fest, without either plates or calculation, first, that still more noxious would this translation of climate supposing the necessary proportion of magnitude have proved to life in the rest of the creation; between the central and the revolving bodies to be and, most perhaps of all, in plants. The habitapreserved, the ignited planet would not be suffi- ble earth, and its beautiful variety, might have cient to illuminate and warm the rest of the sys-been destroyed, by a simple mischance in the axis tem; secondly, that its light and heat would be of rotation. imparted to the other planets much more irregularly than light and heat are now received from

the sun.

(*) III. All this, however, proceeds upon a supposition of the earth having been formed at first an oblate spheroid. There is another supposition; and perhaps our limited information will not enable us to decide between them. The second supposition is, that the earth, being a mixed mass somewhat fluid, took, as it might do, its present form, by the joint action of the mutual gravitation of its parts and its rotatory motion. This, as we have said, is a point in the history of the earth, which our observations are not sufficient to determine. For a very small depth below the surface, (but extremely small, less, perhaps, than an eightthousandth part, compared with the depth of the centre,) we find vestiges of ancient fluidity. But this fluidity must have gone down many hundred times farther than we can penetrate, to enable the earth to take its present oblate form: and whether any traces of this kind exist to that depth, we are ignorant. Calculations were made a few years ago, of the mean density of the earth, by compar ing the force of its attraction with the force of attraction of a rock of granite, the bulk of which

(*) II. Another thing, in which a choice appears to be exercised, and in which, amongst the possibilities out of which the choice was to be made, the number of those which were wrong bore an infinite proportion to the number of those which were right, is in what geometricians call the aris of rotation. This matter I will endeavour to explain. The earth, it is well known, is not an exact globe, but an oblate spheroid, something like an orange. Now the axes of rotation, or the diameters upon which such a body may be made to turn round, are as many as can be drawn through its centre to opposite points upon its whole surface but of these axes none are permanent, except either its shortest diameter, i. e. that which passes through the heart of the orange from the place where the stalk is inserted into it, and which is but one; or its longest diameters, at right angles with the former, which must all terminate in the single circumference which goes round the thickest part of the orange. The short-could be ascertained: and the upshot of the calest diameter is that upon which in fact the earth culation was, that the earth upon an average, turns, and it is, as the reader sees, what it ought through its whole sphere, has twice the density to be, a permanent axis; whereas, had blind of granite, or about five times that of water. chance, had a casual impulse, had a stroke or push Therefore it cannot be a hollow shell, as some at random, set the earth a-spinning, the odds were have formerly supposed; nor can its internal infinite, but that they had sent it round upon a parts be occupied by central fire, or by water. wrong axis. And what would have been the The solid parts must greatly exceed the fluid consequence? The difference between a perma-parts; and the probability is, that it is a solid mass nent axis and another axis is this: When a sphe- throughout, composed of substances more ponderroïd in a state of rotatory motion gets upon a per-ous the deeper we go. Nevertheless, we may conmanent axis, it keeps there; it remains steady ceive the present face of the earth to have origiand faithful to its position; its poles preserve their nated from the revolution of a sphere, covered by direction with respect to the plane and to the cen- a surface of a compound mixture; the fluid and tre of its orbit: but, whilst it turns upon an axis solid parts separating, as the surface becomes which is not permanent (and the number of those quiescent. Here then comes in the moderating we have seen infinitely exceeds the number of the hand of the Creator. If the water had exceeded its other,) it is always liable to shift and vacillate present proportion, even but by a triffing quantity from one axis to another, with a corresponding compared with the whole globe, all the land would change in the inclination of its poles. Therefore, have been covered: had there been much less if a planet once set off revolving upon any other than there is, there would not have been enough than its shortest, or one of its longest axes, the to fertilize the continent. Had the exsiccation poles on its surface would keep perpetually chang-been progressive, such as we may suppose to have ing, and it never would attain a permanent axis been produced by an evaporating heat, how came of rotation. The effect of this unfixedness and it to stop at the point at which we see it? Why instability would be, that the equatorial parts of did it not stop sooner? why at all? The mandate the earth might become the polar, or the polar the of the Deity will account for this; nothing else equatorial; to the utter destruction of plants and will. animals, which are not capable of interchanging IV. OF CENTRIPETAL FORCES. By virtue of their situations, but are respectively adapted to the simplest law that can be imagined, riz. that a their own. As to ourselves, instead of rejoicing body continues in the state in which it is, whein our temperate zone, and annually preparing for ther of motion or rest; and, if in motion, goes on the moderate vicissitude, or rather the agreeable suc-in the line in which it was proceeding, and with cession of seasons, which we experience and ex- the same velocity, unless there be some cause for pect, we might come to be locked up in the ice change: by virtue, I say, of this law, it comes to and darkness of the arctic circle, with bodies nei-pass, (what may appear to be a strange consether inured to its rigours, nor provided with shel-quence,) that cases arise, in which attraction, inter or defence against them. Nor would it be much better, if the trepidation of our pole, taking an opposite course, should place us under the heats of a vertical sun. But if it would fare so ill with the human inhabitant, who can live under greater varieties of latitude than any other animal;

