Popular physical astronomy; or, An exposition of remarkable celestial phenomena

Front matter

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Preface

An extensive department of human knowledge has been laid open in modern times by a study of the forces which pervade nature, and the operations which proceed from their action. It has been found that celestial arrangements depend on the causes which prevail on our planet, and that our experience with terrestrial objects is sufficient to bring us into communion with the most remote parts of the creation. From their conformity to simple and determinate laws, the phenomena of the Heavens are rendered intelligible to the limited powers of the human mind, and we are thus enabled to realize the greatest advantages from the revelations of the telescope, and from the several facts which science has placed at our disposal.

Since the time of Sir I. Xewton, the labors of astronomers and mathematicians have been spent more in perfecting the work which he commenced than in opening new fields of inquiry. The science of Physical Astronomy has been much embarrassed and rendered more inaccessible by the great minuteness which Laplace and other writers have endeavored to attain, and by their superfluous use of mathematical formulas. As it has not been enriched to a corresponding degree by discoveries, it has become less inviting even to the most highly educated minds, and its study is almost exclusively confined to the universities of Europe, where a few favored individuals are permitted to devote to it the amount of time and attention which so difficult and scientific a pursuit demands. The popular sketches of Physical Astronomy sometimes introduced into works are too superficial to be of much value.

It has been the object of the author to render this department of Astronomy more acceptable to the general

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IV PREFACE.

reader by pursuing a plan somewhat different from any hitherto attempted. He has endeavored to make each subject more intelligible by the use of proofs and illustrations more intimately connected with common experience, and he hopes that his contribution to the science will render it more calculated to repay the labor of the student. The greater part of the original views which he introduces have been already laid before scientific men, and have been received with as much interest and favor as new developments in science generally command. The theory of planetary rings, and the stability of satellites, given in the fourth and fifth chapters, were made the subject of a paper read at the American Scientific Convention for 1856, and published in the proceedings, page 111. The theories of the effects of tidal action, and of the origin of solar light, were presented to the British Association for the Advancement of Science during the past year. The greater part of the chapter on variable stars and the sun's spots, was published in the Philosophical Magazine for May, 1858. He hopes, therefore, that the misrepresentations which his views have received from a few public journals will not deter the reader from giving an impartial examination to the original portions of the present work.

The subjects treated of in the following pages have much engaged the author's attention during many years, and he accordingly feels more confidence in offering them to the public. But he cannot expect to present them in so acceptable a form as might be desirable, as the preparation of the work occupied only a very inadequate time, and was undertaken under very unfavorable circumstances. It is to be hoped, however, that a want of literary merit will not detract much from its scientific value, and that a reasonable indulgence will be given for any defects which it may contain.

P P U I A E

PHYSICAL ASTRONOMY

THE INFLUENCE OF MAGNITUDE ON STABILITY.

The great diversity of size in natural objects becomes a source of admiration to all who first direct their attention to the study of the material world. The minute animalcule, sporting with myriads of its fellow beings in a drop of water, presents a singular contrast with the whale or the elephant ; and these animals in turn appear equally insignificant when compared with the globe on which we dwell, or the mighty sun which controls its destiny. By the revelations of the microscope, telescopic wonders are rendered more overpowering to the imagination ; and the panorama of suns and worlds which meets the eye of the astronomer receives a great accession of grandeur from the knowledge that a drop of water or a single leaf may be a world in itself. On examining the works of Nature, from the largest to the smallest scale of being, and discovering the great variety which prevails through her extensive realms, it becomes an object of interest to the reflective mind to ascertain the several conditions on which these manifold forms of existence depend.

The present inquiry shall be devoted to a consideration of physical stability, without which the harmonious career of nature could not be maintained. All material forms, though perishable in their character, have generally assigned to them a term of existence corresponding to the purposes they are called to fulfill, and each enjoys a degree of security in some measure proportionate to its importance, or to the part it serves in the

6 THE INFLUENCE OF MAGNITUDE

economy of creation. The trembling leaf soon falls a victim to the fury of the storm, but our globe is capable of contending successfully with all the destructive agencies to which it can be exposed during many millions of years. Its rapid march through space cannot introduce disorder among its parts, nor can the great heat which appears to prevail in the subterranean regions ever extend its desolating energy at one time over any considerable portion of our habitable lands. The investigations of Lagrange and Laplace have shown ths.t the mutual disturbances between the several planets cannot cause any derangement of our solar system, and our apprehensions in regard to external dangers must vanish when we consider the immense distance that separates us from the dominion of other suns. During less enlightened ages, comets have too frequently spread dismay among mankind, but there seems to be little ground for such apprehensions, for so wide is the planetary domain that many myriads of these celestial wanderers mayfly through it without any serious danger of striking our terrestrial sphere or any other member of the solar family.

