axis and another axis is this: When a sphe- density of the earth, by comparing the force roid in a state of rotatory motion gets upon a of its attraction with the force of attraction permanent axis, it keeps there; it remains of a rock of granite, the bulk of which could steady and faithful to its position; its poles be ascertained; and the upshot of the calculapreserve their direction with respect to the tion was, that the earth upon an average, plane and to the centre of its orbit: but, whilst through its whole sphere, has twice the denit turns upon an axis which is not permanent sity of granite, or about five times that of wa(and the number of those we have seen infi- ter. Therefore, it cannot be a hollow shell, as nitely exceeds the number of the other,) it is some have formerly supposed; nor can its inalways liable to shift and vacillate from one ternal parts be occupied by central fire, or by axis to another, with a corresponding change water. The solid parts must greatly exceed in the inclination of its poles. Therefore, if the fluid parts: and the probability is, that it a planet once set off revolving upon any other is a solid mass throughout composed of subthan its shortest, or one of its longest axes, stances more ponderous the deeper we go. the poles on its surface would keep perpetually Nevertheless, we may conceive the present changing, and it never would attain a perman- face of the earth to have originated from the ent axis of rotation. The effect of this unfix-revolution of a sphere, covered by a surface of edness and instability would be, that the equa- a compound mixture; the fluid and solid parts torial parts of the earth might become the polar, separating, as the surface becomes quiescent. or the polar the equatorial; to the utter de- Here then comes in the moderating hand of struction of plants and animals, which are not the Creator. If the water had exceeded its precapable of interchanging their situations, but sent proportion, even but by a trifling quanare respectively adapted to their own. As to tity, compared with the whole globe, all the ourselves, instead of rejoicing in our temper- land would have been covered: had there been ate zone, and annually preparing for the mo- much less than there is, there would not have derate vicissitude, or rather the agreeable suc-been enough to fertilize the continent. Had cession of seasons, which we experience and the exsiccation been progressive, such as we expect, we might come to be locked up in the may suppose to have been produced by an evaice and darkness of the arctic circle, with bodies porating heat, how came it to stop at the point neither inured to its rigours, nor provided with at which we see it? Why did it not stop shelter or defence against them. Nor would sooner? why at all? The mandate of the it be much better, if the trepidation of our pole, Deity will account for this; nothing else taking an opposite course, should place us un- will.'

der the heats of a vertical sun. But if it would IV. OF CENTRIPETAL FORCES. By vir fare so ill with the human inhabitant, who tue of the simplest law that can be imagined, can live under greater varieties of latitude viz. that a body continues in the state in which than any other animal; still more noxious it is, whether of motion or rest; and, if in mowould this translation of climate have proved to life in the rest of the creation; and, most perhaps of all, in plants. The habitable earth, and its beautiful variety, might have been destroyed, by a simple mischance in the axis of rotation.

tion, goes on in the line in which it was pro ceeding, and with the same velocity, unless there be some cause for change: by virtue, I say, of this law, it comes to pass (what may appear to be a strange consequence,) that cases arise, in which attraction, incessantly (*) III. All this, however, proceeds upon drawing a body towards a centre, never brings, a supposition of the earth having been formed nor ever will bring, the body to that centre, at first an oblate spheroid. There is another but keep it in eternal circulation round it If supposition; and perhaps our limited informa- it were possible to fire off a cannon-ball with tion will not enable us to decide between them. a velocity of five miles in a second, and the The second supposition is, that the earth, be- resistance of the air could be taken away, the ing a mixed mass, somewhat fluid, took, as it cannon-ball would for ever wheel round the might do, its present form, by the joint action earth, instead of falling down upon it. This of the mutual gravitation of its parts and its is the principle which sustains the heavenly rotatory motion. This, as we have said, is a motions. The Deity, having appointed this point in the history of the earth, which our law to matter (than which, as we have said observations are not sufficient to determine. before, no law could be more simple,) has turnFor a very small depth below the surface (but ed it to a wonderful account in constructing extremely small-less, perhaps, than an eight-planetary systems.