cessantly drawing a body towards a centre, never brings, nor ever will bring, the body to that centre, but keep it in eternal circulation round it. If it were possible to fire off a cannon-ball with a velocity of five miles in a second, and the resistance of the air could be taken away, the cannon-ball

these limits bear so small a proportion to the range of possibilities upon which chance might equally have cast it, is not, with any appearance of reason, to be accounted for by any other cause than a regulation proceeding from a designing mind. But our next proposition carries the matter somewhat farther. We say, in the third place, that, out of the different laws which lie within the limits of admissible laws, the best is made choice of; that there are advantages in this particular law which cannot be demonstrated to belong to any other law; and, concerning some of which, it can be demonstrated that they do not belong to any other.

(*) 1. Whilst this law prevails between each particle of matter, the united attraction of a sphere, composed of that matter, observes the same law. This property of the law is necessary, to render it applicable to a system composed of spheres, but it is a property which belongs to no other law of attraction that is admissible. The law of variation of the united attraction is in no other case the same as the law of attraction of each particle, one case excepted, and that is of the attraction varying directly as the distance; the inconveniency of which law, in other respects, we have already noticed.

compared with that of the body at the centre; the orbits not much inclined to one another; and their eccentricity little. In such a system, the grand points are secure. The mean distances and periodic times, upon which depend our temperature, and the regularity of our year, are constant. The eccentricities, it is true, will still vary; but so slowly, and to so small an extent, as to produce no inconveniency from fluctuation of temperature and season. The same as to the obliquity of the planes of the orbits. For instance, the inclination of the ecliptic to the equator will never change above two degrees (out of ninety,) and that will require many thousand years in performing.

It has been rightly also remarked, that, if the great planets, Jupiter and Saturn, had moved in lower spheres, their influences would have had much more effect as to disturbing the planetary motions, than they now have. While they revolve at so great distances from the rest, they act almost equally on the sun and on the inferior planets; which has nearly the same consequences as not acting at all upon either.

If it be said that the planets might have been sent round the sun in exact circles, in which case, no change of distance from the centre taking place, the law of variation of the attracting power would have never come in question, one law would have served as well as another; an answer to the scheme may be drawn from the consideration of these same perturbing forces. The system retaining in other respects its present constitution, though the planets had been at first sent round in exact circular orbits, they could not have kept them; and if the law of attraction had not been what it is, or, at least, if the prevailing law had transgressed the limits above assigned, every evagation would have been fatal: the planet once drawn, as drawn it necessarily must have been, out of its course, would have wandered in endless error.

