve on its axis.

All solids which ring when struck, such as bells, drinking glasses, gongs, &c., have their shape momentarily and forcibly changed by the blow, and from their elasticity, or tendency to resume their natural form, a series of undulations take place, owing to the alternate condensations and rarefactions of the particles of solid matter. These have also their harmonic tones, and consequently nodes. Indeed, generally, when a rigid system of any form whatever vibrates either transversely or longitudinally, it divides itself into a certain number of parts which perform their vibrations without disturbing one another. These parts are at every instant in alternate states of undulation; and, as the points or lines where they join partake of both, they remain at rest, because the opposing motions destroy one another.

The air, notwithstanding its rarity, is capable of transmitting its undulations when in contact with a body susceptible of admitting and exciting them. It is thus that sympathetic undulations are excited by a body vibrating near insulated tended strings, capable of following its undulations, either by vibrating entire, or by separating themselves into their harmonic divisions. If two chords equally stretched, of which one is twice or three times longer than the other, be placed side by side, and if the shorter be sounded, its vibrations will be communicated by the air to the other, which will be thrown into such a state of vibration that it will be spontaneously divided into segments equal in length to the shorter string. When a tuning-fork receives a blow and is made to rest upon a piano-forte during its vibration, every string which, either by its natural length or by its spontaneous subdivisions, is capable of executing corresponding vibrations, responds in a sympathetic note. The same effect will be produced by the stroke of a bell near a piano or harp. Some one or other of the notes of an organ are generally in unison with one of the panes or with the whole sash of a window, which consequently resounds when those notes are sounded. A peal of thunder has frequently the same effect. The sound of very large organ-pipes is generally inaudible till the air be set in motion by the undulations of some of the superior accords, and then the sound becomes extremely energetic. Recurring vibrations occasionally influence each other’s periods. For example, two adjacent organ-pipes nearly in unison may force themselves into concord; and two clocks, whose rates differed considerably when separate, have been known to beat together when fixed to the same wall, and one clock has forced the pendulum of another into motion, when merely standing on the same stone pavement. These forced oscillations, which correspond in their periods with those of the exciting cause, are to be traced in every department of physical science. Several instances of them have already occurred in this work. Such are the tides, which follow the sun and moon in all their motions and periods. The nutation of the earth’s axis also, which corresponds with the period, and represents the motion of the nodes of the moon, is again reflected back to the moon, and may be traced in the nutation of the lunar orbit. And, lastly, the acceleration of the moon’s mean motion represents the action of the planets on the earth reflected by the sun to the moon.

In consequence of the facility with which the air communicates undulations, all the phenomena of vibrating plates may be exhibited by sand strewed on paper or parchment, stretched over a harmonica glass or large bell-shaped tumbler. In order to give due tension to the paper or vellum, it must be wetted, stretched over the glass, gummed round the edges, allowed to dry, and varnished over, to prevent changes in its tension from the humidity of the atmosphere. If a circular disc of glass be held concentrically over this apparatus, with its plane parallel to the surface of the paper, and set in vibration by drawing a bow across its edge, so as to make sand on its surface take any of Chladni’s figures, the sand on the paper will assume the very same form, in consequence of the vibrations of the disc being communicated to the paper by the air. When the disc is removed slowly in a horizontal direction, the forms on the paper will correspond with those on the disc, till the distance is too great for the air to convey the vibrations. If the disc while vibrating be gradually more and more inclined to the horizon, the figures on the paper will vary by degrees; and, when the vibrating disc is perpendicular to the horizon, the sand on the paper will form into straight lines parallel to the surface of the disc, by creeping along it instead of dancing up and down. If the disc be made to turn round its vertical diameter while vibrating, the nodal lines on the paper will revolve, and exactly follow the motion of the disc. It appears, from this experiment, that the motions of the aërial molecules in every part of a spherical wave, propagated from a vibrating body as a centre, are parallel to each other, and not divergent like the radii of a circle. When a slow air is played on a flute near this apparatus, each note calls up a particular form in the sand, which the next note effaces, to establish its own. The motion of the sand will even detect sounds that are inaudible. By the vibrations of sand on a drum-head the besieged have discovered the direction in which a counter-mine was working. M. Savart, who made these beautiful experiments, employed this apparatus to discover nodal lines in masses of air. He found that the air of a room, when thrown into undulations by the continued sound of an organ-pipe, or by any other means, divides itself into masses separated by nodal curves of double curvature, such as spirals, on each side of which the air is in opposite states of vibration. He even traced these quiescent lines going out at an open window, and for a considerable distance in the open air. The sand is violently agitated where the undulations of the air are greatest, and remains at rest in the nodal lines. M. Savart observed, that when he moved his head away from a quiescent line towards the right the sound appeared to come from the right, and when he moved it towards the left the sound seemed to come from the left, because the molecules of air are in different states of motion on each side of the quiescent line.

A musical string gives a very feeble sound when vibrating alone, on account of the small quantity of air set in motion; but when attached to a sounding-board, as in the harp and piano-forte, it communicates its undulations to that surface, and from thence to every part of the instrument; so that the whole system vibrates isochronously, and by exposing an extensive undulating surface, which transmits its undulations to a great mass of air, the sound is much reinforced. The intensity is greatest when the vibrations of the string or sounding body are perpendicular to the sounding-board, and least when they are in the same plane with it. The sounding-board of the piano-forte is better disposed than that of any other stringed instrument, because the hammers strike the strings so as to make them vibrate at right angles to it. In the guitar, on the contrary, they are struck obliquely, which renders the tone feeble, unless when the sides, which also act as a sounding-board, are deep. It is evident that the sounding-board and the whole instrument are agitated at once by all the superposed vibrations excited by the simultaneous or consecutive notes that are sounded, each having its perfect effect independently of the rest. A sounding-board not only reciprocates the different degrees of pitch, but all the nameless qualities of tone. This has been beautifully illustrated by Professor Wheatstone in a series of experiments on the transmission through solid conductors of musical performances, from the harp, piano, violin, clarinet, &c. He found that all the varieties of pitch, quality, and intensity are perfectly transmitted with their relative gradations, and may be communicated, through conducting wires or rods of very considerable length, to a properly disposed sounding-board in a distant apartment. The sounds of an entire orchestra may be transmitted and reciprocated by connecting one end of a metallic rod with a sounding-board near the orchestra, so placed as to resound to all the instruments, and the other end with the sounding-board of a harp, piano, or guitar, in a remote apartment. Professor Wheatstone observes, “The effect of this experiment is very pleasing; the sounds, indeed, have so little intensity as scarcely to be heard at a distance from the reciprocating instrument; but, on placing the ear close to it, a diminutive band is heard in which all the instruments preserve their distinctive qualities, and the pianos and fortes, the crescendos and diminuendos, their relative contrasts. Compared with an ordinary band heard at a distance through the air, the effect is as a landscape seen in miniature beauty through a concave lens, compared with the same scene viewed by ordinary vision through a murky atmosphere.”

Every one is aware of the reinforcement of sound by the resonance of cavities. When singing or speaking near the aperture of a wide-mouthed vessel, the intensity of some one note in unison with the air in the cavity is often augmented to a great degree. Any vessel will resound if a body vibrating the natural note of the cavity be placed opposite to its orifice, and be large enough to cover it, or at least to set a large portion of the adjacent air in motion. For the sound will be alternately reflected by the bottom of the cavity and the undulating body at its mouth. The first impulse of the undulating substance will be reflected by the bottom of the cavity, and then by the undulating body, in time to combine with the second new impulse. This reinforced sound will also be twice reflected in time to conspire with the third new impulse; and, as the same process will be repeated on every new impulse, each will combine with all its echoes to reinforce the sound prodigiously. Professor Wheatstone, to whose ingenuity we are indebted for so much new and valuable information on the theory of sound, has given some very striking instances of resonance. If one of the branches of a vibrating tuning-fork be brought near the embouchure of a flute, the lateral apertures of which are stopped so as to render it capable of producing the same sound as the fork, the feeble and scarcely audible sound of the fork will be augmented by the rich resonance of the column of air within the flute, and the tone will be full and clear. The sound will be found greatly to decrease by closing or opening another aperture; for the alteration in the length of the column of air renders it no longer fit perfectly to reciprocate the sound of the fork. This experiment may be made on a concert flute with a C tuning-fork. But Professor Wheatstone observes, that in this case it is generally necessary to finger the flute for B, because, when blown into with the mouth, the under-lip partly covers the embouchure, which renders the sound about a semitone flatter than it would be were the embouchure entirely uncovered. He has also shown, by the following experiment, that any one among several simultaneous sounds may be rendered separately audible. If two bottles be selected, and tuned by filling them with such a quantity of water as will render them unisonant with two tuning-forks which differ in pitch, on bringing both of the vibrating tuning-forks to the mouth of each bottle alternately, in each case that sound only will be heard which is reciprocated by the unisonant bottle.

Several attempts have been made to imitate the articulation of the letters of the alphabet. About the year 1779, MM. Kratzenstein of St. Petersburg, and Kempelen of Vienna, constructed instruments which articulated many letters, words, and even sentences. Mr. Willis of Cambridge has adapted cylindrical tubes to a reed, whose length can be varied at pleasure by sliding joints. Upon drawing out a tube while a column of air from the bellows of an organ is passing through it, the vowels are pronounced in the order, i, e, a, o, u. On extending the tube, they are repeated after a certain interval, in the inverted order, u, o, a, e, i. After another interval they are again obtained in the direct order, and so on. When the pitch of the reed is very high, it is impossible to sound some of the vowels, which is in perfect correspondence with the human voice, female singers being unable to pronounce u and o in their high notes. From the singular discoveries of M. Savart on the nature of the human voice, and the investigations of Mr. Willis on the mechanism of the larynx, it may be presumed that ultimately the utterance or pronunciation of modern languages will be conveyed, not only to the eye, but also to the ear of posterity. Had the ancients possessed the means of transmitting such definite sounds, the civilised world would still have responded in sympathetic notes at the distance of many ages.

SECTION XVIII.

Refraction—Astronomical Refraction and its Laws—Formation of Tables of Refraction—Terrestrial Refraction—Its Quantity—Instances of extraordinary Refraction—Reflection—Instances of extraordinary Reflection—Loss of Light by the Absorbing Power of the Atmosphere—Apparent Magnitude of Sun and Moon in the Horizon.

NOT only everything we hear but all we see is through the medium of the atmosphere. Without some knowledge of its action upon light, it would be impossible to ascertain the position of the heavenly bodies, or even to determine the exact place of very distant objects upon the surface of the earth; for, in consequence of the refractive power of the air, no distant object is seen in its true position.

All the celestial bodies appear to be more elevated than they really are; because the rays of light, instead of moving through the atmosphere in straight lines, are continually inflected towards the earth. Light passing obliquely out of a rare into a denser medium, as from vacuum into air, or from air into water, is bent or refracted from its course towards a perpendicular to that point of the denser surface where the light enters it (N. 189). In the same medium, the sine of the angle contained between the incident ray and the perpendicular is in a constant ratio to the sine of the angle contained by the refracted ray and the same perpendicular; but this ratio varies with the refracting medium. The denser the medium, the more the ray is bent. The barometer shows that the density of the atmosphere decreases as the height above the earth increases. Direct experiments prove that the refractive power of the air increases with its density. It follows therefore that, if the temperature be uniform, the refractive power of the air is greatest at the earth’s surface, and diminishes upwards.

A ray of light from a celestial object falling obliquely on this variable atmosphere, instead of being refracted at once from its course, is gradually more and more bent during its passage through it so as to move in a vertical curved line, in the same manner as if the atmosphere consisted of an infinite number of strata of different densities. The object is seen in the direction of a tangent to that part of the curve which meets the eye; consequently the apparent altitude (N. 190) of the heavenly bodies is always greater than their true altitude. Owing to this circumstance, the stars are seen above the horizon after they are set, and the day is lengthened from a part of the sun being visible, though he really is behind the rotundity of the earth. It would be easy to determine the direction of a ray of light through the atmosphere if the law of the density were known; but, as this law is perpetually varying with the temperature, the case is very complicated. When rays pass perpendicularly from one medium into another, they are not bent; and experience shows, that in the same surface, though the sines of the angles of incidence and refraction retain the same ratio, the refraction increases with the obliquity of incidence (N. 189). Hence it appears that the refraction is greatest at the horizon, and at the zenith there is none. But it is proved that, at all heights above ten degrees, refraction varies nearly as the tangent of the angular distance of the object from the zenith, and wholly depends upon the heights of the barometer and thermometer. For the quantity of refraction at the same distance from the zenith varies nearly as the height of the barometer, the temperature being constant; and the effect of the variation of temperature is to diminish the quantity of refraction by about its 480th part for every degree in the rise of Fahrenheit’s thermometer. Not much reliance can be placed on celestial observations, within less than ten or twelve degrees of the horizon, on account of irregular variations in the density of the air near the surface of the earth, which are sometimes the cause of very singular phenomena. The humidity of the air produces no sensible effect on its refractive power; and it has been proved that the amount of refraction is the same whatever be the velocity of the incident light, that is whether the light comes from a star in that part of the heavens towards which the earth is going, or from one in that part of the sky whence it is receding.

Bodies, whether luminous or not, are only visible by the rays which proceed from them. As the rays must pass through strata of different densities in coming to us, it follows that, with the exception of stars in the zenith, no object either in or beyond our atmosphere is seen in its true place. But the deviation is so small in ordinary cases that it causes no inconvenience, though in astronomical and trigonometrical observations due allowance must be made for the effects of refraction. Dr. Bradley’s tables of refraction were formed by observing the zenith distances of the sun at his greatest declinations, and the zenith distances of the pole-star above and below the pole. The sum of these four quantities is equal to 180°, diminished by the sum of the four refractions, whence the sum of the four refractions was obtained; and, from the law of the variation of refraction determined by theory, he assigned the quantity due to each altitude (N. 191). The mean horizontal refraction is about 35ʹ 6ʺ, and at the height of forty-five degrees it is 58ʺ·36. The effect of refraction upon the same star above and below the pole was noticed by Alhazen, a Saracen astronomer of Spain, in the ninth century; but its existence was known to Ptolemy in the second, though he was ignorant of its quantity.

The refraction of a terrestrial object is estimated differently from that of a celestial body. It is measured by the angle contained between the tangent to the curvilineal path of the ray where it meets the eye, and the straight line joining the eye and the object (N. 192). Near the earth’s surface the path of the ray may be supposed to be circular; and the angle at the centre of the earth corresponding to this path is called the horizontal angle. The quantity of terrestrial refraction is obtained by measuring contemporaneously the elevation of the top of a mountain above a point in the plain at its base, and the depression of that point below the top of the mountain. The distance between these two stations is the chord of the horizontal angle; and it is easy to prove that double the refraction is equal to the horizontal angle, increased by the difference between the apparent elevation and the apparent depression. Whence it appears that, in the mean state of the atmosphere, the refraction is about the fourteenth part of the horizontal angle.

Some very singular appearances occur from the accidental expansion or condensation of the strata of the atmosphere contiguous to the surface of the earth, by which distant objects, instead of being elevated, are depressed. Sometimes, being at once both elevated and depressed, they appear double, one of the images being direct, and the other inverted. In consequence of the upper edges of the sun and moon being less refracted than the lower, they often appear to be oval when near the horizon. The looming also or elevation of coasts, mountains, and ships, when viewed across the sea, arises from unusual refraction. A friend of the author’s, while standing on the plains of Hindostan, saw the whole upper chain of the Himalaya Mountains start into view, from a sudden change in the density of the air, occasioned by a heavy shower after a very long course of dry and hot weather. Single and double images of objects at sea, arising from sudden changes of temperature which are not so soon communicated to the water on account of its density as to the air, occur more rarely and are of shorter duration than similar appearances on land. In 1818 Captain Scoresby, whose observations on the phenomena of the polar seas are so valuable, recognised his father’s ship by its inverted image in the air, although the vessel itself was below the horizon. He afterwards found that she was seventeen miles beyond the horizon, and thirty miles distant. Two images are sometimes seen suspended in the air over a ship, one direct and the other inverted, with their topmasts or their hulls meeting, according as the inverted image is above or below the direct image (N. 193). Dr. Wollaston has proved that these appearances are owing to the refraction of the rays through media of different densities, by the very simple experiment of looking along a red-hot poker at a distant object. Two images are seen, one direct and another inverted, in consequence of the change induced by the heat in the density of the adjacent air. He produced the same effect by a saline or saccharine solution with water and spirit of wine floating upon it (N. 194).

Many of the phenomena that have been ascribed to extraordinary refraction seem to be occasioned by a partial or total reflection of the rays of light at the surfaces of strata of different densities (N. 189). It is well known that, when light falls obliquely upon the external surface of a transparent medium, as on a plate of glass or a stratum of air, one portion is reflected and the other transmitted. But, when light falls very obliquely upon the internal surface, the whole is reflected, and not a ray is transmitted. In all cases the angles made by the incident and reflected rays with a perpendicular to the surface being equal, as the brightness of the reflected image depends on the quantity of light, those arising from total reflection must be by far the most vivid. The delusive appearance of water, so well known to African travellers and to the Arab of the desert as the Lake of the Gazelles, is ascribed to the reflection which takes place between strata of air of different densities, owing to radiation of heat from the arid sandy plains. The mirage described by Captain Mundy in his Journal of a Tour in India probably arises from this cause. “A deep precipitous valley below us, at the bottom of which I had seen one or two miserable villages in the morning, bore in the evening a complete resemblance to a beautiful lake; the vapour which played the part of water ascending nearly half way up the sides of the vale, and on its bright surface trees and rocks being distinctly reflected. I had not been long contemplating this phenomenon, before a sudden storm came on and dropped a curtain of clouds over the scene.”

An occurrence which happened on the 18th of November, 1804, was probably produced by reflection. Dr. Buchan, while watching the rising sun from the cliff about a mile to the east of Brighton, at the instant the solar disc emerged from the surface of the ocean, saw the cliff on which he was standing, a windmill, his own figure and that of a friend, depicted immediately opposite to him on the sea. This appearance lasted about ten minutes, till the sun had risen nearly his own diameter above the surface of the waves. The whole then seemed to be elevated into the air, and successively vanished. The rays of the sun fell upon the cliff at an incidence of 73° from the perpendicular, and the sea was covered with a dense fog many yards in height, which gradually receded before the rising sun. When extraordinary refraction takes place laterally, the strata of variable density are perpendicular to the horizon, and, if combined with vertical refraction, the objects are magnified as when seen through a telescope. From this cause, on the 26th of July, 1798, the cliffs of France, fifty miles off, were seen as distinctly from Hastings as if they had been close at hand; and even Dieppe was said to have been visible in the afternoon.

The stratum of air in the horizon is so much thicker and more dense than the stratum in the vertical, that the sun’s light is diminished 1300 times in passing through it, which enables us to look at him when setting without being dazzled. The loss of light, and consequently of heat, by the absorbing power of the atmosphere, increases with the obliquity of incidence. Of ten thousand rays falling on its surface, 8123 arrive at a given point of the earth if they fall perpendicularly; 7024 arrive if the angle of direction be fifty degrees; 2831, if it be seven degrees; and only five rays will arrive through a horizontal stratum. Since so great a quantity of light is lost in passing through the atmosphere, many celestial objects are altogether invisible from the plain, which may be seen from elevated situations. Diminished splendour, and the false estimate we make of distance from the number of intervening objects, lead us to suppose the sun and moon to be much larger when in the horizon than at any other altitude, though their apparent diameters are then somewhat less. Instead of the sudden transitions of light and darkness, the reflective power of the air adorns nature with the rosy and golden hues of the Aurora and twilight. Even when the sun is eighteen degrees below the horizon, a sufficient portion of light remains to show that at the height of thirty miles it is still dense enough to reflect light. The atmosphere scatters the sun’s rays, and gives all the beautiful tints and cheerfulness of day. It transmits the blue light in greatest abundance; the higher we ascend, the sky assumes a deeper hue; but, in the expanse of space, the sun and stars must appear like brilliant specks in profound blackness.

SECTION XIX.

Constitution of Light according to Sir Isaac Newton—Absorption of Light—Colours of Bodies—Constitution of Light according to Sir David Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light—The Achromatic Telescope—Homogeneous Light—Accidental and Complementary Colours—M. Plateau’s Experiments and Theory of Accidental Colours.

IT is impossible thus to trace the path of a sunbeam through our atmosphere without feeling a desire to know its nature, by what power it traverses the immensity of space, and the various modifications it undergoes at the surfaces and in the interior of terrestrial substances.

Sir Isaac Newton proved the compound nature of white light, as emitted from the sun, by passing a sunbeam through a glass prism (N. 195), which, separating the rays by refraction, formed a spectrum or oblong image of the sun, consisting of seven colours, red, orange, yellow, green, blue, indigo, and violet—of which the red is the least refrangible, and the violet the most. But, when he reunited these seven rays by means of a lens, the compound beam became pure white as before. He insulated each coloured ray, and, finding that it was no longer capable of decomposition by refraction, concluded that white light consists of seven kinds of homogeneous light, and that to the same colour the same refrangibility ever belongs, and to the same refrangibility the same colour. Since the discovery of absorbent media, however, it appears that this is not the constitution of the solar spectrum.

