The elements of astronomy

Preface

The apology for the present treatise on Astronomy is based on the nature of the subject ; it is one which requires to be presented to the student from more than one point of view. He should learn from the original observer, the profound generalizer, the investigator of cause and effect in detail ; and to prepare him for such studies, he needs the book of one who knows from experience his requirements and his capacity.

As such a book, " The Elements of Astronomy, or the World as it is, and as it appears," is offered by a teacher to the teaching and studying public. Had the writer aimed only to excite an interest in the subject, it would have been shorter and more attractive ; but it is intended, likewise, to exercise the student's memory, reason, and imagination. The details introduced for this purpose serve also to keep each truth before the mind some time ; they present it in different lights, and secure its being perceived by each pupil fully and in all its bearings.

IV PREFACE.

This book has gradually grown out of lessons given orally during many years of teaching. These were written out for the author's own use, not for publication. Originality was not sought for, and all explanations and illustrations which could be of service to the pupils were adopted. As time passed on, and no book appeared precisely suited to the wants of these pupils, or of High Schools in general, the author began to entertain the idea that these lessons might in some measure supply the want so extensively felt. In this hope such completeness has been given to the work as a very limited leisure would allow. It has been revised in manuscript by George P. Bond, Esq., of the Cambridge Observatory, to whom the author is also indebted for superintending its passage through the press.

Boston, 1850.

Contents

Page.

Chapter I. — Definitions. The Sphere. Spherical Distances and Angles. The Spheroid. Earth's Axis and Equator. Terrestrial Latitude and Longitude. The Sphere of the Heavens, Zenith and Horizon. Celestial Pole and Equator. The Ecliptic. The Zodiac. Right Ascension and Declination. Celestial Longitude and Latitude. Parallax. Terms defining the Orbit of a Planet. Sidereal and Apparent Time. 13

Chapter II. — Light and the Telescope. Nature and properties of Light. Velocity of Light. Transmission and Reflection. Lenses, and the Refracting Telescope. Magnifying Power. Fields of View. Distinction between the different powers of a Telescope. Reflecting Telescope. Achromatic Telescope. 25

Chapter II. Light And The Telescope

Nature and properties of Light. Velocity of Light. Transmission and; Reflection. Lenses, and the Refracting Telescope. Magnifying Power. Fields of View. Distinction between the different powers of a Telescope. Reflecting Telescope. Achromatic Telescope.

§ 29. Philosophers are not agreed about the nature of light. Some maintain that it is an emanation from luminous bodies ; others suppose it to be produced like sound, bj the undulations of a subtile fluid diffused throughout space. Many facts favor this last theory. Bays of light cross in every direction without interfering ;. and we can suppose this more easily of waves than of actual particles. If light is a substance, what becomes of it ? where is all that has been emitted since the beginning of the world ? If it is merely a motion of particles, it may cease like any other motion. As the undulatory theory has much in its favor, we shall adopt it and consider light as that vibration of an unknown fluid which causes to our eye the sensation of sight. We cannot attain perfect certainty as to the nature of light, but we can learn its laws, and reason concerning them without this certainty.

§ 30. Bodies are divided into luminous and non-luminous. All light comes originally from some self-luminous body. It is emitted from every point of such a body, and in every direction in which the point is visible. A ray is a single line of light ; a pencil of rays is a collection proceeding from any one point of such a body. These rays move through a uniform medium in straight lines, entirely independent one of another. We know that rays move in straight lines, for no opaque body can screen a luminous point from us unless interposed in a straight line between us and it. Light moves with a velocity of 192,500 miles in a second. It travels from the sun to the earth in eight minutes ; a distance which the earth, moving nineteen miles a second, will take two months to pass through. 3

It moves through a space equal to the circumference of our globe in the eighth part of a second, a flight which the swiftest bird could not perform in less than three weeks. Light diminishes in intensity according to the squares of the distance. At a certain distance let it be diffused over a certain space and have a certain intensity, at twice the distance it is diffused over four times the space, and has but one fourth the intensity.

