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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..66faadf --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #67386 (https://www.gutenberg.org/ebooks/67386) diff --git a/old/67386-0.txt b/old/67386-0.txt deleted file mode 100644 index ddf4590..0000000 --- a/old/67386-0.txt +++ /dev/null @@ -1,2789 +0,0 @@ -The Project Gutenberg eBook of A Preliminary Dissertation on the -Mechanisms of the Heavens, by Mary Somerville - -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this eBook. - -Title: A Preliminary Dissertation on the Mechanisms of the Heavens - -Author: Mary Somerville - -Release Date: February 12, 2022 [eBook #67386] - -Language: English - -Produced by: Laura Natal Rodrigues (Images generously made available by - Hathi Trust Digital Library.) - -*** START OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON -THE MECHANISMS OF THE HEAVENS *** - - -A - -PRELIMINARY DISSERTATION - -ON THE - -MECHANISM OF THE HEAVENS. - - - -BY - -MRS. SOMMERVILLE - - - - -PHILADELPHIA: -CAREY & LEA - -1832 - - - - -In order to convey some idea of the object of this work, it may be -useful to offer a few preliminary observations on the nature of the -subject which it is intended to investigate, and of the means that have -already been adopted with so much success to bring within the reach of -our faculties, those truths which might seem to be placed so far beyond -them. - -All the knowledge we possess of external objects is founded upon -experience, which furnishes a knowledge of facts, and the comparison of -these facts establishes relations, from which, induction, the intuitive -belief that like causes will produce like effects, leads us to general -laws. Thus, experience teaches that bodies fall at the surface of the -earth with an accelerated velocity, and proportional to their masses. -Newton proved, by comparison, 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 induction led him to conclude 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 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 combined efforts of astronomers, from the earliest dawn of -civilization, have been requisite 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 of -matter. On the other hand, descending from the principle of gravitation, -every motion in the system of the world has been so completely -explained, that no astronomical phenomenon can now be transmitted to -posterity of which the laws have not been determined. - -Science, regarded as the pursuit of truth, which can only be attained by -patient and unprejudiced investigation, wherein nothing is too great to -be attempted, nothing so minute as to be justly disregarded, must ever -afford occupation of consummate interest and 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 elegant 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. - -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 -limits. 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 us a base wherewith to measure -the magnitude and distance of the sun and planets, and make the diameter -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 which seem so mighty to us -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 or creation. - -A complete acquaintance with Physical Astronomy can only be attained by -those who are well versed in the higher branches of mathematical and -mechanical science: such alone can appreciate the extreme beauty of -the results, and of the means by which these results are obtained. -Nevertheless a sufficient skill in analysis to follow the general -outline, to see the mutual dependence of the different parts of the -system, and to comprehend by what means some of the most extraordinary -conclusions have been arrived at, is within the reach of many who shrink -from the task, appalled by difficulties, which perhaps are not more -formidable than those incident to the study of the elements of every -branch of knowledge, and possibly overrating them by not making a -sufficient distinction between the degree of mathematical acquirement -necessary for making discoveries, and that which is requisite for -understanding what others have done. That the study of mathematics and -their application to astronomy are full of interest will be allowed by -all who have devoted their time and attention to these pursuits, and -they only can estimate the delight of arriving at truth, whether it be -in the discovery of a world, or of a new property of numbers. - -It has been proved by Newton that a particle of matter placed without -the surface of a hollow sphere is attracted by it in the name manner as -if its mass, or the whole matter it contains, were collected 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. -This however is not the case with a spheroid, but the celestial bodies -are so nearly spherical, and at such remote distances from each other, -that they attract and are attracted as if each were a dense point -situate in its centre of gravity, a circumstance which greatly -facilitates the investigation of their motions. - -The attraction of the earth on bodies at its surface in that latitude, -the square of whose sine is ⅓, 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 of the moon from the earth is about sixty -times the mean radius of the earth. When the number 16.0697 is -diminished in the ratio of 1 to 3600, which is the square of the moon's -distance from the earth, 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 her centrifugal force, arising from the velocity -with which she moves in her orbit. So that the moon is 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; but as experience shows that the action and reaction of matter are -equal and contrary, the moon must attract the earth with an equal and -contrary force. - -Newton proved that a body projected in space will move in a conic -section, if it be attracted by a force directed towards a fixed point, -and having an intensity inversely as the square of the distance; but -that any deviation from that law will cause it to move in a curve of a -different nature. Kepler ascertained by direct observation that the -planets describe ellipses round the sun, and 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 his 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 of the planets, or the times of their revolutions round the sun, -are proportional to the cubes of their mean distances from his centre: -whence it follows, that the intensity of gravitation of all the bodies -towards the sun is the same at equal distances; consequently gravitation -is proportional to the masses, for if the planets and comets be supposed -to be at equal distances from the sun and left to the effects of -gravity, they would arrive at his surface at the same time. The -satellites also gravitate to their primaries according to the same law -that their primaries do to the sun. Hence, by the law of action and -reaction, each body is itself the centre of an attractive force -extending indefinitely in space, whence proceed all the mutual -disturbances that 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 taken in mass; 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 -in other respects they also would 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; 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, which is impossible. - -The form of the planets results 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 revolves about an axis, it becomes flattened at the poles, -and bulges at the equator, in consequence of the centrifugal force -arising from the velocity of rotation. For, the centrifugal force -diminishes the gravity of the particles at the equator, and equilibrium -can only exist when 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 balanced the -centrifugal force by their attraction, consequently the sphere would -become an oblate 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. Such is the form of the earth and planets, -but the compression or flattening at their poles is so small, that even -Jupiter, whose rotation is the most rapid, differs but little from a -sphere. Although the planets attract each other as if they were spheres -on account of their immense distances, yet the satellites 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 in -the axis of rotation, and the reaction of that matter on the moon is the -cause of a corresponding nutation in the lunar orbit. - -If a sphere at rest in space receives 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 give it a -rotatory motion at the same time that it is translated in space. These -motions are independent of one another, so that a contrary impulse -passing through its centre of gravity will impede its progression, -without interfering with its rotation. As the sun rotates about an axis, -it seems probable if an impulse in a contrary direction has not been -given to his centre of gravity, that he moves in space accompanied by -all those bodies which compose the solar system, a circumstance that -would in no way interfere with their relative motions; for, in -consequence of our experience that force is proportional to velocity, -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, -such impulse must have passed through a point about twenty-five miles -from its centre. - -Since the motions of the rotation and translation of the planets are -independent of each other, though probably communicated by the same -impulse, they form separate subjects of investigation. - -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 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 a planet is in its aphelion or at the -point where the orbit is farthest from the sun, his action overcomes its -velocity, and brings it towards him with such an accelerated motion, -that it at last overcomes the sun's attraction, and shoots past him; -then, gradually decreasing in velocity, it arrives at the aphelion where -the sun's attraction again prevails. In this motion the radii vectores, -or imaginary lines joining the centres of the sun and planets, pass over -equal areas in equal times. - -If the planets were attracted by the sun only, this would ever be their -course; and because his action is proportional to his mass, which is -immensely larger than that of all the planets put together, the -elliptical is the nearest approximation to their true motions, which 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, and now receding from the elliptical form, and their -radii vectores do not describe areas exactly proportional to the time. -Thus the areas become a test of the existence 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 arises the celebrated -problem of the three bodies, which originally was that of 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 position at any given instant. - -By this problem the motions of translation of all the celestial bodies -are determined. It is one of extreme difficulty, and would be of -infinitely greater difficulty, if the disturbing action were not very -small, when compared with the central force. 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 on the intensity of the primitive momentum 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 -on 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, their mutual attractions might have changed them into -parabolas or even hyperbolas; so that the earth and planets might ages -ago have been sweeping 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 immensely -greater than those of the planets; and as their inequalities bear the -same ratio to their elliptical motions as their masses do to that of the -sun, their mutual disturbances only increase or diminish the -eccentricities 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 the end, -than is exhibited in the nice adjustment of these forces. - -The orbits of the planets have a very small inclination to the plane of -the ecliptic in which the earth moves; and on that account, astronomers -refer their motions to it at a given epoch as a known and fixed -position. 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; the points where the orbit intersects the -plane of the ecliptic are its nodes. - -The orbits of the recently discovered planets deviate more from the -ecliptic: that of Pallas has an inclination of 35° to it: on that -account it will be more difficult to determine their motions. These -little planets have no sensible effect in disturbing the rest, though -their own motions are rendered very irregular by the proximity of -Jupiter and Saturn. - -The planets are subject to disturbances of two distinct 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 troubled planet is sometimes drawn away from -the sun, sometimes brought nearer to him; 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 on 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. - -In consequence of disturbances of this kind, the apsides, or extremities -of the major axes of all the orbits, have a direct, but variable motion -in space, excepting those of Venus, which are retrograde; and the lines -of the nodes move with a variable velocity in the contrary direction. -The motions of both are extremely slow; it requires more than 109770 -years for the major axis of the earth's orbit to accomplish a sidereal -revolution, and 20935 years to complete its tropical motion. The major -axis of Jupiter's orbit requires no less than 197561 years to perform -its revolution from the disturbing action of Saturn alone. The periods -in which the nodes revolve are also very great. Beside these, the -inclination and eccentricity of every orbit are in a state of perpetual, -but slow change. At the present time, the inclinations of all the orbits -are decreasing; but so slowly, that the inclination of Jupiter's orbit -is only six minutes less now than it was in the age of Ptolemy. The -terrestrial eccentricity is decreasing at the rate of 3914 miles in a -century; and if it were to decrease equably, it would be 36300 years -before the earth's orbit became a circle. But in the midst of all these -vicissitudes, the major axes and 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. - -With the exception of these two elements, it appears, that all the -bodies are in motion, and every orbit is in a state of perpetual change. -Minute as these changes are, they might be supposed liable 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. The -consequences being so dreadful, it is natural to inquire, what proof -exists that creation will be preserved from such a catastrophe? For -nothing can be known from observation, since the existence of the human -race has occupied but a point in duration, while these vicissitudes -embrace myriads of ages. The proof is simple and convincing. All the -variations of the solar system, as well secular as periodic, are -expressed analytically by the sines and cosines of circular arcs, which -increase with the time; and as a sine or cosine never can exceed the -radius, but must oscillate between zero and unity, however much the time -may increase, it follows, that when the variations have by slow changes -accumulated in however long a time to a maximum, they decrease by the -same slow degrees, till they arrive at their smallest value, and then -begin a new course, thus for ever oscillating about a mean value. This, -however, would not be the case if the planets moved in a resisting -medium, for then both the eccentricity and the major axes of the orbits -would vary with the time, so that the stability of the system would be -ultimately destroyed. But if the planets do move in an ethereal medium, -it must be of extreme rarity, since its resistance has hitherto been -quite insensible. - -Three circumstances have generally been supposed necessary to prove the -stability of the system: the small eccentricities of the planetary -orbits, their small inclinations, and the revolution of all the bodies, -as well planets as satellites, in the same direction. These, however, -are not necessary conditions: the periodicity of the terms in which the -inequalities are expressed is sufficient to assure us, that though 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 52"·109, occasioned by the reciprocal action -of the planets; but as this is also periodical, the terrestrial equator, -which is inclined to it at an angle of about 23° 28', will never -coincide with the plane of the ecliptic; so there never can be perpetual -spring. - -The rotation of the earth is uniform; therefore day and night, summer -and winter, will continue their vicissitudes while the system endures, -or is untroubled by foreign causes. - - - Yonder starry sphere - Of planets, and of fix'd, in all her wheels - Resembles nearest, mazes intricate, - Eccentric, intervolv'd, 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 -elliptical orbits of the planets, La Grange's discovery of their -periodical inequalities is without doubt the noblest truth in physical -astronomy; 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. This difficulty is obviated by La Place, who has shown -that whatever changes time may induce either in the orbits themselves, -or in the plane of the ecliptic, there exists an invariable plane -passing through the centre of gravity of the sun, about which the whole -system oscillates within narrow limits, and which is determined by this -property; that if every body in the system be projected on it, and if -the mass of each be multiplied by the area described in a given time by -its projection on this plane, the sum of all these products will be a -maximum. 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 remains parallel to itself, and -maintains a fixed position, whence the oscillations of the system may be -estimated through unlimited time. It is situate nearly half way between -the orbits of Jupiter and Saturn, and is inclined to the ecliptic at an -angle of about 1° 35' 31". - -All the periodic and secular inequalities deduced from the law of -gravitation are so perfectly confirmed by observations, 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 great inequalities of very long periods, forming -what appeared an 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 inequality in the mean -motion of each of these planets, which completes its period in nearly -929 Julian years, the one being retarded, while the other is -accelerated. These inequalities are strictly periodical, since they -depend on the configuration of the two planets; and the theory is -perfectly confirmed by observation, which shows that in the course of -twenty centuries, Jupiter's mean motion has been accelerated by 3° 23', -and Saturn's retarded by 5° 13'. - -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 those bodies were united in their common centre -of gravity; the action of the sun however disturbs in some degree the -motion of the satellites about their primary. - -The changes that take place in the planetary system are exhibited on a -small scale by Jupiter and his satellites; and as the period requisite -for the development of the inequalities of these little 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 -centuries. 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 the compression of Jupiter's spheroid is very great in -consequence of his rapid rotation; and as the masses of the satellites -are nearly 100000 times less than that of Jupiter, 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 further removed from its influence, move in orbits with -a very small eccentricity. The same cause occasions the orbits of the -satellites to remain nearly in the plane of Jupiter's equator, on -account of which they are always seen nearly in the same line; and the -powerful action of that quantity of prominent matter is the reason why -the motion of the nodes of these little bodies is so much more rapid -than those of the planet. The nodes of the fourth satellite accomplish a -revolution in 520 years, while those of Jupiter's orbit require no less -than 50673 years, a proof of the reciprocal attraction between each -particle of Jupiter's equator and of the satellites. Although the two -first satellites sensibly move in circles, they acquire a small -ellipticity from the disturbances they experience. - -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 -further the satellite is removed, a circumstance entirely owing to the -influence of Jupiter's compression. - -A singular law obtains among the mean motions and mean longitudes of the -three first 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. They extend to the synodic motions 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 they are frequently eclipsed by the planet. 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, gives the difference of the meridians in time, and -consequently the longitude of the place of observation. It has required -all the refinements of modern instruments to render the eclipses of -these remote moons available to the mariner; now however, that system of -bodies invisible to the naked eye, known to man by the aid of science -alone, enables him to traverse the ocean, spreading the light of -knowledge and the blessings of civilization over the most remote -regions, and to return loaded with the productions of another -hemisphere. Nor is this all: the eclipses of Jupiter's satellites have -been the means or a discovery, which, though not so immediately -applicable to the wants of man, unfolds a property 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, are later by 16' 26" than those which take place when the -planet is in opposition. But as Jupiter is nearer to us when in -opposition by the whole breadth of the earth's orbit than when in -conjunction, this circumstance was attributed to the time employed by -the rays of light in crossing the earth's orbit, a distance of 192 -millions of miles; whence it is estimated, that light travels at the -rate of 192000 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 -confirmed this astonishing result. - -Objects appear to be situate in the direction of the rays that 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, when Jupiter is in conjunction, we -see him by means of rays that left him 16' 26" 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 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 192000 to 19. In consequence of -aberration, none of the heavenly bodies are in the place in which they -seem to be. 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 never -exceeds twenty seconds, in ordinary cases. - -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 apparently the most unpromising and dissimilar -circumstances, occur in physical astronomy, and prove dependences 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 if light consists in the vibrations of an -elastic fluid or ether filling space, which hypothesis accords best with -observed phenomena, the uniformity of its velocity shows that the -density of the fluid throughout the whole extent of the solar system, -must be proportional to its elasticity. 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." - -As 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 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. - -The little that is known of the theories of the satellites of Saturn and -Uranus is in all respects similar to that of Jupiter. The great -compression of Saturn occasions its satellites to move nearly in the -plane of its equator. Of the situation of the equator of Uranus we know -nothing, nor of its compression. The orbits of its satellites are nearly -perpendicular to the plane of the ecliptic. - -Our constant companion the moon next claims 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. Neither the -eccentricity of the lunar orbit, nor its inclination to the plane of the -ecliptic, have experienced any changes from secular inequalities; but -the mean motion, the nodes, and the perigee, are subject to very -remarkable variations. - -From an eclipse observed at Babylon by the Chaldeans, 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; 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; -all the 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, and it was at one time attributed to the -resistance of an ethereal medium pervading space; 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 or nodes, they could not affect the -mean motion, a variation in the latter from such a cause being -inseparably connected with variations in the two former of these -elements. That great mathematician, however, in studying the theory of -Jupiter's satellites, perceived that the secular variations in the -elements of Jupiter's orbit, from the action of the planets, occasion -corresponding changes in the motions of the satellites: this led him to -suspect that the acceleration in the mean motion of the moon might be -connected with the secular variation in the eccentricity of the -terrestrial orbit; and analysis has proved that he assigned the true -cause. - -If the eccentricity of the earth's orbit were invariable, the moon would -be exposed to a variable disturbance from the action of the sun, in -consequence of the earth's annual revolution; but it would be periodic, -since it would be the same as often as the sun, the earth, and the moon -returned to the same relative positions: on account however of the slow -and incessant diminution in the eccentricity of the terrestrial orbit, -the revolution of our planet is performed at different distances from -the sun every year. The position of the moon with regard to the sun, -undergoes a corresponding change; so that the mean action of the sun on -the moon varies from one century to another, and occasions the secular -increase in the moon's velocity called the acceleration, a name which is -very appropriate in the present age, and which will continue to be so -for a vast number of ages to come; because, as long as the earth's -eccentricity diminishes, the moon's mean motion will be accelerated; but -when the eccentricity has passed its minimum and begins to increase, the -mean motion will be retarded from age to age. At present the secular -acceleration is about 10", but its effect on the moon's place increases -as the square of the time. 