We know of no substance that is either perfectly opaque or perfectly transparent. Even gold may be beaten so thin as to be pervious to light. On the contrary, the clearest crystal, the purest air or water, stops or absorbs its rays when transmitted, and gradually extinguishes them as they penetrate to greater depths. On this account objects cannot be seen at the bottom of very deep water, and many more stars are visible to the naked eye from the tops of mountains than from the valleys. The quantity of light that is incident on any transparent substance is always greater than the sum of the reflected and refracted rays. A small quantity is irregularly reflected in all directions by the imperfections of the polish by which we are enabled to see the surface; but a much greater portion is absorbed by the body. Bodies that reflect all the rays appear white, those that absorb them all seem black; but most substances, after decomposing the white light which falls upon them, reflect some colours and absorb the rest. A violet reflects the violet rays alone and absorbs the others. Scarlet cloth absorbs almost all the colours except red. Yellow cloth reflects the yellow rays most abundantly, and blue cloth those that are blue. Consequently colour is not a property of matter, but arises from the action of matter upon light. In fact, the law of action and reaction obtains in light as in every other department of nature, so that light cannot be reflected, refracted, much less absorbed, by any medium without being reacted upon by it. Thus a white riband reflects all the rays, but, when dyed red, the particles of the silk acquire the property of reflecting the red rays most abundantly and of absorbing the others. Upon this property of unequal absorption the colours of transparent media depend; for they also receive their colour from their power of stopping or absorbing some of the colours of white light, and transmitting others. As, for example, black and red inks, though equally homogeneous, absorb different kinds of rays; and, when exposed to the sun, they become heated in different degrees; while pure water seems to transmit all rays equally, and is not sensibly heated by the passing light of the sun. The rich dark light transmitted by a smalt-blue finger-glass is not a homogeneous colour like the blue or indigo of the spectrum, but is a mixture of all the colours of white light which the glass has not absorbed. The colours absorbed are such as mixed with the blue tint would form white light. When the spectrum of seven colours is viewed through a thin plate of this glass, they are all visible; and, when the plate is very thick, every colour is absorbed between the extreme red and the extreme violet, the interval being perfectly black; but, if the spectrum be viewed through a certain thickness of the glass intermediate between the two, it will be found that the middle of the red space, the whole of the orange, a great part of the green, a considerable part of the blue, a little of the indigo, and a very little of the violet, vanish, being absorbed by the blue glass; and that the yellow rays occupy a larger space, covering part of that formerly occupied by the orange on one side and by the green on the other: so that the blue glass absorbs the red light, which when mixed with the yellow constitutes orange; and also absorbs the blue light, which when mixed with the yellow forms the part of the green space next to the yellow. Hence, by absorption, green light is decomposed into yellow and blue, and orange light into yellow and red: consequently the orange and green rays, though incapable of decomposition by refraction, can be resolved by absorption, and actually consist of two different colours possessing the same degree of refrangibility. Difference of colour, therefore, is not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admissible as a general truth. By this analysis of the spectrum, not only with blue glass but with a variety of coloured media, Sir David Brewster, so justly celebrated for his optical discoveries, is of opinion that the solar spectrum consists of three primary colours, red, yellow, and blue, each of which exists throughout its whole extent, but with different degrees of intensity in different parts; and that the superposition of these three produces all the seven hues according as each primary colour is in excess or defect. That since a certain portion of red, yellow, and blue rays constitute white light, the colour of any point of the spectrum may be considered as consisting of the predominating colour at that point mixed with white light. Consequently, “by absorbing the excess of any colour at any point of the spectrum above what is necessary to form white light, such white light will appear at that point as never mortal eye looked upon before this experiment, since it possesses the remarkable property of remaining the same after any number of refractions, and of being capable of decomposition by absorption alone.” This analysis of light has been called in question by Professor Challis, of Cambridge, who does not admit of any resolution by absorbing media different from that by the prism, though he admits that a mixture of blue and yellow solar light produces green. Professor Stokes, on the contrary, does not allow that a mixture of blue and yellow solar light produces green, although that mixture produces green when the light is from other sources, for he found the gradation from sunlight to pass from yellow through diluted yellow, white, diluted blue to blue; so he does not admit of Sir David Brewster’s analysis of the spectrum; however, there appears to be still a doubt as to the real character of the phenomena presented by certain absorbing substances.

In addition to the seven colours of the Newtonian spectrum, Sir John Herschel has discovered a set of very dark red rays beyond the red extremity of the spectrum which can only be seen when the eye is defended from the glare of the other colours by a dark blue cobalt glass. He has also found that beyond the extreme violet there are visible rays of a lavender gray colour, which may be seen by throwing the spectrum on a sheet of paper moistened by the carbonate of soda. The illuminating power of the different rays of the spectrum varies with the colour. The most intense light is in the mean yellow ray, or, according to M. Fraunhofer, at the boundary of the orange and yellow.

When the prism is very perfect and the sunbeam small, so that the spectrum may be received on a sheet of white paper in its utmost state of purity, it presents the appearance of a riband shaded with all the prismatic colours, having its breadth irregularly striped or subdivided by an indefinite number of dark, and sometimes black lines. The greater number of these rayless lines are so extremely narrow that it is impossible to see them in ordinary circumstances. The best method is to receive the spectrum on the object-glass of a telescope, so as to magnify them sufficiently to render them visible. This experiment may also be made, but in an imperfect manner, by viewing a narrow slit between two nearly closed window-shutters through a very excellent glass prism held close to the eye, with its refracting angle parallel to the line of light. The rayless lines in the red portion of the spectrum become most visible as the sun approaches the horizon, while those in the blue extremity are most obvious in the middle of the day. When the spectrum is formed by the sun’s rays, either direct or indirect—as from the sky, clouds, rainbow, moon, or planets—the black bands are always found to be in the same parts of the spectrum, and under all circumstances to maintain the same relative positions. Similar dark lines are also seen in the light of the stars, in the electric light, and in the flame of combustible substances, though differently arranged, each star and each flame having a system of dark lines peculiar to itself. Dr. Wollaston and M. Fraunhofer, of Munich, discovered these lines deficient of rays independently of each other. M. Fraunhofer found that their number extends to nearly six hundred, but they are much more numerous. There are bright lines in the solar spectrum which also maintain a fixed position. Among the dark lines, M. Fraunhofer selected seven of the most remarkable, and determined their distances so accurately, that they now form standard and invariable points of reference for measuring the refractive powers of different media on the rays of light, which renders this department of optics as exact as any of the physical sciences. These lines are designated by the letters of the alphabet, beginning with B, which is in the red near the end of the spectrum; C is farther advanced in the red; D is in the orange; E in the green; F in the blue; G in the indigo; and H in the violet. By means of these fixed points, M. Fraunhofer has ascertained from prismatic observation the refrangibility of seven of the principal rays in each of ten different substances solid and liquid. The refraction increased in all from the red to the violet end of the spectrum. The rays that are wanting in the solar spectrum, which occasion the dark lines, were supposed to be absorbed by the atmosphere of the sun. But the annular eclipse which happened on the 15th of May, 1836, afforded Professor Forbes the means of proving that the dark lines in question cannot be attributed to the absorption of the solar atmosphere; they were neither broader nor more numerous in the spectrum formed during that phenomenon than at any other time, though the rays came only from the circumference of the sun’s disc, and consequently had to traverse a greater depth of his atmosphere.

Sir David Brewster found that in certain states of the atmosphere the obscure lines become much broader, and some of them deeply black; and he observed also, that, at the time the sun was setting in a veil of red light, part of the luminous spectrum was absorbed, whence he concluded that the earth’s atmosphere had absorbed the rays of light which occupied the dark bands. By direct experiments also the atmosphere was observed to act powerfully upon the rayless lines.

When a lens is used along with a prism, longitudinal dark lines of different breadths are seen to cross the bands, already described, at right angles; these M. Ragona-Scina and M. Babinet believe to be lines of interference which exist in light that has passed through a convex lens.

The lines are different both in kind and number in the spectra of gases and flames. In a highly-magnified spectrum from light passed through nitrous acid gas, Sir David Brewster counted 2000 dark bands. In the spectrum of a lamp, and generally of all white flames, none of the defective lines are found; so all such flames contain rays which do not exist in the light of the sun or stars. Brilliant red lines appear in the spectrum produced by the combustion of nitre upon charcoal; and in all artificial flames dark and bright bands exist, sometimes corresponding in position with those in the solar spectrum, and sometimes not.

A sunbeam received on a screen, after passing through a small round hole in a window-shutter, appears like a round white spot; but when a prism is interposed, the beam no longer occupies the same space. It is separated into the prismatic colours, and spread over a line of considerable length, while its breadth remains the same with that of the white spot. The act of spreading or separation is called the dispersion of the coloured rays. Dispersion always takes place in the plane of refraction, and is greater as the angle of incidence is greater. It varies inversely as the length of a wave of light, and directly as its velocity: hence towards the blue end of the spectrum, where the undulations of the rays are least, the dispersion is greatest. Substances have very different dispersive powers; that is to say, the spectra formed by two equal prisms of different substances, under precisely the same circumstances, are of different lengths. Thus, if a prism of flint-glass and one of crown-glass of equal refracting angles be presented to two rays of white light at equal angles, it will be found that the space over which the coloured rays are dispersed by the flint-glass is much greater than the space occupied by that produced by the crown-glass: and as the quantity of dispersion depends upon the refracting angle of the prism, the angles of the two prisms may be made such that, when the prisms are placed close together with their edges turned opposite ways, they will exactly oppose each other’s action, and will refract the coloured rays equally, but in contrary directions, so that an exact compensation will be effected, and the light will be refracted without colour (N. 195). The achromatic telescope is constructed on this principle. It consists of a tube with an object-glass or lens at one end to bring the rays to a focus, and form an image of the distant object, and a magnifying-glass at the other end to view the image thus formed. Now it is found that the object-glass, instead of making the rays converge to one point, disperses them, and gives a confused and coloured image: but by constructing it of two lenses in contact, one of flint and the other of crown-glass of certain forms and proportions, the dispersion is counteracted, and a perfectly well-defined and colourless image of the object is formed (N. 196). It was thought to be impossible to produce refraction without colour, till Mr. Hall, a gentleman of Worcestershire, constructed a telescope on this principle in the year 1733; and twenty-five years afterwards the achromatic telescope was brought to perfection by Mr. Dollond, a celebrated optician in London.

By means of Mr. Fraunhofer’s determination of the refraction of the principal rays in substances, their dispersive powers may be found (N. 197).

A perfectly homogeneous colour is very rarely to be found; but the tints of all substances are most brilliant when viewed in light of their own colour. The red of a wafer is much more vivid in red than in white light; whereas, if placed in homogeneous yellow light, it can no longer appear red, because there is not a ray of red in the yellow light. Were it not that the wafer, like all other bodies, whether coloured or not, reflects white light at its outer surface, it would appear absolutely black when placed in yellow light.

After looking steadily for a short time at a coloured object, such as a red wafer, on turning the eyes to a white substance, a green image of the wafer appears, which is called the accidental colour of red. All tints have their accidental colours: thus the accidental colour of orange is blue; that of yellow is indigo; of green, reddish white; of blue, orange-red; of violet, yellow; and of white, black; and vice versâ. When the direct and accidental colours are of the same intensity, the accidental is then called the complementary colour, because any two colours are said to be complementary to one another which produce white when combined.

From experiments by M. Plateau of Brussels, it appears that two complementary colours from direct impression, which would produce white when combined, produce black, or extinguish one another, by their union, when accidental; and also that the combination of all the tints of the solar spectrum produces white light if they be from a direct impression on the eye, whereas blackness results from a union of the same tints if they be accidental; and in every case where the real colours produce white by their combination, the accidental colours of the same tints produce black. When the image of an object is impressed on the retina only for a few moments, the picture left is exactly of the same colour with the object, but in an extremely short time the picture is succeeded by the accidental image. M. Plateau attributes this phenomenon to a reaction of the retina after being excited by direct vision, so that the accidental impression is of an opposite nature to the corresponding direct impression. He conceives that when the eye is excited by being fixed for a time on a coloured object, and then withdrawn from the excitement, it endeavours to return to its state of repose; but in so doing, that it passes this point, and spontaneously assumes an opposite condition, like a spring which, bent in one direction, in returning to its state of rest bends as much the contrary way. The accidental image thus results from a particular modification of the organ of sight, in virtue of which it spontaneously gives us a new sensation after it has been excited by direct vision. If the prevailing impression be a very strong white light, its accidental image is not black, but a variety of colours in succession. According to M. Plateau, the retina offers a resistance to the action of light, which increases with the duration of this action; whence, after looking intently at an object for a long time, it appears to decrease in brilliancy. The imagination has a powerful influence on our optical impressions, and has been known to revive the images of highly luminous objects months, and even years, afterwards.

SECTION XX.

Interference of Light—Undulatory Theory of Light—Propagation of Light—Newton’s Rings—Measurement of the Length of the Waves of Light, and of the Frequency of the Vibrations of Ether for each Colour—Newton’s Scale of Colours—Diffraction of Light—Sir John Herschel’s Theory of the Absorption of Light—Refraction and Reflection of Light.

NEWTON and most of his immediate successors imagined light to be a material substance, emitted by all self-luminous bodies in extremely minute particles, moving in straight lines with prodigious velocity, which, by impinging upon the optic nerves, produce the sensation of light. Many of the observed phenomena have been explained by this theory; it is, however, totally inadequate to account for the following circumstances.

When two equal rays of red light, proceeding from two luminous points, fall upon a sheet of white paper in a dark room, they produce a red spot on it which will be twice as bright as either ray would produce singly, provided the difference in the lengths of the two beams, from the luminous points to the red spot on the paper, be exactly the 0·0000258th part of an inch. The same effect will take place if the difference in the lengths be twice, three times, four times, &c., that quantity. But if the difference in the lengths of the two rays be equal to one-half of the 0·0000258th part of an inch, or to its 1-1/2, 2-1/2, 3-1/2, &c., part, the one light will entirely extinguish the other, and will produce absolute darkness on the paper where the united beams fall. If the difference in the lengths of their paths be equal to the 1-1/4, 2-1/4, 3-1/4, &c., of the 0·0000258th part of an inch, the red spot arising from the combined beams will be of the same intensity which one alone would produce. If violet light be employed, the difference in the lengths of the two beams must be equal to the 0·0000157th part of an inch, in order to produce the same phenomena; and for the other colours, the difference must be intermediate between the 0·0000258th and the 0·0000157th part of an inch. Similar phenomena may be seen by viewing the flame of a candle through two very fine slits in a card extremely near to one another (N. 198); or by admitting the sun’s light into a dark room through a pin-hole about the fortieth of an inch in diameter, receiving the image on a sheet of white paper, and holding a slender wire in the light. Its shadow will be found to consist of a bright white bar or stripe in the middle, with a series of alternate black and brightly-coloured stripes on each side. The rays which bend round the wire in two streams are of equal lengths in the middle stripe; it is consequently doubly bright from their combined effect; but the rays which fall on the paper on each side of the bright stripe, being of such unequal lengths as to destroy one another, form black lines. On each side of these black lines the rays are again of such lengths as to combine to form bright stripes, and so on alternately till the light is too faint to be visible. When any homogeneous light is used, such as red, the alternations are only black and red; but on account of the heterogeneous nature of white light, the black lines alternate with vivid stripes or fringes of prismatic colours, arising from the superposition of systems of alternate black lines and lines of each homogeneous colour. That the alternation of black lines and coloured fringes actually does arise from the mixture of the two streams of light which flow round the wire, is proved by their vanishing the instant one of the streams is interrupted. It may therefore be concluded, as often as these stripes of light and darkness occur, that they are owing to the rays combining at certain intervals to produce a joint effect, and at others to extinguish one another. Now it is contrary to all our ideas of matter to suppose that two particles of it should annihilate one another under any circumstances whatever; while, on the contrary, two opposing motions may; and it is impossible not to be struck with the perfect similarity between the interferences of small undulations of air or of water and the preceding phenomena. The analogy is indeed so perfect, that philosophers of the highest authority concur in the belief that the celestial regions are filled with an extremely rare and highly elastic medium or ether, whose particles are capable of receiving the vibrations communicated to them by self-luminous bodies, and of transmitting them to the optic nerves, so as to produce the sensation of light. The acceleration in the mean motion of Encke’s comet, as well as of the comet discovered by M. Biela, renders the existence of such a medium certain. It is clear that, in this hypothesis, the alternate stripes of light and darkness are entirely the effect of the interference of the undulations; for, by actual measurement, the length of a wave of the mean red rays of the solar spectrum is equal to the 0·0000258th part of an inch; consequently, when the elevations of the waves combine, they produce double the intensity of light that each would do singly; and when half a wave combines with a whole—that is, when the hollow of one wave is filled up by the elevation of another—darkness is the result. At intermediate points between these extremes, the intensity of the light corresponds to intermediate differences in the lengths of the rays.

The theory of interferences is a particular case of the general mechanical law of the superposition of small motions; whence it appears that the disturbance of a particle of an elastic medium, produced by two co-existent undulations, is the sum of the disturbances which each undulation would produce separately; consequently, the particle will move in the diagonal of a parallelogram, whose sides are the two undulations. If, therefore, the two undulations agree in direction, or nearly so, the resulting motion will be very nearly equal to their sum, and in the same direction; if they nearly oppose one another, the resulting motion will be nearly equal to their difference; and, if the undulations be equal and opposite, the resultant will be zero, and the particle will remain at rest.

The preceding experiments, and the inferences deduced from them, which have led to the establishment of the doctrine of the undulations of light, are the most splendid memorials of our illustrious countryman Dr. Thomas Young, though Huygens was the first to originate the idea.

It is supposed that the particles of luminous bodies are in a state of perpetual agitation, and that they possess the property of exciting regular vibrations in the molecules of the ethereal medium, corresponding to the vibrations of their own molecules; and that, on account of its elastic nature, one particle of the ether when set in motion communicates its vibrations to those adjacent, which in succession transmit them to those farther off; so that the primitive impulse is transferred from particle to particle, and the undulating motion darts through ether like a wave in water; so that light is motion, and therefore subject to the laws of dynamics and mathematical analysis. Although the progressive motion of light is known by experience to be uniform and in a straight line, the vibrations of the particles are always at right angles to the direction of the ray. The propagation of light is like the spreading of waves in water; but, if one ray alone be considered, its motion may be conceived by supposing a rope of indefinite length stretched horizontally, one end of which is held in the hand. If it be agitated to and fro at regular intervals, with a motion perpendicular to its length, a series of similar and equal tremors or waves will be propagated along it; and if the regular impulses be given in a variety of planes, as up and down, from right to left, and also in oblique directions, the successive undulations will take place in every possible plane. An analogous motion in the ether, when communicated to the optic nerves, would produce the sensation of common light. It is evident that the waves which flow from end to end of the cord in a serpentine form are altogether different from the perpendicular vibratory motion of each particle of the rope, which never deviates far from a state of rest. So, in ether, each particle vibrates perpendicularly to the direction of the ray; but these vibrations are totally different from and independent of the undulations which are transmitted through it, in the same manner as the vibrations of each particular ear of corn are independent of the waves that rush from end to end of a harvest-field when agitated by the wind.

The intensity of light depends upon the amplitude or extent of the vibrations of the particles of ether, while its colour depends upon their frequency. The time of the vibration of a particle of ether is, by theory, as the length of a wave directly, and inversely as its velocity. Now, as the velocity of light is known to be 190,000 miles in a second, if the lengths of the waves of the different coloured rays could be measured, the number of vibrations in a second corresponding to each could be computed. That has been accomplished as follows:—All transparent substances of a certain thickness, with parallel surfaces, reflect and transmit white light; but, if they be extremely thin, both the reflected and transmitted light is coloured. The vivid hues on soap-bubbles, the iridescent colours produced by heat on polished steel and copper, the fringes of colour between the laminæ of Iceland spar and sulphate of lime, all consist of a succession of hues disposed in the same order, totally independent of the colour of the substance, and determined solely by its greater or less thickness—a circumstance which affords the means of ascertaining the length of the waves of each coloured ray, and the frequency of the vibrations of the particles producing them. If a plate of glass be laid upon a lens of almost imperceptible curvature, before an open window, when they are pressed together a black spot will be seen in the point of contact, surrounded by seven rings of vivid colours, all differing from one another (N. 199). In the first ring, estimated from the black spot, the colours succeed each other in the following order:—black, very faint blue, brilliant white, yellow, orange, and red. They are quite different in the other rings, and in the seventh the only colours are pale bluish green and very pale pink. That these rings are formed between the two surfaces in apparent contact may be proved by laying a prism on the lens instead of the plate of glass, and viewing the rings through the inclined side of it that is next to the eye, which arrangement prevents the light reflected from the upper surface mixing with that from the surfaces in contact, so that the intervals between the rings appear perfectly black—one of the strongest circumstances in favour of the undulatory theory; for, although the phenomena of the rings can be explained by either hypothesis, there is this material difference, that, according to the undulatory theory, the intervals between the rings ought to be absolutely black, which is confirmed by experiment; whereas, by the doctrine of emanation, they ought to be half illuminated, which is not found to be the case. M. Fresnel, whose opinion is of the first authority, thought this test conclusive. It may therefore be concluded that the rings arise entirely from the interference of the rays: the light reflected from each of the surfaces in apparent contact reaches the eye by paths of different lengths, and produces coloured and dark rings alternately, according as the reflected waves coincide or destroy one another. The breadths of the rings are unequal; they decrease in width, and the colours become more crowded, as they recede from the centre. Coloured rings are also produced by transmitting light through the same apparatus; but the colours are less vivid, and are complementary to those reflected, consequently the central spot is white.

The size of the rings increases with the obliquity of the incident light, the same colour requiring a greater thickness or space between the glasses to produce it than when the light falls perpendicularly upon them. Now, if the apparatus be placed in homogeneous instead of white light, the rings will all be of the same colour with that of the light employed, that is to say, if the light be red, the rings will be red, divided by black intervals. The size of the rings varies with the colour of the light. They are largest in red, and decrease in magnitude with the succeeding prismatic colours, being smallest in violet light.

Since one of the glasses is plane and the other spherical, it is evident that from the point of contact the space between them gradually increases in thickness all round, so that a certain thickness of air corresponds to each colour, which in the undulatory system measures the length of the wave producing it (N. 200). By actual measurement Sir Isaac Newton found that the squares of the diameters of the brightest part of each ring are as the odd numbers, 1, 3, 5, 7, &c.; and that the squares of the diameters of the darkest parts are as the even numbers, 0, 2, 4, 6, &c. Consequently, the intervals between the glasses at these points are in the same proportion. If, then, the thickness of the air corresponding to any one colour could be found, its thickness for all the others would be known. Now, as Sir Isaac Newton knew the radius of curvature of the lens, and the actual breadth of the rings in parts of an inch, it was easy to compute that the thickness of air at the darkest part of the first ring is the 1/89000 part of an inch, whence all the others have been deduced. As these intervals determine the length of the waves on the undulatory hypothesis, it appears that the length of a wave of the extreme red of the solar spectrum is equal to the 0·0000266th part of an inch; that the length of a wave of the extreme violet is equal to the 0·0000167th part of an inch; and, as the time of a vibration of a particle of ether producing any particular colour is directly as the length of a wave of that colour, and inversely as the velocity of light, it follows that the molecules of ether producing the extreme red of the solar spectrum perform 458 millions of millions of vibrations in a second; and that those producing the extreme violet accomplish 727 millions of millions of vibrations in the same time. The lengths of the waves of the intermediate colours, and the number of their vibrations, being intermediate between these two, white light, which consists of all the colours, is consequently a mixture of waves of all lengths between the limits of the extreme red and violet. The determination of these minute portions of time and space, both of which have a real existence, being the actual results of measurement, do as much honour to the genius of Newton as that of the law of gravitation.

The number of advancing waves of light in an inch is known to be from 37,600 to 59,880, and the number of lateral vibrations is from 458 to 727 billions in a second, but the extent of these lateral vibrations of the particles of the ethereal medium is not known, though both their extent and velocity are probably very small compared with the length of the advancing waves and the velocity of propagation. Colour is identified with the number of vibrations; but whether reflection, refraction, absorption, &c., have any relations to the lateral vibrations, or whether they are dependent in part upon some physical action of the ethereal medium unknown and unsuspected, are points as yet undetermined. To ascertain these circumstances, Dr. Faraday instituted a series of the most refined experiments upon the relation of the minute particles of metals to the vibrations of light.