§ 31. Luminous bodies, probably from being themselves in agitation, cause vibrations in some medium which excites our optic nerve, and makes us conscious of the object at which the vibration began. Hearing, which seems to be a coarser sense, is excited in the same manner. But we know that the air, wood, ice, rock, or almost any substance, may serve as a medium for the vibrations which affect the auditory nerve. While we cannot detect the medium which transmits vibrations to the optic nerve, as the transmission is so much more rapid than in case of sounds, and as we see to far greater distances than we hear, we cannot but feel it probable that the medium is more thin and subtile, and that no other can be substituted for it. This medium must extend to the stars, otherwise no vibrations from them could reach us ; it must exist in interstices of transparent bodies, such as air, water, and glass. Other facts also make it probable that regions beyond our earth are occupied by a thin ether. The comets, whose frequent returns enable us to calculate their periodic times, seem to be drawn nearer and nearer to the sun, their times are diminishing. If so, they must meet some resistance which gradually diminishes their projectile power, and this resistance must come from an invisible thin fluid. A fluid too thin to act sensibly upon the planets, but dense enough to derange the lighter comets, and to transmit light.

§ 32. Non-luminous bodies are either opaque or transparent. When light falls on an opaque body, a part of it is reflected, a part enters the body and is lost. When the body is transparent, the greater part is transmitted, and but little is reflected. Both reflection and transmission follow particular laws, which must be understood previous to studying astronomy.

Bodies are referred to the direction from which the ray by which we see them comes to our eyes. We cannot know, except by reasoning, what changes this direction may have undergone.

§ 33. Reflected light serves as well as original light to show us the direction of bodies. We see the moon, and the clouds, we see objects around us by light which may have been many times reflected. Reflected light is however weak, because a great portion of that which falls on bodies is usually absorbed. There is one condition necessary to our seeing a body by reflected light. The angle by which the light passes to us is always equal to that by which it strikes upon the reflecting body. The angle of reflection is equal to the angle of incidence. We must, therefore, be in such a position that the ray reflected at this angle shall enter our eye, or we shall not see the body.

§ 34. When light passes obliquely from a medium to one more dense, it is bent at the surface of the denser medium into a line more nearly approaching a perpendicular. It passes without bending through the medium, and if it again passes into the thinner medium, it is turned away from the perpendicular by an angle equal to that at which it entered. The more obliquely it enters the more it is turned aside ; the sine of the angle of incidence always bears the same ratio to the sine of the angle of refraction, when the same media are compared. When light passes perpendicularly from one medium to another, it suffers no refraction.

By interposing between the eye and the object a material of higher refractive power than air, and making it of such a form that the refraction at one or both surfaces shall bring the rays to a focus behind it, we bring the image of the object nearer to the eye, and thus increase its apparent size, brightness, and rapidity of motion.

§ 35. The material used for the lenses of telescopes is glass. The lenses used are chiefly the plano-convex, the double convex and the double concave. Lenses of the same material converge the rays in proportion to the convexity of their form. A small portion of a large sphere refracts to a longer focus than a large portion of a small sphere.

The simplest telescope consists of a plano-convex lens, whose focal length exceeds six inches, placed at one end of a tube whose length must be six inches greater than the focal length of the lens. Six inches being the distance at which an eye sees small objects with ease. An eye placed at the other end of the tube will see an inverted image of distant objects magnified in proportion to the focal length of the lens. If the lens has a focal length of from ten to twelve feet, the magnifying power will be from twenty to twenty- four ; to a very shortsighted person, who sees objects distinctly at three inches, the magnifying power would be from forty to forty-eight.

§ 36. It is well known that the same object brought nearer to the eye subtends a larger angle, and therefore appears larger than when more distant. It is also true that a small body, very near, subtends a larger angle, and therefore appears larger than a distant object of greater size.

Let us examine the effects of placing convex lenses at different distances between the eye and an object. We will suppose a man to be 100 feet from the eye. We will place a convex glass of twenty-five feet focal distance half way between the man and the eye. The inverted image of the man will be formed fifty feet behind the lens, of the same size as the object. This image can be seen by the eye placed six inches behind it with great distinctness, and nearly as well as if the man had been brought from the distance of 100 feet to six inches. Thus the man, though seen no larger than life, would be apparently magnified, because his apparent magnitude would be increased in the proportion of 100 feet to six inches. If a lens of shorter focus be placed between them in such a way that the man is twenty feet before the lens, and his image eighty feet behind it, the size of the image would be four times that of the object. The man would be magnified four times directly by the lens, and 200 times by being brought nearer to the eye ; in the whole 800 times.

§ 37. When the focal length of the lens is quite inconsiderable compared with the distance of the object, as it is in viewing the heavenly bodies, the rule becomes this :— -

Divide the focal length of the lens by the distance at which the eye looks at the image. If we use a lens with a focal distance of ten feet, on account of the sun's being 95,000,000 miles distant, the image of the sun formed in the focus will be only ~^ ^miiea °^ ^e true s ^ ze °f tne sun's disc. But this image is viewed at a distance of six inches instead of 95,000,000, therefore it is magnified ^ZToT^T (=20 times.