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 eccentricity, 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 1° 48' in the moon's longitude, -and of 7° 12' in her mean anomaly. - -The action of the sun occasions a rapid but variable motion in the nodes -and perigee of the lunar orbit; the former, though they recede during -the greater part of the moon's revolution, and advance during the -smaller, perform their sidereal revolutions in 6793^days.4212, and the -latter, though its motion is sometimes retrograde and sometimes direct, -in 3232^days.5807, or a little more than nine years: 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 109770 years for the -greater axis of the terrestrial orbit to do the same. 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 motion of the nodes and perigee; and 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 eccentricity -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, and 0.265, or according -to the most recent investigations as 1, 4, 6776 and 0.391. A comparison -of ancient eclipses observed by the Arabs, Greeks, and Chaldeans, -imperfect as they are, with modern observations, perfectly confirms -these results of analysis. - -Future ages will develop these great inequalities, which at some most -distant period will amount to many circumferences. They are indeed -periodic; but who shall tell their period? Millions of years must elapse -before that great cycle is accomplished; but 'such changes, though rare -in time, are frequent in eternity.' - -The moon is so near, that the excess of matter at the earth's equator -occasions periodic variations in her longitude and latitude; and, 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 equatorial diameter 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 square of the distance, were to revolve about an axis, as the -earth, it would assume the form of a spheroid, whose compression is -1/230. Whence it appears, that the earth is not homogeneous, but decreases -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 the internal structure of our planet; results of analysis which -could not have been anticipated. Similar inequalities in Jupiter's -satellites prove that his mass is not homogeneous, and that his -compression is 1/13·8. - -The motions of the moon have now become of more importance to the -navigator and geographer than those of any other body, from the -precision with which the longitude is determined by the occultations of -stars and lunar distances. The lunar theory is brought to such -perfection, that the times of these phenomena, observed under any -meridian, when compared with that computed for Greenwich in the Nautical -Almanack, gives the longitude of the observer within a few miles. The -accuracy of that work is obviously of extreme importance to a maritime -nation; we have reason to hope that the new Ephemeris, now in -preparation, will be by far the most perfect work of the kind that ever -has been published. - -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 distance of the sun and -moon from the earth is obtained: whence it appears that the sun's -distance from the earth is nearly 396 times greater than that of the -moon. - -The method however of finding the absolute distances of the celestial -bodies in miles, is in fact the same with that employed in measuring -distances of terrestrial objects. From the extremities of a known base -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 at all from the celestial bodies. But the globe -itself whose dimensions are ascertained by actual admeasurement, -furnishes a standard of measures, with which we compare the distances, -masses, densities, and volumes of the sun and planets. - -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, at any rate, quite 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 gravity, 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 contemporaneously the same noon. 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 will -be greatest where the curvature is least; a comparison of the length of -the degrees in different parts of the earth's surface will therefore -determine its size and form. - -An arc of the meridian may be measured by observing the latitude of its -extreme points, 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, the sides and angles of which are either measured -or computed, so that the length of the arc is ascertained with much -laborious computation. In consequence of the inequalities 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 is spherical, they -require a correction to reduce them from plane to spherical triangles. - -Arcs of the meridian have been measured in a variety of latitudes, both -north and south, as well as arcs perpendicular to the meridian. From -these measurements it appears that the length of the degrees increase -from the equator to the poles, nearly as the square of the sine of the -latitude; consequently, the convexity of the earth diminishes from the -equator to the poles. Many discrepancies occur, but the figure that most -nearly follows this law is an ellipsoid of revolution, whose equatorial -radius is 3962.6 miles, and the polar radius 3949.7; the difference, or -12.9 miles, divided by the equatorial radius, is 1/308·7, or 1/309 -nearly; this fraction is called the compression of the earth, because, -according as it is greater or less, the terrestrial ellipsoid is more -or less flattened at the poles; it does not differ much from that given -by the lunar inequalities. If we assume the earth to be a sphere, the -length of a degree of the meridian is 69 1/22 British miles; therefore -360 degrees, or the whole circumference of the globe is 24856, and the -diameter, which is something less than a third of the circumference, is -7916 or 8000 miles nearly. Eratosthenes, who died 194 years before the -Christian era, was the first to give an approximate value of the earth's -circumference, by the mensuration of an arc between Alexandria and Syene. - -But there is another method of finding the figure of the earth, totally -independent of either of the preceding. 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, the force of gravity -theoretically ought to increase, from the equator to the pole as the -square of the sine of the latitude; but for a spheroid in rotation, by -the laws of mechanics the centrifugal force varies 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 effects 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 in going 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; for if the fall of bodies be -accelerated, the oscillations will be more rapid; and that they may -always be performed in the same time, the length of the pendulum must -be altered. Now, by numerous and very careful experiments, it is proved -that a pendulum, which makes 86400 oscillations in a mean day at the -equator, will do the same at every point of the earth's surface, if -its length be increased in going to the pole, as the square of the -sine of the latitude. From the mean of these it appears that the -compression of the terrestrial spheroid is about 1/342, which does not -differ much from that given by the lunar inequalities, and from the arcs -of the meridian. 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, -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 1/578. - -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 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 to be about 1/320; that given by the lunar theory has the advantage -of being independent of the irregularities at the earth's surface, -and of local attractions. The form and size of the earth being determined, -it furnishes a standard of measure with which the dimensions of the -solar system may be compared. - -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. Suppose that, when the moon is in the horizon at the -instant of rising or setting, lines were 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 3454"·2; whence the mean distance -of the moon is about sixty times the mean terrestrial radius, or 240000 -miles nearly. Since the parallax is equal to the radius of the earth -divided by the distance of the moon; under the same parallel of latitude -it varies with the distance of the moon from the earth, and proves the -ellipticity of the lunar orbit; and when the moon is at her mean -distance, it varies with the terrestrial radii, thus showing that the -earth is not a sphere. - -Although the method described is sufficiently accurate for finding the -parallax of an object so 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 by the transits of Venus that difficulty -is obviated. When that planet is in her nodes, 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 block 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 sun is not so remote but that -the semidiameter of the earth has a sensible magnitude when viewed from -his centre, 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. 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, are 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 Otaheite in the South Sea, -the latter observation being the object of Cook's first voyage. The -transit lasted about six hours at Otaheite, and the difference in the -duration at these two stations was eight minutes; whence the sun's -parallax was found to be 8"·72; but by other considerations it has -subsequently been reduced to 8"·575; from which the mean distance of -the sun appears to be about 95996000, or ninety-six millions of miles -nearly. This is confirmed by an inequality in the motion of the moon, -which depends on the parallax of the sun, and which when compared -with observation gives 8"·6 for the sun's parallax. - -The parallax of Venus is determined by her transits, that of Mars -by direct observation. The distances of these two planets from the -earth are 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, -their absolute distances in miles are easily found. - -Far as the earth seems to be from the sun, it is near to him when -compared with Uranus; that planet is no less than 1843 millions of -miles from the luminary that warms and enlivens the world; to it, -situate on the verge of the system, the sun must appear not much -larger than Venus does to us. The earth cannot even be visible as a -telescopic object to a body so remote; 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, for -the apparent places of the fixed stars are not sensibly changed by -the earth's annual revolution; and with the aid derived from the -refinements of modern astronomy and the most perfect instruments, -it is still a matter of doubt whether a sensible parallax has been -detected, even in the nearest of these remote suns. If a fixed star -had the parallax of one second, its distance from the sun would be -20500000 millions of miles. At such a distance not only the terrestrial -orbit shrinks to a point, but, where the whole solar system, when -seen in the focus of the most powerful telescope, might be covered -by the thickness of a spider's thread. Light, flying at the rate -of 200000 miles in a second, would take three years and seven days -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 rationally be supposed to be -situated many thousand times further 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 dim and remote companion.' - -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. 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, 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 354936 times greater than that of the earth; -whence the great perturbations of the moon and the rapid motion of the -perigee and nodes of her orbit. Even Jupiter, the largest of the -planets, is 1070.5 times less than the sun. The mass of the moon is -determined from four different sources,--from her action on the -terrestrial equator, which occasions the rotation 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 titles. 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 very much from each -other; but, from her action in raising the tides, which furnishes -the fourth method, her mass appears to be about the seventy-fifth 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 8000 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 The mean apparent diameter of the sun -is 1920", and with the solar parallax 8"·65, it will be found that -the diameter of the sun is about 888000 miles; therefore, 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 mean radius or 240000 miles; so that twice the distance of -the moon is 480000 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 -88000 miles is incomparably less than that of the sun The diameter of -Pallas does not much exceed 71 miles, so that an inhabitant of that -planet, in one of our steam-carriages, might go round his world in five -or six hours. - -The oblate form of the celestial bodies indicates rotatory motion, and -this has been confirmed, in most cases, by tracing spots on their -surfaces, whence their poles and times of rotation have been determined. -The rotation of Mercury is unknown, on account of his proximity to the -sun; and that of the new planets has not yet been ascertained. The sun -revolves in twenty-five days ten hours, about an axis that is directed -towards a point half way between the pole star and Lyra, the plane of -rotation being inclined a little more than 70° to that on which the -earth revolves. From the rotation of the sun, there is every reason to -believe that he has a progressive motion in space, although the -direction to which he tends is as yet unknown; but in consequence of the -reaction of the planets, he describes a small irregular orbit about the -centre of inertia of the system, never deviating from his position by -more than twice his own diameter, or about 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 in every point of their orbit, and -with angular velocities that are sensibly uniform. 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 causes which have -determined the planetary motions. - -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, similar to that which obtains in -the terrestrial spheroid from the attraction of the sun and moon on the -prominent matter at the equator. 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 surrounded by a ring even brighter than himself, which always remains -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. 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 about the -planet in 10 1/2 hours, which is considerably less than 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 31°; and in consequence -of this obliquity of position they always appear elliptical to us, but -with an eccentricity so variable as even to be occasionally like a -straight line drawn across the planet. At present the apparent axes of -the rings are as 1000 to 160; and on the 29th of September, 1832, -the plane of the rings will pass through the centre of the earth -when they will be visible only with superior instruments, and will -appear like a fine line across the disc of Saturn. On the 1st of -December in the same year, the plane of the rings will pass through -the centre of the sun. - -It is a singular result of the 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 the 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 ring 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 ring on one -side, is 11"·073, and on the other side the interval is 11"·288; -consequently there is an eccentricity of the globe in the ring of -0"·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. - -The periods of the 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, 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 other 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 the poles from her centrifugal -force, therefore her polar axis is least; the other two are in the plane -of her equator, but that directed towards the earth is the greatest. 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 in 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 earth and moon; so that it would vibrate 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; for if it -had been only the hundred-thousandth part of that of the earthy it would -have rendered the libration sensible. A similar libration exists in the -motions of Jupiter's satellites; but although the comet of 1767 and 1779 -passed through the midst of them, their libration still remains -insensible. It is true, the moon is liable to librations depending on -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 moon exhibiting a surface thirteen times -larger than ours, with all the varieties of clouds, land, and water -coming successively into view, would 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 determined with as much accuracy as those -of many of the most remarkable places on the surface of our globe. - -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 that prevail throughout creation, the period of -the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage -observes, in 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 -its 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 again by removing matter to a greater distance from the centre, -destroy the velocity generated by its previous approach; so that the -descent of the 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 inefficient, -a variation in the mean temperature would certainly occasion a -corresponding change in the velocity of rotation: for 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 an -external 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 nature of fossil -remains, that the mean temperature of the globe is decreasing. - -The high temperature of mines, hot springs, and above all, the internal -fires that have produced, and do still occasion such devastation on our -planet, indicate an augmentation of heat towards its centre the increase -of density in the strata corresponding to the depth and the form of the -spheroid, being what theory assigns to a fluid mass in rotation, concur -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, 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. But even if this cause 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 hundredth part -of a second since the observations of Hipparchus two thousand years ago, -it would have diminished the secular equation of the moon by 4"·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 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 indication of the -primitive fluidity of the earth, as there is no direct proof, it can -only be regarded as a very probable hypothesis; but one of the most -profound philosophers and elegant writers of modern times has found, in -the secular variation of the eccentricity of the terrestrial orbit, an -evident cause of decreasing temperature. That accomplished author, in -pointing out the mutual dependences 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 8 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, _cœteris 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, -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 eccentricity 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 the other inhabitants -of the torrid zone, it is impossible to say. - -The relative quantity of heat received by the earth at different moments -during a single revolution, varies with the position of the perigee of -its orbit, which accomplishes a tropical revolution in 20935 years. In -the year 1250 of our era, and 29653 years before it, the perigee -coincided with the summer solstice; at both these periods the earth was -nearer the sun during the summer, and farther from him in the winter -than in any other position of the apsides: the extremes of temperature -must therefore have been greater than at present; but as the terrestrial -orbit was probably more elliptical at the distant epoch, the heat of the -summers must have been very great though possibly compensated by the -rigour of the winters; at all events, none of these changes affect the -length of the day. - -It appears 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 which -must have engulphed 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 ending to the new equator would leave some portions -of the globe, and overwhelm others. - -But theory 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 some foreign -cause, as the collision of a comet which may have happened in the -immensity of time. Then indeed, the equilibrium could only have been -restored by the rushing of the seas to the new equator, which they would -continue to do, till the surface was every where 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 -even of the Pacific ocean is not more than four miles, whereas the -equatorial radius of the earth exceeds the polar radius by twenty-five -or thirty miles; consequently the influence of the sea on the direction -of gravity is very small; and as it appears that a great change in the -position of the axes is incompatible with the law of equilibrium, the -geological phenomena must be ascribed to an internal cause. 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 axis on -its surface, have undergone but slight variations. - -It is beyond a doubt that the strata increase in density from the -surface of the earth to its centre, which is even proved by the lunar -inequalities; and it is manifest from the mensuration of arcs of the -meridian and the lengths of the seconds pendulum that the strata are -elliptical and concentric. This certainly would 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 -these phenomena. Professor Leslie observes, that air compressed into the -fiftieth part of its volume has its elasticity fifty times augmented; if -it continue 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. In descending therefore towards the centre through -4000 miles, the condensation of ordinary materials would surpass the -utmost powers of conception. But a density so extreme is not borne out -by astronomical observation. It might seem therefore to follow, 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. 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; but, from the experiments of Mr. -Perkins, they appear to be capable of a greater degree of compression -than has generally been imagined. - -It appears then, that the axis of rotation is invariable on the surface -of the earth, and observation shows, that were it not for the action of -the sun and moon on the matter at the equator, it would remain parallel -to itself in every point of its orbit. - -The attraction of an exterior 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 about 23° 28', and the inclination of the lunar orbit on the -same is nearly 5°; 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 about 50"·412 annually. The direct tendency of this action -would be to make the planes of the equator and ecliptic coincide; but in -consequence of the rotation of the earth, the inclination of the two -planes remains constant, as a top in 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 -to the same points of the ecliptic, at least as far as this kind of -action is concerned. But another and totally different cause operates on -this motion, which 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 on -the plane of the equator, and gives the equinoctial points a slow but -direct motion on the ecliptic of 0"·312 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, -but 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 50"·1 annually. 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 then 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 50"·1 annually, the equinoctial points will -accomplish a revolution in 25868 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 -365.242264 days must be increased by the time he takes to move through -an arc of 50"·1, in order to have the length of the sidereal year. By -simple proportion it is the 0.014119th part of a day, so that the -sidereal year is 365.256383. - -The mean annual precession is subject to a secular variation; for -although the change in the plane of the ecliptic which is the orbit of -the sun, 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 -0"·455 now than it was in the lime of Hipparchus; consequently the -actual length of the tropical year is about 4"·154 shorter than it was -at that time. The utmost change that it can experience from this cause -amounts to 43". - -Such is the secular motion of the equinoxes, but it is sometimes -increased and sometimes diminished by periodic variations, whose periods -depend on the relative positions of the sun and moon with regard to the -earth, and 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 -diameters of which are 16" and 20". The period of this inequality is -nineteen 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. -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 -oblique of the ecliptic is annually diminished by 0"·52109. With -regard to the fixed stars, this variation in the course of ages may -amount to tea or eleven degrees; but the obliquity of the ecliptic to -the equator can never vary more than two or three degrees, 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, and therefore all observations of them must -be corrected for these inequalities. - -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 1922" and -17"·08, and the mass of the earth is the 1/354936th part of that of the -sun taken as the unit; it follows therefore, that the earth is nearly -four times as dense as the sun; but the sun is so large that his -attractive force would cause bodies to fall through about 450 feet -in a second; consequently if he were even habitable by human beings, -they would be unable to move, since their weight would be thirty -times as great as it is here. A moderate sized man would weigh about -two tons at the surface of the sun. On the contrary, at the surface -of the four new planets we should be so light, that it would be -impossible to stand from the excess of our muscular force, for a man -would only weigh a few pounds. 