Gold acts powerfully on light, and possesses a real transparency, transmitting green rays when very thin; and being capable of extreme division by solvents without losing its metallic character, its particles transmit rays of various colours according to their size; those that transmit the rose-colour in Bohemian glass are of inconceivable minuteness. The progressive waves of the ether are so long compared with the dimensions of the molecules to which gold can be reduced, that it seemed probable to Dr. Faraday when the latter were placed in a sunbeam that some effective relation might be discovered between them and the smaller vibrations of the ethereal medium; in which case, if reflection, refraction, &c., depended upon such relations, there was reason to expect that these functions would change sensibly by the substitution of different sized particles of the gold for one another. At one time Dr. Faraday hoped he had changed one colour into another by means of gold, which would have been equivalent to a change in the number of vibrations; but although he has not yet confirmed that result, his researches are of the greatest interest.[9]

The phenomenon of the coloured rings takes place in vacuo as well as in air, which proves that it is the distance between the lenses alone, and not the air, which produces the colours. However, if water or oil be put between them, the rings contract, but no other change ensues; and Newton found that the thickness of different media at which a given tint is seen is in the inverse ratio of their refractive indices, so that the thickness of laminæ which could not otherwise be measured may be known by their colour; and, as the position of the colours in the rings is invariable, they form a fixed standard of comparison, well known as Newton’s scale of colours; each tint being estimated according to the ring to which it belongs from the central spot inclusively. Not only the periodical colours which have been described, but the colours seen in thick plates of transparent substances, the variable hues of feathers, of insects’ wings, mother-of-pearl, and of striated substances, all depend upon the same principle. To these may be added the coloured fringes surrounding the shadows of all bodies held in an extremely small beam of light, and the coloured rings surrounding the small beam itself when received on a screen.

When a very slender sunbeam, passing through a small pin-hole into a dark room, is received on a white screen, or plate of ground-glass, at the distance of a little more than six feet, the spot of light on the screen is larger than the pin-hole: and, instead of being bounded by shadow, it is surrounded by a series of coloured rings separated by obscure intervals. The rings are more distinct in proportion to the smallness of the beam (N. 201). When the light is white there are seven rings, which dilate or contract with the distance of the screen from the hole. As the distance of the screen diminishes, the white central spot contracts to a point and vanishes; and, on approaching still nearer, the rings gradually close in upon it, so that the centre assumes successively the most intense and vivid hues. When the light is homogeneous—red, for example—the rings are alternately red and black, and more numerous; and their breadth varies with the colour, being broadest in red light and narrowest in violet. The tints of the coloured fringes from white light, and their obliteration after the seventh ring, arise from the superposition of the different sets of fringes of all the coloured rays. The shadows of objects are also bordered by coloured fringes when held in this slender beam of light. If the edge of a knife or hair, for example, be held in it, the rays, instead of proceeding in straight lines past its edge, are bent when quite close to it, and proceed from thence to the screen in curved lines called hyperbolas; so that the shadow of the object is enlarged, and, instead of being at once bounded by light, is surrounded or edged with coloured fringes alternating with black bands, which are more distinct the smaller the pin-hole (N. 202). The fringes are altogether independent of the form or density of the object, being the same when it is round or pointed, when of glass or platinum. When the rays which form the fringes arrive at the screen, they are of different lengths, in consequence of the curved path they follow after passing the edge of the object. The waves are therefore in different phases or states of vibration, and either conspire to form coloured fringes or destroy one another in the obscure intervals. The coloured fringes bordering the shadows of objects were first described by Grimaldi in 1665; but, besides these, he noticed that there are others within the shadows of slender bodies exposed to a small sunbeam, a phenomenon which has already been mentioned to have afforded Dr. Young the means of proving, beyond all controversy, that coloured rings are produced by the interference of light.

It may be concluded that material substances derive their colours from two different causes: some from the law of interference, such as iridescent metals, peacocks’ feathers, &c.; others from the unequal absorption of the rays of white light, such as vermilion, ultramarine, blue, or green cloth, flowers, and the greater number of coloured bodies. The latter phenomena have been considered extremely difficult to reconcile with the undulatory theory of light, and much discussion has arisen as to what becomes of the absorbed rays. But that embarrassing question has been ably answered by Sir John Herschel in a most profound paper on the Absorption of Light by coloured Media, and cannot be better given than in his own words. It must, however, be premised, that, as all transparent bodies are traversed by light, they are presumed to be permeable to the ether. He says,—“Now, as regards only the general fact of the obstruction and ultimate extinction of light in its passage through gross media, if we compare the corpuscular and undulatory theories, we shall find that the former appeals to our ignorance, the latter to our knowledge, for its explanation of the absorptive phenomena. In attempting to explain the extinction of light on the corpuscular doctrine, we have to account for the light so extinguished as a material body, which we must not suppose annihilated. It may, however, be transformed; and among the imponderable agents, heat, electricity, &c., it may be that we are to search for the light which has become thus comparatively stagnant. The heating power of the solar rays gives a primâ facie plausibility to the idea of the transformation of light into heat by absorption. But, when we come to examine the matter more nearly, we find it encumbered on all sides with difficulties. How is it, for instance, that the most luminous rays are not the most calorific, but that, on the contrary, the calorific energy accompanies, in its greatest intensity, rays which possess comparatively feeble illuminating powers? These and other questions of a similar nature may perhaps admit of answer in a more advanced state of our knowledge; but at present there is none obvious. It is not without reason, therefore, that the question, ‘What becomes of light?’ which appears to have been agitated among the photologists of the last century, has been regarded as one of considerable importance as well as obscurity by the corpuscular philosophers. On the other hand, the answer to this question, afforded by the undulatory theory of light, is simple and distinct. The question, ‘What becomes of light?’ merges in the more general one, ‘What becomes of motion?’ And the answer, on dynamical principles, is, that it continues for ever. No motion is, strictly speaking, annihilated; but it may be divided, and the divided parts made to oppose and in effect destroy one another. A body struck, however perfectly elastic, vibrates for a time, and then appears to sink into its original repose. But this apparent rest (even abstracting from the inquiry that part of the motion which may be conveyed away by the ambient air) is nothing else than a state of subdivided and mutually destroying motion, in which every molecule continues to be agitated by an indefinite multitude of internally reflected waves, propagated through it in every possible direction, from every point in its surface on which they successively impinge. The superposition of such waves will, it is easily seen, at length operate their mutual destruction, which will be the more complete the more irregular the figure of the body, and the greater the number of internal reflections.” Thus Sir John Herschel, by referring the absorption of light to the subdivision and mutual destruction of the vibrations of ether in the interior of bodies, brings another class of phenomena under the laws of the undulatory theory.

According to Mr. Rankin’s hypothesis of Molecular Vortices[10] the absorption of light and radiant heat consists in the transference of motion from the molecules to their atmospheres, and conversely the emission of light and radiant heat is the transmission of motion from the atmospheres to the molecules. The great velocity of light and heat is a natural consequence of this hypothesis, according to which the vibratory masses must be extremely small compared with the forces exerted by them.

The ethereal medium pervading space is supposed to penetrate all material substances, occupying the interstices between their molecules; but in the interior of refracting media it exists in a state of less elasticity compared with its density in vacuo; and, the more refractive the medium, the less the elasticity of the ether within it. Hence the waves of light are transmitted with less velocity in such media as glass and water than in the external ether. As soon as a ray of light reaches the surface of a diaphanous reflecting substance, for example a plate of glass, it communicates its undulations to the ether next in contact with the surface, which thus becomes a new centre of motion, and two hemispherical waves are propagated from each point of this surface; one of which proceeds forward into the interior of the glass, with a less velocity than the incident waves; and the other is transmitted back into the air, with a velocity equal to that with which it came (N. 203). Thus, when refracted, the light moves with a different velocity without and within the glass; when reflected, the ray comes and goes with the same velocity. The particles of ether without the glass, which communicate their motions to the particles of the dense and less elastic ether within it, are analogous to small elastic balls striking large ones; for some of the motion will be communicated to the large balls, and the small ones will be reflected. The first would cause the refracted wave, and the last the reflected. Conversely, when the light passes from glass to air, the action is similar to large balls striking small ones. The small balls receive a motion which would cause the refracted ray, and the part of the motion retained by the large ones would occasion the reflected wave; so that, when light passes through a plate of glass or of any other medium differing in density from the air, there is a reflection at both surfaces; but this difference exists between the two reflections, that one is caused by a vibration in the same direction with that of the incident ray, and the other by a vibration in the opposite direction.

A single wave of air or ether would not produce the sensation of sound or light. In order to excite vision, the vibrations of the molecules of ether must be regular, periodical, and very often repeated: and, as the ear continues to be agitated for a short time after the impulse by which alone a sound becomes continuous, so also the fibres of the retina, according to M. d’Arcet, continue to vibrate for about the eighth part of a second after the exciting cause has ceased. The interval of time during which the impression lasts is longer for the blue than for red or white light: it must not be less than 0ʺ·34. Every one must have observed, when a strong impression is made by a bright light, that an object remains visible for a short time after shutting the eyes, which is supposed to be in consequence of the continued vibrations of the fibres of the retina. Occasionally the retina becomes insensible to feebly illuminated objects when continuously presented. If the eye be turned aside for a moment, the object becomes again visible. It is probably on this account that the owl makes so peculiar a motion with its head when looking at objects in the twilight. It is quite possible that many vibrations may be excited in the ethereal medium incapable of producing undulations in the fibres of the human retina, which yet have a powerful effect on those of other animals or of insects. Such may receive luminous impressions of which we are totally unconscious, and at the same time they may be insensible to the light and colours which affect our eyes, their perceptions beginning where ours end.

SECTION XXI.

Polarization of Light—Defined—Polarization by Refraction—Properties of the Tourmaline—Double Refraction—All doubly Refracted Light is Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the two Refracted Rays—Undulations of Natural Light—Undulations of Polarized Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries on the Rays passing along the Optic Axis—Polarization by Reflection.

IN giving a sketch of the constitution of light, it is impossible to omit the extraordinary property of its polarization, “the phenomena of which,” Sir John Herschel says, “are so singular and various, that to one who has only studied the common branches of physical optics it is like entering into a new world, so splendid as to render it one of the most delightful branches of experimental inquiry, and so fertile in the views it lays open of the constitution of natural bodies, and the minuter mechanism of the universe, as to place it in the very first rank of the physico-mathematical sciences, which it maintains by the rigorous application of geometrical reasoning its nature admits and requires.”

Light is said to be polarized, which, by being once reflected or refracted, is rendered incapable of being again reflected or refracted at certain angles. In general, when a ray of light is reflected from a pane of plate-glass, or any other substance, it may be reflected a second time from another surface, and it will also pass freely through transparent bodies. But, if a ray of light be reflected from a pane of plate-glass at an angle of 57°, it is rendered totally incapable of reflection at the surface of another pane of glass in certain definite positions, but it will be completely reflected by the second pane in other positions. It likewise loses the property of penetrating transparent bodies in particular positions, whilst it is freely transmitted by them in others. Light, so modified as to be incapable of reflection and transmission in certain directions, is said to be polarized.

Light may be polarized by reflection from any polished surface, and the same property is also imparted by refraction. It is proposed to explain these methods of polarizing light, to give a short account of its most remarkable properties, and to endeavour to describe a few of the splendid phenomena it exhibits.

If a brown tourmaline, which is a mineral generally crystallized in the form of a long prism, be cut longitudinally, that is, parallel to the axis of the prism, into plates about the thirtieth of an inch in thickness, and the surfaces polished, luminous objects may be seen through them, as through plates of coloured glass. The axis of each plate is in its longitudinal section parallel to the axis of the prism whence it was cut (N. 204). If one of these plates be held perpendicularly between the eye and a candle, and turned slowly round in its own plane, no change will take place in the image of the candle. But if the plate be held in a fixed position, with its axis or longitudinal section vertical, when a second plate of tourmaline is interposed between it and the eye, parallel to the first, and turned slowly round in its own plane, a remarkable change will be found to have taken place in the nature of the light. For the image of the candle will vanish and appear alternately at every quarter revolution of the plate, varying through all degrees of brightness down to total or almost total evanescence, and then increasing again by the same degrees as it had before decreased. These changes depend upon the relative positions of the plates. When the longitudinal sections of the two plates are parallel, the brightness of the image is at its maximum; and, when the axes of the sections cross at right angles, the image of the candle vanishes. Thus the light, in passing through the first plate of tourmaline, has acquired a property totally different from the direct light of the candle. The direct light would have penetrated the second plate equally well in all directions, whereas the refracted ray will only pass through it in particular positions, and is altogether incapable of penetrating it in others. The refracted ray is polarized in its passage through the first tourmaline, and experience shows that it never loses that property, unless when acted upon by a new substance. Thus, one of the properties of polarized light is the incapability of passing through a plate of tourmaline perpendicular to it, in certain positions, and its ready transmission in other positions at right angles to the former.

Many other substances have the property of polarizing light. If a ray of light falls upon a transparent medium, which has the same temperature, density, and structure throughout every part, as fluids, gases, glass, &c., and a few regularly crystallized minerals, it is refracted into a single pencil of light by the laws of ordinary refraction, according to which the ray, passing through the refracting surface from the object to the eye, never quits a plane perpendicular to that surface. Almost all other bodies, such as the greater number of crystallized minerals, animal and vegetable substances, gums, resins, jellies, and all solid bodies having unequal tensions, whether from unequal temperature or pressure, possess the property of doubling the image or appearance of an object seen through them in certain directions; because a ray of natural light falling upon them is refracted into two pencils which move with different velocities, and are more or less separated, according to the nature of the body and the direction of the incident ray. Whenever a ray of natural light is thus divided into two pencils in its passage through a substance, both of the transmitted rays are polarized. Iceland spar, a carbonate of lime, which by its natural cleavage may be split into the form of a rhombohedron, possesses the property of double refraction in an eminent degree, as may be seen by pasting a piece of paper, with a large pin-hole in it, on the side of the spar farthest from the eye. The hole will appear double when held to the light (N. 205). One of these pencils is refracted according to the same law as in glass or water, never quitting the plane perpendicular to the refracting surface, and is therefore called the ordinary ray. But the other does quit the plane, being refracted according to a different and much more complicated law, and on that account is called the extraordinary ray. For the same reason one image is called the ordinary, and the other the extraordinary image. When the spar is turned round in the same plane, the extraordinary image of the hole revolves about the ordinary image, which remains fixed, both being equally bright. But if the spar be kept in one position, and viewed through a plate of tourmaline, it will be found that, as the tourmaline revolves, the images vary in their relative brightness—one increases in intensity till it arrives at a maximum, at the same time that the other diminishes till it vanishes, and so on alternately at each quarter revolution, proving both rays to be polarized. For in one position the tourmaline transmits the ordinary ray, and reflects the extraordinary; and, after revolving 90°, the extraordinary ray is transmitted, and the ordinary ray is reflected. Thus another property of polarized light is, that it cannot be divided into two equal pencils by double refraction, in positions of the doubly refracting bodies in which a ray of common light would be so divided.

Were tourmaline like other doubly refracting bodies, each of the transmitted rays would be double; but that mineral, when of a certain thickness, after separating the light into two polarized pencils, absorbs that which undergoes ordinary refraction, and consequently shows only one image of an object. On this account tourmaline is peculiarly fitted for analyzing polarized light, which shows nothing remarkable till viewed through it or something equivalent.

The pencils of light, on leaving a double refracting substance, are parallel; and it is clear, from the preceding experiments, that they are polarized in planes at right angles to each other (N. 206). But that will be better understood by considering the change produced in common light by the action of the polarizing body. It has been shown that the undulations of ether, which produce the sensation of common light, are performed in every possible plane, at right angles to the direction in which the ray is moving. But the case is very different after the ray has passed through a doubly refracting substance, like Iceland spar. The light then proceeds in two parallel pencils, whose undulations are still indeed transverse to the direction of the rays, but they are accomplished in planes at right angles to one another, analogous to two parallel stretched cords, one of which performs its undulations only in a horizontal plane, and the other in a vertical or upright plane (N. 206). Thus the polarizing action of Iceland spar and of all doubly refracting substances is to separate a ray of common light, whose waves or undulations are in every plane, into two parallel rays, whose waves or undulations lie in planes at right angles to each other. By a simple mechanical law each vibratory motion of the first is resolved into two vibratory motions at right angles to one another. The ray of common light may be assimilated to a round rod, whereas the two polarized rays are like two parallel long flat rulers, one of which is laid horizontally on its broad surface, and the other horizontally on its edge. The alternate transmission and obstruction of one of these flattened beams by the tourmaline is similar to the facility with which a card may be passed between the bars of a grating or wires of a cage, if presented edgeways, and the impossibility of its passing in a transverse direction.

Although it generally happens that a ray of light, in passing through Iceland spar, is separated into two polarized rays, yet there is one direction along which it is refracted in one ray only, and that according to the ordinary law. This direction is called the optic axis (N. 207). Many crystals and other substances have two optic axes, inclined to each other, along which a ray of light is transmitted in one pencil by the law of ordinary refraction. The extraordinary ray is sometimes refracted towards the optic axis, as in quartz, zircon, ice, &c., which are therefore said to be positive crystals; but when it is bent from the optic axis, as in Iceland spar, tourmaline, emerald, beryl, &c., the crystals are negative, which is the most numerous class. The ordinary ray moves with uniform velocity within a doubly refracting substance, but the velocity of the extraordinary ray varies with the position of the ray relatively to the optic axis, being a maximum when its motion within the crystal is at right angles to the optic axis, and a minimum when parallel to it. Between these extremes its velocity varies according to a determinate law.

It had been inferred, from the action of Iceland spar on light, that in all doubly refracting substances one only of two rays is turned aside from the plane of ordinary refraction, while the other follows the ordinary law; and the great difficulty of observing the phenomena tended to confirm that opinion. M. Fresnel, however, proved by a most profound mathematical inquiry, à priori, that the extraordinary ray must be wanting in glass and other uncrystallized substances, and that it must necessarily exist in carbonate of lime, quartz, and other bodies having one optic axis, but that in a numerous class of substances, which possess two optic axes, both rays must undergo extraordinary refraction, and consequently that both must deviate from their original plane; and these results have been perfectly confirmed by subsequent experiments. This theory of refraction, which for generalization is perhaps only inferior to the law of gravitation, has enrolled the name of Fresnel among those which pass not away, and makes his early loss a subject of deep regret to all who take an interest in the higher paths of scientific research.

When a beam of common light is partly reflected at, and partly transmitted through a transparent surface, the reflected and refracted pencils contain equal quantities of polarized light, and their planes of polarization are at right angles to one another: hence, a pile of panes of glass will give a polarized beam by refraction. For, if a ray of common light pass through them, part of it will be polarized by the first plate, the second plate will polarize a part of what passes through it, and the rest will do the same in succession, till the whole beam is polarized, except what is lost by reflection at the different surfaces, or by absorption. This beam is polarized in a plane at right angles to the plane of reflection, that is, at right angles to the plane passing through the incident and reflected ray (N. 208).

By far the most convenient way of polarizing light is by reflection. A plane of plate-glass laid upon a piece of black cloth, on a table at an open window, will appear of a uniform brightness from the reflection of the sky or clouds. But if it be viewed through a plate of tourmaline, having its axis vertical, instead of being illuminated as before, it will be obscured by a large cloudy spot, having its centre quite dark, which will readily be found by elevating or depressing the eye, and will only be visible when the angle of incidence is 57°, that is, when the line from the eye to the centre of the black spot makes an angle of 33° with the surface of the reflector (N. 209). When the tourmaline is turned round in its own plane, the dark cloud will diminish, and entirely vanish when the axis of the tourmaline is horizontal, and then every part of the surface of the glass will be equally illuminated. As the tourmaline revolves, the cloudy spot will appear and vanish alternately at every quarter revolution. Thus, when a ray of light is incident on a pane of plate-glass at an angle of 57°, the reflected ray is rendered incapable of penetrating a plate of tourmaline whose axis is in the plane of incidence. Consequently it has acquired the same character as if it had been polarized by transmission through a plate of tourmaline, with its axis at right angles to the plane of reflection. It is found by experience that this polarized ray is incapable of a second reflection at certain angles and in certain positions of the incident plane. For if another pane of plate-glass, having one surface blackened, be so placed as to make an angle of 33° with the reflected ray, the image of the first pane will be reflected in its surface, and will be alternately illuminated and obscured at every quarter revolution of the blackened pane, according as the plane of reflection is parallel or perpendicular to the plane of polarization. Since this happens by whatever means the light has been polarized, it evinces another general property of polarized light, which is, that it is incapable of reflection in a plane at right angles to the plane of polarization.

All reflecting surfaces are capable of polarizing light, but the angle of incidence at which it is completely polarized is different in each substance (N. 210). It appears that the angle for plate-glass is 57°; in crown-glass it is 56° 55ʹ, and no ray will be completely polarized by water unless the angle of incidence be 53° 11ʹ. The angles at which different substances polarize light are determined by a very simple and elegant law, discovered by Sir David Brewster, “That the tangent of the polarizing angle for any medium is equal to the sine of the angle of incidence divided by the sine of the angle of refraction of that medium.” Whence also the refractive power even of an opaque body is known when its polarizing angle has been determined.

If a ray, polarized by refraction or by reflection from any substance not metallic, be viewed through a piece of Iceland spar, each image will alternately vanish and reappear at every quarter revolution of the spar, whether it revolves from right to left or from left to right; which shows that the properties of the polarized ray are symmetrical on each side of the plane of polarization.

Although there be only one angle in each substance at which light is completely polarized by one reflection, yet it may be polarized at any angle of incidence by a sufficient number of reflections. For, if a ray falls upon the upper surface of a pile of plates of glass at an angle greater or less than a polarizing angle, a part only of the reflected ray will be polarized, but a part of what is transmitted will be polarized by reflection at the surface of the second plate, part at the third, and so on till the whole is polarized. This is the best apparatus; but one plate of glass having its inferior surface blackened, or even a polished table, will answer the purpose.

SECTION XXII.

Phenomena exhibited by the Passage of Polarized Light through Mica and Sulphate of Lime—The Coloured Images produced by Polarized Light passing through Crystals having one and two Optic Axes—Circular Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel, and Professor Airy—Coloured Images produced by the Interference of Polarized Rays—Fluorescence.

SUCH is the nature of polarized light and of the laws it follows. But it is hardly possible to convey an idea of the splendour of the phenomena it exhibits under circumstances which an attempt will now be made to describe.

If light polarized by reflection from a pane of glass be viewed through a plate of tourmaline, with its longitudinal section vertical, an obscure cloud, with its centre totally dark, will be seen on the glass. Now, let a plate of mica, uniformly about the thirtieth of an inch in thickness, be interposed between the tourmaline and the glass; the dark spot will instantly vanish, and, instead of it, a succession of the most gorgeous colours will appear, varying with every inclination of the mica, from the richest reds, to the most vivid greens, blues, and purples (N. 211). That they may be seen in perfection, the mica must revolve at right angles to its own plane. When the mica is turned round in a plane perpendicular to the polarized ray, it will be found that there are two lines in it where the colours entirely vanish. These are the optic axes of the mica, which is a doubly refracting substance, with two optic axes, along which light is refracted in one pencil.