The mind which would embark in the investigation of the causes that uphold so many suns and worlds, must first be provided with a store of facts and principles derived from the observation of the course of nature around us. It may be also advisable to make the study of the works of art a standing point of our inquiries, for man's achievements, though far inferior to those of nature, are much better understood, and involve principles which lie more within the range of human comprehension. Believing that the knowledge which has enabled the architect to adorn the Earth with so many monuments of his skill may not be unprofitable to the student of the architecture of the Heavens, I shall begin with the consideration of a subject which is generally regarded as entirely foreign to this department of physical science.

The degree of firmness or solidity which it is possible to impart to all artificial structures depends not only on the skill of the artisan, but also on the passive strength of the materials placed at his disposal. In consequence of the cohesion and the elasticity of their particles, solid bodies are enabled to with-

ON STABILITY. 7

stand, to a certain extent, all the strains to which they are subjected, and man is thus furnished with the means for constructing his most imposing works. Of the various materials called into requisition by art, iron occupies the most prominent place in respect to passive strength. A tun weight might be suspended by an iron wire not more than one-fifth of an inch in diameter ; and a similar wire, if quite free from defects, would be capable of supporting about seven miles of its own length without being torn asunder. When bars of the same metal are exposed to transverse or lateral strains, their strength is exhibited in a much less degree, and it is proportional to their breadth multiplied by the square of the depth and divided by their length.

A bar of cast iron, five feet long and one inch square, would be capable of bearing only about five hundred pounds, if supported at both ends and loaded at the middle point. By doubling the length, the breadth and the depth of the bar, we should give it four times the strength and eight times the weight it previously possessed ; and it may be shown that in similar solids the resistance to fracture is proportional to the square of any of the linear dimensions, while their own weight is proportional to the cube of the same quantities. A beam of iron, 500 feet long and 100 inches square, with its ends resting on two supports, would be inevitably broken by its own weight, which must exceed 8,000 tons. From this we may infer the impossibility of extending the size of structures beyond a certain limit; and it appears that those of enormous magnitude suffer most from the pressure and the inertia of their own parts. The most lofty buildings are the most certain victims to the violence of an earthquake ; the tallest trees are the first to yield to the rage of the tempest ; and, though a small boat may strike a rock with impunity, a similar collision would consign the majestic ship to inevitable ruin.

In the animal frame, where such complicated movements are inseparable from existence, undue size operates to the greatest disadvantage. Whatever be the source of vital power or the, intensity which it is capable of attaining, there must be a limit to its efficiency, in consequence of the fragility of the solid

8 THE INFLUENCE OF MAGNITUDE

frame-work of the system when strained beyond a certain degree ; and the maximum power of animals of similar organization may therefore be regarded as proportional to the square of their linear dimensions. If men attained a stature of five or six fathoms, with a corresponding development of bone and muscle, they might indeed be about thirty-six times as strong as the present members of the human race, but they would be encumbered by a weight over two hundred times as great as that of our bodies, and accordingly it must be very dangerous and difficult for them to move about or to maintain an erect position. We may therefore condemn the unnatural fictions of the ancient poets, who represent their giants as rivaling in stature the tallest trees of the primitive forest. Such unwieldy monsters could only walk on the bottoms of seas or deep rivers, where the sustaining power of the liquid element almost deprived them of weight, but their huge frames would be quite immovable on the land.

In consequence of the diminution of their weight by the presence of the water, the tenants of the deep are permitted to attain a far greater size than any terrestrial animal. But, even here, an undue size exposes the larger tribes to much inconvenience from the inertia of their bodies, and their movements display less vigor of action than we should expect to result from their amazing strength. The gigantic whale, notwithstanding his high organization and the elevated character of his instinct, is far from being the lord or the tyrant of the ocean, and he falls a victim not only to the ingenuity of man, but also to the activity of animals far inferior to him in size and in bodily power.

If the relative force which land animals need for supporting the weight of their bodies is much greater than is necessary for fishes to propel themselves through the water, it is far inferior to what the winged tribes must possess for soaring into the air. Accordingly, the capability of flying can be conferred only on animals of much smaller dimensions than the most gigantic tenants of the land and water. Some species of the whale, when full grown, are about seventy times as large and as heavy as the most gigantic elephant, and the elephant, in

ON STABILITY. 9

turn, lias a still more decided superiority in size and weight over the greatest bird that traverses the atmosphere. Some of the largest birds now living, though possessed of wings, onlyuse them to accelerate their motions on the land, and it is probable that the same may be said of the colossal winged tribes which tenanted the geological world.