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; and -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. - -Astronomy has been of immediate and essential use in affording -invariable standards for measuring duration, distance, magnitude, and -velocity. The sidereal day, measured by the time elapsed between two -consecutive transits of any star at the same meridian, and the sidereal -year, are immutable units with which to compare all great periods of -time; 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 in the -lapse of ages. - -The returns of the sun to the same 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 in the -equinoxes the arc of the equator is less than the corresponding arc of -the ecliptic, and in the solstices it is greater. 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 59' 8"·3 -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 in the equator, is denominated mean solar -time, such as 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 apparent -time, such as 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, and sometimes amounts to as much as sixteen minutes. The -apparent and mean time coincide four times in the year. - -Astronomers begin the day 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 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 system of -weights and measures. This subdivision is not used in common life, nor -has it been adopted in any other country, though their scientific -writers still employ that division of time. The mean length of the day, -though accurately determined, is not sufficient for the purposes either -of astronomy or civil life. The length of the year is pointed out by -nature as a measure of long periods; but the incommensurability that -exists between the lengths of the day, and the revolutions 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, four years are nearly equal to four revolutions 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. 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 new moon immediately following the winter solstice in the 707th year -of Rome was made the 1st of January of the first year of Cæsar; the -25th of December in his 45th year, is considered as the date of Christ's -nativity; and Cæsar's 46th year 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 actually elapsed -since that time. - -Some remarkable astronomical eras are determined by the position of the -major axis of the solar ellipse. Moving at the rate of 61"·906 -annually, it accomplishes a tropical revolution in 20935 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 6485 the major axis will again coincide with the line of the -equinoxes, but then the solar perigee will coincide with the equinox of -spring; whereas at the creation of man it coincided with the autumnal -equinox. In the year 1250 the major axis was perpendicular to the line -of the equinoxes, and then the solar perigee coincided with the solstice -of winter, and the apogee with the solstice of summer. On that account -La Place proposed the year 1250 as a universal epoch, and that the -vernal equinox of that year should be the first day of the first year. - -The variations in the positions of the solar ellipse occasion -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 about seven days. These intervals will be -equal towards the year 6485, when the perigee comes to the equinox of -spring. Were the earth's orbit circular, the seasons would be equal; -their differences arise from the eccentricity of the earth's orbit, -small as it is; but the changes are so gradual as to be imperceptible in -the short space 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 language, arts and -sciences, leaving but confused masses of ruin 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 period 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 computation 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 show to how many centuries they may be extended, -without the fear of error. A few examples will show the importance of -this 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, which in former times was determined from the meridian -length of the shadow of the style of a dial on the day of the solstice. -The lengths of the meridian shadow at the summer and winter solstice 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 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 in the obliquity is known, both the time -and place of the observations have been verified by computation from -modern tables. Thus the Chinese had made some advances in the science of -astronomy at that early period; the whole chronology of the Chinese 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 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. The great inequality of Jupiter and -Saturn whose cycle embraces 929 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 menu 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 from computation it -appears that _χ_ Draconis was not very far from that place about 3000 -years ago; but as Eudoxus lived only about 2150 years ago, he must have -described an anterior state of the heavens, supposed to be the same that -was determined by Chiron, about the time of the siege of Troy. Every -circumstance concurs in showing that astronomy was cultivated in the -highest ages of antiquity. - -A knowledge of astronomy leads to the interpretation of hieroglyphical -characters, since astronomical signs are often found on the ancient -Egyptian monuments, which were probably employed by the priests to -record dates. On the ceiling of the portico of a temple among the ruins -of Tentyris, there is a long row of figures of men and animals, -following each other in the some direction among these are the twelve -signs of the zodiac, placed according to the motion of the sun: it is -probable that the first figure in the procession represents the -beginning of the year. Now the first is the Lion as if coming out of the -temple; and as it is well known that the agricultural year of the -Egyptians commenced at the solstice of summer, the epoch of the -inundations of the Nile, if the preceding hypothesis be true, the -solstice at the time the temple was built must have happened in the -constellation of the lion; but as the solstice now happens 21° 6' north -of the constellation of the Twins, it is easy to compute that the zodiac -of Tentyris must have been made 4000 years ago. - -The author had occasion to witness an instance of this most interesting -application of astronomy, in ascertaining the dale 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 not only -to his country, but 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 antiquity 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 in the latitude of London forms the standard of the -British measure of extension. Its length oscillating in vacuo at the -temperature of 62° of Fahrenheit, and reduced to the level of the sea, -was determined by Captain Kater, in parts of the imperial standard yard, -to be 39.1387 inches. The weight of a cubic inch of water at the -temperature of 62° Fahrenheit, barometer 30, was also determined in -parts of the imperial troy pound, whence a standard both of weight and -capacity is deduced. The French have adopted the metre for their unit of -linear measure, which is the ten millionth part of that quadrant of the -meridian passing through Formentera and Greenwich, the middle of which -is nearly in the forty-fifth degree of latitude. Should the national -standards of the two countries be lost in the vicissitudes of human -affairs, both may be recovered, since they are derived from natural -standards presumed to be invariable. The length of the pendulum would be -found again with more facility than the metre; 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 is rendered -totally insensible by subdivision in taking its ten millionth part. The -French have adopted the decimal division not only in time, but in their -degrees, weights, and measures, which affords very great facility in -computation. It has not been adopted by any other people; though nothing -is more desirable than that all nations should concur in using the same -division and standards, not only on account of the convenience, but as -affording a more definite idea of quantity. It is singular that the -decimal division of the day, of degrees, weights and measures, was -employed in China 4000 years ago; and that, at the time Ibn Yunus made -his observations at Cairo, about the year 1000, the Arabians were in the -habit of employing the vibrations of the pendulum in their astronomical -observations. - -One of the most immediate and striking 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 48^s of mean solar -time. As it depends on the action of the sun and moon, it is classed -among astronomical problems, of which it is by far the most difficult -and 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 -trouble the equilibrium. - -It is proved by daily experience, as well as by strict mechanical -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 distinct -kinds of oscillations, depending on different causes, 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 on the motion of the -disturbing body in its orbit, they are of long periods. The second kind -of oscillations depends on the rotation of the earth, therefore their -period is nearly a day: and the oscillations of the third kind depend on -an angle equal to twice the angular rotation of the earth; and -consequently happen twice in twenty-four hours. The first afford no -particular interest, and are extremely small; but the difference of two -consecutive tides depends on the second. At the time of the solstices, -this difference which, according to Newton's theory, ought to be very -great, is hardly sensible on our shores. La Place has shown that this -discrepancy arises from the depth of the sea, and that if the depth were -uniform, there would be no difference in the consecutive tides, were it -not for 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 miles, that of the Atlantic -only three. From the formulæ which determine the difference of the -consecutive tides it is also proved that the precession of the -equinoxes, and the nutation in the earth's axis, are the same as if the -sea formed one solid mass with the earth. - -The third kind of oscillations are the semidiurnal tides, so remarkable -on our coasts; they are occasioned by the combined action of the sun and -moon, but as the effect of each is independent of the other, they may be -considered separately. - -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 -distances; hence they have a tendency to leave the earth, but are -retained by their gravitation, which this tendency diminishes. 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 this tendency again diminishes. 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 above the -surface of equilibrium of nearly the same height; 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 -water 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 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. The effects -of the sun's attraction are in all respects similar to those of the -moon's, though really less in degree, on account of his distance; he -therefore only modifies the form of this spheroid a little. If the -waters were capable of instantly assuming the form of equilibrium, 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 on them requires. Hence, on account of the inertia of the -waters, if the tides be considered relatively to the whole earth and -open sea, 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 the meridian at 90° distant, -it is everywhere low water. It is evident that these tides must happen -twice in a day, since in that time the rotation of the earth brings the -same point twice under the meridian of the moon, once under the superior -and once under the inferior meridian. - -In the semidiurnal tides there are two phenomena particularly to be -distinguished, one that happens twice in a month, and the other twice in -a year. - -The first phenomenon is, that the tides are much increased in the -syzigies, 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 the -full tide, the lower it is in the ebb. The neap tides lake place when -the moon is in quadrature, they neither rise so high nor sink so low as -the spring tides. The spring tides are much increased when the moon is -in perigee. It is evident that the spring tides must happen twice a -month, since in that time the moon is once new and once full. - -The second phenomenon in the tides is the augmentation which occurs at -the time of the equinoxes when the sun's declination is zero, which -happens twice every year. The greatest tides take place when a new or -full moon happens, near the equinoxes while the moon is in perigee. The -inclination of the moon's orbit on the ecliptic is 5° 9'; hence in -the equinoxes the action of the moon would be increased if her node were -to coincide with her perigee. The equinoctial gales often raise these -tides to a great height. Beside these remarkable variations, there are -others arising from the declination of the moon, which has a great -influence on the ebb and flow of the waters. - -Both the height and time of high water are thus perpetually changing; -therefore, in solving the problem, it is required to determine the -heights to which they rise, the times at which they happen, and the -daily variations. - -The periodic motions of the waters of the ocean on the hypothesis of an -ellipsoid of revolution entirely covered by the sea, are very far from -according with observation; this arises from the very great -irregularities in the surface of the earth, which is but partially -covered by the sea, 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, the resistance the waters meet with, all of -them causes which it is impossible to estimate, 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 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. Thus the -problem of the tides does not admit of a general solution; it is -certainly necessary to analyse the funeral phenomena which ought to -result from the attraction of the sun and moon, but these must be -corrected in each particular case by those local observations which are -modified by the extent and depth of the sea, and the peculiar -circumstances of the port. - -Since the disturbing action of the sun and moon can only become sensible -in a very great extent of water, it is evident that the Pacific ocean is -one of the principal sources of our tides; but in consequence of the -rotation of the earth, and the inertia of the ocean, high water does not -happen till some time after the moon's southing. The tide raised in that -world of waters is transmitted to the Atlantic, and from that sea it -moves in a northerly direction along the coasts of Africa and Europe, -arriving later and later at each place. This great wave however is -modified by the tide raised in the Atlantic, which sometimes combines -with that from the Pacific in raising the sea, and sometimes is in -opposition to it, so that the tides only rise in proportion to their -difference. This great combined wave, reflected by the shores of the -Atlantic, extending nearly from pole to pole, still coming northward, -occurs through the Irish and British channels into the North sea, so -that the tides in our ports are modified by those of another hemisphere. -Thus the theory of the tides in each port, both as to their height and -the times at which they take place, is really a matter of experiment, -and can only be perfectly determined by the mean of a very great number -of observations including several revolutions of the moon's nodes. - -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. In -high latitudes where the ocean is less directly under the influence of -the luminaries, the rise and fall of the sea is inconsiderable, so that, -in all probability, there is no tide at the poles, or only a small -annual and monthly one. The ebb and flow of the sea are perceptible in -rivers to a very great distance from their estuaries. In the straits 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 in 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 of the ocean 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. From this -ratio the mass of the moon is found to be only 1/15 part of that of the -earth. 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, the stability of the equilibrium of the -ocean never can be subverted by any physical cause whatever. A general -inundation arising from the mere instability of the ocean is therefore -impossible. - -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, and it is -sensibly of finite extent, whether it consists of particles infinitely -divisible or not. On the latter hypothesis it must really be finite; and -even if the particles of matter be infinitely divisible, it is known by -experience to be of extreme tenuity at very small heights. The barometer -rises in proportion to the superincumbent pressure. Now at the -temperature of melting ice, the density of mercury is to that of air as -10320 to 1; and as the mean height of the barometer is 29.528 inches, -the height of the atmosphere by simple proportion is 30407 feet, at the -mean temperature of 62°, or 34153 feet, which is extremely small, when -compared with the radius of the earth. The action of the sun and moon -disturbs the equilibrium of the atmosphere, producing oscillations -similar to those in the ocean, which occasion periodic variations in the -heights of the barometer. These, however, are so extremely small, that -their existence in latitudes so far removed from the equator is -doubtful; a series of observations within the tropics can alone decide -this delicate point. La Place seems to think that the flux and reflux -distinguishable at Paris may be occasioned by the rise and fall of the -ocean, which forms a variable base to so great a portion of the -atmosphere. - -The attraction of the sun and moon has no sensible effect on the trade -winds; the heat of the sun occasions these aerial currents, by rarefying -the air at the equator, which causes the cooler and more dense part of -the atmosphere to rush along the surface of the earth to the equator, -while that which is heated is carried along the higher strata to the -poles, forming two currents in the direction of the meridian. But the -rotatory velocity of the air corresponding to its geographical situation -decreases towards the poles; in approaching the equator it must -therefore revolve more slowly than the corresponding parts of the earth, -and the bodies on the surface of the earth must strike against it with -the excess of their velocity, and by its reaction they will meet with a -resistance contrary to their motion of rotation; so that the wind will -appear, to a person supposing himself to be at rest, to blow in a -contrary direction to the earth's rotation, or from east to west, which -is the direction of the trade winds. 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. - -The sun and most of the planets appear to be surrounded with atmospheres -of considerable density. The attraction of the earth has probably -deprived the moon of hers, for the refraction of the air at the surface -of the earth is at least a thousand times as great as at the moon. The -lunar atmosphere, therefore, must be of a greater degree of rarity than -can be produced by our best air-pumps; consequently no terrestrial -animal could exist in it. - -Many philosophers of the highest authority concur in the belief that -light consists in the undulations of a highly elastic ethereal medium -pervading space, which, communicated to the optic nerves produce the -phenomena of vision. The experiments of our illustrious countryman, Dr. -Thomas Young, and those of the celebrated Fresnel, show that this theory -accords better with all the observed phenomena than that of the emission -of particles from the luminous body. As sound is propagated by the -undulations of the air, its theory is in a great many respects similar -to that of light. The grave or low tones are produced by very slow -vibrations, which increase in frequency progressively as the note -becomes more acute. When the vibrations of a musical chord, for example, -are less than sixteen in a second, it will not communicate a continued -sound to the ear; the vibrations or pulses increase in number with the -acuteness of the note, till at last all sense of pitch is lost. The -whole extent of human hearing, from the lowest notes of the organ to the -highest known cry of insects, as of the cricket, includes about nine -octaves. - -The undulations of light are much more rapid than those of sound, but -they are analogous in this respect, that as the frequency of the -pulsations in sound increases from the low tones to the higher, so those -of light augment in frequency, from the red rays of the solar spectrum -to the extreme violet. By the experiments of Sir William Herschel, it -appears that the heat communicated by the spectrum increases from the -violet to the red rays; but that the maximum of the hot invisible rays -is beyond the extreme red. Heat in all probability consists, like light -and sound, in the undulations of an elastic medium. All the principal -phenomena of heat may actually be illustrated by a comparison with those -of sound. The excitation of heat and sound are not only similar, but -often identical, as in friction and percussion; they are both -communicated by contact and by radiation; and Dr. Young observes, that -the effect of radiant heat in raising the temperature of a body upon -which it falls, resembles the sympathetic agitation of a string, when -the sound of another string, which is in unison with it, is transmitted -to it through the air. Light, heat, sound, and the waves of fluids are -all subject to the same laws of reflection, and, indeed, their -undulating theories are perfectly similar. If, therefore, we may judge -from analogy, the undulations of the heat producing rays must be less -frequent than those of the extreme red of the solar spectrum; but if the -analogy were perfect, the interference of two hot rays ought to produce -cold, since darkness results from the interference of two undulations of -light, silence ensues from the interference of two undulations of sound; -and still water, or no tide, is the consequence of the interference of -two tides. - -The propagation of sound requires a much denser medium than that of -either light or heat; its intensity diminishes as the rarity of the air -increases; so that, at a very small height above the surface of the -earth, the noise of the tempest ceases, and the thunder is heard no more -in those boundless regions where the heavenly bodies accomplish their -periods in eternal and sublime silence. - -What the body of the sun may be, it is impossible to conjecture; but he -seems to be surrounded by an ocean of flame through which his dark -nucleus appears like black spots, often of enormous size. The solar -rays, which probably arise from the chemical processes that continually -take place at his surface, are transmitted through space in all -directions; but, notwithstanding the sun's magnitude, and the -inconceivable heat that must exist where such combustion is going on, as -the intensity both of his light and heat diminishes with the square of -the distance, his kindly influence can hardly be felt at the boundaries -of our system. Much depends on the manner in which the rays fall, as we -readily perceive from the different climates on our globe. In winter the -earth is nearer the sun by 1/30th than in summer, but the rays strike -the northern hemisphere more obliquely in winter than in the other half -of the year. In Uranus the sun must be seen like a small but brilliant -star, not above the hundred and fiftieth part so bright as he appears -to us; that is however 2000 times brighter than our moon to us, so -that he really is a sun to Uranus, and probably imparts 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, unless indeed the -ether has a temperature. The climate of Venus more nearly resembles -that of the earth, though, excepting perhaps at her poles, much too -hot for animal and vegetable life as they exist here; but in Mercury -the mean heat, arising only from the intensity of the sun's rays, -must be above that of boiling quick-silver, and water would boil even -at his poles. Thus the planets, though kindred with the earth in -motion and structure, are totally unfit for the habitation of such -a being as man. - -The direct light of the sun has been estimated to be equal to that of -5563 wax candles of a moderate size, supposed to be placed at the -distance of one foot from the object: that of the moon is probably only -equal to the light of one candle at the distance of twelve feet; -consequently the light of the sun is more than three hundred thousand -times greater than that of the moon; for which reason the light of the -moon imparts no heat, even when brought to a focus by a mirror. - -In adverting to the peculiarities in the form and nature of the earth -and planets, it is impossible to pass in silence the magnetism of the -earth, the director of the mariner's compass, and his guide through the -ocean. This property probably arises from metallic iron in the interior -of the earth, or from the circulation of currents of electricity round -it: its influence extends over every part of its surface, but its -accumulation and deficiency determine the two poles of this great -magnet, which are by no means the same as the poles of the earth's -rotation. In consequence of their attraction and repulsion, a needle -freely suspended, whether it be magnetic or not, only remains in -equilibrio when in the magnetic meridian, that is, in the plane which -passes through the north and south magnetic poles. There are places -where the magnetic meridian coincides with the terrestrial meridian; in -these a magnetic needle freely suspended, points to the true north, but -if it be carried successively to different places on the earth's -surface, its direction will deviate sometimes to the east and sometimes -to the west of north. Lines drawn on the globe through all the places -where the needle points due north and south, are called lines of no -variation, and are extremely complicated. The direction of the needle is -not even constant in the same place, but changes in a few years, -according to a law not yet determined. In 1657, the line of no variation -passed through London. In the year 1819, Captain Parry, in his voyage to -discover