We may follow this regulation somewhat farther, and still more strikingly perceive that it proceeded from a designing mind. A law both admissible and convenient was requisite. In what way is the law of the attracting globes obtained? Astronomical observations and terrestrial experiments show that the attraction of the globes of the system is made up of the attraction of their parts; the attraction of each globe being compounded of the attractions of its parts. Now the admissible and convenient law which exists, could not be obtained in a system of bodies gravitating by the united gravitation of their parts, unless each particle of matter were attracted by a force varying by one particular law, viz. varying inversely as the square of the distance: for, if the action of the particles be according to any other law whatever, the admissible and convenient law, which is adopted, could not be obtained. Here then are clearly shown regulation and design. A law both admissible and convenient was to be obtained: the mode chosen for obtaining that law was by making each particle of matter act. After this choice was made, then farther attention was to be given to each particle of matter, and one, and one only, particular law of action to be assigned to it. No other law would have answered the pur-comets actually move in orbits of this sort: and, pose intended.

(*) 2. All systems must be liable to perturbations. And, therefore, to guard against these perturbations, or rather to guard against their running to destructive lengths, is perhaps the strongest evidence of care and foresight that can be given. Now, we are able to demonstrate of our law of attraction, what can be demonstrated of no other, and what qualifies the dangers which arise from cross but unavoidable influences; that the action of the parts of our system upon one another will not cause permanently increasing irregularities, but merely periodical or vibratory ones; that is, they will come to a limit, and then go back again. This we can demonstrate only of a system, in which the following properties concur, viz. that the force shall be inversely as the square of the distance; the masses of the revolving bodies small,

(*) V. What we have seen in the law of the centripetal force, viz. a choice guided by views of utility, and a choice of one law out of thousands which might equally have taken place, we see no less in the figures of the planetary orbits. It was not enough to fix the law of the centripetal force, though by the wisest choice; for, even under that law, it was still competent to the planets to have moved in paths possessing so great a degree of eccentricity, as, in the course of every revolution, to be brought very near to the sun, and carried away to immense distances from him.

The

had the planets done so, instead of going round in orbits nearly circular, the change from one extremity of temperature to another must, in ours at least, have destroyed every animal and plant upon its surface. Now, the distance from the centre at which a planet sets off, and the absolute force of attraction at that distance, being fixed, the figure of its orbit, its being a circle, or nearer to, or farther off from a circle, riz. a rounder or a longer oval, depends upon two things, the velocity with, and the direction in which, the planet is projected. And these, in order to produce a right result, must be both brought within certain narrow limits. One, and only one, velocity, united with one, and only one, direction, will produce a perfect circle. And the velocity must be near to this velocity, and the direction also near to this direction, to produce orbits, such as the planetary

have been carried to their proper distances, before they were projected.*

orbits are, nearly circular; that is, ellipses with i small eccentricities. The velocity and the direction must both be right. If the velocity be wrong. To conclude: in astronomy, the great thing is no direction will cure the error; if the direction to raise the imagination to the subject, and that be in any considerable degree oblique, no velocity oftentimes in opposition to the impression made will produce the orbit required. Take for exam- upon the senses. An illusion, for example, must ple the attraction of gravity at the surface of the be gotten over, arising from the distance at which earth. The force of that attraction being what we view the heavenly bodies, riz. the apparent it is, out of all the degrees of velocity, swift and slowness of their motions. The moon shall take slow, with which a ball might be shot off, none some hours in getting half a yard from a star would answer the purpose of which we are speak-which it touched. A motion so deliberate, we may ing, but what was nearly that of five miles in a think easily guided. But what is the fact? The second. If it were less than that, the body would moon, in fact, is, all this while, driving through not get round at all, but would come to the ground; the heavens, at the rate of considerably more than if it were in any considerable degree more than two thousand miles in an hour; which is more that, the body would take one of those eccentric than double of that with which a ball is shot off courses, these long ellipses, of which we have from the mouth of a cannon. Yet is this prodinoticed the inconveniency. If the velocity reached gious rapidity as much under government, as if the rate of seven miles in a second, or went be- the planet proceeded ever so slowly, or were conyond that, the ball would fly off from the earth, ducted in its course inch by inch. It is also diffiand never be heard of more. In like manner with cult to bring the imagination to conceive (what respect to the direction; out of the innumerable yet, to judge tolerably of the matter, it is necesangles in which the ball might be sent off (I mean sary to conceive) how loose, if we may so express angles formed with a line drawn to the centre,) it, the heavenly bodies are. Enormous globes, none would serve but what was nearly a right held by nothing, confined by nothing, are turned one: out of the various directions in which the into free and boundless space, each to seek its cannon might be pointed, upwards and down- course by the virtue of an invisible principle; wards, every one would fail, but what was exactly but a principle, one, common, and the same in or nearly horizontal. The same thing holds true all; and ascertainable. To preserve such bodies of the planets: of our own amongst the rest. We from being lost, from running together in heaps, are entitled therefore to ask, and to urge the ques-from hindering and distracting one another's motion, Why did the projectile velocity and projections in a degree inconsistent with any continutile direction of the earth happen to be nearly those which would retain it in a circular form? Why not one of the infinite number of velocities, one of the infinite number of directions, which would have made it approach much nearer to, or recede much farther from, the sun?