95,000,000 miles X 6 inches. J

§ 38. A lens placed in a telescope as we have described it, is called an object glass. It bestows on a telescope the power of bringing the image near, which is evidently the same thing as transporting the observer to the distant regions of space. But there is another way of increasing the apparent magnitude of objects, particularly of those which are within our reach, which is of great importance in optics. Rays from each point of a distant object enter the eye in parallel lines, and the object is distinctly seen. If we bring an object very near, so as to give it great apparent magnitude, it becomes indistinct ; because the rays diverge from each point so much that the eye cannot bring them to a focus. But if we can make the rays from it enter the eye nearly parallel, it will be distinctly seen. Since parallel rays are brought to a focus by a lens, if we place an object or its image in the focus of the lens, the rays will come out from it parallel. We shall see the object very distinctly, and it will be magnified in the proportion of six inches, at which we see small objects most distinctly, to its present short distance from the eye. But this short distance is equal to the focal length of the lens, so that the magnifying power produced by the lens is equal to six inches divided by the focal length of the lens.

Such a lens is called the eyepiece of the telescope. These two lenses together constitute a simple form of the astronomical refracting telescope.

§ 39. Let us consider the effect of each of these

glasses upon the apparent motion and brightness of objects

seen through them. Distant motions appear slow, because

the space passed through subtends so small an angle at the

3* eye. The moon wheels round the earth 2,000 miles an hour ; yet owing to her distance from it her motion is not visible to the naked eye. The same space described by two objects, one a hundred times more distant than the other, would seem a hundred times smaller in the former case than in the latter. The object-glass, since it brings objects nearer, must therefore increase their apparent motion in the same ratio.

§ 40. A very rapid motion may be imperceptible, if the distance of the moving body be sufficiently great. For, the greater the distance, the smaller the angle under which the motion appears to the eye ; and if the arc which a body describes in an hour does not subtend an angle of more than 20°, its motion is imperceptible. The greatest apparent motion in the heavens does not exceed 15° in an hour, being that produced by the rotation of the earth. The greatest central motion is that of the moon and does not exceed about 13° a day.

The apparent motion of heavenly bodies caused by the rotation of the earth is magnified by the object glass. The field of view appearing larger than it really is, bodies appear to pass through it in the same time more swiftly than they would to the naked eye.

The eye piece also increases apparent motion in proportion to its power of magnifying. As in the solar microscope where the motions of animalcules appear prodigiously swift.

Since the object and the eye glasses affect motion similarly, we shall in the following calculations consider not the power of each separately, but the whole power of the telescope.

§ 41. Let a person direct the tubes of a telescope (without the lenses) to any celestial object, and there fix them ; he will soon find that in a short space of time the object will have removed from before the mouth of the tube. Now this motion of the celestial bodies, which is only apparent, arises from the rotation of the earth upon her axis ; and the quantity of this motion may be determined with facility thus : the earth is known to revolve once about her axis in twenty-four hours, and as every circle is supposed to be divided into 360 equal parts or degrees, the apparent time any celestial body takes to describe one degree will be found by dividing the 24 hours by 360, which gives us four minutes as the time an object in the celestial equator would take to pass the mouth of the tube if it only takes in one degree of the heavens.

In ordinary telescopes the field of view is about half a degree, and an equatorial star will cross it in two minutes. The moon's diameter is 30', it will therefore fill the field of such a telescope, and the whole moon, from the time one edge enters till the other leaves, will require four minutes. If now we suppose the glasses to be put in the tube, the magnifying power will cause all bodies nearer than the fixed stars to look larger, and to appear to move faster, but the size of the tube remaining the same, no larger portion of the heavens from side to side can be seen through it than before. On the contrary, as a general rule, the higher the magnifying power the smaller are the linear dimensions of the field of view, while the apparent diameter and motion of objects is increased.

§ 42. For convenience of calculation the linear dimensions have been used. But in truth when a surface is magnified it is so in all directions, and the increase of surface will be according to the square of the linear increase. Thus when the moon is brought by the telescope ten times nearer, its disc is one hundred times increased, and the area of the field of view one hundred times diminished. In the case of the fixed stars, while the telescope increases their brilliancy, no magnifying power that has yet been applied has shown their true discs, owing to their immense distance from us.

§ 43. There are three modes in use among astronomers of designating the capacity of a telescope. The first is by its illuminating power, which is proportioned to the area of its object glass ; the second by its magnifying power, which may be increased to any extent by changing the lenses of the eye pieces ; and the third is by its space-penetrating power, by which is meant such a relation between the illuminating and the magnifying powers that the object viewed shall appear with its natural brightness.