the north-west passage round America, sailed directly over the -magnetic pole; and in 1824, Captain Lyon, when on en expedition for the -same purpose, found that the variation of the compass was 37° 30' -west, and that the magnetic pole was then situate in 63° 26' 51" -north latitude, and in 80° 51' 25" west longitude. It appears -however from later researches that the law of terrestrial magnetism is -of considerable complication, and the existence of more than one -magnetic pole in either hemisphere has been rendered highly probable. -The needle is also subject to diurnal variations; in our latitudes it -moves slowly westward from about three in the morning till two, and -returns to its former position in the evening. - -A needle suspended so as only to be moveable in the vertical plane, dips -or become more and more inclined to the horizon the nearer it is brought -to the magnetic pole. Captain Lyon found that the dip in the latitude -and longitude mentioned was 86° 32'. What properties the planets may -have in this respect, it is impossible to know, but it is probable that -the moon has become highly magnetic, in consequence of her proximity to -the earth, and because her greatest diameter always points towards it. - -The passage of comets has never sensibly disturbed the stability of the -solar system; their nucleus is rare, and their transit so rapid, that -the time has not been long enough to admit of a sufficient accumulation -of impetus to produce a perceptible effect. The comet of 1770 passed -within 80000 miles of the earth without even affecting our tides, and -swept through the midst of Jupiter's satellites without deranging the -motions of those little moons. Had the mass of that comet been equal to -the mass of the earth, its disturbing action would have shortened the -year by the ninth of a day; but, as Delambre's computations from the -Greenwich observations of the sun, show that the length of the year has -not been sensibly affected by the approach of the comet. La Place proved -that its mass could not be so much as the 5000th part of that of the -earth. The paths of comets have every possible inclination to the plane -of the ecliptic, and unlike the planets, their motion is frequently -retrograde. Comets are only visible when near their perihelia. Then -their velocity is such that its square is twice as great as that of a -body moving in a circle at the same distance; they consequently remain a -very short time within the planetary orbits; and as all the conic -sections of the same focal distance sensibly coincide through a small -arc on each side of the extremity of their axis, it is difficult to -ascertain in which of these curves the comets move, from observations -made, as they necessarily must be, at their perihelia: but probably they -all move in extremely eccentric ellipses, although, in most cases, the -parabolic curve coincides most nearly with their observed motions. Even -if the orbit be determined with all the accuracy that the case admits -of, it may be difficult, or even impossible, to recognise a comet on its -return, because its orbit would be very much changed if it passed near -any of the large planets of this or of any other system, in consequence -of their disturbing energy, which would be very great on bodies of so -rare a nature. Halley and Clairaut predicted that, in consequence of the -attraction of Jupiter and Saturn, the return of the comet of 1759 would -be retarded 618 days, which was verified by the event as nearly as could -be expected. - -The nebulous appearance of comets is perhaps occasioned by the vapours -which the solar heat raises at their surfaces in their passage at the -perihelia, and which are again condensed as they recede from the sun. -The comet of 1680 when in its perihelion was only at the distance of -one-sixth of the sun's diameter, or about 148000 miles from its surface; -it consequently would be exposed to a heat 27500 times greater than that -received by the earth. As the sun's heat is supposed to be in proportion -to the intensity of his height, it is probable that a degree of heat so -very intense would be sufficient to convert into vapour every -terrestrial substance with which we are acquainted. - -In those positions of comets where only half of their enlightened -hemisphere ought to be seen, they exhibit no phases even when viewed -with high magnifying powers. Some slight indications however were once -observed by Hevelius and La Hire in 1682; and in 1811 Sir William -Herschel discovered a small luminous point, which he concluded to be the -disc of the comet. In general their masses are so minute, that they have -no sensible diameters, the nucleus being principally formed of denser -strata of the nebulous matter, but so rare that stars have been seen -through them. The transit of a comet over the sun's disc would afford -the best information on this point. It was computed that such an event -was to take place in the year 1627; unfortunately the sun was hid by -clouds in this country, but it was observed at Viviers and at Marseilles -at the time the comet must have been on it, but no spot was seen. The -tails are often of very great length, and are generally situate in the -planes of their orbits; they follow them in their descent towards the -sun, but precede them in their return, with a small degree of curvature; -but their extent and form must vary in appearance, according to the -position of their orbits with regard to the ecliptic. The tail of the -comet of 1680 appeared, at Paris, to extend over sixty-two degrees. The -matter of which the tail is composed must be extremely buoyant to -precede a body moving with such velocity; indeed the rapidity of its -ascent cannot be accounted for. The nebulous part of comets diminishes -every time they return to their perihelia; after frequent returns they -ought to lose it altogether, and present the appearance of a fixed -nucleus; this ought to happen sooner in comets of short periods. La -Place supposes that the comet of 1682 must be approaching rapidly to -that state. Should the substances be altogether or even to a great -degree evaporated, the comet wilt disappear for ever. Possibly comets -may have vanished from our view sooner than they otherwise would have -done from this cause. Of about six hundred comets that have been seen at -different times, three are now perfectly ascertained to form part of our -system; that is to say, they return to the sun at intervals of 76, 6 1/3, -and 3 1/4 years nearly. - -A hundred and forty comets have appeared within the earth's orbit during -the last century that have not again been seen; if a thousand years be -allowed as the average period of each, it may be computed by the theory -of probabilities, that the whole number that range within the earth's -orbit must be 1400; but Uranus being twenty times more distant, there -may be no less than 11,200,000 comets that come within the known extent -of our system. In such a multitude of wandering bodies it is just -possible that one of them may come in collision with the earth; but even -if it should, the mischief would be local, and the equilibrium soon -restored. It is however more probable that the earth would only be -deflected a little from its course by the near approach of the comet, -without being touched. Great as the number of comets appears to be, it -is absolutely nothing when compared to the number of the fixed stars. -About two thousand only are visible to the naked eye, but when we view -the heavens with a telescope, their number seems to be limited only by -the imperfection of the instrument. In one quarter of an hour Sir -William Herschel estimated that 116000 stars passed through the field of -his telescope, which subtended an angle of 15'. This however was -stated as a specimen of extraordinary crowding; but at an average the -whole expanse of the heavens must exhibit about a hundred millions of -fixed stars that come within the reach of telescopic vision. - -Many of the stars have a very small progressive motion, especially _μ_ -Cassiopeia and 61 Cygni, both small stars; and, as the sun is decidedly -a star, it is an additional reason for supposing the solar system to be -in motion. The distance of the fixed stars is too great to admit of -their exhibiting a sensible disc; but in all probability they are -spherical, and must certainly be so, if gravitation pervades all space. -With a fine telescope they appear like a point of light; their twinkling -arises from sudden changes in the refractive power of the air, which -would not be sensible if they had discs like the planets. Thus we can -learn nothing of the relative distances of the stars from us and from -one another, by their apparent diameters; but their annual parallax -being insensible, shows that we must be one hundred millions of millions -of miles from the nearest; many of them however must be vastly more -remote, for of two stars that appear close together, one may be far -beyond the other in the depth of space. The light of Sirius, according -to the observations of Mr. Herschel, is 324 times greater than that of a -star of the sixth magnitude; if we suppose the two to be really of the -same size, their distances from us must be in the ratio of 57.3 to 1, -because light diminishes as the square of the distance of the luminous -body increases. - -Of the absolute magnitude of the stars, nothing is known, only that many -of them must be much larger than the sun, from the quantity of light -emitted by them. Dr. Wollaston determined the approximate ratio that the -light of a wax candle bears to that of the sun, moon, and stars, by -comparing their respective images reflected from small glass globes -filled, with mercury, whence a comparison was established between the -quantities of light emitted by the celestial bodies themselves. By this -method he found that the light of the sun is about twenty millions of -millions of times greater than that of Sirius, the brightest, and -supposed to be the nearest of the fixed stars. If Sirius had a parallax -of half a second, its distance from the earth would be 525481 times the -distance of the sun from the earth; and therefore Sirius, placed where -the sun is, would appear to us to be 3.7 times as large as the sun, and -would give 13.8 times more light; but many of the fixed stars must be -immensely greater than Sirius. Sometimes stars have all at once -appeared, shone with a brilliant light, and then vanished. In 1572 a -star was discovered in Cassiopeia, which rapidly increased in brightness -till it even surpassed that of Jupiter; it then gradually diminished in -splendour, and after exhibiting all the variety of tints that indicates -the changes of combustion, vanished sixteen months after its discovery, -without altering its position. It is impossible to imagine any thing -more tremendous than a conflagration that could be visible at such a -distance. Some stars are periodic, possibly from the intervention of -opaque bodies revolving about them, or from extensive spots on their -surfaces. Many thousands of stars that seem to be only brilliant points, -when carefully examined are found to be in reality systems of two or -more suns revolving about a common centre. These double and multiple -stars are extremely remote, requiring the most powerful telescopes to -show them separately. - -The first catalogue of double stars in which their places and relative -positions are determined, was accomplished by the talents and industry -of Sir William Herschel, to whom astronomy is indebted for so many -brilliant discoveries, and with whom originated the idea of their -combination in binary and multiple systems, an idea which his own -observations had completely established, but which has since received -additional confirmation from those of his son and Sir James South, the -former of whom, as well as Professor Struve of Dorpat, have added many -thousands to their numbers. The motions of revolution round a common -centre of many have been clearly established, and their periods -determined with considerable accuracy. Some have already since their -first discovery accomplished nearly a whole revolution, and one, if the -latest observations can be depended on, is actually considerably -advanced in its second period. These interesting systems thus present a -species of sidereal chronometer, by which the chronology of the heavens -will be marked out to future ages by epochs of their own, liable to no -fluctuations from planetary disturbances such as obtain in our system. - -Possibly among the multitudes of small stars, whether double or -insulated, some may be found near enough to exhibit distinct parallactic -motions, or perhaps something approaching to planetary motion, which may -prove that solar attraction is not confined to our system, or may lead -to the discovery of the proper motion of the sun. The double stars are -of various hues, but most frequently exhibit the contrasted colours. The -large star is generally yellow, orange, or red; and the small star blue, -purple, or green. Sometimes a white star is combined with a blue or -purple, and more rarely a red and white are united. In many cases, these -appearances are due to the influences of contrast on our judgment of -colours. For example, in observing a double star where the large one is -of a full ruby red, or almost blood colour, and the small one a fine -green, the latter lost its colour when the former was hid by the cross -wires of the telescope. But there are a vast number of instances where -the colours are too strongly marked to be merely imaginary. Mr. Herschel -observes in one of his papers in the _Philosophical Transactions_, as a -very remarkable fact, that although red single stars are common enough, -no example of an insulated blue, green, or purple one has as yet been -produced. - -In some parts of the heavens, the stars are so near together as to form -clusters, which to the unassisted eye appear like thin white clouds; -such is the milky way, which has its brightness from the diffused light -of myriads of stars. Many of these clouds, however, are never resolved -into separate stars, even by the highest magnifying powers. This -nebulous matter exists in vast abundance in space. No fewer than 2500 -nebulæ were observed by Sir William Herschel, whose places have been -computed from his observations, reduced to a common epoch, and arranged -into a catalogue in order of right ascension by his sister Miss Caroline -Herschel, a lady so justly celebrated for astronomical knowledge and -discovery. The nature and use of this matter scattered over the heavens -in such a variety of forms is involved in the greatest obscurity. That -it is a self-luminous, phosphorescent material substance, in a highly -dilated or gaseous state, but gradually subsiding by the mutual -gravitation of its particles into stars and sidereal systems, is the -hypothesis which seems to be most generally received; but the only way -that any real knowledge on this mysterious subject can be obtained, is -by the determination of the form, place, and present state of each -individual nebula, and a comparison of these with future observations -will show generations to come the changes that may now be going on in -these rudiments of future systems. With this view, Mr. Herschel is now -engaged in the difficult and laborious investigation, which is -understood to be nearly approaching its completion, and the results of -which we may therefore hope ere long to see made public. The most -conspicuous of these appearances are found in Orion, and in the girdle -of Andromeda. It is probable that light must be millions of years -travelling to the earth from some of the nebulæ. - -So numerous are the objects which meet our view in the heavens, that we -cannot imagine a part of space where some light would not strike the -eye: but as the fixed stars would not be visible at such distances, if -they did not shine by their own light, it is reasonable to infer that -they are suns; and if so, they are in all probability attended by -systems of opaque bodies, revolving about them as the planets do about -ours. But although there be no proof that planets not seen by us revolve -about these remote suns, certain it is, that there are many invisible -bodies wandering in space, which, occasionally coming within the sphere -of the earth's attraction, are ignited by the velocity with which they -pass through the atmosphere, and are precipitated with great violence on -the earth. The obliquity of the descent of meteorites, the peculiar -matter of which they are composed, and the explosion with which their -fall is invariably accompanied, show that they are foreign to our -planet. Luminous spots altogether independent of the phases have -occasionally appeared on the dark part of the moon, which have been -ascribed to the light arising from the eruption of volcanoes; whence it -has been supposed that meteorites have been projected from the moon by -the impetus of volcanic eruption; it has even been computed, that if a -stone were projected from the moon in a vertical line, and with an -initial velocity of 10992 feet in a second, which is more than four -times the velocity of a ball when first discharged from a cannon, -instead of falling back to the moon by the attraction of gravity, it -would come within the sphere of the earth's attraction, and revolve -about it like a satellite. These bodies, impelled either by the -direction of the primitive impulse, or by the disturbing action of the -sun, might ultimately penetrate the earth's atmosphere, and arrive at -its surface. But from whatever source meteoric stones may come, it seems -highly probable, that they have a common origin, from the uniformity, we -may almost say identity, of their chemical composition. - -The known quantity of matter bears a very small proportion to the -immensity of space. Large as the bodies are, the distances that separate -them are immeasurably greater; but as design is manifest in every part -of creation, it is probable that if the various systems in the universe -had been nearer to one another, their mutual disturbances would have -been inconsistent with the harmony and stability of the whole. It is -clear that space is not pervaded by atmospheric air, since its -resistance would long ere this have destroyed the velocity of the -planets; neither can we affirm it to be void, when it is traversed in -all directions by light, heat, gravitation, and possibly by influences -of which we can form no idea; but whether it be replete with an ethereal -medium, time alone will show. - -Though totally ignorant of the laws which obtain in the more distant -regions of creation, we are assured, that one alone regulates the -motions of our own system; and as general laws form the ultimate object -of philosophical research, we cannot conclude these remarks without -considering the nature of that extraordinary power, whose effects we -have been endeavouring to trace through some of their mazes. It was at -one time imagined, that the acceleration in the moon's mean motion was -occasioned by the successive transmission of the gravitating force; but -it has been proved, that, in order to produce this effect, its velocity -must be about fifty millions of times greater than that of light, which -flies at the rate of 200000 miles in a second; its action even at the -distance of the sun may therefore be regarded as instantaneous; yet so -remote are the nearest of the fixed stars, that it may be doubted -whether the sun has any sensible influence on them. - -The analytical expression for the gravitating force is a straight line; -the curves in which the celestial bodies move by the force of -gravitation are only lines of the second order; the attraction of -spheroids according to any other law would be much more complicated; and -as it is easy to prove that matter might have been moved according to an -infinite variety of laws, it may be concluded, that gravitation must -have been selected by Divine wisdom out of an infinity of other laws, -its being the most simple, and that which gives the greatest stability -to the celestial motions. - -It is a singular result of the simplicity of the laws of nature, which -admit only of the observation and comparison of ratios, that the -gravitation and theory of the motions of the celestial bodies are -independent of their absolute magnitudes and distances; consequently if -all the bodies in the solar system, their mutual distances, and their -velocities, were to diminish proportionally, they would describe curves -in all respect similar to those in which they now move; and the system -might be successively reduced to the smallest sensible dimensions, and -still exhibit the same appearances. Experience shows that a very -different law of attraction prevails when the particles of matter are -placed within inappreciable distances from each other, as in chemical -and capillary attractions, and the attraction of cohesion; whether it be -a modification of gravity, or that some new and unknown power comes into -action, does not appear; but as a change in the law of the force takes -place at one end of the scale, it is possible that gravitation may not -remain the same at the immense distance of the fixed stars. Perhaps the -day may come when even gravitation, no longer regarded as an ultimate -principle, may be resolved into a yet more general cause, embracing -every law that regulates the material world. - -The action of the gravitating force is not impeded by the intervention -even of the densest substances. If the attraction of the sun for the -centre of the earthy and for the hemisphere diametrically opposite to -him, was diminished by a difficulty in penetrating the interposed -matter, the tides would be more obviously affected. Its attraction is -the same also, whatever the substances of the celestial bodies may be, -for if the action of the sun on the earth differed by a millionth part -from his action on the moon, the difference would occasion a variation -in the sun's parallax amounting to several seconds, which is proved to -be impossible by the agreement of theory with observation. Thus all -matter is pervious to gravitation, and is equally attracted by it. - -As far as human knowledge goes, the intensity of gravitation, has never -varied within the limits of the solar system; nor does even analogy lead -us to expect that it should; on the contrary, there is every reason to -be assured, that the great laws of the universe are immutable like their -Author. Not only the sun and planets, but the minutest particles in all -the varieties of their attractions and repulsions, nay even the -imponderable matter of the electric, galvanic, and magnetic fluids are -obedient to permanent laws, though we may not be able in every case to -resolve their phenomena into general principles. Nor can we suppose the -structure of the globe alone to be exempt from the universal fiat, -though ages may pass before the changes it has undergone, or that are -now in progress, can be referred to existing causes with the same -certainty with which the motions of the planets and all their secular -variations are referable to the law of gravitation. The traces of -extreme antiquity perpetually occurring to the geologist, give that -information as to the origin of things which we in vain look for in the -other parts of the universe. They date the beginning of time; since -there is every reason to believe, that the formation of the earth was -contemporaneous with that of the rest of the planets; but they show that -creation is the work of Him with whom 'a thousand years are as one day, -and one day as a thousand years.' - -*** END OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON -THE MECHANISMS OF THE HEAVENS *** - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the -United States without permission and without paying copyright -royalties. Special rules, set forth in the General Terms of Use part -of this license, apply to copying and distributing Project -Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm -concept and trademark. 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You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online -at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you -are not located in the United States, you will have to check the laws of the -country where you are located before using this eBook. -</div> - -<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: A Preliminary Dissertation on the Mechanisms of the Heavens</p> -<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Mary Somerville</p> -<p style='display:block; text-indent:0; margin:1em 0'>Release Date: February 12, 2022 [eBook #67386]</p> -<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p> - <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: Laura Natal Rodrigues (Images generously made available by Hathi Trust Digital Library.)</p> -<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***</div> - -<div class="figcenter" style="width: 500px;"> -<img src="images/dissertation_cover.jpg" width="500" alt="" /> -</div> - - - -<h1>A -<br /> -PRELIMINARY DISSERTATION -<br /> -ON THE -<br /> -MECHANISM OF THE HEAVENS.</h1> - -<p><br /></p> - -<h5>BY</h5> - -<h2>MRS. SOMMERVILLE</h2> - -<p><br /></p> - -<h4>PHILADELPHIA:</h4> - -<h3>CAREY & LEA</h3> - -<h5>1832</h5> - -<p><br /><br /><br /></p> - -<p> -In order to convey some idea of the object of this work, it may be -useful to offer a few preliminary observations on the nature of the -subject which it is intended to investigate, and of the means that have -already been adopted with so much success to bring within the reach of -our faculties, those truths which might seem to be placed so far beyond -them. -</p> - -<p> -All the knowledge we possess of external objects is founded upon -experience, which furnishes a knowledge of facts, and the comparison of -these facts establishes relations, from which, induction, the intuitive -belief that like causes will produce like effects, leads us to general -laws. Thus, experience teaches that bodies fall at the surface of the -earth with an accelerated velocity, and proportional to their masses. -Newton proved, by comparison, 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 induction led him to conclude 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. -</p> - -<p> -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 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. -</p> - -<p> -The combined efforts of astronomers, from the earliest dawn of -civilization, have been requisite 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 of -matter. On the other hand, descending from the principle of gravitation, -every motion in the system of the world has been so completely -explained, that no astronomical phenomenon can now be transmitted to -posterity of which the laws have not been determined. -</p> - -<p> -Science, regarded as the pursuit of truth, which can only be attained by -patient and unprejudiced investigation, wherein nothing is too great to -be attempted, nothing so minute as to be justly disregarded, must ever -afford occupation of consummate interest and 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 elegant 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. -</p> - -<p> -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 -limits. 