ing order; h. e. to cause them to form planetary systems, systems that, when formed, can be upheld, and most especially, systems accommodated to the organized and sensitive natures which the planets sustain, as we know to be the case, where alone we can know what the case is, upon our

tion, because it can be demonstrated concerning it, that it requires an adjustment of force, dis tance, direction, and velocity, out of the reach of chance to have produced; an adjustment, in its view to utility, similar to that which we see in ten thousand subjects of nature which are nearer to us, but in power, and in the extent of space through which that power is exerted, stupendous.

But many of the heavenly bodies, as the sun and fixed stars, are stationary. Their rest must be the effect of an absence or of an equilibrium of attractions. It proves also that a projectile impulse was originally given to some of the heavenly bodies, and not to others. But farther; if attraction act at all distances, there can only be one quiescent centre of gravity in the universe: and all bodies whatever must be approaching this centre, or revolving round it. According to the

The planets going round, all in the same direc-earth: all this requires an intelligent interposition, and all nearly in the same plane, afforded to Buffon a ground for asserting that they had all been shivered from the sun by the same stroke of a comet, and by that stroke projected into their present orbits. Now, beside that this is to attribute to chance the fortunate concurrence of velocity and direction which we have been here noticing, the hypothesis, as I apprehend, is inconsistent with the physical laws by which the heavenly motions are governed. If the planets were struck off from the surface of the sun, they would return to the surface of the sun again. Nor will this difficulty be got rid of, by supposing that the same violent blow which shattered the sun's surface, and separated large fragments from it, pushed the sun himself out of his place; for, the consequence of this would be, that the sun and system of shattered fragments would have a progressive motion, which, indeed, may possibly be the case with our system; but then each fragment would, in every revolution, return to the surface of the sun again. The hypothesis is also contradicted, by the vast difference which subsists between the diameters of the planetary orbits. The distance of Saturn from the sun (to say nothing of the Georgium Sidus) is nearly five-and-twenty times that of Mercury; a disparity, which it seems impossible to reconcile with Buffon's scheme. Bodies starting from the same place, with whatever difference of direction or velocity they set off, could not have been found at these different distances from the centre, still retaining their nearly circular orbits. They must

* If we suppose the matter of the system to be accumulated in the centre by its gravity, no mechanical principles, with the assistance of this power of gravity, could separate the vast mass into such parts as the sun and planets; and, after carrying them to their different distances, project them in their several directions, preserving still the quality of action, and reaction, or the state of the centre of gravity of the system. Such an exquise structure of things could only arise from the contrivance and powerful influences of an intelligent, free, and most potent agent. The same powers, therefore, which, at present, govern the material universe, and conduct its various motions, are very different from those which were necessary to have produced it from nothing, or to have disposed it in the admirable form in which it now proceeds."-Maclaurin's Account of Newton's Philos. p. 407. ed. 3.