thousandth part, compared with the depth of The actuating cause in these systems, is an the centre,) we find vestiges of ancient fluidity. attraction which varies reciprocally as the But this fluidity must have gone down many square of the distance; that is, at double the hundred times farther than we can penetrate, distance, has a quarter of the force; at half to enable the earth to take its present oblate the distance, four times the strength, and so form: and whether any traces of this kind ex-on. Now concerning this law of variation, ist to that depth, we are ignorant. Calcula-we have three things to observe: First, that tions were made a few years ago, of the mean attraction, for any thing we know about it, was

NATURAL THEOLOGY.

just as capable of one law of variation, as of imply a contrariety of properties, to suppose another Secondly, that out of an infinite an ethereal fluid to act, but not to resisi; number of possible laws, those which were ad-powerful enough to carry down bodies with missible for the purpose of supporting the hea-great force towards a centre, yet, inconsistentvenly motions, lay within certain narrow li-ly with the nature of inert matter, powerless mits: Thirdly, that of the admissible laws, and perfectly yielding with respect to the moor those which come within the limits pre- tions which result from the projectile impulse. scribed, the law that actually prevails is the By calculations drawn from ancient notices of most beneficial. So far as these propositions eclipses of the moon, we can prove that, if can be made out, we may be said, I think, to such a fluid exist at all, its resistance has had prove choice and regulation: choice, out of no sensible effect upon the moon's motion for boundless variety; and regulation, of that two thousand five hundred years. The truth which, by its own nature, was in respect of is, that, except this one circumstance of the the property regulated, indifferent and indefi- variation of the attracting force at different spissitude, there is no reason whatever to supdistances agreeing with the variation of the port the hypothesis of an emanation; and, as it seems to me, almost insuperable reasons against it.

nite.

I. First then, attraction, for any thing we know about it, was originally indifferent to all laws of variation depending upon change of distance, i. e. just as susceptible of one law as of another. It might have been the same at all distances; it might have increased as the whilst the possible laws of variation were in(*) II. Our second proposition is, that, distance increased: or it might have diminish-finite, the admissible laws, or the laws compaed with the increase of the distance, yet in tible with the preservation of the system, lie ten thousand different proportions from the within narrow limits. If the attracting force present; it might have followed no stated law had varied according to any direct law of the at all. If attraction be what Cotes, with many distance, let it have been what it would, great other Newtonians, thought it to be, a primor-destruction and confusion would have taken dial property of matter, not dependent upon, place. The direct simple proportion of the or traceable to, any other material casue; then, by the very nature and definition of a primordial property, it stood indifferent to all laws. If it be the agency of something immaterial; then also, for any thing we know of it, it was indifferent to all laws. If the revolution of bodies round a centre depend upon vortices, neither are these limited to one law more than another.

distance would, it is true, have produced an ellipse; but the perturbing forces would have acted with so much advantage, as to be continually changing the dimensions of the ellipse, in a manner inconsistent with our terrestrial creation. For instance, if the planet Saturn, so large and so remote, had attracted the earth, both in proportion to the quantity of There is, I know, an account given of at- also in any proportion to its distance, i. e. if it matter contained in it, which it does; and traction, which should seem, in its very cause, had pulled the harder for being the farther off, to assign to it the law which we find it to ob. (instead of the reverse of it,) it would have serve; and which, therefore, makes that law, dragged out of its course the globe which we a law, not of choice, but of necessity: and it inhabit, and have perplexed its motions, to a is the account which ascribes attraction to an degree incompatible with our security, our enemanation from the attracting body. It is pro-joyments, and probably our existence. Of the bable, that the influence of such an emanation inverse laws, if the centripetal force had changwill be proportioned to the spissitude of the ed as the cube of the distance, or in any higher rays of which it is composed; which spissitude, proportion, that is, (for I speak to the unlearnsupposing the rays to issue in right lines on ed,) if, at double the distance, the attractive all sides from a point, will be reciprocally as force had been diminished to an eighth part, the square of the distance. The mathematics or to less than that, the consequence would of this solution we do not call in question: have been, that the planets, if they once bethe question with us is, whether there be any gan to approach the sun, would have fallen sufficient reason for believing that attraction into his body; if they once, though by ever is produced by an emanation. For my part, so little, increased their distance from the I am totally at a loss to comprehend how par-centre, would for ever have receded from it. ticles streaming from a centre should draw a The laws therefore of attraction, by which a body towards it. The impulse, if impulse it system of revolving bodies could be upholden be, is all the other way. Nor shall we find in their motions, lie within narrow limits, comless difficulty in conceiving a conflux of par-pared with the possible laws. I much underticles, incessantly flowing to a centre, and car-rate the restriction, when I say, that, in a rying down all bodies along with it, that cen-scale of a mile, they are confined to an inch. tre also itself being in a state of rapid motion All direct ratios of the distance are excluded, through absolute space; for, by what source is the stream fed, or what becomes of the accumulation? Add to which, that it seems to