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 us a base wherewith to measure -the magnitude and distance of the sun and planets, and make the diameter -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 which seem so mighty to us -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 or creation. -</p> - -<p> -A complete acquaintance with Physical Astronomy can only be attained by -those who are well versed in the higher branches of mathematical and -mechanical science: such alone can appreciate the extreme beauty of -the results, and of the means by which these results are obtained. -Nevertheless a sufficient skill in analysis to follow the general -outline, to see the mutual dependence of the different parts of the -system, and to comprehend by what means some of the most extraordinary -conclusions have been arrived at, is within the reach of many who shrink -from the task, appalled by difficulties, which perhaps are not more -formidable than those incident to the study of the elements of every -branch of knowledge, and possibly overrating them by not making a -sufficient distinction between the degree of mathematical acquirement -necessary for making discoveries, and that which is requisite for -understanding what others have done. That the study of mathematics and -their application to astronomy are full of interest will be allowed by -all who have devoted their time and attention to these pursuits, and -they only can estimate the delight of arriving at truth, whether it be -in the discovery of a world, or of a new property of numbers. -</p> - -<p> -It has been proved by Newton that a particle of matter placed without -the surface of a hollow sphere is attracted by it in the name manner as -if its mass, or the whole matter it contains, were collected 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. -This however is not the case with a spheroid, but the celestial bodies -are so nearly spherical, and at such remote distances from each other, -that they attract and are attracted as if each were a dense point -situate in its centre of gravity, a circumstance which greatly -facilitates the investigation of their motions. -</p> - -<p> -The attraction of the earth on bodies at its surface in that latitude, -the square of whose sine is ⅓, 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 of the moon from the earth is about sixty -times the mean radius of the earth. When the number 16.0697 is -diminished in the ratio of 1 to 3600, which is the square of the moon's -distance from the earth, 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 her centrifugal force, arising from the velocity -with which she moves in her orbit. So that the moon is 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; but as experience shows that the action and reaction of matter are -equal and contrary, the moon must attract the earth with an equal and -contrary force. -</p> - -<p> -Newton proved that a body projected in space will move in a conic -section, if it be attracted by a force directed towards a fixed point, -and having an intensity inversely as the square of the distance; but -that any deviation from that law will cause it to move in a curve of a -different nature. Kepler ascertained by direct observation that the -planets describe ellipses round the sun, and 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 his 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. -</p> - -<p> -Kepler also deduced from observation, that the squares of the periodic -times of the planets, or the times of their revolutions round the sun, -are proportional to the cubes of their mean distances from his centre: -whence it follows, that the intensity of gravitation of all the bodies -towards the sun is the same at equal distances; consequently gravitation -is proportional to the masses, for if the planets and comets be supposed -to be at equal distances from the sun and left to the effects of -gravity, they would arrive at his surface at the same time. The -satellites also gravitate to their primaries according to the same law -that their primaries do to the sun. Hence, by the law of action and -reaction, each body is itself the centre of an attractive force -extending indefinitely in space, whence proceed all the mutual -disturbances that render the celestial motions so complicated, and their -investigation so difficult. -</p> - -<p> -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 taken in mass; 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 -in other respects they also would 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; 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, which is impossible. -</p> - -<p> -The form of the planets results 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 revolves about an axis, it becomes flattened at the poles, -and bulges at the equator, in consequence of the centrifugal force -arising from the velocity of rotation. For, the centrifugal force -diminishes the gravity of the particles at the equator, and equilibrium -can only exist when 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 balanced the -centrifugal force by their attraction, consequently the sphere would -become an oblate 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. Such is the form of the earth and planets, -but the compression or flattening at their poles is so small, that even -Jupiter, whose rotation is the most rapid, differs but little from a -sphere. Although the planets attract each other as if they were spheres -on account of their immense distances, yet the satellites 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 in -the axis of rotation, and the reaction of that matter on the moon is the -cause of a corresponding nutation in the lunar orbit. -</p> - -<p> -If a sphere at rest in space receives 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 give it a -rotatory motion at the same time that it is translated in space. These -motions are independent of one another, so that a contrary impulse -passing through its centre of gravity will impede its progression, -without interfering with its rotation. As the sun rotates about an axis, -it seems probable if an impulse in a contrary direction has not been -given to his centre of gravity, that he moves in space accompanied by -all those bodies which compose the solar system, a circumstance that -would in no way interfere with their relative motions; for, in -consequence of our experience that force is proportional to velocity, -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, -such impulse must have passed through a point about twenty-five miles -from its centre. -</p> - -<p> -Since the motions of the rotation and translation of the planets are -independent of each other, though probably communicated by the same -impulse, they form separate subjects of investigation. -</p> - -<p> -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 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 a planet is in its aphelion or at the -point where the orbit is farthest from the sun, his action overcomes its -velocity, and brings it towards him with such an accelerated motion, -that it at last overcomes the sun's attraction, and shoots past him; -then, gradually decreasing in velocity, it arrives at the aphelion where -the sun's attraction again prevails. In this motion the radii vectores, -or imaginary lines joining the centres of the sun and planets, pass over -equal areas in equal times. -</p> - -<p> -If the planets were attracted by the sun only, this would ever be their -course; and because his action is proportional to his mass, which is -immensely larger than that of all the planets put together, the -elliptical is the nearest approximation to their true motions, which 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, and now receding from the elliptical form, and their -radii vectores do not describe areas exactly proportional to the time. -Thus the areas become a test of the existence of disturbing forces. -</p> - -<p> -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 arises the celebrated -problem of the three bodies, which originally was that of 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 position at any given instant. -</p> - -<p> -By this problem the motions of translation of all the celestial bodies -are determined. It is one of extreme difficulty, and would be of -infinitely greater difficulty, if the disturbing action were not very -small, when compared with the central force. 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. -</p> - -<p> -On account of the reciprocal action of matter, the stability of the -system depends on the intensity of the primitive momentum 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 -on 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, their mutual attractions might have changed them into -parabolas or even hyperbolas; so that the earth and planets might ages -ago have been sweeping 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 immensely -greater than those of the planets; and as their inequalities bear the -same ratio to their elliptical motions as their masses do to that of the -sun, their mutual disturbances only increase or diminish the -eccentricities 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 the end, -than is exhibited in the nice adjustment of these forces. -</p> - -<p> -The orbits of the planets have a very small inclination to the plane of -the ecliptic in which the earth moves; and on that account, astronomers -refer their motions to it at a given epoch as a known and fixed -position. 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; the points where the orbit intersects the -plane of the ecliptic are its nodes. -</p> - -<p> -The orbits of the recently discovered planets deviate more from the -ecliptic: that of Pallas has an inclination of 35° to it: on that -account it will be more difficult to determine their motions. These -little planets have no sensible effect in disturbing the rest, though -their own motions are rendered very irregular by the proximity of -Jupiter and Saturn. -</p> - -<p> -The planets are subject to disturbances of two distinct 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 troubled planet is sometimes drawn away from -the sun, sometimes brought nearer to him; 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. -</p> - -<p> -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 on 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. -</p> - -<p> -In consequence of disturbances of this kind, the apsides, or extremities -of the major axes of all the orbits, have a direct, but variable motion -in space, excepting those of Venus, which are retrograde; and the lines -of the nodes move with a variable velocity in the contrary direction. -The motions of both are extremely slow; it requires more than 109770 -years for the major axis of the earth's orbit to accomplish a sidereal -revolution, and 20935 years to complete its tropical motion. The major -axis of Jupiter's orbit requires no less than 197561 years to perform -its revolution from the disturbing action of Saturn alone. The periods -in which the nodes revolve are also very great. Beside these, the -inclination and eccentricity of every orbit are in a state of perpetual, -but slow change. At the present time, the inclinations of all the orbits -are decreasing; but so slowly, that the inclination of Jupiter's orbit -is only six minutes less now than it was in the age of Ptolemy. The -terrestrial eccentricity is decreasing at the rate of 3914 miles in a -century; and if it were to decrease equably, it would be 36300 years -before the earth's orbit became a circle. But in the midst of all these -vicissitudes, the major axes and 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. -</p> - -<p> -With the exception of these two elements, it appears, that all the -bodies are in motion, and every orbit is in a state of perpetual change. -Minute as these changes are, they might be supposed liable 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. The -consequences being so dreadful, it is natural to inquire, what proof -exists that creation will be preserved from such a catastrophe? For -nothing can be known from observation, since the existence of the human -race has occupied but a point in duration, while these vicissitudes -embrace myriads of ages. The proof is simple and convincing. All the -variations of the solar system, as well secular as periodic, are -expressed analytically by the sines and cosines of circular arcs, which -increase with the time; and as a sine or cosine never can exceed the -radius, but must oscillate between zero and unity, however much the time -may increase, it follows, that when the variations have by slow changes -accumulated in however long a time to a maximum, they decrease by the -same slow degrees, till they arrive at their smallest value, and then -begin a new course, thus for ever oscillating about a mean value. This, -however, would not be the case if the planets moved in a resisting -medium, for then both the eccentricity and the major axes of the orbits -would vary with the time, so that the stability of the system would be -ultimately destroyed. But if the planets do move in an ethereal medium, -it must be of extreme rarity, since its resistance has hitherto been -quite insensible. -</p> - -<p> -Three circumstances have generally been supposed necessary to prove the -stability of the system: the small eccentricities of the planetary -orbits, their small inclinations, and the revolution of all the bodies, -as well planets as satellites, in the same direction. These, however, -are not necessary conditions: the periodicity of the terms in which the -inequalities are expressed is sufficient to assure us, that though 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. -</p> - -<p> -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 52"·109, occasioned by the reciprocal action -of the planets; but as this is also periodical, the terrestrial equator, -which is inclined to it at an angle of about 23° 28', will never -coincide with the plane of the ecliptic; so there never can be perpetual -spring. -</p> - -<p> -The rotation of the earth is uniform; therefore day and night, summer -and winter, will continue their vicissitudes while the system endures, -or is untroubled by foreign causes. -</p> - -<div class="poem"><div class="stanza"> -<span class="i12">Yonder starry sphere</span><br /> -<span class="i2">Of planets, and of fix'd, in all her wheels</span><br /> -<span class="i2">Resembles nearest, mazes intricate,</span><br /> -<span class="i2">Eccentric, intervolv'd, yet regular</span><br /> -<span class="i2">Then most, when most irregular they seem.</span> -</div></div> - -<p> -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 -elliptical orbits of the planets, La Grange's discovery of their -periodical inequalities is without doubt the noblest truth in physical -astronomy; and, in respect of the doctrine of final causes, it may be -regarded as the greatest of all.' -</p> - -<p> -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. This difficulty is obviated by La Place, who has shown -that whatever changes time may induce either in the orbits themselves, -or in the plane of the ecliptic, there exists an invariable plane -passing through the centre of gravity of the sun, about which the whole -system oscillates within narrow limits, and which is determined by this -property; that if every body in the system be projected on it, and if -the mass of each be multiplied by the area described in a given time by -its projection on this plane, the sum of all these products will be a -maximum. 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 remains parallel to itself, and -maintains a fixed position, whence the oscillations of the system may be -estimated through unlimited time. It is situate nearly half way between -the orbits of Jupiter and Saturn, and is inclined to the ecliptic at an -angle of about 1° 35' 31". -</p> - -<p> -All the periodic and secular inequalities deduced from the law of -gravitation are so perfectly confirmed by observations, 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 great inequalities of very long periods, forming -what appeared an 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 inequality in the mean -motion of each of these planets, which completes its period in nearly -929 Julian years, the one being retarded, while the other is -accelerated. These inequalities are strictly periodical, since they -depend on the configuration of the two planets; and the theory is -perfectly confirmed by observation, which shows that in the course of -twenty centuries, Jupiter's mean motion has been accelerated by 3° 23', -and Saturn's retarded by 5° 13'. -</p> - -<p> -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 those bodies were united in their common centre -of gravity; the action of the sun however disturbs in some degree the -motion of the satellites about their primary. -</p> - -<p> -The changes that take place in the planetary system are exhibited on a -small scale by Jupiter and his satellites; and as the period requisite -for the development of the inequalities of these little 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 -centuries. 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 the compression of Jupiter's spheroid is very great in -consequence of his rapid rotation; and as the masses of the satellites -are nearly 100000 times less than that of Jupiter, 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 further removed from its influence, move in orbits with -a very small eccentricity. The same cause occasions the orbits of the -satellites to remain nearly in the plane of Jupiter's equator, on -account of which they are always seen nearly in the same line; and the -powerful action of that quantity of prominent matter is the reason why -the motion of the nodes of these little bodies is so much more rapid -than those of the planet. The nodes of the fourth satellite accomplish a -revolution in 520 years, while those of Jupiter's orbit require no less -than 50673 years, a proof of the reciprocal attraction between each -particle of Jupiter's equator and of the satellites. Although the two -first satellites sensibly move in circles, they acquire a small -ellipticity from the disturbances they experience. -</p> - -<p> -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 -further the satellite is removed, a circumstance entirely owing to the -influence of Jupiter's compression. -</p> - -<p> -A singular law obtains among the mean motions and mean longitudes of the -three first 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. They extend to the synodic motions 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 they are frequently eclipsed by the planet. 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, gives the difference of the meridians in time, and -consequently the longitude of the place of observation. It has required -all the refinements of modern instruments to render the eclipses of -these remote moons available to the mariner; now however, that system of -bodies invisible to the naked eye, known to man by the aid of science -alone, enables him to traverse the ocean, spreading the light of -knowledge and the blessings of civilization over the most remote -regions, and to return loaded with the productions of another -hemisphere. Nor is this all: the eclipses of Jupiter's satellites have -been the means or a discovery, which, though not so immediately -applicable to the wants of man, unfolds a property 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, are later by 16' 26" than those which take place when the -planet is in opposition. But as Jupiter is nearer to us when in -opposition by the whole breadth of the earth's orbit than when in -conjunction, this circumstance was attributed to the time employed by -the rays of light in crossing the earth's orbit, a distance of 192 -millions of miles; whence it is estimated, that light travels at the -rate of 192000 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 -confirmed this astonishing result. -</p> - -<p> -Objects appear to be situate in the direction of the rays that 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, when Jupiter is in conjunction, we -see him by means of rays that left him 16' 26" 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 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 192000 to 19. In consequence of -aberration, none of the heavenly bodies are in the place in which they -seem to be. 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 never -exceeds twenty seconds, in ordinary cases. -</p> - -<p> -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 apparently the most unpromising and dissimilar -circumstances, occur in physical astronomy, and prove dependences 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 if light consists in the vibrations of an -elastic fluid or ether filling space, which hypothesis accords best with -observed phenomena, the uniformity of its velocity shows that the -density of the fluid throughout the whole extent of the solar system, -must be proportional to its elasticity. 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." -</p> - -<p> -As 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 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. -</p> - -<p> -The little that is known of the theories of the satellites of Saturn and -Uranus is in all respects similar to that of Jupiter. The great -compression of Saturn occasions its satellites to move nearly in the -plane of its equator. Of the situation of the equator of Uranus we know -nothing, nor of its compression. The orbits of its satellites are nearly -perpendicular to the plane of the ecliptic. -</p> - -<p> -Our constant companion the moon next claims 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. Neither the -eccentricity of the lunar orbit, nor its inclination to the plane of the -ecliptic, have experienced any changes from secular inequalities; but -the mean motion, the nodes, and the perigee, are subject to very -remarkable variations. -</p> - -<p> -From an eclipse observed at Babylon by the Chaldeans, 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; 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; -all the 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, and it was at one time attributed to the -resistance of an ethereal medium pervading space; 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 or nodes, they could not affect the -mean motion, a variation in the latter from such a cause being -inseparably connected with variations in the two former of these -elements. That great mathematician, however, in studying the theory of -Jupiter's satellites, perceived that the secular variations in the -elements of Jupiter's orbit, from the action of the planets, occasion -corresponding changes in the motions of the satellites: this led him to -suspect that the acceleration in the mean motion of the moon might be -connected with the secular variation in the eccentricity of the -terrestrial orbit; and analysis has proved that he assigned the true -cause. -</p> - -<p> -If the eccentricity of the earth's orbit were invariable, the moon would -be exposed to a variable disturbance from the action of the sun, in -consequence of the earth's annual revolution; but it would be periodic, -since it would be the same as often as the sun, the earth, and the moon -returned to the same relative positions: on account however of the slow -and incessant diminution in the eccentricity of the terrestrial orbit, -the revolution of our planet is performed at different distances from -the sun every year. The position of the moon with regard to the sun, -undergoes a corresponding change; so that the mean action of the sun on -the moon varies from one century to another, and occasions the secular -increase in the moon's velocity called the acceleration, a name which is -very appropriate in the present age, and which will continue to be so -for a vast number of ages to come; because, as long as the earth's -eccentricity diminishes, the moon's mean motion will be accelerated; but -when the eccentricity has passed its minimum and begins to increase, the -mean motion will be retarded from age to age. At present the secular -acceleration is about 10", but its effect on the moon's place increases -as the square of the time. 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 eccentricity, 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 1° 48' in the moon's longitude, -and of 7° 12' in her mean anomaly. -</p> - -<p> -The action of the sun occasions a rapid but variable motion in the nodes -and perigee of the lunar orbit; the former, though they recede during -the greater part of the moon's revolution, and advance during the smaller, -perform their sidereal revolutions in 6793<sup>days</sup>.4212, and the -latter, though its motion is sometimes retrograde and sometimes direct, -in 3232<sup>days</sup>.5807, or a little more than nine years: 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 109770 years for the -greater axis of the terrestrial orbit to do the same. 