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of one aw out of thousands which mignt equally have taken p ace, 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 comets actually move in orbits of this sort; and 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 his orbit, its being a circle, or nearer to, or farther off from a circle, viz. a rounder or a longer oval, depends upon two things, the velocity with which, 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 orbits are, nearly circular; that is, ellipses with small eccentricities. The velocity and the direction must both be right. If the velocity be wrong, no direction will cure the error; if the direction be in any considerable degree oblique, no velocity will produce the orbit required. Take for example the attraction of gravity at the surface of the earth. The force of that attraction being what it is, out of all the degrees 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
*The moon describes in one second of time nearly two-thirds of a mile in its orbit round the earth: and if its distance were diminished it might still continue to revolve nearly in a circle round the same centre, if its velocity were increased so as to compensate for the greater attraction, which would now draw it constantly out of the lectilinear direction, in which it would otherwise move. This distance may be supposed to be diminished till the moon is brought near to the earth's surface, and t would, under these circumstances, still continue to complete its revolution, if its velocity were increased to about five miles in a second. Now for the description of such a revolution, there is no difference between the moon and any other matelial substance at the same distance; for they would box be drawn down through the same space in the same time by 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 he 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 the cannon might be pointed, upwards and downwards, every one would fail, but what was exactly or nearly horizontal. The same thing holds true of the planets; of our own among 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 ?
the force of attraction towards the earth's centre; and therefore a cannon ball projected parallel to the horizon with this velocity would (if there were no resistance from the air or other accidental circumstance) complete its circular revolution, and come back to the place from which it had set out, in a few minutes less than an hour and a half, which is equivalent to the velocity of about five miles in a second.—Parton.
* The ball is supposed to be fired from a place not far from the earth's surface, it can therefore be easily conceived that if its direction is much depressed below the horizon, it must be soon brought down to the ground; out it is not equally obvious that an elevation of any magnitude would ikewise prevent its completing its revolution round the earth. Abstracting from the air's resistance, and of course omitting the supposition of a projectile force sufficient to carry the ball off into infinite space, it will move in the curve of an ellipse, of which one of the foci is situated in the centre of the earth. Now a body moving uninterruptedly in an ellipse must return in time to the same point from which it set out. The body therefore which, when projected from A, Fig. 6, Pl. XXXIX, comes down to the earth at C, would have continued its course along the dotted line and returned to A, if the mass of matter in the earth had ween collected together at its centre, so as not to interfere with the motion of the projectile. Let us now conceive the body to be projected back from C, with the velocity which it had acquired in its fall, and with the direction in which it reached the earth, it would then pass through A, and come down on the other side of A I, in just the same curve, in which it had fallen from A to C. The same would apply to bodies projected upwards from B or D; and if the velocities of projection were less or greater than what would have been acquired in fall.ng from A, the bodies would still turn, but at some less or more distant point. The longest diameter, however, of the ellipsis in which they move must always pass through the earth's centre, and if the bodies rise on one side of this diameter they must fall down on the other. Now it will be seen that the curves at B, C, and D, make the angles ABI, ACI, ADI less, as the body is supposed to go farther and farther before it falls, and that the curves, in which the body can complete a revolution near the surface, will in all its parts be nearly parallel to it. Hence the canaon ball fired upwards will come back again to the ground and not be able completely to go round the earth upon any other supposition exceptng that of its being fired in nearly an horizontal direction. – Parton.
.The planets going round, all in the same direction, 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, besides 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 aws by which the heavenly motions are governed. If the planets were struck off from the surface of the sun, they
would return to 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 twenty-five times that of Mercury; a disparity which it seems impossible to reconcile with Buffon's scheme Bodies starting from the same place, with whatever differ. ence of direction or velocity they could set off, could not nave been found, at these different distances from 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 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 equality ow action and reaction, or the state of the centre of gravity of the system. Such an exquisite 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.”—JMaclaurin’s Account of Mewton’s Phil. p. 407, ed. 3.
To conclude: In astronomy, the great thing is to raise the imagination to the subject, and that oftentimes in opposition to the impression made upon the senses. An allusion, for example, must be gotten over, arising from the distance at which we view the heavenly bodies, viz. the apparent slowness of their motions. The moon shall take some hours in getting half a yard from a star which it touched. A motion so deliberate, we may think easily guided. But what is the fact? The moon, in fact, is, all this while, driving through the heavens, at the rate of considerably more than two thousand miles in an hour; which is more than double of that with which a ball is shot off from the mouth of a cannon. Yet is this prodigious rapidity as much under government, as if the planet proceeded ever so slowly, or were conducted in its course inch by inch. It is also difficult to bring the imagination to conceive (what yet, to judge tolerably of the matter, it is necessary to conceive) how loose, if we may so express it, the heavenly bodies are. Enormous globes, held by nothing, confined by nothing, are turned into free and boundless space, each to seek its course by the virtue of an invisible principle; but a principle, one, common, and the same in all; and ascertainable. To preserve such bodies from being lost, from running together in heaps, from hindering and distracting one another's motions, in a degree inconsistent with any continuing order; i. e. to cause them to form planetary systems, systems that, when formed, can be upheld, and more 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 earth: all this requires an intelligent interposition, because it can be demonstrated concerning it, that it requires an adjustment of force, distance, 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 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 be only one quiescent centre of gravity in the universe: and all bodies whatever must be approaching this centre, or revolving round it. According to the first of these suppositions, if the duration of the world had been long enough to allow of it, all its parts, all the great bodies of which it is composed, must have been gathered together in a heap round this point. No changes, however, which have been observed, afford us the smallest reason for believing, that either the one sur position or the other is true: and then it will follow, that attraction itself is controlled or suspended by a superior agent: that there is a power above the highest of the powers of material nature; a will which restrains and cireumscribes the operations of the most extensive.”
CoNTRIvance, if established, appears to me to prove everything which we wish to prove. Amongst other things, it proves the personality of the Deity, as distinguished from what is sometimes called nature, sometimes called a prin
* It must here, however, be stated, that many astronomers deny that any of the heavenly bodies are absolutely stationary. Some of the brightest of the fixed stars have certainly small motions; and of the rest the distance is too great, and the intervals of our observation too short, to enable us to pronounce with certainty that they may not have the same. The motions in the fixed stars which have been observed, are considered ei:her as proper to each of them, or as compounded of the motion of our system, and of motions proper to each star. By a comparison of these motions, a motion in our system is supposed to be discovered. By continuing this anology to other, and to all systems, it is possible to suppose that attraction is unlimited, and that the whole material universe is revolving round some fixed point within its containing sphere or space.—Paley.
The milky way is known to derive its appearance from a congeries of
very small stars, but there are luminous spots in the heaven, which cannot
be separated into distinct stars by the most powerful telescopes; these have been observed in some instances to alter their form, which Sir W. Herschell attributed to the mutual attraction of the luminous particles which composed them.