It thus appears that mere mechanical conditions are not without their influence in determining the characters of life in the three departments of our planet, so that the air, notwithstanding its numerous population of living beings, can never furnish such gigantic inhabitants as dwell on the land or in the ocean. In consequence of the superior size of man, his relative strength is much inferior to that of birds, and this precludes the possibility of his ever using machinery with success for flying through the air. If terrestrial gravity were reduced to one-tenth of its present force, and a tenfold increase were given to the air which surrounds our globe, artificial flying would no longer be impossible, and our atmosphere would soon become a highway between nations. Such an arrangement, 1 owever, though conferring some privileges on man, would afford at least a possibility of the existence of flying monsters, who might become troublesome enemies to the human race. But we should have far more to fear from the depravity of our own species, for, as nations could then have little means of protection from invaders, wars would be attended with the most horrible consequences, while crime obtained more chances of impunity. Accordingly, though we may envy the enjoyment of the feathered tribes who sport over our heads, we have no just cause to be displeased with the restraints which have been imposed on human liberty by the fixed laws of nature.

In setting limits to human possibility, it is not to be supposed that no allowance is made for future improvements in the arts. In the execution of all his works, man makes continual advances to perfection ; and in every succeeding age he is able to leave more stupendous monuments of his skill behind him. As his knowledge of the properties of bodies increases, he is enabled to derive more advantage from the resources which have been placed within his reach ; by studying the

10 THE INFLUENCE OF. MAGNITUDE

laws of nature, he obtains a more extensive command of her potent agencies, and new inventions ever furnish him with more effective means for the accomplishment of his designs. The invention of the arch enabled the Romans to give their public edifices a scale of magnitude far surpassing what the Grecian architecture could attain. By the use of the suspension bridge during the present age, highways have been formed over the largest rivers without destroying their utility for the purposes of navigation. The great strength of wrought iron tubes, in proportion to their weight, has been recognized hj modern art ; and to their use are we indebted for the construction of the largest vessel that ever braved the fury of the waves.

But no materials placed at man's disposal have a degree of strength sufficiently great to afford unlimited scope for architectural ambition, and their power of resistance seems taxed to the utmost extent in many works of modern times. The frequent failures of suspension bridges and other edifices may be regarded as warnings to those who are desirous of giving structures a greater magnitude than the character of the materials will justify. In sounding great depths of the ocean, it was long found impossible to prevent the line from being broken by a weight sufficient to sink it ; and at last success could be only attained by sacrificing a ball at every attempt. The chief difficulty in forming a telegraphic communication between the Old and New World arises from the liability of the cable to break by its own weight while sinking to the bed of the ocean. Towers and massive pyramids exhibit their strength to the greatest advantage, and man cannot expect to be able to give such structures the size which would be fatal to their stability. It may be safely asserted, however, that if a pyramid of granite were fifteen miles high, its base should be crushed by the weight it had to bear; end, though giants had the power of piling one. mountain on another, they could never raise so lofty an edifice from the rocks found at the earth's surface.

There are, indeed, in the laboratory of nature giant forces, whose incessant action would be capable of forming such high

ON STABILITY. 11

pinnacles on our globe, if the frailty of terrestrial matter put no obstacles in their way. Of the water annually evaporated from the ocean and conveyed by the winds to many lands, a vast quantity falls as snow on the tops of high mountains, where the temperature never rises sufficiently high to restore it to a liquid state. At great distances from the sea the air is so dry that much of the snowy mantle gradually disappears by evaporation, and in these localities perpetual snow is found considerably above the elevation which temperature would prescribe to it under different circumstances. But near the ocean the evaporation is checked by the moisture of the air, and in such localities the snowy deposit accumulates every year on those mountains which pierce the frigid strata of the atmosphere. It might be expected, that in the course of a few thousand years, the height of such mountains would be considerably augmented by repeated atmospheric deposition of this character. This, however, is not the case. The piles of snow are soon taxed beyond their strength, crushed by their own weight and precipitated into the valleys below. Such is the origin of the avalanches which often occur in the Pyrenean and the Dofrafield Mountains, but which are most frequent in the Alps, and the hardy tenant of these bleak regions is exposed to perpetual dangers from the fall of these frail edifices, which atmospheric influences are continually raising around him.