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 motion of the nodes and perigee; and 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 eccentricity -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, and 0.265, or according -to the most recent investigations as 1, 4, 6776 and 0.391. A comparison -of ancient eclipses observed by the Arabs, Greeks, and Chaldeans, -imperfect as they are, with modern observations, perfectly confirms -these results of analysis. -</p> - -<p> -Future ages will develop these great inequalities, which at some most -distant period will amount to many circumferences. They are indeed -periodic; but who shall tell their period? Millions of years must elapse -before that great cycle is accomplished; but 'such changes, though rare -in time, are frequent in eternity.' -</p> - -<p> -The moon is so near, that the excess of matter at the earth's equator -occasions periodic variations in her longitude and latitude; and, 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 equatorial diameter 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 square of the distance, were to revolve about an axis, as the -earth, it would assume the form of a spheroid, whose compression is -¹⁄₂₃₀. Whence it appears, that the earth is not homogeneous, but decreases -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 the internal structure of our planet; results of analysis which -could not have been anticipated. Similar inequalities in Jupiter's -satellites prove that his mass is not homogeneous, and that his -compression is ¹⁄₁₃.₈. -</p> - -<p> -The motions of the moon have now become of more importance to the -navigator and geographer than those of any other body, from the -precision with which the longitude is determined by the occultations of -stars and lunar distances. The lunar theory is brought to such -perfection, that the times of these phenomena, observed under any -meridian, when compared with that computed for Greenwich in the Nautical -Almanack, gives the longitude of the observer within a few miles. The -accuracy of that work is obviously of extreme importance to a maritime -nation; we have reason to hope that the new Ephemeris, now in -preparation, will be by far the most perfect work of the kind that ever -has been published. -</p> - -<p> -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 distance of the sun and -moon from the earth is obtained: whence it appears that the sun's -distance from the earth is nearly 396 times greater than that of the -moon. -</p> - -<p> -The method however of finding the absolute distances of the celestial -bodies in miles, is in fact the same with that employed in measuring -distances of terrestrial objects. From the extremities of a known base -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 at all from the celestial bodies. But the globe -itself whose dimensions are ascertained by actual admeasurement, -furnishes a standard of measures, with which we compare the distances, -masses, densities, and volumes of the sun and planets. -</p> - -<p> -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, at any rate, quite 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 gravity, 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:— -</p> - -<p> -A terrestrial meridian is a line passing through both poles, all the -points of which have contemporaneously the same noon. 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 will -be greatest where the curvature is least; a comparison of the length of -the degrees in different parts of the earth's surface will therefore -determine its size and form. -</p> - -<p> -An arc of the meridian may be measured by observing the latitude of its -extreme points, 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, the sides and angles of which are either measured -or computed, so that the length of the arc is ascertained with much -laborious computation. In consequence of the inequalities 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 is spherical, they -require a correction to reduce them from plane to spherical triangles. -</p> - -<p> -Arcs of the meridian have been measured in a variety of latitudes, both -north and south, as well as arcs perpendicular to the meridian. From -these measurements it appears that the length of the degrees increase -from the equator to the poles, nearly as the square of the sine of the -latitude; consequently, the convexity of the earth diminishes from the -equator to the poles. Many discrepancies occur, but the figure that most -nearly follows this law is an ellipsoid of revolution, whose equatorial -radius is 3962.6 miles, and the polar radius 3949.7; the difference, or -12.9 miles, divided by the equatorial radius, is ¹⁄₃₀₈.₇, or ¹⁄₃₀₉ -nearly; this fraction is called the compression of the earth, because, -according as it is greater or less, the terrestrial ellipsoid is more -or less flattened at the poles; it does not differ much from that given -by the lunar inequalities. If we assume the earth to be a sphere, the -length of a degree of the meridian is 69 ¹⁄₂₂ British miles; therefore -360 degrees, or the whole circumference of the globe is 24856, and the -diameter, which is something less than a third of the circumference, is -7916 or 8000 miles nearly. Eratosthenes, who died 194 years before the -Christian era, was the first to give an approximate value of the earth's -circumference, by the mensuration of an arc between Alexandria and Syene. -</p> - -<p> -But there is another method of finding the figure of the earth, totally -independent of either of the preceding. 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, the force of gravity -theoretically ought to increase, from the equator to the pole as the -square of the sine of the latitude; but for a spheroid in rotation, by -the laws of mechanics the centrifugal force varies 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 effects 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 in going 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; for if the fall of bodies be -accelerated, the oscillations will be more rapid; and that they may -always be performed in the same time, the length of the pendulum must -be altered. Now, by numerous and very careful experiments, it is proved -that a pendulum, which makes 86400 oscillations in a mean day at the -equator, will do the same at every point of the earth's surface, if -its length be increased in going to the pole, as the square of the -sine of the latitude. From the mean of these it appears that the -compression of the terrestrial spheroid is about ¹⁄₃₄₂, which does not -differ much from that given by the lunar inequalities, and from the arcs -of the meridian. 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, -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 ¹⁄₅₇₈. -</p> - -<p> -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 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 to be about ¹⁄₅₇₈; that given by the lunar theory has the advantage -of being independent of the irregularities at the earth's surface, -and of local attractions. The form and size of the earth being determined, -it furnishes a standard of measure with which the dimensions of the -solar system may be compared. -</p> - -<p> -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. Suppose that, when the moon is in the horizon at the -instant of rising or setting, lines were 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 3454"·2; whence the mean distance -of the moon is about sixty times the mean terrestrial radius, or 240000 -miles nearly. Since the parallax is equal to the radius of the earth -divided by the distance of the moon; under the same parallel of latitude -it varies with the distance of the moon from the earth, and proves the -ellipticity of the lunar orbit; and when the moon is at her mean -distance, it varies with the terrestrial radii, thus showing that the -earth is not a sphere. -</p> - -<p> -Although the method described is sufficiently accurate for finding the -parallax of an object so 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 by the transits of Venus that difficulty -is obviated. When that planet is in her nodes, or within 1 ¼° of them, -that is, in, or nearly in the plane of the ecliptic, she is occasionally -seen to pass over the sun like a block 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 sun is not so remote but that -the semidiameter of the earth has a sensible magnitude when viewed from -his centre, 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. 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, are 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 Otaheite in the South Sea, -the latter observation being the object of Cook's first voyage. The -transit lasted about six hours at Otaheite, and the difference in the -duration at these two stations was eight minutes; whence the sun's -parallax was found to be 8"·72; but by other considerations it has -subsequently been reduced to 8"·575; from which the mean distance of -the sun appears to be about 95996000, or ninety-six millions of miles -nearly. This is confirmed by an inequality in the motion of the moon, -which depends on the parallax of the sun, and which when compared -with observation gives 8"·6 for the sun's parallax. -</p> - -<p> -The parallax of Venus is determined by her transits, that of Mars -by direct observation. The distances of these two planets from the -earth are 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, -their absolute distances in miles are easily found. -</p> - -<p> -Far as the earth seems to be from the sun, it is near to him when -compared with Uranus; that planet is no less than 1843 millions of -miles from the luminary that warms and enlivens the world; to it, -situate on the verge of the system, the sun must appear not much -larger than Venus does to us. The earth cannot even be visible as a -telescopic object to a body so remote; 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. -</p> - -<p> -Sublime as the idea is, this assumption proves ineffectual, for -the apparent places of the fixed stars are not sensibly changed by -the earth's annual revolution; and with the aid derived from the -refinements of modern astronomy and the most perfect instruments, -it is still a matter of doubt whether a sensible parallax has been -detected, even in the nearest of these remote suns. If a fixed star -had the parallax of one second, its distance from the sun would be -20500000 millions of miles. At such a distance not only the terrestrial -orbit shrinks to a point, but, where the whole solar system, when -seen in the focus of the most powerful telescope, might be covered -by the thickness of a spider's thread. Light, flying at the rate -of 200000 miles in a second, would take three years and seven days -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 rationally be supposed to be -situated many thousand times further 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 dim and remote companion.' -</p> - -<p> -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. 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, 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 354936 times greater than that of the earth; -whence the great perturbations of the moon and the rapid motion of the -perigee and nodes of her orbit. Even Jupiter, the largest of the -planets, is 1070.5 times less than the sun. The mass of the moon is -determined from four different sources,—from her action on the -terrestrial equator, which occasions the rotation 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 titles. 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 very much from each -other; but, from her action in raising the tides, which furnishes -the fourth method, her mass appears to be about the seventy-fifth part -of that of the earth, a value that cannot differ much from the truth. -</p> - -<p> -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 8000 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 The mean apparent diameter of the sun -is 1920", and with the solar parallax 8"·65, it will be found that -the diameter of the sun is about 888000 miles; therefore, 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 mean radius or 240000 miles; so that twice the distance of -the moon is 480000 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. -</p> - -<p> -The diameter of the moon is only 2160 miles; and Jupiter's diameter of -88000 miles is incomparably less than that of the sun The diameter of -Pallas does not much exceed 71 miles, so that an inhabitant of that -planet, in one of our steam-carriages, might go round his world in five -or six hours. -</p> - -<p> -The oblate form of the celestial bodies indicates rotatory motion, and -this has been confirmed, in most cases, by tracing spots on their -surfaces, whence their poles and times of rotation have been determined. -The rotation of Mercury is unknown, on account of his proximity to the -sun; and that of the new planets has not yet been ascertained. The sun -revolves in twenty-five days ten hours, about an axis that is directed -towards a point half way between the pole star and Lyra, the plane of -rotation being inclined a little more than 70° to that on which the -earth revolves. From the rotation of the sun, there is every reason to -believe that he has a progressive motion in space, although the -direction to which he tends is as yet unknown; but in consequence of the -reaction of the planets, he describes a small irregular orbit about the -centre of inertia of the system, never deviating from his position by -more than twice his own diameter, or about seven times the distance of -the moon from the earth. -</p> - -<p> -The sun and all his attendants rotate from west to east on axes that -remain nearly parallel to themselves in every point of their orbit, and -with angular velocities that are sensibly uniform. 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 causes which have -determined the planetary motions. -</p> - -<p> -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, similar to that which obtains in -the terrestrial spheroid from the attraction of the sun and moon on the -prominent matter at the equator. 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. -</p> - -<p> -The appearance of Saturn is unparalleled in the system of the world; he -is surrounded by a ring even brighter than himself, which always remains -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. 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 about the -planet in 10 ½ hours, which is considerably less than 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 31°; and in consequence -of this obliquity of position they always appear elliptical to us, but -with an eccentricity so variable as even to be occasionally like a -straight line drawn across the planet. At present the apparent axes of -the rings are as 1000 to 160; and on the 29th of September, 1832, -the plane of the rings will pass through the centre of the earth -when they will be visible only with superior instruments, and will -appear like a fine line across the disc of Saturn. On the 1st of -December in the same year, the plane of the rings will pass through -the centre of the sun. -</p> - -<p> -It is a singular result of the 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 the different parts -of the circumference, so that their centres of gravity do not coincide -with the centres of their figures. -</p> - -<p> -Professor Struve has also discovered that the centre of the ring 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 ring on one -side, is 11"·073, and on the other side the interval is 11"·288; -consequently there is an eccentricity of the globe in the ring of -0"·215. -</p> - -<p> -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. -</p> - -<p> -The periods of the 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, 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 other 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 the poles from her centrifugal -force, therefore her polar axis is least; the other two are in the plane -of her equator, but that directed towards the earth is the greatest. 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 in 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 earth and moon; so that it would vibrate 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. -</p> - -<p> -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; for if it -had been only the hundred-thousandth part of that of the earthy it would -have rendered the libration sensible. A similar libration exists in the -motions of Jupiter's satellites; but although the comet of 1767 and 1779 -passed through the midst of them, their libration still remains -insensible. It is true, the moon is liable to librations depending on -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 moon exhibiting a surface thirteen times -larger than ours, with all the varieties of clouds, land, and water -coming successively into view, would be a splendid object to a lunar -traveller in a journey to his antipodes. -</p> - -<p> -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. -</p> - -<p> -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 determined with as much accuracy as those -of many of the most remarkable places on the surface of our globe. -</p> - -<p> -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 that prevail throughout creation, the period of -the earth's diurnal rotation is immutable. A fluid, as Mr. Babbage -observes, in 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 -its 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 again by removing matter to a greater distance from the centre, -destroy the velocity generated by its previous approach; so that the -descent of the 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 inefficient, -a variation in the mean temperature would certainly occasion a -corresponding change in the velocity of rotation: for 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 an -external 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 nature of fossil -remains, that the mean temperature of the globe is decreasing. -</p> - -<p> -The high temperature of mines, hot springs, and above all, the internal -fires that have produced, and do still occasion such devastation on our -planet, indicate an augmentation of heat towards its centre the increase -of density in the strata corresponding to the depth and the form of the -spheroid, being what theory assigns to a fluid mass in rotation, concur -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, 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. But even if this cause 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 hundredth part -of a second since the observations of Hipparchus two thousand years ago, -it would have diminished the secular equation of the moon by 4"·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 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 indication of the -primitive fluidity of the earth, as there is no direct proof, it can -only be regarded as a very probable hypothesis; but one of the most -profound philosophers and elegant writers of modern times has found, in -the secular variation of the eccentricity of the terrestrial orbit, an -evident cause of decreasing temperature. That accomplished author, in -pointing out the mutual dependences 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 8 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, <i>cœteris paribus</i>, 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, -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 eccentricity 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 the other inhabitants -of the torrid zone, it is impossible to say. -</p> - -<p> -The relative quantity of heat received by the earth at different moments -during a single revolution, varies with the position of the perigee of -its orbit, which accomplishes a tropical revolution in 20935 years. In -the year 1250 of our era, and 29653 years before it, the perigee -coincided with the summer solstice; at both these periods the earth was -nearer the sun during the summer, and farther from him in the winter -than in any other position of the apsides: the extremes of temperature -must therefore have been greater than at present; but as the terrestrial -orbit was probably more elliptical at the distant epoch, the heat of the -summers must have been very great though possibly compensated by the -rigour of the winters; at all events, none of these changes affect the -length of the day. -</p> - -<p> -It appears 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 which -must have engulphed 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 ending to the new equator would leave some portions -of the globe, and overwhelm others. -</p> - -<p> -But theory 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 some foreign -cause, as the collision of a comet which may have happened in the -immensity of time. Then indeed, the equilibrium could only have been -restored by the rushing of the seas to the new equator, which they would -continue to do, till the surface was every where 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 -even of the Pacific ocean is not more than four miles, whereas the -equatorial radius of the earth exceeds the polar radius by twenty-five -or thirty miles; consequently the influence of the sea on the direction -of gravity is very small; and as it appears that a great change in the -position of the axes is incompatible with the law of equilibrium, the -geological phenomena must be ascribed to an internal cause. 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 axis on -its surface, have undergone but slight variations. -</p> - -<p> -It is beyond a doubt that the strata increase in density from the -surface of the earth to its centre, which is even proved by the lunar -inequalities; and it is manifest from the mensuration of arcs of the -meridian and the lengths of the seconds pendulum that the strata are -elliptical and concentric. This certainly would 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 -these phenomena. Professor Leslie observes, that air compressed into the -fiftieth part of its volume has its elasticity fifty times augmented; if -it continue 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. In descending therefore towards the centre through -4000 miles, the condensation of ordinary materials would surpass the -utmost powers of conception. But a density so extreme is not borne out -by astronomical observation. It might seem therefore to follow, 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. 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; but, from the experiments of Mr. -Perkins, they appear to be capable of a greater degree of compression -than has generally been imagined. -</p> - -<p> -It appears then, that the axis of rotation is invariable on the surface -of the earth, and observation shows, that were it not for the action of -the sun and moon on the matter at the equator, it would remain parallel -to itself in every point of its orbit. -</p> - -<p> -The attraction of an exterior 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. -</p> - -<p> -The plane of the equator is inclined to the plane of the ecliptic at an -angle of about 23° 28', and the inclination of the lunar orbit on the -same is nearly 5°; 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 about 50"·412 annually. The direct tendency of this action -would be to make the planes of the equator and ecliptic coincide; but in -consequence of the rotation of the earth, the inclination of the two -planes remains constant, as a top in 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 -to the same points of the ecliptic, at least as far as this kind of -action is concerned. But another and totally different cause operates on -this motion, which 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 on -the plane of the equator, and gives the equinoctial points a slow but -direct motion on the ecliptic of 0"·312 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, -but 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 50"·1 annually. 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 then 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 50"·1 annually, the equinoctial points will -accomplish a revolution in 25868 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 -365.242264 days must be increased by the time he takes to move through -an arc of 50"·1, in order to have the length of the sidereal year. By -simple proportion it is the 0.014119th part of a day, so that the -sidereal year is 365.256383. -</p> - -<p> -The mean annual precession is subject to a secular variation; for -although the change in the plane of the ecliptic which is the orbit of -the sun, 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 -0"·455 now than it was in the lime of Hipparchus; consequently the -actual length of the tropical year is about 4"·154 shorter than it was -at that time. The utmost change that it can experience from this cause -amounts to 43". -</p> - -<p> -Such is the secular motion of the equinoxes, but it is sometimes -increased and sometimes diminished by periodic variations, whose periods -depend on the relative positions of the sun and moon with regard to the -earth, and 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 -diameters of which are 16" and 20". The period of this inequality is -nineteen 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. -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 -oblique of the ecliptic is annually diminished by 0"·52109. With -regard to the fixed stars, this variation in the course of ages may -amount to tea or eleven degrees; but the obliquity of the ecliptic to -the equator can never vary more than two or three degrees, since the -equator will follow in some measure the motion of the ecliptic. -</p> - -<p> -It is evident that the places of all the celestial bodies are affected -by precession and nutation, and therefore all observations of them must -be corrected for these inequalities. -</p> - -<p> -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 1922" and -17"·08, and the mass of the earth is the ¹⁄₃₅₄₉₃₆th part of that of the -sun taken as the unit; it follows therefore, that the earth is nearly -four times as dense as the sun; but the sun is so large that his -attractive force would cause bodies to fall through about 450 feet -in a second; consequently if he were even habitable by human beings, -they would be unable to move, since their weight would be thirty -times as great as it is here. A moderate sized man would weigh about -two tons at the surface of the sun. On the contrary, at the surface -of the four new planets we should be so light, that it would be -impossible to stand from the excess of our muscular force, for a man -would only weigh a few pounds. 