on account of danger from perturbing forces:
all reciprocal ratios, except what lie beneath
the cube of the distance, by the demonstrable

consequence, that every the least change of ther attention was to be given to each particle distance would, under the operation of such of matter, and one, and one only particular laws, have been fatal to the repose and order law of action to be assigned to it. No other of the system. We do not know, that is, we law would have answered the purpose intended. seldom reflect, how interested we are in this (*) 2. All systems must be liable to permatter. Small irregularities may be endured; turbations. And therefore, to guard against but, changes within these limits being allowed these perturbations, or rather to guard against for, the permanency of our ellipse is a question their running to destructive lengths, is perof life and death to our whole sensitive world. haps the strongest evidence of care and fore(*) III. That the subsisting law of at- sight that can be given. Now, we are able traction falls within the limits which utility to demonstrate of our law of attraction, what requires, when these limits bear so small a can be demonstrated of no other, and what proportion to the range of possibilities upon qualifies the dangers which arise from cross which chance might equally have cast it, is but unavoidable influences; that the action not, with any appearance of reason, to be ac- of the parts of our system upon one another, counted for, by any other cause than a regu- will not cause permanently increasing irregu'ation proceeding from a designing mind. But larities, but merely periodical or vibratory our next proposition carries the matter some- ones; that is, they will come to a limit, and what farther. We say, in the third place, then go back again. This we can demonstrate 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.

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, compared with that of the body at the centre; the orbits not much inclined to one another; and their eccentricity little. In such a sys(*) 1. Whilst this law prevails between each tem, the grand points are secure. The mean particle of matter, the united attraction of a distances and periodic times, upon which desphere, composed of that matter, observes the pend our temperature, and the regularity of same law. This property of the law is neces- our year, are constant. The eccentricities, sary, to render it applicable to a system com- it is true, will still vary; but so slowly, and posed of spheres, but it is a property which be- to so small an extent, as to produce no inconlongs to no other law of attraction that is ad-veniency from fluctuation of temperature and missible. The law of variation of the united season. The same as to the obliquity of the attraction is in no other case the same as the planes of the orbits. For instance, the inclilaw of attraction of each particle, one case ex-nation of the ecliptic to the equator will necepted, and that is, of the attraction varying ver change above two degrees (out of ninety), directly as the distance; the inconveniency of and that will require many thousand years in which law, in other respects, we have already performing. noticed.

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 consequence as not acting at all upon either.