Had snow and ice been as unyielding as the rocks on the earth's crust, such catastrophes would be averted for a longer time ; but when they occurred, they would be attended with the most awful consequences. If the constituents of granite were sublimed, like water, by solar heat, and deposited in a compact form on the tops of mountains, it would give them a continual augmentation of stature, until at last they must be crushed by the great weight of the pinnacles which they bore. In the present course of nature, atmospheric ^influences serve only to destroy mountain chains as they are raised by subterranean movements. But, in- whatever manner they may have originated, their height must have a limit depending on the strength of the materials which compose them ; and no

12 THE INFLUENCE OF MAGNITUDE

peak or table- lands could have an elevation of twenty miles above the level of the sea. If we could depend on the observations of some astronomers who announce the existence of so high a mountain on Venus, it may be regarded as an evidence that this planet can furnish much stronger materials than we find in our terrestrial abode.

It may be necessary to observe that the intensity of gravity is nearly equal on the surfaces of Venus and the earth, but it is -about twenty-seven times as powerful on the surface of the sun. If so great an attractive force prevailed on our planet, it would destroy all our lofty mountains and the great works of art ; while the larger animals would be crushed by the weight of their own bodies. Some phenomena exhibited by the sun have been ascribed to the presence of mountains several thousand feet high, and of valleys of corresponding magnitude ; but, to render the existence of such eminences and depressions possible, the solar matter must have many thousand times more passive strength than wrought iron ; and so extravagant a hypothesis cannot be admitted on the slender evidence which some astronomers adduce to support it.

There is much greater scope for inequalities on the surfaces of small worlds. On the secondary planets the force of gravity is very small ; and it is so feeble on some of the asteroids, that a full grown man, translated to their surfaces, would weigh less than a pound. On such small celestial bodies, mountains might attain so great a size as to cause a considerable distortion from the planetary form peculiar to larger worlds ; and many facts show that the asteroids deviate very widely from exact spheres. . If the attractive power of the earth were so much reduced, our mountain chains could attain a most gigantic size, the snows of unnumbered ages would be permitted to repose on their summits, and ice and snow might collect at the polar regions in so great a quantity as to lead to a change in the axis of rotation of our planet. Any of the asteroids which may contain a large proportion of air and water, would present very strange scenes to an inhabitant of the larger class of worlds.

In investigating the conditions of stability, it has been usual

ON STABILITY. 13

for writers to regard solid bodies as absolutely unyielding in their character, while fluids are obedient to every impulse they receive. But, to obtain strict accuracy, it is necessary to consider how the cohesive strength of all material forms compares with the forces to which it is subjected, and how far it is influenced by their magnitude. The drop of water ready to fall from a leaf has about the same relative strength and solidity as a ball of iron ten miles in diameter. Each of them would be crushed by its own weight if placed on an unyielding surface ; and even the latter would fall to pieces if it were raised from the ground by some superhuman power. Were our earth moulded into a cubical form, it would be soon crushed by the weight of its more prominent parts, until it acquired a shape differing little from that which it now possesses. Whenever matter is congregated into large masses, it pays little allegiance to the restraint of solidity, and complies with the conditions of equilibrium in fluid bodies. The existence of rivers of ice would not be credited if the movements of glaciers were not established by observation.

The study of the conditions which give security to the works of art will serve to check some of the puerilities into which persons are liable to fall while speculating on the condition of other worlds. A little experience might have convinced the ancient astronomers of the impossibility of the existence of the large hollow spheres, in which they supposed that the stars and planets were fixed. Almost as extravagant a demand on the strength of materials was made in the seventeenth century by Riccioli, who regarded Saturn's ring as a mighty arch, supported by two gigantic pillars, which rested on the planet. More recently, astronomers have regarded these rings as two flat solid masses revolving around the planet, and having their weight equipoised by centrifugal force. It will be shown, however, that such an arrangement could only partially neutralize the weight, and that, under the most favorable conditions, they must be subjected to a strain about one hundred times as great as they could withstand if they were composed of wrought iron. All the knowledge which we can gain by experience, however, discountenances the idea that the preser-

14: INFLUENCE OF MAGNITUDE ON STABILITY.

vation of so vast a mundane structure should be confided to the mere strength of the materials of which it is composed. When we observe the manner in which the works of art fall a victim to their inability to support their own weight, and how even the earth's crust has been rent by the convulsions of geological times, we cannot but rejoice that the destiny of our world does not depend on the infirmities of its component parts. Whatever advantage the passive strength of materials may confer on man in the structure of his puny edifices, we may be assured that it has very little committed to its trust in the structure and arrangement of suns and worlds.