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; and -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. -</p> - -<p> -Astronomy has been of immediate and essential use in affording -invariable standards for measuring duration, distance, magnitude, and -velocity. The sidereal day, measured by the time elapsed between two -consecutive transits of any star at the same meridian, and the sidereal -year, are immutable units with which to compare all great periods of -time; 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 in the -lapse of ages. -</p> - -<p> -The returns of the sun to the same 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 in the -equinoxes the arc of the equator is less than the corresponding arc of -the ecliptic, and in the solstices it is greater. 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 59' 8"·3 -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 in the equator, is denominated mean solar -time, such as 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 apparent -time, such as 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, and sometimes amounts to as much as sixteen minutes. The -apparent and mean time coincide four times in the year. -</p> - -<p> -Astronomers begin the day 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 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 system of -weights and measures. This subdivision is not used in common life, nor -has it been adopted in any other country, though their scientific -writers still employ that division of time. The mean length of the day, -though accurately determined, is not sufficient for the purposes either -of astronomy or civil life. The length of the year is pointed out by -nature as a measure of long periods; but the incommensurability that -exists between the lengths of the day, and the revolutions 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, four years are nearly equal to four revolutions 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. 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. -</p> - -<p> -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 Cæsar; the -25th of December in his 45th year, is considered as the date of Christ's -nativity; and Cæsar's 46th year 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 actually elapsed -since that time. -</p> - -<p> -Some remarkable astronomical eras are determined by the position of the -major axis of the solar ellipse. Moving at the rate of 61"·906 -annually, it accomplishes a tropical revolution in 20935 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 6485 the major axis will again coincide with the line of the -equinoxes, but then the solar perigee will coincide with the equinox of -spring; whereas at the creation of man it coincided with the autumnal -equinox. In the year 1250 the major axis was perpendicular to the line -of the equinoxes, and then the solar perigee coincided with the solstice -of winter, and the apogee with the solstice of summer. On that account -La Place proposed the year 1250 as a universal epoch, and that the -vernal equinox of that year should be the first day of the first year. -</p> - -<p> -The variations in the positions of the solar ellipse occasion -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 about seven days. These intervals will be -equal towards the year 6485, when the perigee comes to the equinox of -spring. Were the earth's orbit circular, the seasons would be equal; -their differences arise from the eccentricity of the earth's orbit, -small as it is; but the changes are so gradual as to be imperceptible in -the short space of human life. -</p> - -<p> -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 language, arts and -sciences, leaving but confused masses of ruin 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 period they must have made -considerable progress in science.' -</p> - -<p> -The ancient state of the heavens may now be computed with great -accuracy; and by comparing the results of computation 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 show to how many centuries they may be extended, -without the fear of error. A few examples will show the importance of -this subject. -</p> - -<p> -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, which in former times was determined from the meridian -length of the shadow of the style of a dial on the day of the solstice. -The lengths of the meridian shadow at the summer and winter solstice 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 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 in the obliquity is known, both the time -and place of the observations have been verified by computation from -modern tables. Thus the Chinese had made some advances in the science of -astronomy at that early period; the whole chronology of the Chinese 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 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. The great inequality of Jupiter and -Saturn whose cycle embraces 929 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 menu 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. -</p> - -<p> -The returns of comets to their perihelia may possibly mark the present -state of astronomy to future ages. -</p> - -<p> -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 from computation it -appears that <i>χ</i> Draconis was not very far from that place about 3000 -years ago; but as Eudoxus lived only about 2150 years ago, he must have -described an anterior state of the heavens, supposed to be the same that -was determined by Chiron, about the time of the siege of Troy. Every -circumstance concurs in showing that astronomy was cultivated in the -highest ages of antiquity. -</p> - -<p> -A knowledge of astronomy leads to the interpretation of hieroglyphical -characters, since astronomical signs are often found on the ancient -Egyptian monuments, which were probably employed by the priests to -record dates. On the ceiling of the portico of a temple among the ruins -of Tentyris, there is a long row of figures of men and animals, -following each other in the some direction among these are the twelve -signs of the zodiac, placed according to the motion of the sun: it is -probable that the first figure in the procession represents the -beginning of the year. Now the first is the Lion as if coming out of the -temple; and as it is well known that the agricultural year of the -Egyptians commenced at the solstice of summer, the epoch of the -inundations of the Nile, if the preceding hypothesis be true, the -solstice at the time the temple was built must have happened in the -constellation of the lion; but as the solstice now happens 21° 6' north -of the constellation of the Twins, it is easy to compute that the zodiac -of Tentyris must have been made 4000 years ago. -</p> - -<p> -The author had occasion to witness an instance of this most interesting -application of astronomy, in ascertaining the dale 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 not only -to his country, but 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 antiquity was determined from the configuration of the -heavens at the time of its construction. -</p> - -<p> -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 in the latitude of London forms the standard of the -British measure of extension. Its length oscillating in vacuo at the -temperature of 62° of Fahrenheit, and reduced to the level of the sea, -was determined by Captain Kater, in parts of the imperial standard yard, -to be 39.1387 inches. The weight of a cubic inch of water at the -temperature of 62° Fahrenheit, barometer 30, was also determined in -parts of the imperial troy pound, whence a standard both of weight and -capacity is deduced. The French have adopted the metre for their unit of -linear measure, which is the ten millionth part of that quadrant of the -meridian passing through Formentera and Greenwich, the middle of which -is nearly in the forty-fifth degree of latitude. Should the national -standards of the two countries be lost in the vicissitudes of human -affairs, both may be recovered, since they are derived from natural -standards presumed to be invariable. The length of the pendulum would be -found again with more facility than the metre; 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 is rendered -totally insensible by subdivision in taking its ten millionth part. The -French have adopted the decimal division not only in time, but in their -degrees, weights, and measures, which affords very great facility in -computation. It has not been adopted by any other people; though nothing -is more desirable than that all nations should concur in using the same -division and standards, not only on account of the convenience, but as -affording a more definite idea of quantity. It is singular that the -decimal division of the day, of degrees, weights and measures, was -employed in China 4000 years ago; and that, at the time Ibn Yunus made -his observations at Cairo, about the year 1000, the Arabians were in the -habit of employing the vibrations of the pendulum in their astronomical -observations. -</p> - -<p> -One of the most immediate and striking 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<sup>h</sup> 50<sup>m</sup> 48<sup>s</sup> of mean solar -time. As it depends on the action of the sun and moon, it is classed -among astronomical problems, of which it is by far the most difficult -and 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. -</p> - -<p> -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 -trouble the equilibrium. -</p> - -<p> -It is proved by daily experience, as well as by strict mechanical -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 distinct -kinds of oscillations, depending on different causes, producing their -effects independently of each other, which may therefore be estimated -separately. -</p> - -<p> -The oscillations of the first kind which are very small, are independent -of the rotation of the earth; and as they depend on the motion of the -disturbing body in its orbit, they are of long periods. The second kind -of oscillations depends on the rotation of the earth, therefore their -period is nearly a day: and the oscillations of the third kind depend on -an angle equal to twice the angular rotation of the earth; and -consequently happen twice in twenty-four hours. The first afford no -particular interest, and are extremely small; but the difference of two -consecutive tides depends on the second. At the time of the solstices, -this difference which, according to Newton's theory, ought to be very -great, is hardly sensible on our shores. La Place has shown that this -discrepancy arises from the depth of the sea, and that if the depth were -uniform, there would be no difference in the consecutive tides, were it -not for 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 miles, that of the Atlantic -only three. From the formulæ which determine the difference of the -consecutive tides it is also proved that the precession of the -equinoxes, and the nutation in the earth's axis, are the same as if the -sea formed one solid mass with the earth. -</p> - -<p> -The third kind of oscillations are the semidiurnal tides, so remarkable -on our coasts; they are occasioned by the combined action of the sun and -moon, but as the effect of each is independent of the other, they may be -considered separately. -</p> - -<p> -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 -distances; hence they have a tendency to leave the earth, but are -retained by their gravitation, which this tendency diminishes. 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 this tendency again diminishes. 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 above the -surface of equilibrium of nearly the same height; 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 -water 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 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. The effects -of the sun's attraction are in all respects similar to those of the -moon's, though really less in degree, on account of his distance; he -therefore only modifies the form of this spheroid a little. If the -waters were capable of instantly assuming the form of equilibrium, 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 on them requires. Hence, on account of the inertia of the -waters, if the tides be considered relatively to the whole earth and -open sea, 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 the meridian at 90° distant, -it is everywhere low water. It is evident that these tides must happen -twice in a day, since in that time the rotation of the earth brings the -same point twice under the meridian of the moon, once under the superior -and once under the inferior meridian. -</p> - -<p> -In the semidiurnal tides there are two phenomena particularly to be -distinguished, one that happens twice in a month, and the other twice in -a year. -</p> - -<p> -The first phenomenon is, that the tides are much increased in the -syzigies, 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 the -full tide, the lower it is in the ebb. The neap tides lake place when -the moon is in quadrature, they neither rise so high nor sink so low as -the spring tides. The spring tides are much increased when the moon is -in perigee. It is evident that the spring tides must happen twice a -month, since in that time the moon is once new and once full. -</p> - -<p> -The second phenomenon in the tides is the augmentation which occurs at -the time of the equinoxes when the sun's declination is zero, which -happens twice every year. The greatest tides take place when a new or -full moon happens, near the equinoxes while the moon is in perigee. The -inclination of the moon's orbit on the ecliptic is 5° 9'; hence in -the equinoxes the action of the moon would be increased if her node were -to coincide with her perigee. The equinoctial gales often raise these -tides to a great height. Beside these remarkable variations, there are -others arising from the declination of the moon, which has a great -influence on the ebb and flow of the waters. -</p> - -<p> -Both the height and time of high water are thus perpetually changing; -therefore, in solving the problem, it is required to determine the -heights to which they rise, the times at which they happen, and the -daily variations. -</p> - -<p> -The periodic motions of the waters of the ocean on the hypothesis of an -ellipsoid of revolution entirely covered by the sea, are very far from -according with observation; this arises from the very great -irregularities in the surface of the earth, which is but partially -covered by the sea, 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, the resistance the waters meet with, all of -them causes which it is impossible to estimate, 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 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. Thus the -problem of the tides does not admit of a general solution; it is -certainly necessary to analyse the funeral phenomena which ought to -result from the attraction of the sun and moon, but these must be -corrected in each particular case by those local observations which are -modified by the extent and depth of the sea, and the peculiar -circumstances of the port. -</p> - -<p> -Since the disturbing action of the sun and moon can only become sensible -in a very great extent of water, it is evident that the Pacific ocean is -one of the principal sources of our tides; but in consequence of the -rotation of the earth, and the inertia of the ocean, high water does not -happen till some time after the moon's southing. The tide raised in that -world of waters is transmitted to the Atlantic, and from that sea it -moves in a northerly direction along the coasts of Africa and Europe, -arriving later and later at each place. This great wave however is -modified by the tide raised in the Atlantic, which sometimes combines -with that from the Pacific in raising the sea, and sometimes is in -opposition to it, so that the tides only rise in proportion to their -difference. This great combined wave, reflected by the shores of the -Atlantic, extending nearly from pole to pole, still coming northward, -occurs through the Irish and British channels into the North sea, so -that the tides in our ports are modified by those of another hemisphere. -Thus the theory of the tides in each port, both as to their height and -the times at which they take place, is really a matter of experiment, -and can only be perfectly determined by the mean of a very great number -of observations including several revolutions of the moon's nodes. -</p> - -<p> -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. In -high latitudes where the ocean is less directly under the influence of -the luminaries, the rise and fall of the sea is inconsiderable, so that, -in all probability, there is no tide at the poles, or only a small -annual and monthly one. The ebb and flow of the sea are perceptible in -rivers to a very great distance from their estuaries. In the straits 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 in 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. -</p> - -<p> -These perpetual commotions in the waters of the ocean are occasioned by -forces that bear a very small proportion to terrestrial gravitation: the -sun's action in raising the ocean is only the ¹⁄₃₈₄₄₈₀₀₀₀ 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. From this -ratio the mass of the moon is found to be only ¹⁄₁₅ part of that of the -earth. 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, the stability of the equilibrium of the -ocean never can be subverted by any physical cause whatever. A general -inundation arising from the mere instability of the ocean is therefore -impossible. -</p> - -<p> -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, and it is -sensibly of finite extent, whether it consists of particles infinitely -divisible or not. On the latter hypothesis it must really be finite; and -even if the particles of matter be infinitely divisible, it is known by -experience to be of extreme tenuity at very small heights. The barometer -rises in proportion to the superincumbent pressure. Now at the -temperature of melting ice, the density of mercury is to that of air as -10320 to 1; and as the mean height of the barometer is 29.528 inches, -the height of the atmosphere by simple proportion is 30407 feet, at the -mean temperature of 62°, or 34153 feet, which is extremely small, when -compared with the radius of the earth. The action of the sun and moon -disturbs the equilibrium of the atmosphere, producing oscillations -similar to those in the ocean, which occasion periodic variations in the -heights of the barometer. These, however, are so extremely small, that -their existence in latitudes so far removed from the equator is -doubtful; a series of observations within the tropics can alone decide -this delicate point. La Place seems to think that the flux and reflux -distinguishable at Paris may be occasioned by the rise and fall of the -ocean, which forms a variable base to so great a portion of the -atmosphere. -</p> - -<p> -The attraction of the sun and moon has no sensible effect on the trade -winds; the heat of the sun occasions these aerial currents, by rarefying -the air at the equator, which causes the cooler and more dense part of -the atmosphere to rush along the surface of the earth to the equator, -while that which is heated is carried along the higher strata to the -poles, forming two currents in the direction of the meridian. But the -rotatory velocity of the air corresponding to its geographical situation -decreases towards the poles; in approaching the equator it must -therefore revolve more slowly than the corresponding parts of the earth, -and the bodies on the surface of the earth must strike against it with -the excess of their velocity, and by its reaction they will meet with a -resistance contrary to their motion of rotation; so that the wind will -appear, to a person supposing himself to be at rest, to blow in a -contrary direction to the earth's rotation, or from east to west, which -is the direction of the trade winds. 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. -</p> - -<p> -The sun and most of the planets appear to be surrounded with atmospheres -of considerable density. The attraction of the earth has probably -deprived the moon of hers, for the refraction of the air at the surface -of the earth is at least a thousand times as great as at the moon. The -lunar atmosphere, therefore, must be of a greater degree of rarity than -can be produced by our best air-pumps; consequently no terrestrial -animal could exist in it. -</p> - -<p> -Many philosophers of the highest authority concur in the belief that -light consists in the undulations of a highly elastic ethereal medium -pervading space, which, communicated to the optic nerves produce the -phenomena of vision. The experiments of our illustrious countryman, Dr. -Thomas Young, and those of the celebrated Fresnel, show that this theory -accords better with all the observed phenomena than that of the emission -of particles from the luminous body. As sound is propagated by the -undulations of the air, its theory is in a great many respects similar -to that of light. The grave or low tones are produced by very slow -vibrations, which increase in frequency progressively as the note -becomes more acute. When the vibrations of a musical chord, for example, -are less than sixteen in a second, it will not communicate a continued -sound to the ear; the vibrations or pulses increase in number with the -acuteness of the note, till at last all sense of pitch is lost. The -whole extent of human hearing, from the lowest notes of the organ to the -highest known cry of insects, as of the cricket, includes about nine -octaves. -</p> - -<p> -The undulations of light are much more rapid than those of sound, but -they are analogous in this respect, that as the frequency of the -pulsations in sound increases from the low tones to the higher, so those -of light augment in frequency, from the red rays of the solar spectrum -to the extreme violet. By the experiments of Sir William Herschel, it -appears that the heat communicated by the spectrum increases from the -violet to the red rays; but that the maximum of the hot invisible rays -is beyond the extreme red. Heat in all probability consists, like light -and sound, in the undulations of an elastic medium. All the principal -phenomena of heat may actually be illustrated by a comparison with those -of sound. The excitation of heat and sound are not only similar, but -often identical, as in friction and percussion; they are both -communicated by contact and by radiation; and Dr. Young observes, that -the effect of radiant heat in raising the temperature of a body upon -which it falls, resembles the sympathetic agitation of a string, when -the sound of another string, which is in unison with it, is transmitted -to it through the air. Light, heat, sound, and the waves of fluids are -all subject to the same laws of reflection, and, indeed, their -undulating theories are perfectly similar. If, therefore, we may judge -from analogy, the undulations of the heat producing rays must be less -frequent than those of the extreme red of the solar spectrum; but if the -analogy were perfect, the interference of two hot rays ought to produce -cold, since darkness results from the interference of two undulations of -light, silence ensues from the interference of two undulations of sound; -and still water, or no tide, is the consequence of the interference of -two tides. -</p> - -<p> -The propagation of sound requires a much denser medium than that of -either light or heat; its intensity diminishes as the rarity of the air -increases; so that, at a very small height above the surface of the -earth, the noise of the tempest ceases, and the thunder is heard no more -in those boundless regions where the heavenly bodies accomplish their -periods in eternal and sublime silence. -</p> - -<p> -What the body of the sun may be, it is impossible to conjecture; but he -seems to be surrounded by an ocean of flame through which his dark -nucleus appears like black spots, often of enormous size. The solar -rays, which probably arise from the chemical processes that continually -take place at his surface, are transmitted through space in all -directions; but, notwithstanding the sun's magnitude, and the -inconceivable heat that must exist where such combustion is going on, as -the intensity both of his light and heat diminishes with the square of -the distance, his kindly influence can hardly be felt at the boundaries -of our system. Much depends on the manner in which the rays fall, as we -readily perceive from the different climates on our globe. In winter the -earth is nearer the sun by ¹⁄₃₀th than in summer, but the rays strike -the northern hemisphere more obliquely in winter than in the other half -of the year. In Uranus the sun must be seen like a small but brilliant -star, not above the hundred and fiftieth part so bright as he appears -to us; that is however 2000 times brighter than our moon to us, so -that he really is a sun to Uranus, and probably imparts 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, unless indeed the -ether has a temperature. The climate of Venus more nearly resembles -that of the earth, though, excepting perhaps at her poles, much too -hot for animal and vegetable life as they exist here; but in Mercury -the mean heat, arising only from the intensity of the sun's rays, -must be above that of boiling quick-silver, and water would boil even -at his poles. Thus the planets, though kindred with the earth in -motion and structure, are totally unfit for the habitation of such -a being as man. -</p> - -<p> -The direct