No colours are visible in the mica, whatever its position may be with regard to the polarized light, without the aid of the tourmaline, which separates the transmitted ray into two pencils of coloured light complementary to one another, that is, which taken together would make white light. One of these it absorbs, and transmits the other; it is therefore called the analyzing plate. The truth of this will appear more readily if a film of sulphate of lime, between the twentieth and sixtieth of an inch thick, be used instead of the mica. When the film is of uniform thickness, only one colour will be seen when it is placed between the analyzing plate and the reflecting glass; as, for example, red. But, when the tourmaline revolves, the red will vanish by degrees till the film is colourless; then it will assume a green hue, which will increase and arrive at its maximum when the tourmaline has turned through ninety degrees; after that, the green will vanish and the red will reappear, alternating at each quadrant. Thus the tourmaline separates the light which has passed through the film into a red and a green pencil; in one position it absorbs the green and lets the red pass, and in another it absorbs the red and transmits the green. This is proved by analyzing the ray with Iceland spar instead of tourmaline; for, since the spar does not absorb the light, two images of the sulphate of lime will be seen, one red and the other green; and these exchange colours every quarter revolution of the spar, the red becoming green, and the green red; and, where the images overlap, the colour is white, proving the red and green to be complementary to each other. The tint depends on the thickness of the film. Films of sulphate of lime, the 0·00124 and 0·01818 of an inch respectively, give white light in whatever position they may be held, provided they be perpendicular to the polarized ray; but films of intermediate thickness will give all colours. Consequently, a wedge of sulphate of lime, varying in thickness between the 0·00124 and the 0·01818 of an inch, will appear to be striped with all colours when polarized light is transmitted through it. A change in the inclination of the film, whether of mica or sulphate of lime, is evidently equivalent to a variation in thickness.

When a plate of mica, held as close to the eye as possible, at such an inclination as to transmit the polarized ray along one of its optic axes, is viewed through the tourmaline with its axis vertical, a most splendid appearance is presented. The cloudy spot in the direction of the optic axis is seen surrounded by a set of vividly coloured rings of an oval form, divided into two unequal parts by a black curved band passing through the cloudy spot about which the rings are formed. The other optic axis of the mica exhibits a similar image (N. 212).

When the two optic axes of a crystal make a small angle with one another, as in nitre, the two sets of rings touch externally; and, if the plate of nitre be turned round in its own plane, the black transverse bands undergo a variety of changes, till, at last, the whole richly coloured image assumes the form of the figure 8, traversed by a black cross (N. 213). Substances with one optic axis have but one set of coloured circular rings, with a broad black cross passing through its centre, dividing the rings into four equal parts. When the analyzing plate revolves, this figure recurs at every quarter revolution; but in the intermediate positions it assumes the complementary colours, the black cross becoming white.

It is in vain to attempt to describe the beautiful phenomena exhibited by innumerable bodies which undergo periodic changes in form and colour when the analyzing plate revolves, but not one of them shows a trace of colour without the aid of tourmaline, or something equivalent, to analyze the light, and as it were to call these beautiful phantoms into existence. Tourmaline has the disadvantage of being itself a coloured substance; but that inconvenience may be obviated by employing a reflecting surface as an analyzing plate. When polarized light is reflected by a plate of glass at the polarizing angle, it will be separated into two coloured pencils; and, when the analyzing plate is turned round in its own plane, it will alternately reflect each ray at every quarter revolution, so that all the phenomena that have been described will be seen by reflection on its surface.

Coloured rings are produced by analyzing polarized light transmitted through glass melted and suddenly or unequally cooled; also through thin plates of glass bent with the hand, jelly indurated or compressed, &c. &c. In short, all the phenomena of coloured rings may be produced, either permanently or transiently, in a variety of substances, by heat and cold, rapid cooling, compression, dilatation, and induration; and so little apparatus is necessary for performing the experiments, that, as Sir John Herschel says, a piece of window glass or a polished table to polarize the light, a sheet of clear ice to produce the rings, and a broken fragment of plate-glass placed near the eye to analyze the light, are alone requisite to produce one of the most splendid of optical exhibitions.

Pressure produces remarkable changes in the optical properties of crystals. Compression, perpendicular to the axis, transforms a crystal with one optic axis into one with two. A slice of quartz and one of beryl, both cut perpendicularly to their axis, were compressed thus by MM. Moignot and Soleil. They found that the single system in the quartz, which is a positive crystal, was doubled in the direction of the compression, while in the beryl, which is a negative crystal, the duplication was perpendicular to the compression. In the quartz the axis of the double system coincided with the line of pressure, but in the tourmaline, which is a negative crystal, the line which joins the centres of the rings was perpendicular to the pressure.

If a positive crystal be compressed in the direction of its axis the tint of the rings descends, and that of a negative crystal rises. But if the crystals be dilated in the direction of their optic axis, the tints in positive crystals rise, and negative descend.

It has been observed, that when a ray of light, polarized by reflection from any surface not metallic, is analyzed by a doubly refracting substance, it exhibits properties which are symmetrical both to the right and left of the plane of reflection, and the ray is then said to be polarized according to that plane. This symmetry is not destroyed when the ray, before being analyzed, traverses the optic axis of a crystal having but one optic axis, as evidently appears from the circular forms of the coloured rings already described. Regularly crystallized quartz, however, forms an exception. In it, even though the rays should pass through the optic axis itself, where there is no double refraction, the primitive symmetry of the ray is destroyed, and the plane of primitive polarization deviates either to the right or left of the observer, by an angle proportional to the thickness of the plate of quartz. This angular motion, or true rotation of the plane of polarization, which is called circular polarization, is clearly proved by the phenomena. The coloured rings produced by all crystals having but one optic axis are circular, and traversed by a black cross concentric with the rings; so that the light entirely vanishes throughout the space enclosed by the interior ring, because there is neither double refraction nor polarization along the optic axis. But in the system of rings produced by a plate of quartz, whose surfaces are perpendicular to the axis of the crystal, the part within the interior ring, instead of being void of light, is occupied by a uniform tint of red, green, or blue, according to the thickness of the plate (N. 214). Suppose the plate of quartz to be 1/25 of an inch thick, which will give the red tint to the space within the interior ring; when the analyzing plate is turned, in its own plane through an angle of 17-1/2°, the red hue vanishes. If a plate of rock crystal 2/25 of an inch thick be used, the analyzing plate must revolve through 35° before the red tint vanishes, and so on, every additional 25th of an inch in thickness requiring an additional rotation of 17-1/2°; whence it is manifest that the plane of polarization revolves in the direction of a spiral within the rock crystal. It is remarkable that, in some crystals of quartz, the plane of polarization revolves from right to left, and in others from left to right, although the crystals themselves differ apparently only by a very slight, almost imperceptible, variety in form. In these phenomena the rotation to the right is accomplished according to the same laws, and with the same energy, as that to the left. But if two plates of quartz be interposed, which possess different affections, the second plate undoes, either wholly or partly, the rotatory motion which the first had produced, according as the plates are of equal or unequal thickness. When the plates are of unequal thickness, the deviation is in the direction of the strongest, and exactly the same with that which a third plate would produce equal in thickness to the difference of the two.

M. Biot has discovered the same properties in a variety of liquids. Oil of turpentine, and an essential oil of laurel, cause the plane of polarization to turn to the left, whereas the syrup of sugar-cane, and a solution of natural camphor, by alcohol, turn it to the right. A compensation is effected by the superposition or mixture of two liquids which possess these opposite properties, provided no chemical action takes place. A remarkable difference was also observed by M. Biot between the action of the particles of the same substances when in a liquid or solid state. The syrup of grapes, for example, turns the plane of polarization to the left as long as it remains liquid; but, as soon as it acquires the solid form of sugar, it causes the plane of polarization to revolve towards the right, a property which it retains even when again dissolved. Instances occur also in which these circumstances are reversed.

A ray of light passing through a liquid possessing the power of circular polarization is not affected by mixing other fluids with the liquid—such as water, ether, alcohol, &c.—which do not possess circular polarization themselves, the angle of deviation remaining exactly the same as before the mixture. Whence M. Biot infers that the action exercised by the liquids in question does not depend upon their mass, but that it is a molecular action exercised by the ultimate particles of matter, which depends solely upon the individual constitution, and is entirely independent of the positions and mutual distances of the particles with regard to each other. These important discoveries show that circular polarization surpasses the power of chemical analysis in giving certain and direct evidence of the similarity or difference existing in the molecular constitution of bodies, as well as of the permanency of that constitution, or of the fluctuations to which it may be liable. For example, no chemical difference has been discovered between syrup from the sugar-cane and syrup from grapes. Yet the first causes the plane of polarization to revolve to the right, and the other to the left; therefore some essential difference must exist in the nature of their ultimate molecules. The same difference is to be traced between the juices of such plants as give sugar similar to that from the cane, and those which give sugar like that obtained from grapes.

If chlorate of soda be dissolved in water, the liquid has no circular polarization; but if the solution be allowed to crystallize, some of the crystals turn the light to the right and others to the left. Now, if all those of one kind be gathered together and dissolved a second time, the liquid will have no circular polarization; but if crystals be allowed to form, some will turn the light to the right and others to the left, although only one kind was dissolved.[11]

It is a fact established by M. Biot, that in circular polarization the laws of rotation followed by the different simple rays of light are dissimilar in different substances. Whence he infers that the deviation of the simple rays from one another ought not to result from a special property of the luminous principle only, but that the proper action of the molecules must also concur in modifying the deviations of the simple rays differently in different substances.

One of the many brilliant discoveries of M. Fresnel is the production of circular and elliptical polarization by the internal reflection of light from plate-glass. He has shown that, if light polarized by any of the usual methods be twice reflected within a glass rhomb (N. 169) of a given form, the vibrations of the ether that are perpendicular to the plane of incidence will be retarded a quarter of a vibration, which causes the vibrating particles to describe circles, and the succession of such vibrating particles throughout the extent of a wave to form altogether a circular helix, or curve like a corkscrew. However, that only happens when the plane of polarization is inclined at an angle of 45° to the plane of incidence. When these two planes form an angle either greater or less, the succession of vibrating particles forms an elliptical helix, which curve may be represented by twisting a thread in a spiral about an oval rod. These curves will turn to the right or left, according to the position of the incident plane.

The motion of the ethereal medium in elliptical and circular polarization may be represented by the analogy of a stretched cord; for, if the extremity of such a cord be agitated at equal and regular intervals by a vibratory motion entirely confined to one plane, the cord will be thrown into an undulating curve lying wholly in that plane. If to this motion there be superadded another similar and equal, but perpendicular to the first, the cord will assume the form of an elliptical helix; its extremity will describe an ellipse, and every molecule throughout its length will successively do the same. But, if the second system of vibrations commence exactly a quarter of an undulation later than the first, the cord will take the form of a circular helix or corkscrew, the extremity will move uniformly in a circle, and every molecule throughout the cord will do the same in succession. It appears, therefore, that both circular and elliptical polarization may be produced by the composition of the motions of two rays in which the particles of ether vibrate in planes at right angles to one another.

Professor Airy, in a very profound and able paper published in the Cambridge Transactions, has proved that all the different kinds of polarized light are obtained from rock crystal. When polarized light is transmitted through the axis of a crystal of quartz, in the emergent ray the particles of ether move in a circular helix; and when it is transmitted obliquely so as to form an angle with the axis of the prism, the particles of ether move in an elliptical helix, the ellipticity increasing with the obliquity of the incident ray; so that, when the incident ray falls perpendicularly to the axis, the particles of ether move in a straight line. Thus quartz exhibits every variety of elliptical polarization, even including the extreme cases where the excentricity is zero, or equal to the greater axis of the ellipse (N. 215). In many crystals the two rays are so little separated, that it is only from the nature of the transmitted light that they are known to have the property of double refraction. M. Fresnel discovered, by experiments on the properties of light passing through the axis of quartz, that it consists of two superposed rays, moving with different velocities; and Professor Airy has shown that in these two rays the molecules of ether vibrate in similar ellipses at right angles to each other, but in different directions; that their ellipticity varies with the angle which the incident ray makes with the axis; and that, by the composition of their motions, they produce all the phenomena of polarized light observed in quartz.

It appears, from what has been said, that the molecules of ether always perform their vibrations at right angles to the direction of the ray, but very differently in the various kinds of light. In natural light the vibrations are rectilinear, and in every plane. In ordinary polarized light they are rectilinear, but confined to one plane; in circular polarization the vibrations are circular; and in elliptical polarization the molecules vibrate in ellipses. These vibrations are communicated from molecule to molecule, in straight lines when they are rectilinear, in a circular helix when they are circular, and in an oval or elliptical helix when elliptical.

Some fluids possess the property of circular polarization naturally, as oil of turpentine, the essential oils of laurel and lemon, sugar of grapes, and various liquids.

Elliptical polarization is produced by reflection from metallic surfaces. Mr. Baden Powell discovered it also in the light reflected from China ink, chromate of lead, plumbago, &c. Mr. Airy observed that the light reflected from the diamond is elliptically polarized; and Mr. Jamin has shown that this kind of polarization is generally produced by reflection from almost all transparent bodies, whatever their refractive power may be, especially from glass at angles very little different from the law of the tangents.

Water polarizes light circularly when between the points of maximum density and solidification; hence it becomes crystalline.

The coloured images from polarized light arise from the interference of the rays (N. 216). MM. Fresnel and Arago found that two rays of polarized light interfere and produce coloured fringes if they be polarized in the same plane, but that they do not interfere when polarized in different planes. In all intermediate positions, fringes of intermediate brightness are produced. The analogy of a stretched cord will show how this happens. Suppose the cord to be moved backwards and forwards horizontally at equal intervals; it will be thrown into an undulating curve lying all in one plane. If to this motion there be superadded another similar and equal, commencing exactly half an undulation later than the first, it is evident that the direct motion every molecule will assume, in consequence of the first system of waves, will at every instant be exactly neutralized by the retrograde motion it would take in virtue of the second; and the cord itself will be quiescent in consequence of the interference. But, if the second system of waves be in a plane perpendicular to the first, the effect would only be to twist the rope, so that no interference would take place. Rays polarized at right angles to each other may subsequently be brought into the same plane without acquiring the property of producing coloured fringes; but, if they belong to a pencil the whole of which was originally polarized in the same plane, they will interfere.

The manner in which the coloured images are formed may be conceived by considering that, when polarized light passes through the optic axis of a doubly refracting substance,—as mica, for example,—it is divided into two pencils by the analyzing tourmaline; and, as one ray is absorbed, there can be no interference. But, when polarized light passes through the mica in any other direction, it is separated into two white rays, and these are again divided into four pencils by the tourmaline, which absorbs two of them; and the other two, being transmitted in the same plane with different velocities, interfere and produce the coloured phenomena. If the analysis be made with Iceland spar, the single ray passing through the optic axis of the mica will be refracted into two rays, polarized in different planes, and no interference will happen. But, when two rays are transmitted by the mica, they will be separated into four by the spar, two of which will interfere to form one image, and the other two, by their interference, will produce the complementary colours of the other image when the spar has revolved through 90°; because, in such positions of the spar as produce the coloured images, only two rays are visible at a time, the other two being reflected. When the analysis is accomplished by reflection, if two rays are transmitted by the mica, they are polarized in planes at right angles to each other. And, if the plane of reflection of either of these rays be at right angles to the plane of polarization, only one of them will be reflected, and therefore no interference can take place; but in all other positions of the analyzing plate both rays will be reflected in the same plane, and consequently will produce coloured rings by their interference.

It is evident that a great deal of the light we see must be polarized, since most bodies which have the power of reflecting or refracting light also have the power of polarizing it. The blue light of the sky is completely polarized at an angle of 74° from the sun in a plane passing through his centre.

A constellation of talent almost unrivalled at any period in the history of science has contributed to the theory of polarization, though the original discovery of that property of light was accidental, and arose from an occurrence which, like thousands of others, would have passed unnoticed had it not happened to one of those rare minds capable of drawing the most important inferences from circumstances apparently trifling. In 1808, while M. Malus was accidentally viewing with a doubly-refracting prism a brilliant sunset reflected from the windows of the Luxembourg Palace in Paris, on turning the prism slowly round, he was surprised to see a very great difference in the intensity of the two images, the most refracted alternately changing from brightness to obscurity at each quadrant of revolution. A phenomenon so unlooked for induced him to investigate its cause, whence sprung one of the most elegant and refined branches of physical optics.

Fluorescence, or the internal dispersion of light, though far from possessing the beauty or extensive consequences of polarized light, is scarcely less wonderful. A variety of substances, such as canary-glass, a solution of sulphate of quinine, fluor-spar, and a great number of organic substances, have the property of diminishing the refrangibility of light by internal dispersion, consequently of increasing the length of the waves, and lowering the colour in the prismatic scale; it is therefore called degraded light, or fluorescence, because first discovered in fluor-spar.

If a piece of glass coloured by cobalt be fixed in a hole in a window-shutter of a dark room, a slab of white porcelain placed near it will appear blue; but if the slab be viewed through a yellow glass coloured by silver, it will appear to be almost quite black, because the yellow glass absorbs all the rays transmitted by the blue glass. If, however, a piece of canary-glass be laid on the slab while it is dark, every part of the canary-glass will shine as if it were self-luminous, and with so bright a light that anything written on the slab that was invisible before may now be distinctly read. Such is the singular phenomenon of internal dispersion, degraded light, or fluorescence. The brightness is by no means due to phosphorescence, because the canary-glass only shines when under the influence of the active or blue rays, whereas phosphorescent bodies shine by their own light—the latter has independent, the former dependent, emission; it is possible, however, that a connexion may hereafter be traced between them.

It appears from the analytical investigation of this phenomenon that the vibrations of the fluorescent substance are analogous to those of a sonorous body, as a bell or musical cord, which give the fundamental note and its harmonics. Now since there is a reciprocal action between the molecules of matter and light, when the light of the sun is absorbed by a substance capable of fluorescence, it puts the whole of its molecules into vibrations the same as its own, analogous to the fundamental note, while at the same time a certain number of molecules take more rapid vibrations exactly like the harmonics. The latter form new centres of light throughout the substance, which impart their vibrations to the ethereal medium around, and constitute fluorescence or degraded light. For example, in the experiment that has been described, the blue light imparted its own vibrations to all the molecules of the canary-glass, and also more rapid vibrations to a certain number of them. All of the blue rays were excluded by the yellow glass held before the eye; but it was pervious to the rays emanating in more rapid vibrations from the smaller number of molecules, which thus became really new centres of light, different from the sun’s light, though owing to it; the one celestial, the other terrestrial; and the latter vibrations being more rapid than those of the blue light, their refrangibility was less, and therefore their colour lower in the prismatic scale. Mr. Power computed from his formulæ, that fluorescent light is produced by undulations which are a major or minor third below the pitch of the general vibration of the medium—that is to say, below the vibrations which the whole molecules of the body most readily assume.

Professor Stokes, of Cambridge, who made the preceding experiment, found that the chemical rays from a point in the solar spectrum produced, in a solution of the sulphate of quinine, light of a sky-blue colour, which emanates in all directions from the liquid, and that this blue fluorescent light contains, when analysed, all the rays of the spectrum; hence he inferred that the dispersive power or fluorescence had lowered the refrangibility of the chemical rays, so as to make them visible: and Sir David Brewster observes that the new spectrum, of all colours into which they were transformed, must possess the extraordinary property of being a luminous spectrum, either without chemical rays or full of them. The dispersion in the quinine solution is greatest near the surface, but the blue emanation proceeds from every part of the liquid; and Sir John Herschel, who discovered the fluorescent property in this liquid, and gave it the name of epipolic light, found that the remainder of the beam, when it issued from the solution, though not apparently different from the incident white light, is yet so much changed in passing through the liquid, that it is no longer capable of producing fluorescence, though still capable of common dispersion. The blue light from the solution of quinine, when examined, consisted of rays extending over a great part of the spectrum.

By passing a sunbeam through a bluish kind of fluor-spar, Sir David Brewster perceived that the blue colour is not superficial, as it appears to be, but that some veins in the interior of the crystal disperse blue light, others pink, and even white light; in short, he met with fluorescence in such a variety of substances, that he concludes it may prevail more or less in the greater number of solids and liquids.

Professor Draper, of New York, proved that the result is the same whether the incident light be polarized or not, and that the dispersed or degraded light is never polarized, but that it emanates in all directions, as if the substance were self-luminous; he made experiments with light from all parts of the solar spectrum, and with various substances, and always found that the refrangibility of the incident ray was diminished by internal dispersion, and that the colour was changed to suit the new refrangibility. Professor Draper has also shown that the law of action and reaction prevails in all the phenomena of the sunbeam, as in every other department of nature; so that a beam cannot be reflected, refracted, much less absorbed, without producing some change upon the recipient medium; and Mr. Power proved analytically that the solar rays can exercise no action upon any medium through which they are transmitted, without being accompanied by a diminution of refraction. He says, “The new light emanating from the fluorescent media is just like any other light of the same prismatic composition. In its physical properties it retains no trace of its parentage; it is of terrestrial origin, and its colour depends simply on its new refrangibility, having nothing to do with that of the producing rays, nor to the circumstance of their belonging to the visible or invisible part of the spectrum.” These phenomena can only be explained by the undulatory theory of light.

SECTION XXIII.

Objections to the Undulatory Theory, from a difference in the Action of Sound and Light under the same circumstances, removed—The Dispersion of Light according to the Undulatory Theory—Arago’s final proof that the Undulatory Theory is the Law of Nature.

THE numerous phenomena of periodical colours arising from the interference of light, which do not admit of satisfactory explanation on any other principle than the undulatory theory, are the strongest arguments in favour of that hypothesis; and even cases which at one time seemed unfavourable to that doctrine have proved upon investigation to proceed from it alone. Such is the erroneous objection which has been made, in consequence of a difference in the mode of action of light and sound, under the same circumstances, in one particular instance. When a ray of light from a luminous point, and a diverging sound, are both transmitted through a very small hole into a dark room, the light goes straight forward and illuminates a small spot on the opposite wall, leaving the rest in darkness; whereas the sound on entering diverges in all directions, and is heard in every part of the room. These phenomena, however, instead of being at variance with the undulatory theory, are direct consequences of it, arising from the very great difference between the magnitude of the undulations of sound and those of light. The undulations of light are incomparably less than the minute aperture, while those of sound are much greater. Therefore when light, diverging from a luminous point, enters the hole, the rays round its edges are oblique, and consequently of different lengths, while those in the centre are direct, and nearly or altogether of the same lengths. So that the small undulations between the centre and the edges are in different phases, that is, in different states of undulation. Therefore the greater number of them interfere, and by destroying one another produce darkness all around the edges of the aperture; whereas the central rays, having the same phases, combine, and produce a spot of bright light on a wall or screen directly opposite the hole. The waves of air producing sound, on the contrary, being very large compared with the hole, do not sensibly diverge in passing through it, and are therefore all so nearly of the same length, and consequently in the same phase or state of undulation, that none of them interfere sufficiently to destroy one another. Hence all the particles of air in the room are set into a state of vibration, so that the intensity of the sound is very nearly everywhere the same. Strong as the preceding cases may be, the following experiment, made by M. Arago, seems to be decisive in favour of the undulatory doctrine. Suppose a plano-convex lens of very great radius to be placed upon a plate of very highly polished metal. When a ray of polarized light falls upon this apparatus at a very great angle of incidence, Newton’s rings are seen at the point of contact. But as the polarizing angle of glass differs from that of metal, when the light falls on the lens at the polarizing angle of glass, the black spot and the system of rings vanish. For although light in abundance continues to be reflected from the surface of the metal, not a ray is reflected from the surface of the glass that is in contact with it, consequently no interference can take place; which proves beyond a doubt that Newton’s rings result from the interference of the light reflected from both the surfaces apparently in contact (N. 199).