That is, of the brightness with which the object would appear to the naked eye were the observer transported to a point as many times nearer to the object as the magnifying power employed is greater than unity.

In all cases the space-penetrating power of a telescope is limited by the area of its object glass, or of its speculum, if it be a reflector.

§ 44. On account of the difficulty of obtaining large lenses of a sufficiently pure material, a concave mirror is sometimes used instead of an object glass. The telescope is then called a reflector, as the rays of light are brought to a focus by reflection from the polished surface of the speculum. Large reflecting telescopes are not so well adapted to delicate observations and measurements as to discoveries in physical astronomy, the resolution of nebulae, and the examination of extremely faint objects. Those of Herschel and Lord Rosse are the most celebrated. In Herschel's forty foot reflector the observer turns his back to the object and looks in at the mouth of the telescope tube, near to the edge of which the image is thrown by a slight inclination of the mirror. Lord Rosse's telescope has a speculum of six feet diameter and a tube of sixty feet.

§ 45. There is a difficulty both in convex lenses and concave mirrors arising from their shape, called spherical aberration. The rays from the central part of the lens or mirror are brought to a focus later than those from the edges and the rest of the surface. Spherical aberration causes indistinctness of vision by spreading out every mathematical point of the object into a small spot in its picture ; these spots by mixing with each other confuse the whole.

It is avoided in mirrors by making the surface not spherical, but of the shape formed by the revolution of a parabolic curre. The rays reflected from the edges of the mirror are, on account of the form of the surface, brought to a focus as soon as those from the central portion. It is destroyed in refracting telescopes by combining a meniscus with a double convex lens, or by giving certain proportions to the figure of a single lens.

§ 46. Rays from each point of the object spread over the whole lens and should be refracted to a point ; but if refraction is unequal in different parts of the lens, rajs from a point cannot be converged to a point, but either the more or the less converging will be spread out.

There is also a difficulty in refracting telescopes, owing to the differing refractions of the different colored rays. Violet rays, being the most refrangible, come to a focus sooner than those of any other color. Red rays, being less so, will have a longer focus. Any image formed in the focus of violet rays will be violet colored, and images may be formed between this and the focus of red rays of each color of the spectrum. Therefore no white image can be formed, for there is no one spot in which all the colored rays will be present.

§ 47. If the dispersive powers of different media were in proportion to their refractive powers, it would be impossible to correct this chromatic aberration. But fortunately different media produce spectra of different lengths when the mean refraction is the same. Let us compare two prisms, one of crown glass, the other of flint glass, with such a refracting angle that the light shall enter and quit them at equal angles, the mean ray of each will have the same refraction. But the spectrum produced by the flint glass will be longer than that produced by the crown prism. Thus flint glass is said to have a greater dispersive power than crown glass, because at the same angle of mean refraction it separates farther the extreme rays of the spectrum. Diamond has a refraction nearly three times that of glass, while its dispersive power is less than that of glass.

§ 48, ~Now if different media produce different bands of color with the same focal length, it follows that they may produce equal bands of color with different focal lengths. A concave lens may be used with a convex lens of equal dispersive power, but a higher refractive power, and the excess of the refractive power, will be the available power of the lens, and white light will be refracted to the focus. Such a lens is called an achromatic lens, and. the image formed by it would be perfect were there not in equal spectra formed by different media a difference which prevents their entirely neutralising one another's refraction. The bands of the same color in the two spectra are not of equal breadth, and therefore the images seen through such a lens are bordered on one side with a purple, on the other with a green fringe.

A telescope which is free from dispersion is called achromatic ; one which is free from aberration also is called aplanatic, or free from all errors.

Reflecting telescopes are perfectly free from color. For compound light is reflected, though not refracted, entire, all the colors following the same law of equal angles of incidence and reflection.

Chapter III. Astronomical Instruments

Difficulties in the construction of Telescopes. Telescope Stands. Transit Instrument. Graduated Circle and Vernier. Mural Circle. Polar and Horizontal Point. Transit Circle. The Equatorial. The Altitude and Azimuth Instrument. Theodolite. Sextant. Difficulties in Observing. Personal Equation. Lord Rosse's Reflectors.