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 If it be said, that the planets might have its parts. Now the admissible and convenient been sent round the Sun in exact circies, in law which exists, could not be obtained in a which case no change of distance from the system of bodies gravitating by the united gra- centre taking place, the law of variation of vitation of their parts, unless each particle of the attracting power would have never come matter were attracted by a force varying by in question, one law would have served as one particular law, viz. varying inversely as well as another; an answer to the scheme the square of the distance: for, if the action may be drawn from the consideration of these of the particles be according to any other law same perturbing forces. The system retaining whatever, the admissible and convenient law, in other respects its present constitution, which is adopted, could not be obtained. Here though the planets had been at first sent round then are clearly shown regulation and design. in exact circular orbits, they could not have A law both admissible and convenient was to kept them: and if the law of attraction had be obtained; the mode chosen for obtaining not been what it is, or, at least, if the prethat law was by making each particle of mat- vailing law had transgressed the limits above ter act. After this choice was made, then far-assigned, every evagation would have been

fatal: the planet once drawn, as drawn it ne- the cannon might ne pointed, upwards and cessarily must have been, out of its course, downwards, every one would fail, but what would have wandered in endless error.

was exactly or nearly horizontal. The same thing holds true of the planets: of our own amongst the rest. We are entitled, therefore, to ask, and to urge the question, Why did the projectile velocity and projectile 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?

Now,

(*) 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, The planets going round, all in the same and carried away to immense distances from direction, and all nearly in the same plane, afhim. The comets actually move in orbits of forded to Buffon a ground for asserting, that this sort: and, had the planets done so, instead they had all been shivered from the sun by of going round in orbits nearly circular, the the same stroke of a comet, and by that stroke change from one extremity of temperature to projected into their present orbits. another must, in ours at least, have destroyed besides that this is to attribute to chance the every animal and plant upon its surface. Now, fortunate concurrence of velocity and directhe distance from the centre at which a planet | tion which we have been here noticing, the hysets off, and the absolute force of attraction at pothesis, as I apprehend, is inconsistent with that distance, being fixed, the figure of its orbit, the physical laws by which the heavenly moits being a circle, or nearer to, or farther off tions are governed. If the planets were struck from a circle, viz. a rounder or a longer oval, off from the surface of the sun, they would re. depends upon two things, the velocity with turn to the surface of the sun again. Nor which, and the direction in which, the planet will this difficulty be got rid of, by supposing is projected. And these, in order to produce a that the same violent blow which shattered right result, must be both brought within the sun's surface, and separated large frag certain narrow limits. One, and only one, ments from it, pushed the sun himself out o velocity, united with one, and only one, direc- his place; for, the consequence of this woul tion, will produce a perfect circle. And the be, that the sun and system of shattered fragvelocity must be near to this velocity, and the ments would have a progressive motion, which, direction also near to this direction, to produce indeed, may possibly be the case with our orbits, such as the planetary orbits are, nearly system; but then each fragment would, in circular; that is, ellipses with small eccentri- every revolution, return to the surface of the cities. The velocity and the direction must sun again. The hypothesis is also contradict both be right. If the velocity be wrong, no ed by the vast difference which subsists bedirection will cure the error; if the direction tween the diameters of the planetary orbits. be in any considerable degree oblique, no ve- The distance of Saturn from the sun (to say locity will produce the orbit required. Take nothing of the Georgium Sidus) is nearly fivefor example the attraction of gravity at the and-twenty times that of Mercury; a disparisurface of the earth. The force of that at-ty, which it seems impossible to reconcile with action being what it is, out of all the degrees Buffon's scheme. Bodies starting from the of velocity, swift and slow, with which a ball might be shot off, none would answer the purpose of which we are speaking, but what was nearly that of five miles in a second. If it were less than that, the body would not get round at all, but would come to the ground; if it were in any considerable degree more than that, the body would take one of those eccentric courses, those long ellipses, of which we have noticed the inconveniency. If the velocity reached the rate of seven miles in a second, or went beyond that, the ball would fly off from the earth, and never be heard of more. In like manner, with respect to the direction; out of the innumerable angles in which the ball might be sent off, (I mean angles formed with a line drawn to the centre) none would serve but what was nearly a right one out of the various directions in which

same place, with whatever difference of direction or velocity they set off, could not have been found at these different distances fon the centre, still retaining their nearly circular orbits. They must have been carried to their proper distances, before they were projected.

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