Notwithstanding the successful adaptation of the undulatory system to phenomena, the dispersion of light for a long time offered a formidable objection to that theory, which has been removed by Professor Powell of Oxford.

A sunbeam falling on a prism, instead of being refracted to a single point of white light, is separated into its component colours, which are dispersed or scattered unequally over a considerable space, of which the portion occupied by the red rays is the least, and that over which the violet rays are dispersed is the greatest. Thus the rays of the coloured spectrum, whose waves are of different lengths, have different degrees of refrangibility, and consequently move with different velocities, either in the medium which conveys the light from the sun, or in the refracting medium, or in both; whereas rays of all colours come from the sun to the earth with the same velocity. If, indeed, the velocities of the various rays were different in space, the aberration of the fixed stars, which is inversely as the velocity, would be different for different colours, and every star would appear as a spectrum whose length would be parallel to the direction of the earth’s motion, which is not found to agree with observation. Besides, there is no such difference in the velocities of the long and short waves of air in the analogous case of sound, since notes of the lowest and highest pitch are heard in the order in which they are struck. In fact, when the sunbeam passes from air into the prism, its velocity is diminished; and, as its refraction, and consequently its dispersion, depend solely upon the diminished velocity of the transmission of its waves, they ought to be the same for waves of all lengths, unless a connexion exists between the length of a wave and the velocity with which it is propagated. Now, this connexion between the length of a wave of any colour, and its velocity or refrangibility in a given medium, has been deduced by Professor Powell from M. Cauchy’s investigations of the properties of light on a peculiar modification of the undulatory hypothesis. Hence the refrangibility of the various coloured rays, computed from this relation for any given medium, when compared with their refrangibility in the same medium determined by actual observation, will show whether the dispersion of light comes under the laws of that theory. But, in order to accomplish this, it is clear that the length of the waves should be found independently of refraction, and a very beautiful discovery of M. Fraunhofer furnishes the means of doing so.

That philosopher obtained a perfectly pure and complete coloured spectrum, with all its dark and bright lines, by the interference of light alone, from a sunbeam passing through a series of fine parallel wires covering the object glass of a telescope. In this spectrum, formed independently of prismatic refraction, the positions of the coloured rays depend only on the lengths of their waves, and M. Fraunhofer found that the intervals between them are precisely proportional to the differences of these lengths. He measured the lengths of the waves of the different colours at seven fixed points, determined by seven of the principal dark and bright lines. Professor Powell, availing himself of these measures, has made the requisite computations, and has found that the coincidence of theory with observation is perfect for ten substances whose refrangibility had been previously determined by the direct measurements of M. Fraunhofer, and for ten others whose refrangibility has more recently been ascertained by M. Rudberg. Thus, in the case of seven rays in each of twenty different substances, solid and fluid, the dispersion of light takes place according to the laws of the undulatory theory: and there can hardly be a doubt that dispersion in all other bodies will be found to follow the same law. It is, however, an express condition of the connexion between the velocity of light and the length of its undulations, that the intervals between the vibrating molecules of the ethereal fluid should bear a sensible relation to the length of an undulation. The coincidence of the computed with the observed refractions shows that this condition is fulfilled within the refracting media; but the aberration of the fixed stars leads to the inference that it does not hold in the ethereal regions, where the velocities of the rays of all colours are the same. Strong as all that precedes is in favour of the undulatory theory, the relative velocity of light in air and water is the final and decisive proof. By the Newtonian theory the velocity is greater in water than in air, by the undulatory theory it is less; hence if a comparison could be made it would decide which is the law of nature. The difficulty consisted in comparing the velocity of light passing through a small extent of water with the velocity of light in air, which is 10,000 times greater than the velocity of the earth in its orbit. This delicate and difficult experiment was made by means of an instrument invented by Professor Wheatstone for measuring the velocity of electricity. It consists of a small mirror which revolves in its own plane like a coin spinning on its edge. When it revolves very rapidly the reflected image of an object changes its place perceptibly in an inconceivably small fraction of a second. The mirrors used in the experiment were made to revolve more than 1000 times in a second, by which means the places of the two images—one from light passing through air, and the other from light passing through an equal length of water—were found to be such as to prove that the velocity of light in air and in water is as 4 to 3, while by the Newtonian theory it is as 3 to 4. By this final and decisive proof the undulatory theory may from henceforth be regarded as the law of nature. This experiment was accomplished by M. Fizeau and M. Léon-Faucault, at the suggestion of M. Arago, whose eyesight did not permit him to undertake it himself.

SECTION XXIV.

Chemical or Photographic Rays of Solar Spectrum—Scheele, Ritter, and Wollaston’s Discoveries—Wedgwood’s and Sir Humphry Davy’s Photographic Pictures—The Calotype—The Daguerreotype—The Chromatype—The Cyanotype—Collodion—Sir John Herschel’s Discoveries in the Chemical Spectrum—M. Becquerel’s Discoveries of Inactive Lines in ditto—Thermic Spectrum—Phosphoric Spectrum—Electrical Properties—Parathermic Rays—Moser and Hunt’s Experiments—General Structure and antagonist Properties of Solar Spectrum—Defracted Spectrum.

THE Solar Spectrum exercises an energetic action on matter, producing the most wonderful and mysterious changes on the organised and unorganised creation.

All bodies are probably affected by light, but it acts with greatest energy on such as are of weak chemical affinity, imparting properties to them which they did not possess before. Collodion and metallic salts, especially those of silver, whose molecules are held together by an unstable equilibrium, are of all bodies the most susceptible of its influence; the effects, however, vary with the substances employed, and with the different rays of the solar spectrum, the chemical properties of which are by no means alike. As early as 1772 M. Scheele showed that the pure white colour of chloride of silver was rapidly darkened by the blue rays of the solar spectrum, while the red rays had no effect upon it: and in 1801 M. Ritter discovered that invisible rays beyond the violet extremity have the property of blackening argentine salts, that this property diminishes towards the less refrangible part of the spectrum, and that the red rays have an opposite quality, that of restoring the blackened salt of silver to its original purity; from which he inferred that the most refrangible extremity of the spectrum has an oxygenising power, and the other that of deoxygenating. Dr. Wollaston found that gum guaiacum acquires a green colour in the violet and blue rays, and resumes its original tint in the red. No attempt had been made to trace natural objects by means of light reflected from them, till Mr. Wedgwood, together with Sir Humphry Davy, took up the subject: they produced profiles and tracings of objects on surfaces prepared with nitrate and chloride of silver, but they did not succeed in rendering their pictures permanent. This difficulty was overcome in 1814 by M. Niepcé, who produced a permanent picture of surrounding objects by placing in the focus of a camera-obscura a metallic plate covered with a film of asphalt dissolved in oil of lavender.

Mr. Fox Talbot, without any knowledge of M. Niepcé’s experiments, had been engaged in the same pursuit, and must be regarded as an independent inventor of photography, one of the most beautiful arts of modern times: he was the first who succeeded in using paper chemically prepared for receiving impressions from natural objects; and he also discovered a method of fixing permanently the impressions—that is, of rendering the paper insensible to any further action of light. In the calotype, one of Mr. Talbot’s applications of the art, the photographic surface is prepared by washing smooth writing-paper, first with a solution of nitrate of silver, then with bromide of potassium, and again with nitrate of silver, drying it at a fire after each washing; the paper is thus rendered so sensitive to light that even the passage of a thin cloud is perceptible on it, consequently it must be prepared by candle-light. Portraits, buildings, insects, leaves of plants—in short, every object is accurately delineated in a few seconds; and in the focus of a camera-obscura the most minute objects are so exactly depicted that the microscope reveals new beauties.

Since the effect of the chemical agency of light is to destroy the affinity between the salt and the silver, Mr. Talbot found that, in order to render these impressions permanent on paper, it was only necessary to wash it with salt and water, or with a solution of iodide of potassium. For these liquids the liquid hyposulphites have been advantageously substituted, which are the most efficacious in dissolving and removing the unchanged salt, leaving the reduced silver on the paper. The calotype picture is negative, that is, the lights and shadows are the reverse of what they are in nature, and the right-hand side in nature is the left in the picture; but if it be placed with its face pressed against photographic paper, between a board and a plate of glass, and exposed to the sun a short time, a positive and direct picture, as it is in nature, is formed: engravings may be exactly copied by this simple process, and a direct picture may be produced at once by using photographic paper already made brown by exposure to light.

While Mr. Fox Talbot was engaged in these very elegant discoveries in England, M. Daguerre had brought to perfection and made public that admirable process by which he has compelled Nature permanently to engrave her own works; and thus the talents of France and England have been combined in bringing to perfection this useful art. Copper, plated with silver, was successfully employed by M. Daguerre for copying nature by the agency of light. The surface of the plate is converted into an iodide of silver, by placing it horizontally with its face downwards in a covered box, in the bottom of which there is a small quantity of iodine which evaporates spontaneously. In three or four minutes the surface acquires a yellow tint, and then, screening it carefully from light, it must be placed in the focus of a camera obscura, where an invisible image of external objects will be impressed on it in a few minutes. When taken out, the plate must be exposed in another box to the action of mercurial vapour, which attaches itself to those parts of the plate which had been exposed to light, but does not adhere to such parts as had been in shadow; and as the quantity of mercury over the other parts is in exact proportion to the degree of illumination, the shading of the picture is perfect. The image is fixed, first by removing the iodine from the plate by plunging it into hyposulphite of soda, and then washing it in distilled water; by this process the yellow colour is destroyed, and in order to render the mercury permanent, the plate must be exposed a few minutes to nitric vapour, then placed in nitric acid containing copper or silver in solution at a temperature of 61-1/4° of Fahrenheit for a short time, and lastly polished with chalk. This final part of the process is due to Dr. Berre, of Vienna.

Nothing can be more beautiful than the shading of these chiaroscuro pictures when objects are at rest, but the least motion destroys the effect; the method therefore is more applicable to buildings than landscape. Colour is wanting; but the researches of Sir John Herschel give reason to believe that even this will ultimately be attained.

The most perfect impressions of seaweeds, leaves of plants, feathers, &c., may be formed by bringing the object into close contact with a sheet of photographic paper, between a board and plate of glass; then exposing the whole to the sun for a short time, and afterwards fixing it by the process described. The colours of the pictures vary with the preparation of the paper, by which almost any tint may be produced.

In the chromatype, a peculiar photograph discovered by Mr. Hunt, chromate of copper is used, on which a dark brown negative image is first formed, but by the continued action of light it is changed to a positive yellow picture on a white ground; the farther effect of light is checked by washing the picture in pure water.

In cyanotypes, a class of photographs discovered by Sir John Herschel, in which cyanogen in its combinations with iron forms the ground, the pictures are Prussian blue and white. In the chrysotype of the same eminent philosopher, the image is first received on paper prepared with the ammonia-citrate of iron, and afterwards washed with a neutral solution of gold. It is fixed by water acidulated with sulphuric acid, and lastly by hydriodate of potash, from which a white and purple photograph results. It is vain to attempt to describe the various beautiful effects which Sir John Herschel obtained from chemical compounds, and from the juices of plants; the juice of the red poppy gives a positive bluish purple image, that of the ten-week stock a fine rose colour on a pale straw-coloured ground.

Pictures may be made by exposure to sunshine, on all compound substances having a weak chemical affinity; but the image is often invisible, as in the Daguerreotype, till brought out by washing in some chemical preparation. Water is frequently sufficient; indeed Sir John Herschel brought out dormant photographs by breathing on them, and some substances are insensible to the action of light till moistened, as for example, gum guaiacum. Argentine papers, however, are little subject to the influence of moisture. The power of the solar rays is augmented in certain cases by placing a plate of glass in close contact over the sensitive surface.

All these various experiments, though highly interesting, have now been superseded. It was found that paper did not always answer for photography, on account of imperfections in its structure; silver plates were too expensive; and glass was found to be unimpressable. Nevertheless, M. Niepcé de Victor obtained beautiful results upon glass coated with albumen mixed with sensitive substances, which suggested the medium by means of which the art has been brought to its present perfection, and that final step is due to Mr. Scott Archer. He coated a plate of glass thinly with collodion, that is, gun-cotton dissolved in ether and alcohol, which dries into a delicate transparent film of extreme adhesiveness, and of such intense sensibility that the action of light upon it is so instantaneous that it arrests a stormy sea or a fleeting cloud before they have time to change. Now landscapes in chiaroscuro are produced of great beauty, which by the slower methods were mere masses of deep shade and broad light. Architecture is even more perfectly obtained, but it fails to give a pleasing representation of the human countenance.

Chemical action always accompanies the sun’s light, but the analysis of the solar spectrum has partly disclosed the wonderful nature of the emanation. In the research, properties most important and unexpected have been discovered by Sir John Herschel, who imprints the stamp of genius on all he touches—his eloquent papers can alone convey an adequate idea of their value in opening a field of inquiry vast and untrodden. The following brief and imperfect account of his experiments is all that can be attempted here:—

A certain degree of chemical energy is distributed through every part of the solar spectrum, and also to a considerable extent through the dark spaces at each extremity. This distribution does not depend on the refrangibility of the rays alone, but also on the nature of the rays themselves, and on the physical properties of the analyzing medium on which the rays are received, whose changes indicate and measure their action. The length of the photographic image of the same solar spectrum varies with the physical qualities of the surface on which it is impressed. When the solar spectrum is received on paper prepared with bromide of silver, the chemical spectrum, as indicated merely by the length of the darkened part, includes within its limits the whole luminous spectrum, extending in one direction far beyond the extreme violet and lavender rays, and in the other down to the extremest red: with tartrate of silver the darkening occupies not only all the space under the most refrangible rays, but reaches much beyond the extreme red. On paper prepared with formobenzoate of silver the chemical spectrum is cut off at the orange rays, with phosphate of silver in the yellow, and with chloride of gold it terminates with the green, with carbonate of mercury it ends in the blue, and on paper prepared with the percyanide of gold, ammonia, and nitrate of silver, the darkening lies entirely beyond the visible spectrum at its most refrangible extremity, and is only half its length, whereas in some cases chemical action occupies a space more than twice the length of the luminous image.

The point of maximum energy of chemical action varies as much for different preparations as the scale of action. In the greater number of cases the point of deepest blackening lies about the lower edge of the indigo rays, though in no two cases is it exactly the same, and in many substances it is widely different. On paper prepared with the juice of the ten-week stock (Mathiola annua) there are two maxima, one in the mean yellow and a weaker in the violet; and on a preparation of tartrate of silver Sir John Herschel found three, one in the least refrangible blue, one in the indigo, and a third beyond the visible violet. The decrease in photographic energy is seldom perfectly alike on both sides of the maximum. Thus at the most refrangible end of the solar spectrum the greatest chemical power is exerted in most instances where there is least light and heat, and even in the space where both sensibly cease.

Not only the intensity but the kind of action is different in the different points of the solar spectrum, as evidently appears from the various colours that are frequently impressed on the same analyzing surface, each ray having a tendency to impart its own colour. Sir John Herschel obtained a coloured image of the solar spectrum on paper prepared according to Mr. Talbot’s principle, from a sunbeam refracted by a glass prism and then highly condensed by a lens. The photographic image was rapidly formed and very intense, and, when withdrawn from the spectrum and viewed in common daylight, it was found to be coloured with sombre but unequivocal tints imitating the prismatic colours, which varied gradually from red through green and blue to a purplish black. After washing the surface in water, the tints became more decided by being kept a few days in the dark—a phenomenon, Sir John observes, of constant occurrence, whatever be the preparation of the paper, provided colours are produced at all. He also obtained a coloured image on nitrate of silver, the part under the blue rays becoming a blue brown, while that under the violet had a pinkish shade, and sometimes green appeared at the point corresponding to the least refrangible blue. Mr. Hunt found on a paper prepared with fluoride of silver that a yellow line was impressed on the space occupied by the yellow rays, a green band on the space under the green rays, an intense blue throughout the space on which the blue and indigo rays fell, and under the violet rays a ruddy brown appeared; these colours remained clear and distinct after being kept two months.

Notwithstanding the great variety in the scale of action of the solar spectrum, the darkening or deoxydizing principle that prevails in the more refrangible part rarely surpasses or even attains the mean yellow ray which is the point of maximum illumination; it is generally cut off abruptly at that point which seems to form a limit between the opposing powers which prevail at the two ends of the spectrum. The bleaching or oxydizing effect of the red rays on blackened muriate of silver discovered by M. Ritter of Jena, and the restoration by the same rays of discoloured gum guaiacum to its original tint by Dr. Wollaston, have already been mentioned as giving the first indications of that difference in the mode of action of the chemical rays at the two ends of the visible spectrum, now placed beyond a doubt.

The action exerted by the less refrangible rays beyond and at the red extremity of the solar spectrum, in most instances, so far from blackening metallic salts, protects them from the action of the diffused daylight: but, if the prepared surface has already been blackened by exposure to the sun, they possess the remarkable property of bleaching it in some cases, and under other circumstances of changing the black surface into a fiery red.

Sir John Herschel, to whom we owe most of our knowledge of the properties of the chemical spectrum, prepared a sheet of paper by washing it with muriate of ammonia, and then with two coats of nitrate of silver; on this surface he obtained an impression of the solar spectrum exhibiting a range of colours very nearly corresponding with its natural hues. But a very remarkable phenomenon occurred at the end of least refrangibility; the red rays exerted a protecting influence which preserved the paper from the change which it would otherwise have undergone from the deoxydizing influence of the dispersed light which always surrounds the solar spectrum, and this maintained its whiteness. Sir John met with another instance on paper prepared with bromide of silver, on which the whole of the space occupied by the visible spectrum was darkened down to the very extremity of the red rays, but an oxydizing action commenced beyond the extreme red, which maintained the whiteness of the paper to a considerable distance beyond the last traceable limit of the visible rays, thus evincing decidedly the existence of some chemical power over a considerable space beyond the least refrangible end of the spectrum. Mr. Hunt also found that on the Daguerreotype plate a powerful protecting influence is exercised by the extreme red rays. In these cases the red and those dark rays beyond them exert an action of an opposite nature to that of the violet and lavender rays.

The least refrangible part of the solar spectrum possesses also, under certain circumstances, a bleaching property, by which the metallic salts are restored to their original whiteness after being blackened by exposure to common daylight, or to the most refrangible rays of the solar spectrum.

Paper prepared with iodide of silver, when washed over with ferrocyanite of potash, blackens rapidly when exposed to the solar spectrum. It begins in the violet rays and extends over all the space occupied by the dark chemical rays, and over the whole visible spectrum down to the extreme red rays. This image is coloured, the red rays giving a reddish tint and the blue a blueish. In a short time a bleaching process begins under the red rays, and extends upwards to the green, but the space occupied by the extreme red is maintained perfectly dark. Mr. Hunt found that a similar bleaching power is exerted by the red rays on paper prepared with protocyanide of potassium and gold with a wash of nitrate of silver.

The application of a moderately strong hydriodate of potash to darkened photographic paper renders it peculiarly susceptible of being whitened by further exposure to light. If paper prepared with bromide of silver be washed with ferrocyanate of potash while under the influence of the solar spectrum, it is immediately darkened throughout the part exposed to the visible rays down to the end of the red, some slight interference being perceptible about the region of the orange and yellow. After this a bleaching action begins over the part occupied by the red rays, which extends to the green. By longer exposure an oval spot begins again to darken about the centre of the bleached space; but, if the paper receive another wash of the hydriodate of potash, the bleaching action extends up from the green, over the region occupied by the most refrangible rays and considerably beyond them, thus inducing a negative action in the most refrangible part of the spectrum.

In certain circumstances the red rays, instead of restoring darkened photographic paper to its original whiteness, produce a deep red colour. When Sir John Herschel received the spectrum on paper somewhat discoloured by exposure to direct sunshine, instead of whiteness, a red border was formed extending from the space occupied by the orange, and nearly covering that on which the red fell. When, instead of exposing the paper in the first instance to direct sunshine, it was blackened by the violet rays of a prismatic spectrum, or by a sunbeam that had undergone the absorptive action of a solution of ammonia-sulphate of copper, the red rays of the condensed spectrum produced on it, not whiteness, but a full and fiery red, which occupied the whole space on which any of the visible red rays had fallen; and this red remained unchanged, however long the paper remained exposed to the least refrangible rays.

Sunlight transmitted through red glass produces the same effect as the red rays of the spectrum in the foregoing experiment. Sir John Herschel placed an engraving over a paper blackened by exposure to sunshine, covering the whole with a dark red-brown glass previously ascertained to absorb every ray beyond the orange: in this way a photographic copy was obtained in which the shades were black, as in the original engraving; but the lights, instead of being white, were of the red colour of venous blood, and no other colour could be obtained by exposure to light, however long. Sir John ascertained that every part of the spectrum impressed by the more refrangible rays is equally reddened, or nearly so, by the subsequent action of the less refrangible; thus the red rays have the very remarkable property of assimilating to their own colour the blackness already impressed on photographic paper.

That there is a deoxydating property in the more refrangible rays, and an oxydating action in the less refrangible part of the spectrum, is manifest from the blackening of one and the bleaching effect of the other; but the peculiar action of the red rays in the experiments mentioned shows that some other principle exists different from contrariety of action. These opposite qualities are balanced or neutralized in the region of the mean yellow ray. But, although this is the general character of the photographic spectrum, under certain circumstances even the red rays have a deoxydating power, while the blue and violet exert a contrary influence; but these are rare exceptions.

The photographic action of the two portions of the solar spectrum being so different, Sir John Herschel tried the effect of their united action by superposing the less refrangible part of the spectrum over the more refrangible portion by means of two prisms; and he thus discovered that two rays of different refrangibility, and therefore of different lengths of undulation, acting simultaneously, produce an effect which neither, acting separately, can do.