THE DOCTRINE OF GRAVITATION. 15

THE DOCTRINE OF GRAVITATION.

Having shown that the stability of the works of art and the less gigantic works of nature depends on the passive strength of the solids composing them, I shall now proceed to the consideration of those properties from which matter derives its adaptation for purposes of a more sublime character. A general view of the leading properties or qualities of bodies may be requisite for a more extended survey of natural phenomena, but, as the present work is intended to treat only on a limited department of physical science, it will be necessary to confine our inquiries within a less extensive range. The present chapter shall accordingly be devoted to an examination of the mysterious force which takes the most prominent part in establishing the harmony of the material universe and giving a requisite degree of security to the several suns and world's it contains.

While matter in itself cannot be said to have any predilection for rest or motion, nor any power to change its condition, it is associated with forces which, under certain circumstances, are ever ready to compensate for this physical inertia. The alliance between the material creation and the forces which maintain it in a state of activity is such that all bodies are capable of affecting the condition of others by exerting a peculiar influence, to which the term " attractions" has been applied. Among these mysterious attractive influences, Gravitation holds the most important place, both in respect to the universality of its action and the greatness of the task which it is designed to perform. Cohesive attraction acts very energetically at insensible distances, and gives materials the degree of strength from which man derives so many advantages. But it fails to afford the means for extending the size

16 THE DOCTRINE

of structures beyond a certain limit, and it would be utterlyinadequate to act the part which is assigned to Gravitation in the architecture of the heavens.

Before contemplating the great achievements of this power in planetary movements, we must begin by tracing its operation on our own sphere. It is the attraction of the earth that gives weight to all bodies around us, and causes them to descend when left unsupported.

This mysterious influence proceeds from every portion of matter composing our globe; and in obedience to the forces operating in so many directions, bodies fall perpendicularly to the earth's surface. The attraction of mountains is manifested by the deflection of the plumb line, and that of smaller masses is revealed by experiments with the tortion balance ; x but even in bodies weighing a thousand tuns, it is too feeble to be recognized by ordinary observation. The powerful gravity of the earth renders us insensible to that exerted by such small bodies, in the same manner as the overpowering brilliancy of the sun prevents us from seeing the stars during the day. In a region of space where no material action could arise from the presence of suns or planets, small masses should manifest their attractive influence, and if they had been previously at rest they should commence approaching one another with certain velocities. In such circumstances, two globes of lead, each containing one thousand tuns of the metal, and being separated by a distance of seven hundred feet, would be drawn together in the space of five days, and should acquire a relative velocity of about half an inch a second, previous to their collision. But if the earth were deprived of its orbital motion, it would drop to the sun in the course of less than sixty-five days, and on arriving at his surface should have acquired a velocity about two thousand times as great as the most rapid cannon ball.

The vast distances to which gravity extends its action, contributes to render it an effective agent in the government of our universe ; and its control is rendered more conducive to the harmony of nature by the impartial and uniform manner in which it acts on all matter. To lift one of the largest ships

OF GRAVITATION. * 17

without injuring its structure, it would be necessary to have the supports or the ties attached to its numerous parts, and to give a very proper adjustment of the force exerted on each of them. So, in like manner, the safety of each planet requires that the invisible chain which binds it to the sun, should lay hold of all its parts, and observe somewhat of a uniform character in directing the movements of the whole planetary mass. Now this important object is attained by the gravity of the sun and the several other large spheres, for they manifest no partiality to the size or composition of bodies revolving around them, but under the same circumstances they affect the movements of all in a uniform manner.

The first recognition of this important law must be ascribed to the celebrated Galileo. The experiments which he performed on the tower of Pisa proved, in opposition to the dogmas of Aristotle, that small and large bodies fall to the ground from a given height in the same time. On the invention of the air-pump, the law was found to be more general than was first supposed, for in an exhausted receiver the lightest and the heaviest solids were observed to fall with almost the same velocity. The researches of Newton showed that it was not confined to the earth, for the matter of planets and comets, however widely it may differ in density, paid the same allegiance to solar attraction. Experiments with the pendulum also prove the impartial action of terrestrial gravity. Pendulums of equal lengths, or having the same distance between the centers of motion and oscillation, vibrate in the same time, however the weight which they carry may differ in magnitude or composition. The uniform manner in which gravity urges bodies in similar curves we may reasonably pronounce a conclusive evidence of the impartial effect it would exercise on falling masses of every description.