§ 49. Though the theory of the construction of telescopes is attended with many difficulties, those which occur in practice are as numerous, perhaps some of them are insuperable. For a reflector, a perfectly uniform metal is required, free from all microscopic pores, not liable to tarnish, not so hard as to be incapable of taking a good figure and an exquisite polish, not so soft as to be easily scratched. Various compositions of metals are employed, consisting chiefly of copper and tin, with a little zinc, arsenic or silver. After casting they must be ground and polished with the utmost care. Lenses also require the greatest nicety in composition, casting, grinding, polishing, and centering. To ascertain if the shape is perfect, an opaque back is placed behind the lens, the lens is made to revolve, and a lighted candle is brought before it, whose reflected image is attentively watched. If this image has any motion, the lens is not perfect in its adjustment.

§ 50. After an instrument is completed the next desideratum is a steady and immovable stand, free from vibration. The instrument should be supported at both ends to give steadiness, and to prevent its being aifected by the wind ; for every vibration will be increased in the same ratio as the amplification of the instrument, and produce a tremulous or dancing motion in the objects. Thus a superior telescope badly supported may be inferior to a common one on an immovable stand.

The materials of which stands are composed should be capable of transmitting as little vibration as possible ; the vibration of a frame of cast iron in one piece, though otherwise perfectly steady, would be sufficient to destroy distinct vision. The difficulty of preventing vibrations in reflecting telescopes greatly impairs their value, as they are more affected by such disturbance than refractors. A telescope, which taken from its stand and placed on a lump of soft clay would enable a person to read a bill placed at a distance of 900 feet, would on its stand make it distinct only at a distance of 650 feet, although no tremor would be discerned on the stand.

§51. A difficulty in placing an instrument arises from the absence of natural indications, other than those afforded by astronomical observations themselves, whether an instrument has or has not its true position with respect to the horizon and its cardinal points, the axis of the earth, or to other principal astronomical lines and circles. For instance, to place a transit instrument correctly, we must know the direction of our meridian, but we must first learn this meridian approximately by observing the shadow cast by the sun at noon.

The transit instrument consists of an astronomical telescope with wires and a micrometer, and is mounted on a nicely formed axis at right angles to itself. This axis remaining always horizontal and directed to the east and west points of the horizon rests at its extremities in two sockets perfectly even, and set in two blocks of stone of a size and weight sufficient to prevent all agitation. The smooth extremities of the axis are capable of nice adjustment by screws, both in a vertical and horizontal direction. By placing a spirit level on the points, the axis can be made perfectly horizontal. Whether the axis lies precisely east and west can only be nicely ascertained by observations made with the instrument itself. When it is perfectly well adjusted the central line of the telescope will not quit the plane of the meridian when the instrument is turned round on its axis. The transit instrument is used to note the passage of bodies over the meridian, to note the right ascension of the fixed stars, the upper and lower culminations of the circumpolar stars, and for various problems in time and longitude.

§ 52. In the focus of the eye-piece and at right angles to the length of the telescope is placed the system of wires. This consists of one horizontal and five equidistant vertical threads or wires, which always appear in the field of view when properly illuminated, by day by the light of the sky, by night by that of a lamp. The horizontal wire is fixed, the middle vertical wire is brought to bisect the axis of the telescope, and thus to coincide with and represent that portion of the celestial meridian which appears in the field of view. When a star crosses this wire it culminates, or passes the celestial meridian. The instant of this event is noted by a clock or chronometer, an indispensable accompaniment of the transit instrument. For greater precision, the moment of crossing each of the five or seven vertical threads is noted and a mean taken between the times thus obtained, the threads being equidistant ; this tends to subdivide and destroy the errors.

An important observation of its correctness consists in reversing the ends of the axis, or turning it east for west. If this be done, and it gives the same results, we may be sure that the line of collimation of the telescope is at right angles to its axis, and marks out in the heavens a great circle.

§ 53. To measure any small angular distance with a micrometer, as the diameter of a planet, two parallel wires are made to approach to or recede from each other till the body to be measured is exactly inclosed by them. Having accurately measured the planet by the two cross

The wires are moved by screws. The very slow motion which may be imparted to the end of a screw by a very considerable motion in the power, makes it very useful •in the measurement of minute motions and spaces. Suppose a screw cut so as to have fifty threads in an inch> each revolution of the screw will advance its point through the fiftieth part of an inch. Now suppose the head of the screw to be a circle whose diameter is one inch, the circumference of the head will be 3.14 inches. This may easily be divided into a hundred equal parts distinctly visible. If a fixed index be presented to this graduated circumference, the hundredth part of a revolution of the screw may be observed by noting the passage of one division of the head under the index. Since one entire revolution of the head moves the point through the fiftieth of an inch, one division will correspond to the five thousandth part of an inch.