Some circumstances that occurred during the analysis of the chemical spectrum seem to indicate an absorptive action in the sun’s atmosphere. The spectral image impressed on paper prepared with nitrate of silver and Rochelle salt commenced at, or very little below, the mean yellow ray, of a delicate lead colour; and when the action was arrested, such was the character of the whole photographic spectrum. But, when the light of the solar spectrum was allowed to continue its action, there was observed to come on suddenly a new and much more intense impression of darkness, confined in length to the blue and violet rays; and, what is most remarkable, confined also in breadth to the middle of the sun’s image, so far at least as to leave a border of the lead-coloured spectrum traceable, not only round the clear and well-defined convexity of the dark interior spectrum at the less refrangible end, but also laterally along both its edges; and this border was the more easily traced, and less liable to be mistaken, from its striking contrast of colour with the interior spectrum, the former being lead gray, the latter an extremely rich deep velvety brown. The less refrangible end of this interior brown spectrum presented a sharply terminated and regularly elliptical contour, the more refrangible a less decided one. “It may seem too hazardous,” Sir John continues, “to look for the cause of this very singular phenomenon in a real difference between the chemical agencies of those rays which issue from the central portion of the sun’s disc, and those which, emanating from its borders, have undergone the absorptive action of a much greater depth of its atmosphere; and yet I confess myself somewhat at a loss what other cause to assign for it. It must suffice, however, to have thrown out the hint, remarking only, that I have other, and I am disposed to think decisive, evidence of the existence of an absorptive solar atmosphere extending beyond the luminous one.” M. Arago observed that the rays from the centre of the sun have a greater photographic power than those from the edges, and the photographic images of the sun, taken on glass by M. Niepcé, were blood-red, much deeper in the centre, and on one occasion the image was surrounded by an auriol. Several circumstances concur in showing that there are influences also concerned in the transmission of the photographic action which have not yet been explained, as, for example, the influence which the time of the day exercises on the rapidity with which photographic impressions are made, the sun being much less effective two hours after passing the meridian than two hours before. There is also reason to suspect that the effect in some way depends on the latitude, since a much longer time is required to obtain an image under the bright skies of the tropics than in England; and it is even probable that there is a difference in the sun’s light in high and low latitudes, because an image of the solar spectrum, obtained on a Daguerreotype plate in Virginia, by Dr. Draper, differed from a spectral image obtained by Mr. Hunt on a similar plate in England. The inactive spaces discovered in the photographic spectrum by M. E. Becquerel, similar to those in the luminous spectrum, and coinciding with them, is also a phenomenon of which no explanation has yet been given; possibly the chemical rays may be absorbed by the atmosphere with those of light. Although chemical action extends over the whole luminous spectrum, and much beyond it, in gradations of more or less intensity, it is found by careful investigation to be by no means continuous; numerous inactive lines cross it, coinciding with those in the luminous image as far as it extends; besides, a very great number exist in the portions that are obscure, and which overlap the visible part. There are three extraspectral lines beyond the red, and some strongly marked groups on the obscure part beyond the violet; but the whole number of those inactive lines, especially in the dark spaces, is so great that it is impossible to count them.

Notwithstanding this coincidence in the inactive lines of the two spectra, photographic energy is independent of both light and heat, since it exerts the most powerful influence in those rays where they are least, and also in spaces where neither sensibly exist; but the transmission of the sun’s light through coloured media makes that independence quite evident. Heat and light pass abundantly through yellow glass, or a solution of chromate of potash; but the greater part of the chemical rays are excluded, and chlorine gas diluted with common air, though highly pervious to the luminous and calorific principles, has the same effect. Sir John Herschel found that a slight degree of yellow London fog had a similar effect with that of pale yellow media: he also remarked that a weak solution of azolitmine in potash, which admits a great quantity of green light, excludes chemical action; and some years ago the author, while making experiments on the transmission of chemical rays, observed that green glass, coloured by oxide of copper about the 20th of an inch thick, excludes the photographic rays; and, as M. Melloni has shown that substance to be impervious to the most refrangible calorific rays, it has the property of excluding the whole of the most refrangible part of the solar spectrum, visible and invisible. Green mica, if not too thin, has also the same effect, whereas amethyst, deep blue, and violet-coloured glasses, though they transmit a very little light, allow the chemical rays to pass freely. Thus light and photographic energy may be regarded as distinct parts of the solar beam, and both being propagated by vibrations of the etherial medium they are merely motion. Excellent images have been obtained of the moon in its different phases by Professor Secchi, at Rome; candlelight is nearly deficient of the chemical rays. How far they may influence crystallization and other molecular arrangements is unknown, but their power is universal wherever the solar beam falls, although their effect only becomes evident in cases of unstable molecular equilibrium.

It is not by vision alone that a knowledge of the sun’s rays is acquired: touch proves that they have the power of raising the temperature of substances exposed to their action. Sir William Herschel discovered that rays which produce the sensation of heat exist in the solar spectrum independent of those of light; when he used a prism of flint glass, he found that the warm rays are most abundant in the dark space a little beyond the red extremity of the spectrum, that from thence they decrease towards the violet, beyond which they are insensible. It may be concluded therefore, that the calorific rays vary in refrangibility, and that those beyond the extreme red are less refrangible than any rays of light. Since Sir William Herschel’s time it has been discovered that the calorific spectrum exceeds the luminous one in length in the ratio of 42 to 25, but the most singular phenomenon is its want of continuity. Sir John Herschel blackened the under side of a sheet of very thin white paper by the smoke of a lamp, and, having exposed the white side to the solar spectrum, he drew a brush dipped in spirit of wine over it, by which the paper assumed a black hue when sufficiently saturated. The heat in the spectrum evaporated the spirit first on those parts of the paper where it fell with greatest intensity, thereby restoring their white colour, and he thus discovered that the heat increases uniformly and gradually throughout the luminous spectrum, and that it comes to a maximum and forms a spot at a considerable distance beyond the extreme red. It then decreases, but again increasing it forms a second maximum spot, after which it ceases altogether through a short space, but is again renewed and forms two more insulated spots, and even a fifth may be traced at a little distance from the latter. These circumstances are probably owing to the absorbing action of the atmospheres of the sun and earth. “The effect of the former,” says Sir John, “is beyond our control, unless we could carry our experiments to such a point of delicacy as to operate separately on rays emanating from the centre and borders of the sun’s disc; that of the earth’s, though it cannot be eliminated any more than in the case of the sun’s, may yet be varied to a considerable extent by experiments made at great elevations, under a vertical sun, and compared with others where the sun is more oblique, the situation lower, and the atmospheric pressure of a temporarily high amount. Should it be found that this cause is in reality concerned in the production of the spots, we should see reason to believe that a large portion of solar heat never reaches the earth’s surface, and that what is incident on the summits of lofty mountains differs not only in quantity but also in quality from what the plains receive.”

A remarkable phosphorescent property was discovered by M. E. Becquerel in the solar spectrum. Two luminous bands separated by a dark one are excited by the solar spectrum on paper covered with a solution of gum arabic, and strewed with powdered sulphuret of calcium or Canton’s phosphorus. One of the luminous bands occupies the space under the least refrangible violet rays, and the other that beyond the lavender rays, so that the dark band lies under the extreme violet and lavender rays. When the action of the light is continued, the whole surface beyond the least refrangible violet shines, the luminous bands already mentioned brightest; but all the space from the least refrangible violet to the extreme red remains dark. If the surface, prepared either with the sulphuret of calcium or Bologna stone, be exposed to the sun’s light for a little time, it becomes luminous all over; but when, in this state, a solar spectrum is thrown upon it, the whole remains luminous except the part from the least refrangible violet to the extreme red, on which space the light is extinguished; and when the temperature of the surface is raised by a lamp, the bright parts become more luminous and the dark parts remain dark. Glass stained by the protoxide of copper, which transmits only the red and orange rays, has the same effect with the less refrangible part of the spectrum; hence there can be no doubt that the most refrangible and obscure rays of the spectrum excite phosphorescence, while all the less refrangible rays of light and heat extinguish it.

Paper prepared with the sulphuret of barium, when under the solar spectrum, shows only one space of maximum luminous intensity, and the destroying rays are the same as in the sulphuret of calcium. Thus the obscure rays beyond the extreme violet produce light, while the luminous rays extinguish it.

The phosphoric spectrum has inactive lines which coincide with those in the luminous and chemical spectra, at least as far as it extends; but in order to be seen the spectrum must be received for a few seconds upon the prepared surface through an aperture in a dark room, then the aperture must be closed, and the temperature of the surface raised two or three hundred degrees; the phosphorescent parts then shine brilliantly and the dark lines appear black. Since the parts of similar refrangibility in different spectra are traversed by the same dark lines, rays of the same refrangibility are probably absorbed at the same time by the different media through which they pass.

It appears from the experiments of MM. Becquerel and Biot, that electrical disturbances produce these phosphorescent effects. There is thus a mysterious connexion between the most refrangible rays and electricity which the experiments of M. E. Becquerel confirm, showing that electricity is developed during chemical action by the violet rays, that it is feebly developed by the blue and indigo, but that none is excited by the less refrangible part of the spectrum.

A series of experiments by Sir John Herschel have disclosed a new set of obscure rays in the solar spectrum, which seem to bear the same relation to those of heat that the photographic or chemical rays bear to the luminous. They are situate in that part of the spectrum which is occupied by the less refrangible visible colours, and have been named by their discoverer Parathermic rays. It must be held in remembrance that the region of greatest heat in the solar spectrum lies in the dark space beyond the visible red. Now, Sir John Herschel found that in experiments with a solution of gum guaiacum in soda, which gives the paper a green colour, the green, yellow, orange, and red rays of the spectrum invariably discharged the colour, while no effect was produced by the extra-spectral rays of heat, which ought to have had the greatest effect had heat been the cause of the phenomenon. When an aqueous solution of chlorine was poured over a slip of paper prepared with gum guaiacum dissolved in soda, a colour varying from a deep somewhat greenish hue to a fine celestial blue was given to it; and, when the solar spectrum was thrown on the paper while moist, the colour was discharged from all the space under the less refrangible luminous rays, at the same time that the more distant thermic rays beyond the spectrum evaporated the moisture from the space on which they fell; so that the heat spots became apparent. But the spots disappeared as the paper dried, leaving the surface unchanged; while the photographic impression within the visible spectrum increased in intensity; the non-luminous thermic rays, though evidently active as to heat, were yet incapable of effecting that peculiar chemical change which other rays of much less heating power were all the time producing. Sir John having ascertained that an artificial heat from 180° to 280° of Fahrenheit changed the green tint of gum guaiacum to its original yellow hue when moist, but that it had no effect when dry, he therefore tried whether heat from a hot iron applied to the back of the paper used in the last-mentioned experiment while under the influence of the solar spectrum might not assist the action of the calorific rays; but, instead of doing so, it greatly accelerated the discoloration over the spaces occupied by the less refrangible rays, but had no effect on the extra-spectral region of maximum heat. Obscure terrestrial heat, therefore, is capable of assisting and being assisted in effecting this peculiar change by those rays of the spectrum, whether luminous or thermic, which occupy its red, yellow, and green regions; while, on the other hand, it receives no such assistance from the purely thermic rays beyond the spectrum acting under similar circumstances and in an equal state of condensation.

The conclusions drawn from these experiments are confirmed by that which follows: a photographic picture formed on paper prepared with a mixture of the solutions of ammonia-citrate of iron and ferro-sesquicyanite of potash in equal parts, then thrown into water and afterwards dried, will be blue and negative, that is to say, the lights and shadows will be the reverse of what they are in nature. If in this state the paper be washed with a solution of proto-nitrate of mercury, the picture will be discharged; but if it be well washed and dried, and a hot smoothing-iron passed over it, the picture instantly reappears, not blue, but brown; if kept some weeks in this state in perfect darkness between the leaves of a portfolio, it fades, and almost entirely vanishes, but a fresh application of heat restores it to its full original intensity. This curious change is not the effect of light, at least not of light alone. A certain temperature must be attained, and that suffices in total darkness; yet, on exposing to a very concentrated spectrum a slip of the paper used in the last experiment, after the uniform blue colour has been discharged and a white ground left, this whiteness is changed to brown over the whole region of the red and orange rays, but not beyond the luminous spectrum.

Sir John thence concludes:—1st. That it is the heat of these rays, not their light, which operates the change; 2ndly. That this heat possesses a peculiar chemical quality which is not possessed by the purely calorific rays outside of the visible spectrum, though far more intense; and, 3rdly. That the heat radiated from obscurely hot iron abounds especially in rays analogous to those of the region of the spectrum above indicated.

Another instance of these singular transformations may be noticed. The pictures formed on cyanotype paper rendered more sensitive by the addition of corrosive sublimate are blue on a white ground and positive, that is, the lights and shadows are the same as in nature, but, by the application of heat, the colour is changed from blue to brown, from positive to negative; even by keeping in darkness the blue colour is restored, as well as the positive character. Sir John attributes this, as in the former instance, to certain rays, which, regarded as rays of heat or light, or of some influence sui generis accompanying the red and orange rays of the spectrum, are also copiously emitted by bodies heated short of redness. He thinks it probable that these invisible parathermic rays are the rays which radiate from molecule to molecule in the interior of bodies, that they determine the discharge of vegetable colours at the boiling temperature, and also the innumerable atomic transformations of organic bodies which take place at the temperature below redness, that they are distinct from those of pure heat, and that they are sufficiently identified by these characters to become legitimate objects of scientific discussion.

The calorific and parathermic rays appear to be intimately connected with the discoveries of Messrs. Draper and Moser. Daguerre has shown that the action of light on the iodide of silver renders it capable of condensing the vapour of mercury which adheres to the parts affected by it. Professor Moser of Königsberg has proved that the same effect is produced by the simple contact of bodies, and even by their very near juxtaposition, and that in total darkness as well as in light. This discovery he announced in the following words:—“If a surface has been touched in any particular parts by any body, it acquires the property of precipitating all vapours, and these adhere to it or combine chemically with it on these spots differently from what they do on the untouched parts.” If we write on a plate of glass or any smooth surface whatever with blotting-paper, a brush, or anything else, and then clean it, the characters always reappear if the plate or surface be breathed upon, and the same effect may be produced even on the surface of mercury; nor is absolute contact necessary. If a screen cut in a pattern be held over a polished metallic surface at a small distance, and the whole breathed on, after the vapour has evaporated so that no trace is left on the surface, the pattern comes out when it is breathed on again.

Professor Moser proved that bodies exert a very decided influence upon each other, by placing coins, cut stones, pieces of horn, and other substances, for a short time on a warm metallic plate: when the substance was removed, no impression appeared on the plate till it was breathed upon or exposed to the vapour of mercury, and then these vapours adhered only to the parts where the substance had been placed, making distinct images, which in some cases were permanent after the vapour was removed. Similar impressions were obtained on glass and other substances even when the bodies were not in contact, and the results were the same whether the experiments were performed in light or in darkness.

Mr. Grove found, when plates of zinc and copper were closely approximated, but not in contact, and suddenly separated, that one was positively and the other negatively electric; whence he inferred that the intervening medium was either polarised, or that a radiation analogous, if not identical, with that which produces Moser’s images takes place from plate to plate.

Mr. Hunt has shown that many of these phenomena depend on difference of temperature, and that, in order to obtain good impressions, dissimilar metals must be used. For example, gold, silver, bronze, and copper coins were placed on a plate of copper too hot to be touched, and allowed to remain till the plate cooled: all the coins had made an impression, the distinctness and intensity of which were in the order of the metals named. When the plate was exposed to the vapour of mercury the result was the same, but, when the vapour was wiped off, the gold and silver coins only had left permanent images on the copper. These impressions are often minutely perfect, whether the coins are in actual contact with the plate or one-eighth of an inch above it. The mass of the metal has a material influence on the result; a large copper coin makes a better impression on a copper plate than a small silver coin. When coins of different metals are placed on the same plate they interfere with each other.

When, instead of being heated, the copper plate was cooled by a freezing mixture, and bad conductors of heat laid upon it, as wood, paper, glass, &c., the result was similar.

Mr. Hunt, observing that a black substance leaves a stronger impression on a metallic surface than a white, applied the property to the art of copying prints, woodcuts, writing, and printing, on copper amalgamated on one surface and highly polished, merely by placing the object to be copied smoothly on the metal, and pressing it into close contact by a plate of glass: after some hours the plate is subjected to the vapour of mercury, and afterwards to that of iodine, when a black and accurate impression of the object comes out on a grey ground. Effects similar to those attributed to heat may also be produced by electricity. Mr. Karsten, by placing a glass plate upon one of metal, and on the glass plate a medal subjected to discharges of electricity, found a perfect image of the medal impressed on the glass, which could be brought into evidence by either mercury or iodine; and, when several plates of glass were interposed between the medal and the metallic plate, each plate of glass received an image on its upper surface after the passage of electrical discharges. These discharges have the remarkable power of restoring impressions that have been long obliterated from plates by polishing—a proof that the disturbances upon which these phenomena depend are not confined to the surface of the metals, but that a very decided molecular change has taken place to a considerable depth. Mr. Hunt’s experiments prove that the electro-negative metals make the most decided images upon electro-negative plates, and vice versâ. M. Matteucci has shown that a discharge of electricity does not visibly affect a polished silver plate, but that it produces an alteration which renders it capable of condensing vapour.

The impression of an engraving was made by laying it face downwards on a silver plate iodized, and placing an amalgamated copper plate upon it; it was left in darkness fifteen hours, during which time an impression of the engraving had been made on the amalgamated plate through the paper.

An iodized silver plate was placed in darkness with a coil of string laid on it, and with a polished silver plate suspended one-eighth of an inch above it: after four hours they were exposed to the vapours of mercury, which became uniformly deposited on the iodized plate, but on the silver one there was a sharp image of the string, so that this image was formed in the dark, and even without contact. Coins or other objects leave their impressions in the same manner with perfect sharpness and accuracy, when brought out by vapour without contact, in darkness, and on simple metals.

Red and orange coloured media, smoked glass, and all bodies that transmit or absorb the hot rays freely, leave strong impressions on a plate of copper, whether they be in contact or one-eighth of an inch above it. Heat must be concerned in this, for a solar spectrum concentrated by a lens was thrown on a polished plate of copper, and kept on the same spot by a heliostat for two or three hours: when exposed to mercurial vapour, a film of the vapour covered the plate where the diffused light which always accompanies the solar spectrum had fallen. On the obscure space occupied by the maximum heating power of Sir William Herschel, and also on the great heat spot in the thermic spectrum of Sir John Herschel, the condensation of the mercury was so thick that it stood out a distinct white spot on the plate, while over the whole space that had been under the visible spectrum the quantity of vapour was much less than that which covered the other parts, affording distinct evidence of a negative effect in the luminous spectrum and of the power of the hot rays, which is not always confined to the surface of the metal, since in many instances the impressions penetrated to a considerable depth below it, and consequently were permanent.

Several of these singular effects appear to be owing to the mutual action of molecules in contact while in a different state, whether of electricity or temperature: others clearly point at some unknown influence exerted between surfaces at a distance, and affecting their molecular structure: possibly it may be the parathermic rays, which have a peculiar chemical action even in total darkness. In the last experiment the effect is certainly produced by the positive portion of one of those remarkable antagonist principles which characterise the solar spectrum.

Thus it appears that the prism resolves the pure white sunbeam into three superposed spectra, each varying in refrangibility and intensity throughout its whole length; the visible part is overlapped at one end by the chemical or photographic rays, and at the other by the thermic, but the two latter so much exceed the visible part, that the linear dimensions of the three—the luminous, thermic, and photographic—are in proportion to the numbers 25, 42·10, and 55·10, so that the whole solar spectrum is twice as long as its visible part. The two extremities exert a decided antagonist energy. The least refrangible luminous rays obliterate the action of the photographic rays, while the latter produce phosphorescent light, which is extinguished by the least refrangible luminous rays. According to Mr. Hunt’s experiment, the hot rays condense mercurial vapour on a polished metallic plate, while the luminous rays prevent its formation. Electricity is excited by the chemical rays, while the parathermic are found in the less refrangible rays alone. Each of the spectra is crossed by coloured and rayless lines peculiar to itself, and these are traversed at right angles by innumerable dark lines of various breadths, the whole forming an inexpressibly wonderful and glorious creation.

The arrangement varies a little according to the material of the prism and the manner of producing the spectrum, as in that obtained by Professor Draper from diffracted light. It was formed by a beam diffracted by passing through a netting of fine wire, or by reflection from a polished surface of steel, having fine parallel lines drawn on it. This diffracted spectrum is divided into two equal parts in the centre of the yellow; and as in the prismatic spectrum, one half is antagonist to the other half, the red or negative end undoing what the positive or violet end has done. The centre of the yellow is the hottest part, and the heat decreases to both extremities. A line of cold is supposed to exist on this spectrum answering to Fraunhofer’s dark line H.

The undulations of the ethereal medium which constitute a sunbeam must be infinitely varied, each influence having a vibration peculiar to itself. Those of light are certainly transverse to the direction of the ray; while Professor Draper believes that those of heat are normal, that is, in the direction of the ray, like those of sound. A doubt exists whether the vibrations of polarised light are perpendicular to the plane of polarisation or in that plane. Professor Stokes of Cambridge has come to the conclusion, both from the diffracted spectrum and theory, that they are perpendicular to the plane of polarisation, but M. Holtzmann is of opinion that they are in that plane, so the subject is still open to discussion.

SECTION XXV.

Size and Constitution of the Sun—The Solar Spots—Intensity of the Sun’s Light and Heat—The Sun’s Atmosphere—His influence on the Planets—Atmospheres of the Planets—The Moon has none—Lunar heat—The Differential Telescope—Temperature of Space—Internal Heat of the Earth—Zone of constant Temperature—Increase of Heat With the Depth—Central Heat—Volcanic Action—Quantity of Heat received from the Sun—Isogeothermal Lines—Line of perpetual Congelation—Climate—Isothermal Lines—Same quantity of Heat annually received and radiated by the Earth.

THE sun is a globe 880,000 miles in diameter: what his body may be it is impossible to conjecture, but it seems to be a dark mass surrounded by an extensive atmosphere at a certain height in which there is a stratum of luminous clouds which constitutes the photosphere of the sun. Above it rises the true solar atmosphere, visible as an aureola or corona during annular and total eclipses, and probably the cause of the peculiar phenomena in the photographic image of the sun already mentioned. Through occasional openings in the photosphere or mottled ocean of flame, the dark nucleus appears like black spots, often of enormous size. These spots are almost always comprised within a zone of the sun’s surface, whose breadth measured on a solar meridian does not extend beyond 30-1/2° on each side of his equator, though they have been seen at a distance of 39-1/2°. The dark central part of the spots is surrounded by a succession of obscure cloudy envelopes increasing in brightness up to a penumbra, sometimes there are three or more shades, but it requires a good telescope to distinguish the intermediate ones. The spots gradually increase in size and number from year to year to a maximum, and then as gradually decrease to a minimum, accomplishing regular vicissitudes in periods of about eleven years, and are singularly connected with the cycles of terrestrial magnetism. From their extensive and rapid changes, there is every reason to believe that the exterior and incandescent part of the sun is gaseous.