light of the sun has been estimated to be equal to that of -5563 wax candles of a moderate size, supposed to be placed at the -distance of one foot from the object: that of the moon is probably only -equal to the light of one candle at the distance of twelve feet; -consequently the light of the sun is more than three hundred thousand -times greater than that of the moon; for which reason the light of the -moon imparts no heat, even when brought to a focus by a mirror. -</p> - -<p> -In adverting to the peculiarities in the form and nature of the earth -and planets, it is impossible to pass in silence the magnetism of the -earth, the director of the mariner's compass, and his guide through the -ocean. This property probably arises from metallic iron in the interior -of the earth, or from the circulation of currents of electricity round -it: its influence extends over every part of its surface, but its -accumulation and deficiency determine the two poles of this great -magnet, which are by no means the same as the poles of the earth's -rotation. In consequence of their attraction and repulsion, a needle -freely suspended, whether it be magnetic or not, only remains in -equilibrio when in the magnetic meridian, that is, in the plane which -passes through the north and south magnetic poles. There are places -where the magnetic meridian coincides with the terrestrial meridian; in -these a magnetic needle freely suspended, points to the true north, but -if it be carried successively to different places on the earth's -surface, its direction will deviate sometimes to the east and sometimes -to the west of north. Lines drawn on the globe through all the places -where the needle points due north and south, are called lines of no -variation, and are extremely complicated. The direction of the needle is -not even constant in the same place, but changes in a few years, -according to a law not yet determined. In 1657, the line of no variation -passed through London. In the year 1819, Captain Parry, in his voyage to -discover the north-west passage round America, sailed directly over the -magnetic pole; and in 1824, Captain Lyon, when on en expedition for the -same purpose, found that the variation of the compass was 37° 30' -west, and that the magnetic pole was then situate in 63° 26' 51" -north latitude, and in 80° 51' 25" west longitude. It appears -however from later researches that the law of terrestrial magnetism is -of considerable complication, and the existence of more than one -magnetic pole in either hemisphere has been rendered highly probable. -The needle is also subject to diurnal variations; in our latitudes it -moves slowly westward from about three in the morning till two, and -returns to its former position in the evening. -</p> - -<p> -A needle suspended so as only to be moveable in the vertical plane, dips -or become more and more inclined to the horizon the nearer it is brought -to the magnetic pole. Captain Lyon found that the dip in the latitude -and longitude mentioned was 86° 32'. What properties the planets may -have in this respect, it is impossible to know, but it is probable that -the moon has become highly magnetic, in consequence of her proximity to -the earth, and because her greatest diameter always points towards it. -</p> - -<p> -The passage of comets has never sensibly disturbed the stability of the -solar system; their nucleus is rare, and their transit so rapid, that -the time has not been long enough to admit of a sufficient accumulation -of impetus to produce a perceptible effect. The comet of 1770 passed -within 80000 miles of the earth without even affecting our tides, and -swept through the midst of Jupiter's satellites without deranging the -motions of those little moons. Had the mass of that comet been equal to -the mass of the earth, its disturbing action would have shortened the -year by the ninth of a day; but, as Delambre's computations from the -Greenwich observations of the sun, show that the length of the year has -not been sensibly affected by the approach of the comet. La Place proved -that its mass could not be so much as the 5000th part of that of the -earth. The paths of comets have every possible inclination to the plane -of the ecliptic, and unlike the planets, their motion is frequently -retrograde. Comets are only visible when near their perihelia. Then -their velocity is such that its square is twice as great as that of a -body moving in a circle at the same distance; they consequently remain a -very short time within the planetary orbits; and as all the conic -sections of the same focal distance sensibly coincide through a small -arc on each side of the extremity of their axis, it is difficult to -ascertain in which of these curves the comets move, from observations -made, as they necessarily must be, at their perihelia: but probably they -all move in extremely eccentric ellipses, although, in most cases, the -parabolic curve coincides most nearly with their observed motions. Even -if the orbit be determined with all the accuracy that the case admits -of, it may be difficult, or even impossible, to recognise a comet on its -return, because its orbit would be very much changed if it passed near -any of the large planets of this or of any other system, in consequence -of their disturbing energy, which would be very great on bodies of so -rare a nature. Halley and Clairaut predicted that, in consequence of the -attraction of Jupiter and Saturn, the return of the comet of 1759 would -be retarded 618 days, which was verified by the event as nearly as could -be expected. -</p> - -<p> -The nebulous appearance of comets is perhaps occasioned by the vapours -which the solar heat raises at their surfaces in their passage at the -perihelia, and which are again condensed as they recede from the sun. -The comet of 1680 when in its perihelion was only at the distance of -one-sixth of the sun's diameter, or about 148000 miles from its surface; -it consequently would be exposed to a heat 27500 times greater than that -received by the earth. As the sun's heat is supposed to be in proportion -to the intensity of his height, it is probable that a degree of heat so -very intense would be sufficient to convert into vapour every -terrestrial substance with which we are acquainted. -</p> - -<p> -In those positions of comets where only half of their enlightened -hemisphere ought to be seen, they exhibit no phases even when viewed -with high magnifying powers. Some slight indications however were once -observed by Hevelius and La Hire in 1682; and in 1811 Sir William -Herschel discovered a small luminous point, which he concluded to be the -disc of the comet. In general their masses are so minute, that they have -no sensible diameters, the nucleus being principally formed of denser -strata of the nebulous matter, but so rare that stars have been seen -through them. The transit of a comet over the sun's disc would afford -the best information on this point. It was computed that such an event -was to take place in the year 1627; unfortunately the sun was hid by -clouds in this country, but it was observed at Viviers and at Marseilles -at the time the comet must have been on it, but no spot was seen. The -tails are often of very great length, and are generally situate in the -planes of their orbits; they follow them in their descent towards the -sun, but precede them in their return, with a small degree of curvature; -but their extent and form must vary in appearance, according to the -position of their orbits with regard to the ecliptic. The tail of the -comet of 1680 appeared, at Paris, to extend over sixty-two degrees. The -matter of which the tail is composed must be extremely buoyant to -precede a body moving with such velocity; indeed the rapidity of its -ascent cannot be accounted for. The nebulous part of comets diminishes -every time they return to their perihelia; after frequent returns they -ought to lose it altogether, and present the appearance of a fixed -nucleus; this ought to happen sooner in comets of short periods. La -Place supposes that the comet of 1682 must be approaching rapidly to -that state. Should the substances be altogether or even to a great -degree evaporated, the comet wilt disappear for ever. Possibly comets -may have vanished from our view sooner than they otherwise would have -done from this cause. Of about six hundred comets that have been seen at -different times, three are now perfectly ascertained to form part of our -system; that is to say, they return to the sun at intervals of 76, 6 ⅓, -and 3 ¼ years nearly. -</p> - -<p> -A hundred and forty comets have appeared within the earth's orbit during -the last century that have not again been seen; if a thousand years be -allowed as the average period of each, it may be computed by the theory -of probabilities, that the whole number that range within the earth's -orbit must be 1400; but Uranus being twenty times more distant, there -may be no less than 11,200,000 comets that come within the known extent -of our system. In such a multitude of wandering bodies it is just -possible that one of them may come in collision with the earth; but even -if it should, the mischief would be local, and the equilibrium soon -restored. It is however more probable that the earth would only be -deflected a little from its course by the near approach of the comet, -without being touched. Great as the number of comets appears to be, it -is absolutely nothing when compared to the number of the fixed stars. -About two thousand only are visible to the naked eye, but when we view -the heavens with a telescope, their number seems to be limited only by -the imperfection of the instrument. In one quarter of an hour Sir -William Herschel estimated that 116000 stars passed through the field of -his telescope, which subtended an angle of 15'. This however was -stated as a specimen of extraordinary crowding; but at an average the -whole expanse of the heavens must exhibit about a hundred millions of -fixed stars that come within the reach of telescopic vision. -</p> - -<p> -Many of the stars have a very small progressive motion, especially <i>μ</i> -Cassiopeia and 61 Cygni, both small stars; and, as the sun is decidedly -a star, it is an additional reason for supposing the solar system to be -in motion. The distance of the fixed stars is too great to admit of -their exhibiting a sensible disc; but in all probability they are -spherical, and must certainly be so, if gravitation pervades all space. -With a fine telescope they appear like a point of light; their twinkling -arises from sudden changes in the refractive power of the air, which -would not be sensible if they had discs like the planets. Thus we can -learn nothing of the relative distances of the stars from us and from -one another, by their apparent diameters; but their annual parallax -being insensible, shows that we must be one hundred millions of millions -of miles from the nearest; many of them however must be vastly more -remote, for of two stars that appear close together, one may be far -beyond the other in the depth of space. The light of Sirius, according -to the observations of Mr. Herschel, is 324 times greater than that of a -star of the sixth magnitude; if we suppose the two to be really of the -same size, their distances from us must be in the ratio of 57.3 to 1, -because light diminishes as the square of the distance of the luminous -body increases. -</p> - -<p> -Of the absolute magnitude of the stars, nothing is known, only that many -of them must be much larger than the sun, from the quantity of light -emitted by them. Dr. Wollaston determined the approximate ratio that the -light of a wax candle bears to that of the sun, moon, and stars, by -comparing their respective images reflected from small glass globes -filled, with mercury, whence a comparison was established between the -quantities of light emitted by the celestial bodies themselves. By this -method he found that the light of the sun is about twenty millions of -millions of times greater than that of Sirius, the brightest, and -supposed to be the nearest of the fixed stars. If Sirius had a parallax -of half a second, its distance from the earth would be 525481 times the -distance of the sun from the earth; and therefore Sirius, placed where -the sun is, would appear to us to be 3.7 times as large as the sun, and -would give 13.8 times more light; but many of the fixed stars must be -immensely greater than Sirius. Sometimes stars have all at once -appeared, shone with a brilliant light, and then vanished. In 1572 a -star was discovered in Cassiopeia, which rapidly increased in brightness -till it even surpassed that of Jupiter; it then gradually diminished in -splendour, and after exhibiting all the variety of tints that indicates -the changes of combustion, vanished sixteen months after its discovery, -without altering its position. It is impossible to imagine any thing -more tremendous than a conflagration that could be visible at such a -distance. Some stars are periodic, possibly from the intervention of -opaque bodies revolving about them, or from extensive spots on their -surfaces. Many thousands of stars that seem to be only brilliant points, -when carefully examined are found to be in reality systems of two or -more suns revolving about a common centre. These double and multiple -stars are extremely remote, requiring the most powerful telescopes to -show them separately. -</p> - -<p> -The first catalogue of double stars in which their places and relative -positions are determined, was accomplished by the talents and industry -of Sir William Herschel, to whom astronomy is indebted for so many -brilliant discoveries, and with whom originated the idea of their -combination in binary and multiple systems, an idea which his own -observations had completely established, but which has since received -additional confirmation from those of his son and Sir James South, the -former of whom, as well as Professor Struve of Dorpat, have added many -thousands to their numbers. The motions of revolution round a common -centre of many have been clearly established, and their periods -determined with considerable accuracy. Some have already since their -first discovery accomplished nearly a whole revolution, and one, if the -latest observations can be depended on, is actually considerably -advanced in its second period. These interesting systems thus present a -species of sidereal chronometer, by which the chronology of the heavens -will be marked out to future ages by epochs of their own, liable to no -fluctuations from planetary disturbances such as obtain in our system. -</p> - -<p> -Possibly among the multitudes of small stars, whether double or -insulated, some may be found near enough to exhibit distinct parallactic -motions, or perhaps something approaching to planetary motion, which may -prove that solar attraction is not confined to our system, or may lead -to the discovery of the proper motion of the sun. The double stars are -of various hues, but most frequently exhibit the contrasted colours. The -large star is generally yellow, orange, or red; and the small star blue, -purple, or green. Sometimes a white star is combined with a blue or -purple, and more rarely a red and white are united. In many cases, these -appearances are due to the influences of contrast on our judgment of -colours. For example, in observing a double star where the large one is -of a full ruby red, or almost blood colour, and the small one a fine -green, the latter lost its colour when the former was hid by the cross -wires of the telescope. But there are a vast number of instances where -the colours are too strongly marked to be merely imaginary. Mr. Herschel -observes in one of his papers in the <i>Philosophical Transactions</i>, as -a very remarkable fact, that although red single stars are common enough, -no example of an insulated blue, green, or purple one has as yet been -produced. -</p> - -<p> -In some parts of the heavens, the stars are so near together as to form -clusters, which to the unassisted eye appear like thin white clouds; -such is the milky way, which has its brightness from the diffused light -of myriads of stars. Many of these clouds, however, are never resolved -into separate stars, even by the highest magnifying powers. This -nebulous matter exists in vast abundance in space. No fewer than 2500 -nebulæ were observed by Sir William Herschel, whose places have been -computed from his observations, reduced to a common epoch, and arranged -into a catalogue in order of right ascension by his sister Miss Caroline -Herschel, a lady so justly celebrated for astronomical knowledge and -discovery. The nature and use of this matter scattered over the heavens -in such a variety of forms is involved in the greatest obscurity. That -it is a self-luminous, phosphorescent material substance, in a highly -dilated or gaseous state, but gradually subsiding by the mutual -gravitation of its particles into stars and sidereal systems, is the -hypothesis which seems to be most generally received; but the only way -that any real knowledge on this mysterious subject can be obtained, is -by the determination of the form, place, and present state of each -individual nebula, and a comparison of these with future observations -will show generations to come the changes that may now be going on in -these rudiments of future systems. With this view, Mr. Herschel is now -engaged in the difficult and laborious investigation, which is -understood to be nearly approaching its completion, and the results of -which we may therefore hope ere long to see made public. The most -conspicuous of these appearances are found in Orion, and in the girdle -of Andromeda. It is probable that light must be millions of years -travelling to the earth from some of the nebulæ. -</p> - -<p> -So numerous are the objects which meet our view in the heavens, that we -cannot imagine a part of space where some light would not strike the -eye: but as the fixed stars would not be visible at such distances, if -they did not shine by their own light, it is reasonable to infer that -they are suns; and if so, they are in all probability attended by -systems of opaque bodies, revolving about them as the planets do about -ours. But although there be no proof that planets not seen by us revolve -about these remote suns, certain it is, that there are many invisible -bodies wandering in space, which, occasionally coming within the sphere -of the earth's attraction, are ignited by the velocity with which they -pass through the atmosphere, and are precipitated with great violence on -the earth. The obliquity of the descent of meteorites, the peculiar -matter of which they are composed, and the explosion with which their -fall is invariably accompanied, show that they are foreign to our -planet. Luminous spots altogether independent of the phases have -occasionally appeared on the dark part of the moon, which have been -ascribed to the light arising from the eruption of volcanoes; whence it -has been supposed that meteorites have been projected from the moon by -the impetus of volcanic eruption; it has even been computed, that if a -stone were projected from the moon in a vertical line, and with an -initial velocity of 10992 feet in a second, which is more than four -times the velocity of a ball when first discharged from a cannon, -instead of falling back to the moon by the attraction of gravity, it -would come within the sphere of the earth's attraction, and revolve -about it like a satellite. These bodies, impelled either by the -direction of the primitive impulse, or by the disturbing action of the -sun, might ultimately penetrate the earth's atmosphere, and arrive at -its surface. But from whatever source meteoric stones may come, it seems -highly probable, that they have a common origin, from the uniformity, we -may almost say identity, of their chemical composition. -</p> - -<p> -The known quantity of matter bears a very small proportion to the -immensity of space. Large as the bodies are, the distances that separate -them are immeasurably greater; but as design is manifest in every part -of creation, it is probable that if the various systems in the universe -had been nearer to one another, their mutual disturbances would have -been inconsistent with the harmony and stability of the whole. It is -clear that space is not pervaded by atmospheric air, since its -resistance would long ere this have destroyed the velocity of the -planets; neither can we affirm it to be void, when it is traversed in -all directions by light, heat, gravitation, and possibly by influences -of which we can form no idea; but whether it be replete with an ethereal -medium, time alone will show. -</p> - -<p> -Though totally ignorant of the laws which obtain in the more distant -regions of creation, we are assured, that one alone regulates the -motions of our own system; and as general laws form the ultimate object -of philosophical research, we cannot conclude these remarks without -considering the nature of that extraordinary power, whose effects we -have been endeavouring to trace through some of their mazes. It was at -one time imagined, that the acceleration in the moon's mean motion was -occasioned by the successive transmission of the gravitating force; but -it has been proved, that, in order to produce this effect, its velocity -must be about fifty millions of times greater than that of light, which -flies at the rate of 200000 miles in a second; its action even at the -distance of the sun may therefore be regarded as instantaneous; yet so -remote are the nearest of the fixed stars, that it may be doubted -whether the sun has any sensible influence on them. -</p> - -<p> -The analytical expression for the gravitating force is a straight line; -the curves in which the celestial bodies move by the force of -gravitation are only lines of the second order; the attraction of -spheroids according to any other law would be much more complicated; and -as it is easy to prove that matter might have been moved according to an -infinite variety of laws, it may be concluded, that gravitation must -have been selected by Divine wisdom out of an infinity of other laws, -its being the most simple, and that which gives the greatest stability -to the celestial motions. -</p> - -<p> -It is a singular result of the simplicity of the laws of nature, which -admit only of the observation and comparison of ratios, that the -gravitation and theory of the motions of the celestial bodies are -independent of their absolute magnitudes and distances; consequently if -all the bodies in the solar system, their mutual distances, and their -velocities, were to diminish proportionally, they would describe curves -in all respect similar to those in which they now move; and the system -might be successively reduced to the smallest sensible dimensions, and -still exhibit the same appearances. Experience shows that a very -different law of attraction prevails when the particles of matter are -placed within inappreciable distances from each other, as in chemical -and capillary attractions, and the attraction of cohesion; whether it be -a modification of gravity, or that some new and unknown power comes into -action, does not appear; but as a change in the law of the force takes -place at one end of the scale, it is possible that gravitation may not -remain the same at the immense distance of the fixed stars. Perhaps the -day may come when even gravitation, no longer regarded as an ultimate -principle, may be resolved into a yet more general cause, embracing -every law that regulates the material world. -</p> - -<p> -The action of the gravitating force is not impeded by the intervention -even of the densest substances. If the attraction of the sun for the -centre of the earthy and for the hemisphere diametrically opposite to -him, was diminished by a difficulty in penetrating the interposed -matter, the tides would be more obviously affected. Its attraction is -the same also, whatever the substances of the celestial bodies may be, -for if the action of the sun on the earth differed by a millionth part -from his action on the moon, the difference would occasion a variation -in the sun's parallax amounting to several seconds, which is proved to -be impossible by the agreement of theory with observation. Thus all -matter is pervious to gravitation, and is equally attracted by it. -</p> - -<p> -As far as human knowledge goes, the intensity of gravitation, has never -varied within the limits of the solar system; nor does even analogy lead -us to expect that it should; on the contrary, there is every reason to -be assured, that the great laws of the universe are immutable like their -Author. Not only the sun and planets, but the minutest particles in all -the varieties of their attractions and repulsions, nay even the -imponderable matter of the electric, galvanic, and magnetic fluids are -obedient to permanent laws, though we may not be able in every case to -resolve their phenomena into general principles. Nor can we suppose the -structure of the globe alone to be exempt from the universal fiat, -though ages may pass before the changes it has undergone, or that are -now in progress, can be referred to existing causes with the same -certainty with which the motions of the planets and all their secular -variations are referable to the law of gravitation. The traces of -extreme antiquity perpetually occurring to the geologist, give that -information as to the origin of things which we in vain look for in the -other parts of the universe. They date the beginning of time; since -there is every reason to believe, that the formation of the earth was -contemporaneous with that of the rest of the planets; but they show that -creation is the work of Him with whom 'a thousand years are as one day, -and one day as a thousand years.' -</p> - -<p><br /><br /><br /></p> - -<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK A PRELIMINARY DISSERTATION ON THE MECHANISMS OF THE HEAVENS ***</div> -<div style='text-align:left'> - -<div style='display:block; margin:1em 0'> -Updated editions will replace the previous one—the old editions will -be renamed. -</div> - -<div style='display:block; margin:1em 0'> -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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