Doubts have arisen as to the uniformity of the quantity of heat emitted by the sun. Sir William Herschel was the first to suspect that it was affected by the quantity and magnitude of the spots on his surface; Professor Secchi has observed that the spots are less hot than the luminous part; and now Professor Wolf has perceived that the amount of heat emitted by the sun varies periodically with the spots every 11·11 years, or nearly nine times in a century, beginning at the commencement of the present one. He has discovered a sub-period in that of the spots, which no doubt has an effect on the quantity of solar heat. So the unaccountable vicissitudes in the temperature of different years may ultimately be found to depend upon the constitution of the sun himself.

The intensity of the sun’s light diminishes from the centre to the circumference of the solar disc. His direct light has been estimated to be equal to that of 5563 wax candles of moderate size placed at the distance of one foot from an object; that of the moon is probably only equal to the light of one candle at the distance of 12 feet: consequently the light of the sun is more than three hundred thousand times greater than that of the moon. According to Professor Secchi’s experiments at Rome, the heat of the solar image is almost twice as great at the centre as at the edge. The maximum heat, however, is not in the centre, but in the solar equator, and the spots are less hot than the rest of the surface.

The oceans of light and heat probably arising from electric or chemical processes of immense energy that continually take place at the sun’s surface (N. 217) are transmitted in undulations by the ethereal medium in all directions; but notwithstanding the sun’s magnitude and the inconceivable intensity of light and heat that must exist at his surface, as the intensity of both diminishes as the square of the distance increases, his kindly influence can hardly be felt at the boundaries of our system. In Uranus the sun must be seen like a small brilliant star not above the hundred and fiftieth part as bright as he appears to us, but that is 2000 times brighter than our moon, so that he is really a sun to Uranus, and may impart some degree of warmth. But if we consider that water would not remain fluid in any part of Mars, even at his equator, and that, in the temperate zones of the same planet, even alcohol and quicksilver would freeze, we may form some idea of the cold that must reign in Uranus and Neptune. The climate of Venus more nearly resembles that of the earth, though, excepting at her poles, much too hot for animal and vegetable life such as they exist here, for she receives seven times as much light and heat as the earth does; but in Mercury the mean heat from the intensity of the sun’s rays must be above that of boiling quicksilver, and water would boil even at his poles. Thus the planets, though kindred with the earth in motion and form, are, according to our experience, totally unfit for the habitation of such a being as man, unless indeed their temperature should be modified by circumstances of which we are not aware, and which may increase or diminish the sensible heat so as to render them habitable. In our utter ignorance it may be observed, that the earth, if visible at all from Neptune, can only be a minute telescopic object; that from the nearest fixed star the sun must dwindle to a mere point of light; that the whole solar system would there be hid by a spider’s thread; and that the starry firmament itself is only the first series of starry systems, the numbers of which are bounded alone by the imperfection of our space-penetrating instruments. In this overwhelming majesty of creation, it seems rash to affirm that the earth alone is inhabited by intelligent beings, and thus to limit the Omnipotent, who has made nothing in vain.

Several of the planets have extensive and dense atmospheres: according to Schroëter the atmosphere of Ceres is more than 668 miles high, and that of Pallas has an elevation of 465 miles, but not a trace of an atmosphere can be perceived round Vesta. The attraction of the earth has probably deprived the moon of hers, for the refractive power of the air at the surface of the earth is at least a thousand times as great as at the surface of the moon: the lunar atmosphere must therefore be of a greater degree of rarity than can be produced by our best air-pumps. This is confirmed by Arago’s observations during a solar eclipse, when no trace of a lunar atmosphere could be seen. Since then, however, some indications of air have been perceived in the lunar valleys. In taking photographic images of the moon and Jupiter at Rome, Professor Secchi found that the light of the full moon is to that of the quarter moon as 3 to 1. Jupiter gives a photographic image as bright and vigorous as the brightest part of the moon; but although the light of Jupiter is less than that of the moon, he is nearly five times farther from the sun; and as light diminishes as the square of the distance increases, the light of Jupiter is proportionally greater than that of the moon, consequently Jupiter’s atmosphere reflects more light than the dark volcanic soil of the moon; thus Professor Secchi observes photography may in time reveal the quality of the materials of which the celestial bodies are formed.

The effect of the earth’s atmosphere on lunar heat is remarkable. Professor Forbes proved that the direct light of the full moon is incapable of raising a thermometer the one three thousandth part of a Centigrade degree, at least in England; but at an elevation of 8870 feet on the Peak of Teneriffe, Mr. Piazzi Smyth found a very sensible heat from the moon, although she was then 19° south of the equator; so it is no doubt absorbed by our atmosphere at lower levels.

Some exceedingly interesting experiments might be made by means of a telescope having a prism attached to its objective extremity, and furnished with a micrometer, because by it the difference of the illumination of objects might be determined with extreme accuracy—as for example, the comparative intensity between the bright and dark parts of the moon, the comparative intensity of the solar light reflected by the moon, and the lumière cendré, or the light of the earth reflected on the moon, whence a comparison might be made between the light of the sun and that of the earth. Hence also it might be known whether the terrestrial hemispheres successively visible from the moon are more or less luminous, according as they contain more land or water, and at the same time it might be possible to appreciate the more or less cloudy or clear state of our atmosphere, so that in time we might ultimately find in the lumière cendré of the moon data upon the mean diaphaneity of different terrestrial hemispheres which are of different temperatures.

It is found by experience that heat is developed in opaque and translucent substances by their absorption of solar light, but that the sun’s rays do not sensibly alter the temperature of perfectly transparent bodies through which they pass. As the temperature of the pellucid planetary space can be but little affected by the passage of the sun’s light and heat, neither can it be sensibly raised by the heat now radiated from the earth.

Doubtless the radiation of all the bodies in the universe maintains the ethereal medium at a higher temperature than it would otherwise have, and must eventually increase it, but by a quantity so evanescent that it is hardly possible to conceive a time when a change will become perceptible.

The temperature of space being so low as -239° Fahrenheit, it becomes a matter of no small interest to ascertain whether the earth may not be ultimately reduced by radiation to the temperature of the surrounding medium; what the sources of heat are; and whether they be sufficient to compensate the loss, and to maintain the earth in a state fit for the support of animal and vegetable life in time to come. All observations that have been made under the surface of the ground concur in proving that there is a stratum at the depth of from 40 to 100 feet throughout the whole earth where the temperature is invariable at all times and seasons, and which differs but little from the mean annual temperature of the country above. According to M. Boussingault, that stratum at the equator is at the depth of little more than a foot in places sheltered from the direct rays of the sun; but in our climates it is at a much greater depth. In the course of more than half a century the temperature of the earth at the depth of 90 feet, in the cellars of the Observatory at Paris, has never been above or below 53° of Fahrenheit’s thermometer, which is only 2° above the mean annual temperature at Paris. This zone, unaffected by the sun’s rays from above, or by the internal heat from below, serves as an origin whence the effects of the external heat are estimated on one side, and the internal temperature of the globe on the other.

As early as the year 1740 M. Gensanne discovered in the lead-mines of Giromagny, in the Vosges mountains, three leagues from Béfort, that the heat of the ground increases with the depth below the zone of constant temperature. A vast number of observations have been made since that time, in the mines of Europe and America, by MM. Saussure, Daubuisson, Humboldt, Cordier, Fox, Reich, and others, which agree, without an exception, in proving that the temperature of the earth becomes higher in descending towards its centre. The greatest depth that has been attained is in the silver-mine of Guanaxato, in Mexico, where M. de Humboldt found a temperature of 98° at the depth of 285 fathoms, the mean annual temperature of the country being only 61°. Next to that is the Dalcoath copper-mine, in Cornwall, where Mr. Fox’s thermometer stood at 68° in a hole in the rock at the depth of 230 fathoms, and at 82° in water at the depth of 240 fathoms, the mean annual temperature at the surface being about 50°. But it is needless to multiply examples, all of which concur in showing that there is a very great difference between the temperature in the interior of the earth and at its surface. Mr. Fox’s observations on the temperature of springs which rise at profound depths in mines afford the strongest testimony. He found considerable streams flowing into some of the Cornish mines at the temperature of 80° or 90°, which is about 30° or 40° above that of the surface, and also ascertained that nearly 2,000,000 gallons of water are daily pumped from the bottom of the Poldice mine, which is 176 fathoms deep at 90° or 100°. As this is higher than the warmth of the human body, Mr. Fox justly observes that it amounts to a proof that the increased temperature cannot proceed from the persons of the workmen employed in the mines. Neither can the warmth of mines be attributed to the condensation of the currents of air which ventilate them. Mr. Fox, whose opinion is of high authority in these matters, states that, even in the deepest mines, the condensation of the air would not raise the temperature more than 5° or 6°; and that, if the heat could be attributed to this cause, the seasons would sensibly affect the temperature of mines, which it appears they do not where the depth is great. Besides, the Cornish mines are generally ventilated by numerous shafts opening into the galleries from the surface or from a higher level. The air circulates freely in these, descending in some shafts and ascending in others. In all cases Mr. Fox found that the upward currents are of a higher temperature than the descending currents; so much so, that in winter the moisture is often frozen in the latter to a considerable depth; the circulation of air, therefore, tends to cool the mine instead of increasing the heat. Mr. Fox has also removed the objections arising from the comparatively low temperature of the water in the shafts of abandoned mines, by showing that observations in them, from a variety of circumstances which he enumerates, are too discordant to furnish any conclusion as to the actual heat of the earth. The high temperature of mines might be attributed to the effects of the fires, candles, and gunpowder used by the miners, did not a similar increase obtain in deep wells, and in borings to great depths in search of water, where no such causes of disturbance occur. In a well dug with a view to discover salt in the canton of Berne, and long deserted, M. de Saussure had the most complete evidence of increasing heat. The same has been confirmed by the temperature of many wells, both in France and England, especially by the Artesian wells, so named from a peculiar method of raising water first resorted to in Artois, and since become very general. An Artesian well consists of a shaft a few inches in diameter, bored into the earth till a spring is found. To prevent the water being carried off by the adjacent strata, a tube is let down which exactly fills the bore from top to bottom, in which the water rises pure to the surface. It is clear the water could not rise unless it had previously descended from high ground through the interior of the earth to the bottom of the well. It partakes of the temperature of the strata through which it passes, and in every instance has been warmer in proportion to the depth of the well; but it is evident that the law of increase cannot be obtained in this manner. Perhaps the most satisfactory experiments on record are those made by MM. Auguste de la Rive and F. Marcet during the year 1833, in a boring for water about a league from Geneva, at a place 318 feet above the level of the lake. The depth of the bore was 727 feet, and the diameter only between four and five inches. No spring was ever found; but the shaft filled with mud, from the moisture of the ground mixing with the earth displaced in boring, which was peculiarly favourable for the experiments, as the temperature at each depth may be considered to be that of the particular stratum. In this case, where none of the ordinary causes of disturbance could exist, and where every precaution was employed by scientific and experienced observers, the temperature was found to increase regularly and uniformly with the depth at the rate of about 1° of Fahrenheit for every 52 feet. Professor Reich of Freyberg has found that the mean of a great number of observations both in mines and wells is 1° of Fahrenheit for every 55 feet of depth; and from M. Arago’s observations in the Grenelle Artesian well at Paris, the increase is 1° of Fahrenheit for every 45 feet. Though there can be no doubt as to the increase of temperature in penetrating the crust of the earth, there is still much uncertainty as to the law of increase, which varies with the nature of the soil and other local circumstances; but, on an average, it has been estimated at the rate of 1° for every 50 or 60 feet, which corresponds with the observations of MM. Marcet and De la Rive. In consequence of the rapid increase of internal heat, thermal springs, or such as are independent of volcanic action, rising from a great depth, must necessarily be very rare and of a high temperature; and it is actually found that none are so low as 68° of Fahrenheit; that of Chaudes Aigues, in Auvergne, is about 136°. In many places warm water from Artesian wells will probably come into use for domestic purposes, and it is even now employed in manufactories near Stutgardt, in Alsace, &c.

It is hardly to be expected that at present any information with regard to the actual internal temperature of the earth should be obtained from that of the ocean, on account of the mobility of fluids, by which the colder masses sink downwards, while those that are warmer rise to the surface. Nevertheless, it may be stated that the temperature of the sea decreases with the depth between the tropics; while, on the contrary, all our northern navigators found that the temperature increases with the depth in the polar seas. The change takes place about the 70th parallel of latitude. Some ages hence, however, it may be known whether the earth has arrived at a permanent state as to heat, by comparing secular observations of the temperature of the ocean if made at a great distance from the land.

Should the earth’s temperature increase at the rate of 1° for every 50 feet, it is clear that at the depth of 200 miles the hardest substances must be in a state of fusion, and our globe must in that case either be encompassed by a stratum of melted lava at that depth, or it must be a ball of liquid fire 7600 miles in diameter, enclosed in a thin coating of solid matter; for 200 miles are nothing when compared with the size of the earth. No doubt the form of the earth, as determined by the pendulum and arcs of the meridian, as well as by the motions of the moon, indicates original fluidity and subsequent consolidation and reduction of temperature by radiation; but whether the law of increasing temperature is uniform at still greater depths than those already attained by man, it is impossible to say. At all events, internal fluidity is not inconsistent with the present state of the earth’s surface, since earthy matter is as bad a conductor of heat as lava, which often retains its heat at a very little depth for years after its surface is cool. Whatever the radiation of the earth might have been in former times, certain it is that it goes on very slowly in our days; for M. Fourier has computed that the central heat is decreasing from radiation by only about the 1/30000th part of a degree in a century. If so, there can be no doubt that it will ultimately be dissipated; but as far as regards animal and vegetable life, it is of very little consequence whether the centre of our planet be liquid fire or ice, since its condition in either case could have no sensible effect on the climate at its surface. The internal fire does not even impart heat enough to melt the snow at the poles, though nearer to the centre than any other part of the globe.

The immense extent of active volcanic fire is one of the causes of heat which must not be overlooked.

The range of the Andes from Chile to the north of Mexico, probably from Cape Horn to Behring Straits, is one vast district of igneous action, including the Caribbean and the West Indian Islands on one hand; and stretching quite across the Pacific Ocean, through the Polynesian Archipelago, the New Hebrides, the Georgian and Friendly Islands, on the other. Another chain begins with the Aleutian Islands, extends to Kamtschatka, and from thence passes through the Kurile, Japanese, and Philippine Islands, to the Moluccas, whence it spreads with terrific violence through the Indian Archipelago, even to the Bay of Bengal. Volcanic action may again be followed from the entrance of the Persian Gulf to Madagascar, Bourbon, the Canaries, and Azores. Thence a continuous igneous region extends through about 1000 geographical miles to the Caspian Sea, including the Mediterranean, and extending north and south between the 35th and 40th parallels of latitude; and in central Asia a volcanic region occupies 2500 square geographical miles. The volcanic fires are developed in Iceland in tremendous force; and the antarctic land discovered by Sir James Ross is an igneous formation of the boldest structure, where a volcano in high activity rises 12,000 feet above the perpetual ice of these polar deserts, and within 19-1/2° of the south pole. Throughout this vast portion of the world the subterraneous fire is often intensely active, producing such violent earthquakes and eruptions that their effects, accumulated during millions of years, may account for many of the great geological changes of igneous origin that have already taken place in the earth, and may occasion others not less remarkable, should time—that essential element in the vicissitudes of the globe—be granted, and their energy last.

Sir Charles Lyell, who has shown the power of existing causes with great ingenuity, estimates that on an average twenty eruptions take place annually in different parts of the world; and many must occur or have happened, even on the most extensive and awful scale, among people equally incapable of estimating their effects and of recording them. We should never have known the extent of the fearful eruption which took place in the island of Sumbawa, in 1815, but for the accident of Sir Stamford Raffles having been governor of Java at the time. It began on the 5th of April, and did not entirely cease till July. The ground was shaken through an area of 1000 miles in circumference; the tremors were felt in Java, the Moluccas, a great part of Celebes, Sumatra, and Borneo. The detonations were heard in Sumatra, at the distance of 970 geographical miles in a straight line; and at Ternate, 720 miles in the opposite direction. The most dreadful whirlwinds carried men and cattle into the air; and with the exception of 26 persons, the whole population of the island perished to the amount of 12,000. Ashes were carried 300 miles to Java in such quantities that the darkness during the day was more profound than ever had been witnessed in the most obscure night. The face of the country was changed by the streams of lava, and by the upheaving and sinking of the soil. The town of Tomboro was submerged, and water stood to the depth of 18 feet in places which had been dry land. Ships grounded where they had previously anchored, and others could hardly penetrate the mass of cinders which floated on the surface of the sea for several miles to the depth of two feet. A catastrophe similar to this, though of less magnitude, took place in the island of Bali in 1808, which was not heard of in Europe till years afterwards. The eruption of Coseguina in the Bay of Fonseca, which began on the 19th of January, 1835, and lasted many days, was even more dreadful and extensive in its effects than that of Sumbawa. The ashes during this eruption were carried by the upper current of the atmosphere as far north as Chiassa, which is upwards of 400 leagues to the windward of that volcano. Many volcanoes supposed to be extinct have all at once burst out with inconceivable violence. Witness Vesuvius, on historical record; and the volcano in the island of St. Vincent in our own days, whose crater was lined with large trees, and which had not been active in the memory of man. Vast tracts are of volcanic origin where volcanoes have ceased to exist for ages. Whence it may be inferred that in some places the subterraneous fires are in the highest state of activity, in some they are inert, and in others they appear to be extinct. Yet there are few countries that are not subject to earthquakes of greater or less intensity; the tremors are propagated like a sonorous undulation to such distances that it is impossible to say in what point they originate. In some recent instances their power must have been tremendous. In South America, so lately as 1822, an area of 100,000 square miles, which is equal in extent to the half of France, was raised several feet above its present level—a most able account of which is given in the ‘Transactions of the Geological Society,’ by an esteemed friend of the author’s, the late Mrs. Graham, who was present during the whole time of that formidable earthquake, which recurred at short intervals for more than two months, and who possessed talents to appreciate, and had opportunities of observing, its effects under the most favourable circumstances at Valparaiso, and for miles along the coast where it was most intense. A considerable elevation of the land has again taken place along the coast of Chile, in consequence of the violent earthquake which happened on the 20th of February, 1835. In 1819 a ridge of land stretching for 50 miles across the delta of the Indus, 16 feet broad, was raised 10 feet above the plain. The reader is referred to Sir Charles Lyell’s excellent ‘Principles of Geology,’ already mentioned, for most interesting details of the phenomena and extensive effects of volcanoes and earthquakes, too numerous to find a place here. It may however be mentioned that innumerable earthquakes are from time to time shaking the solid crust of the globe, and carrying destruction to distant regions, progressively though slowly accomplishing the great work of change. A most disastrous instance took place on the 15th of December, 1857, in the Neapolitan provinces of La Basilicata and Principato Citeriore, where the destruction was extensive and terrible; the number of victims, according to the official accounts, being returned at upwards of ten thousand. These terrible engines of ruin, fitful and uncertain as they may seem, must, like all durable phenomena, have a law which may in time be discovered by long-continued and accurate observations.

The shell of volcanic fire that girds the globe at a small depth below our feet has been attributed to different causes. By some it is supposed to originate in an ocean of incandescent matter, still existing in the central abyss of the earth. Some conceive it to be superficial, and due to chemical action, in strata at no very great depth when compared with the size of the globe. The more so as matter on a most extensive scale is passing from old into new combinations, which, if rapidly effected, are capable of producing the most intense heat. According to others, electricity, which is so universally diffused in all its forms throughout the earth, if not the immediate cause of the volcanic phenomena, at least determines the chemical affinities that produce them. It is clear that a subject so involved in mystery must give rise to much speculation, in which every hypothesis is attended with difficulties that observation alone can remove.

But the views of Mr. Babbage and Sir John Herschel on the general cause of volcanic action, and the changes in the equilibrium of the internal heat of the globe, accord more with the laws of mechanics and radiant heat than any that have been proposed. The theory of these distinguished philosophers, formed independently of each other, is equally consistent with observed phenomena, whether the earth be a solid crust encompassing a nucleus of liquid lava, or that there is merely a vast reservoir or stratum of melted matter at a moderate depth below the superficial crust. The author is indebted to the kindness of Sir Charles Lyell for the perusal of a most interesting letter from Sir John Herschel, in which he states his views on the subject.

Supposing that the globe is merely a solid crust, resting upon fluid or semi-fluid matter, whether extending to the centre or not, the transfer of pressure from one part of its surface to another by the degradation of existing continents, and the formation of new ones, would be sufficient to subvert the equilibrium of heat in the interior, and occasion volcanic eruptions. For, since the internal heat of the earth is transmitted outwards by radiation, an accession of new matter on any part of the surface, like an addition of clothing, by keeping it in, would raise the temperature of the strata below, and in the course of ages would even reduce those at a great depth to a state of fusion. Some of the substances might be converted into gases; and should the accumulation of new matter take place at the bottom of the sea, as is generally the case, this lava would be mixed with water in a state of ignition in consequence of the enormous pressure of the ocean, and of the newly superimposed matter which would prevent it from expanding into steam. Now Sir Charles Lyell has shown, with his usual talent, that the quantity of matter carried down by rivers from the surface of the continents is comparatively trifling, and that the great transfer to the bottom of the ocean is produced at the coast-line by the action of the sea; hence, says Sir John Herschel, “the greatest accumulation of local pressure is in the central area of the deep sea, while the greatest local relief takes place along the abraded coast-lines. Here then should occur the chief volcanic vents.” As the crust of the earth is much weaker on the coasts than elsewhere, it is more easily ruptured, and, as Mr. Babbage observes, immense rents might be produced there by its contraction in cooling down after being deprived of a portion of its original thickness. The pressure on the bottom of the ocean would force a column of lava mixed with ignited water and gas to rise through an opening thus formed, and, says Sir John Herschel, “when the column attains such a height that the ignited water can become steam, the joint specific gravity of the column is suddenly diminished, and up comes a jet of mixed steam and lava, till so much has escaped that the matter deposited at the bottom of the ocean takes a fresh bearing, when the evacuation ceases and the crack becomes sealed up.”

This theory perfectly accords with the phenomena of nature, since there are very few active volcanoes at a distance from the sea, and the exceptions that do occur are generally near lakes, or they are connected with volcanoes on the maritime coasts. Many break out even in the bottom of the ocean, probably owing to some of the supports of the superficial crust giving way, so that the steam and lava are forced up through the fissures.

Finally, Mr. Babbage observes that, “in consequence of changes continually going on, by the destruction of forests, the filling up of seas, the wearing down of elevated lands, the heat radiated from the earth’s surface varies considerably at different periods. In consequence of this variation, and also in consequence of the covering up of the bottom of the sea by the detritus of the land, the surfaces of equal temperature within the earth are continually changing their form, and exposing thick beds near the exterior to alterations of temperature. The expansion and contraction of these strata may form rents and veins, produce earthquakes, determine volcanic eruptions, elevate continents, and, possibly, raise mountain chains.”

The numerous vents for the internal heat formed by volcanoes, hot springs, and the emission of steam, so frequent in volcanic regions, no doubt maintain the tranquillity of the interior fluid mass, which seems to be perfectly inert unless when put in motion by unequal pressure.

But, to whatever cause the increasing heat of the earth and the subterranean fires may ultimately be referred, it is certain that, except in some local instances, they have no sensible effect on the temperature of its surface. It may therefore be concluded that the heat of the earth, above the zone of uniform temperature, is entirely owing to the sun.

The power of the solar rays depends much upon the manner in which they fall, as we readily perceive from the different climates on our globe. Although the sun is about three millions of miles nearer to the earth in winter than in summer, his rays strike the atmosphere in the northern hemisphere so obliquely that it absorbs a much greater quantity of heat than when they are more direct (N. 217). Indeed it is so great that, when the sun has an altitude of 30°, one half of his heat is absorbed by the atmosphere, and it increases very rapidly as he sinks towards the horizon. However, that heat is not lost: it is most beneficial to the earth, being really the heat which supplies the greatest part of that which is radiated into space during the absence of the sun. Professor Dove has shown, by taking at all seasons the mean of the temperatures of points on the earth’s surface diametrically opposite to each other, that the average temperature of the whole earth’s surface in June, when we are farthest from the sun, considerably exceeds that in December, when we are nearest to him, owing to the excess of water in the southern hemisphere, and that of land in the northern, which gives a general insular climate to the former, and a continental climate to the latter.

The observations of the north polar navigators, and those of Sir John Herschel at the Cape of Good Hope, show that the direct heating influence of the solar rays is greatest at the equator, and that it diminishes gradually as the latitude increases. At the equator the maximum is 48-3/4°, while in Europe it has never exceeded 29-1/2°.

M. Pouillet has estimated with singular ingenuity, from a series of observations made by himself, that the whole quantity of heat which the earth receives annually from the sun is such as would be sufficient to melt a stratum of ice covering the whole globe 46 feet deep. Part of this heat is radiated back into space; but by far the greater part descends into the earth during the summer, towards the zone of uniform temperature, whence it returns to the surface in the course of the winter, and tempers the cold of the ground and the atmosphere in its passage to the ethereal regions, where it is lost, or rather where it combines with the radiation from the other bodies of the universe in maintaining the temperature of space. The sun’s power being greatest between the tropics, the heat sinks deeper there than elsewhere, and the depth gradually diminishes towards the poles; but the heat is also transmitted laterally from the warmer to the colder strata north and south of the equator, and aids in tempering the severity of the polar regions.

The mean heat of the earth, above the stratum of constant temperature, is determined from that of springs; and, if the spring be on elevated ground, the temperature is reduced by computation to what it would be at the level of the sea, assuming that the heat of the soil varies according to the same law as the heat of the atmosphere, which is about 1° of Fahrenheit’s thermometer for every 333·7 feet. From a comparison of the temperature of numerous springs with that of the air, Sir David Brewster concludes that there is a particular line passing nearly through Berlin, at which the temperature of springs and that of the atmosphere coincide; that in approaching the arctic circle the temperature of springs is always higher than that of the air, while, proceeding towards the equator, it is lower.

Since the warmth of the superficial strata of the earth decreases from the equator to the poles, there are many places in both hemispheres where the ground has the same mean temperature. If lines were drawn through all those points in the upper strata of the globe which have the same mean annual temperature, they would be nearly parallel to the equator between the tropics, and would become more and more irregular and sinuous towards the poles. These are called isogeothermal lines. A variety of local circumstances disturb their parallelism, even between the tropics.

The temperature of the ground at the equator is lower on the coasts and islands than in the interior of continents; the warmest part is in the interior of Africa; but it is obviously affected by the nature of the soil, especially if it be volcanic.

Much has been done to ascertain the manner in which heat is distributed over the surface of our planet, and the variations of climate, which, in a general view, mean every change of the atmosphere, such as of temperature, humidity, variations of barometric pressure, purity of air, the serenity of the heavens, the effects of winds, and electric tension. Temperature depends upon the property which all bodies possess, more or less, of perpetually absorbing and emitting or radiating heat. When the interchange is equal, the temperature of a body remains the same; but, when the radiation exceeds the absorption, it becomes colder, and vice versâ. In order to determine the distribution of heat over the surface of the earth, it is necessary to find a standard by which the temperature in different latitudes may be compared. For that purpose it is requisite to ascertain, by experiment, the mean temperature of the day, of the month, and of the year, at as many places as possible throughout the earth. The annual average temperature may be found by adding the mean temperatures of all the months in the year, and dividing the sum by twelve. The average of ten or fifteen years will give it approximately; for, although the temperature in any place maybe subject to very great variations, yet it never deviates more than a few degrees from its mean state, which consequently offers a good standard of comparison. As a standard, however, much greater accuracy is required.

If climate depended solely upon the heat of the sun, all places having the same latitude would have the same mean annual temperature. The motion of the sun in the ecliptic, indeed, occasions perpetual variations in the length of the day, and in the direction of the rays with regard to the earth; yet, as the cause is periodic, the mean annual temperature from the sun’s motion alone must be constant in each parallel of latitude; for it is evident that the accumulation of heat in the long days of summer, which is but little diminished by radiation during the short nights, is balanced by the small quantity of heat received during the short days in winter, and its radiation in the long, frosty, and clear nights. In fact, if the globe were everywhere on a level with the surface of the sea, and of uniform substance, so as to absorb and radiate heat equally, the mean heat of the sun would be regularly distributed over its surface in zones of equal annual temperature parallel to the equator, from which it would decrease to each pole as the square of the cosine of the latitude; and its quantity would only depend upon the altitude of the sun and atmospheric currents. The distribution of heat, however, in the same parallel, is very irregular in all latitudes except between the tropics, where the isothermal lines, or the lines passing through places of equal mean annual temperature, are more nearly parallel to the equator. The causes of disturbance are very numerous; but such as have the greatest influence, according to M. de Humboldt, to whom we are indebted for the greater part of what is known on the subject, are the elevation of the continents, the distribution of land and water over the surface of the globe exposing different absorbing and radiating powers; the variations in the surface of the land, as forests, sandy deserts, verdant plains, rocks, &c.; mountain-chains covered with masses of snow, which diminish the temperature; the reverberation of the sun’s rays in the valleys, which increases it; and the interchange of currents, both of air and water, which mitigates the rigour of climates; the warm currents from the equator softening the severity of the polar frosts, and the cold currents from the poles tempering the intense heat of the equatorial regions. To these may be added cultivation, though its influence extends over but a small portion of the globe, only a fourth part of the land being inhabited.

Temperature decreases with the height above the level of the sea, as well as with the latitude. The air in the higher regions of the atmosphere is much cooler than that below, because the warm air expands as it rises, by which its capacity for heat is increased, a great proportion becomes latent or absorbed, and less of it sensible. A portion of air at the surface of the earth whose temperature is 70° of Fahrenheit, if carried to the height of two miles and a half, would expand so much that its temperature would be reduced 50°; and in the ethereal regions the temperature is 239° below the zero point of Fahrenheit.

The height at which snow lies perpetually decreases from the equator to the poles, and is higher in summer than in winter; but it varies from many circumstances. Snow rarely falls when the cold is intense and the atmosphere dry. Extensive forests produce moisture by their evaporation; and high table-lands, on the contrary, dry and warm the air, because the air at great elevations is too rare to absorb much of the sun’s heat. In the Cordilleras of the Andes, plains of only twenty-five square leagues from their extent raise the temperature as much as 3° or 4° above what is found at the same altitude on the rapid declivity of a mountain, consequently the line of perpetual snow varies according as one or other of these causes prevails. Aspect in general has also a great influence; yet the line of perpetual snow is much higher on the northern than on the southern side of the Himalaya, partly because the air is nearly deprived of its moisture by precipitation before it arrives at the northern side of the mountains. On the whole, it appears that the mean height between the tropics at which the snow lies perpetually is about 15,207 feet above the level of the sea; whereas snow does not cover the ground continually at the level of the ocean till near the north pole. In the southern hemisphere, however, the cold is greater than in the northern. In Sandwich Land, between the 54th and 58th degrees of latitude, perpetual snow and ice extend to the sea-level; and in the island of S. Georgia, in the 53rd degree of south latitude, which corresponds with the latitude of the central counties of England, perpetual snow descends even to the level of the ocean. It has been shown that this excess of cold in the southern hemisphere cannot be attributed to the winter being longer than ours by 7-3/4 days. It is probably owing to the open sea surrounding the south pole, which permits the icebergs to descend to a lower latitude by 10° than they do in the northern hemisphere, on account of the numerous obstructions opposed to them by the islands and continents about the north pole. Icebergs from the Arctic seas seldom float farther to the south than the Azores; whereas those that come from the south pole descend to as low a latitude as that of the Cape of Good Hope.

The influence of mountain-chains does not wholly depend upon the line of perpetual congelation. They attract and condense the vapours floating in the air, and send them down in torrents of rain. They radiate heat into the atmosphere at a lower elevation, and increase the temperature of the valleys by the reflection of the sun’s rays, and by the shelter they afford against prevailing winds. But, on the contrary, one of the most general and powerful causes of cold arising from the vicinity of mountains is the freezing currents of wind which rush from their lofty peaks along the rapid declivities, chilling the surrounding valleys: such is the cutting north wind called the bise in Switzerland.

Next to elevation, the difference in the radiating and absorbing powers of the sea and land has the greatest influence in disturbing the regular distribution of heat. The extent of the dry land is not above the fourth part of that of the ocean; so that the general temperature of the atmosphere, regarded as the result of the partial temperatures of the whole surface of the globe, is most powerfully modified by the sea. Besides, the ocean acts more uniformly on the atmosphere than the diversified surface of the solid mass does, both by the equality of its curvature and its homogeneity. In opaque substances the accumulation of heat is confined to the stratum nearest the surface. The seas become less heated at their surface than the land, because the solar rays, before being extinguished, penetrate the transparent liquid to a greater depth and in greater numbers than in the opaque masses. On the other hand, water has a considerable radiating power, which, together with evaporation, would reduce the surface of the ocean to a very low temperature, if the cold particles did not sink to the bottom on account of their superior density. The seas preserve a considerable portion of the heat they receive in summer, and from their saltness do not freeze so soon as fresh water. So that, in consequence of all these circumstances, the ocean is not subject to such variations of heat as the land, and, by imparting its temperature to the winds and by its currents, it diminishes the rigour of climate on the coasts and in the islands, which are never subject to such extremes of heat and cold as are experienced in the interior of continents, though they are liable to fogs and rain from the evaporation of the adjacent seas. On each side of the equator to the 48th degree of latitude, the surface of the ocean is in general warmer than the air above it. The mean of the difference of the temperature at noon and midnight is about 1°·37, the greatest deviation never exceeding from 0°·36 to 2°·16, which is much cooler than the air over the land.

On land the temperature depends upon the nature of the soil and its products, its habitual moisture or dryness. From the eastern extremity of the Sahara desert quite across Africa, the soil is almost entirely barren sand; and the Sahara desert itself extends over an area of 194,000 square leagues, equal to twice the area of the Mediterranean Sea, and raises the temperature of the air by radiation from 90° to 100°, which must have a most extensive influence. On the contrary, vegetation cools the air by evaporation and the apparent radiation of cold from the leaves of plants, because they absorb more caloric than they give out. The graminiferous plains of South America cover an extent ten times greater than France, occupying no less than about 50,000 square leagues, which is more than the whole chain of the Andes, and all the scattered mountain-groups of Brazil. These, together with the plains of North America and the steppes of Europe and Asia, must have an extensive cooling effect on the atmosphere if it be considered that in calm and serene nights they cause the thermometer to descend 12° or 14°, and that in the meadows and heaths in England the absorption of heat by the grass is sufficient to cause the temperature to sink to the point of congelation during the night for ten months in the year. Forests cool the air also by shading the ground from the rays of the sun, and by evaporation from the boughs. Hales found that the leaves of a single plant of helianthus three feet high exposed nearly forty feet of surface; and, if it be considered that the woody regions of the river Amazons, and the higher part of the Orinoco, occupy an area of 260,000 square leagues, some idea may be formed of the torrents of vapour which rise from the leaves of the forests all over the globe. However, the frigorific effects of their evaporation are counteracted in some measure by the perfect calm which reigns in the tropical wildernesses. The innumerable rivers, lakes, pools, and marshes interspersed through the continents absorb caloric, and cool the air by evaporation; but, on account of the chilled and dense particles sinking to the bottom, deep water diminishes the cold of winter, so long as ice is not formed.

In consequence of the difference in the radiating and absorbing powers of the sea and land, their configuration greatly modifies the distribution of heat over the surface of the globe. Under the equator only one-sixth part of the circumference is land; and the superficial extent of land in the northern and southern hemispheres is in the proportion of three to one. The effect of this unequal division is greater in the temperate than in the torrid zones, for the area of land in the northern temperate zone is to that in the southern as thirteen to one, whereas the proportion of land between the equator and each tropic is as five to four. It is a curious fact, noticed by Mr. Gardner, that only one twenty-seventh part of the land of the globe has land diametrically opposite to it. This disproportionate arrangement of the solid part of the globe has a powerful influence on the temperature of the southern hemisphere. But, besides these greater modifications, the peninsulas, promontories, and capes, running out into the ocean, together with bays and internal seas, all affect temperature. To these may be added the position of continental masses with regard to the cardinal points. All these diversities of land and water influence temperature by the agency of the winds. On this account the temperature is lower on the eastern coasts both of the New and Old World than on the western; for, considering Europe as an island, the general temperature is mild in proportion as the aspect is open to the Atlantic Ocean, the superficial temperature of which, as far north as the 45th and 50th degrees of latitude, does not fall below 48° or 51° of Fahrenheit, even in the middle of winter. On the contrary, the cold of Russia arises from its exposure to the northern and eastern winds. But the European part of that empire has a less rigorous climate than the Asiatic, because it does not extend to so high a latitude.

The interposition of the atmosphere modifies all the effects of the sun’s heat. The earth communicates its temperature so slowly, that M. Arago has occasionally found as much as from 14° to 18° of difference between the heat of the soil and that of the air two or three inches above it.

The circumstances which have been enumerated, and many more, concur in disturbing the regular distribution of heat over the globe, and occasion numberless local irregularities. Nevertheless the mean annual temperature becomes gradually lower from the equator to the poles. But the diminution of mean heat is most rapid between the 40th and 45th degrees of latitude both in Europe and America, which accords perfectly with theory; whence it appears that the variation in the square of the cosine of the latitude (N. 127), which expresses the law of the change of temperature, is a maximum towards the 45th degree of latitude. The mean annual temperature under the equator in America is about 81-1/2° of Fahrenheit: in Africa it is said to be nearly 83°. The difference probably arises from the winds of Siberia and Canada, whose chilly influence is sensibly felt in Asia and America, even within 18° of the equator.

The isothermal lines are nearly parallel to the equator, till about the 22nd degree of latitude on each side of it, where they begin to lose their parallelism, and continue to do so more and more as the latitude augments. With regard to the northern hemisphere, the isothermal line of 59° of Fahrenheit passes between Rome and Florence in latitude 43°; and near Raleigh in North Carolina, latitude 36°: that of 50° of equal annual temperature runs through the Netherlands, latitude 51°; and near Boston in the United States, latitude 42-1/2°: that of 41° passes near Stockholm, latitude 59-1/2°; and St. George’s Bay, Newfoundland, latitude 48°: and lastly, the line of 32°, the freezing point of water, passes between Ulea in Lapland, latitude 66°, and Table Bay, on the coast of Labrador, latitude 54°.

Thus it appears that the isothermal lines, which are nearly parallel to the equator for about 22°, afterwards deviate more and more. From observations made during the numerous voyages in the Arctic Seas, it is found that the isothermal lines of Europe and America entirely separate in the high latitudes, and surround two poles of maximum cold: one, in 79° N. lat. and 120° E. long., has a mean temperature of 2° Fahrenheit; and the other, whose temperature was determined by Sir David Brewster to be 3-1/2° Fahrenheit, from the observations of Sir Edward Parry is near Melville Island. The pole of the earth’s rotation, whose mean temperature is probably not below 15° Fahrenheit, is nearly midway between the two; and the line which joins these points of maximum cold is almost coincident with that diameter of the polar basin which bisects it, and passes through its two great outlets into the Pacific and Atlantic Oceans, a most remarkable feature, and strongly indicative of the absence of land, and of the prevalence of a materially milder climate in the polar Ocean, probably not under 15° Fahrenheit.[12] It is believed that two corresponding poles of maximum cold exist in the southern hemisphere, though observations are wanting to trace the course of the southern isothermal lines with the same accuracy as the northern.

The isothermal lines, or such as pass through places where the mean annual temperature of the air is the same, do not always coincide with the isogeothermal lines, which are those passing through places where the mean temperature of the ground is the same. Sir David Brewster, in discussing this subject, finds that the isogeothermal lines are always parallel to the isothermal lines; consequently the same general formula will serve to determine both, since the difference is a constant quantity obtained by observation, and depending upon the distance of the place from the neutral isothermal line. These results are confirmed by the observations of M. Kupffer of Kasan during his excursions to the north, which show that the European and the American portions of the isogeothermal line of 32° of Fahrenheit actually separate, and go round the two poles of maximum cold. This traveller remarked, also, that the temperature both of the air and of the soil decreases most rapidly towards the 45th degree of latitude.

It is evident that places may have the same mean annual temperature, and yet differ materially in climate. In one, the winters may be mild and the summers cool; whereas another may experience the extremes of heat and cold. Lines passing through places having the same mean summer or winter temperature are neither parallel to the isothermal, the geothermal lines, nor to one another, and they differ still more from the parallels of latitude. In Europe, the latitude of two places which have the same annual heat never differs more than 8° or 9°; whereas the difference in the latitude of those having the same mean winter temperature is sometimes as much as 18° or 19°. At Kasan, in the interior of Russia, in latitude 55°·48, nearly the same with that of Edinburgh, the mean annual temperature is about 37°·6; at Edinburgh it is 47°·84. At Kasan the mean summer temperature is 64°·84, and that of winter 2°·12; whereas at Edinburgh the mean summer temperature is 58°·28, and that of winter 38°·66. Whence it appears that the difference of winter temperature is much greater than that of summer. At Quebec the summers are as warm as those in Paris, and grapes sometimes ripen in the open air: whereas the winters are as severe as in Petersburgh; the snow lies five feet deep for several months, wheel carriages cannot be used, the ice is too hard for skating, travelling is performed in sledges, and frequently on the ice of the river St. Lawrence. The cold at Melville Island on the 15th of January, 1820, according to Sir Edward Parry, was 55° below the zero of Fahrenheit’s thermometer; and when Dr. Kane was on the northern coast of Greenland it was 70° below that point; yet the summer heat during the day in these high latitudes is insupportable.

Observations tend to prove that all the climates of the earth are stable, and that their vicissitudes are only periods or oscillations of more or less extent, which vanish in the mean annual temperature of a sufficient number of years. This constancy of the mean annual temperature of the different places on the surface of the globe shows that the same quantity of heat which is annually received by the earth is annually radiated into space; and that would be the case even if the quantity of heat emitted by the sun should vary with his spots, for, if more were received, more would be radiated. Nevertheless, a variety of causes may disturb the climate of a place; cultivation may make it warmer; but it is at the expense of some other place, which becomes colder in the same proportion. There may be a succession of cold summers and mild winters, but in some other country the contrary takes place to effect the compensation; wind, rain, snow, fog, and the other meteoric phenomena, are the ministers employed to accomplish the changes. The distribution of heat may vary with a variety of circumstances; but the absolute quantity lost and gained by the whole earth in the course of a year, if not invariably the same, is at least periodical.

SECTION XXVI.

Influence of Temperature on Vegetation—Vegetation varies with the Latitude and Height above the Sea—Geographical Distribution of Land Plants—Distribution of Marine Plants—Corallines, Shell-fish, Reptiles, Insects, Birds, and Quadrupeds—Varieties of Mankind, yet identity of Species.

THE gradual decrease of temperature in the air and in the earth, from the equator to the poles, is clearly indicated by its influence on vegetation. In the valleys of the torrid zone, where the mean annual temperature is very high, and where there is abundance of light and moisture, nature adorns the soil with all the luxuriance of perpetual summer. The palm, the bombax ceiba, and a variety of magnificent trees, tower to the height of 150 or 200 feet above the banana, the bamboo, the arborescent fern, and numberless other tropical productions, so interlaced by creeping and parasitical plants, as often to present an impenetrable barrier. But the richness of vegetation gradually diminishes with the temperature; the splendour of the tropical forest is succeeded by the regions of the vine and olive; these again yield to the verdant meadows of more temperate climes; then follow the birch and the pine, which probably owe their existence in very high latitudes more to the warmth of the soil than to that of the air. But even these enduring plants become dwarfish shrubs, till a verdant carpet of mosses and lichens, enamelled with flowers, exhibits the last sign of vegetable life during the short but fervid summers at the polar regions. Such is the effect of cold and diminished light on the vegetable kingdom, that the number of species growing under the equator and in the northern latitudes of 45° and 68° are in the proportion of the numbers 12, 4, and 1. Notwithstanding the remarkable difference between a tropical and polar flora, light and moisture seem to be almost the only requisites for vegetation, since neither heat, cold, nor even comparative darkness, absolutely destroy the fertility of nature. In salt plains and sandy deserts alone hopeless barrenness prevails. Plants grow on the borders of hot springs: they form the oases wherever moisture exists among the burning sands of Africa; they are found in caverns almost void of light, though generally blanched and feeble. The ocean teems with vegetation. The snow itself not only produces a red lichen, discovered by Saussure in the frozen declivities of the Alps, found in abundance by the author crossing the Col de Bonhomme from Savoy to Piedmont, and by the polar navigators in the Arctic regions, but it affords shelter to the productions of these inhospitable climes against the piercing winds that sweep over fields of everlasting ice. Those undaunted mariners narrate that under this cold defence plants spring up, dissolve the snow a few inches round, and the part above, being again quickly frozen into a transparent sheet of ice, admits the sun’s rays, which warm and cherish the plants in this natural hothouse, till the returning summer renders such protection unnecessary.

The chemical action of light is, however, absolutely requisite for the growth of plants which derive their principal nourishment from the atmosphere. They consume the carbonic acid gas, nitrogen, aqueous vapour, and ammonia it contains; but it is the chemical agency of light that enables them to absorb, decompose, and consolidate these substances into wood, leaves, flowers, and fruit. The atmosphere would soon be deprived of these elements of vegetable life were they not perpetually supplied by the animal creation; while, in return, plants decompose the moisture they imbibe, and, having assimilated the carbonic acid gas, they exhale oxygen for the maintenance of the animated creation, and thus preserve a just equilibrium. Hence it is the combined and powerful influences of the whole solar beams that give such brilliancy to the tropical forests, while, with their decreasing energy in the higher latitudes, vegetation becomes less vigorous. On that account it is vain to expect that the fruit and flowers raised in our hothouses can ever have the flavour, perfume, or colouring equal to that which they acquire from the vivid light of their native skies.

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