will depend, he shows, in any assigned case, upon the particular circumstances of velocity, distance, and direction, which of these curves shall be described, — whether an ellipse, a circle, a parabola, or an hyperbola; but one or other it must be; and any one of any degree of eccentricity it may be, according to the circumstances of the case; and, in all cases, the point to which the motion is referred, whether it be the center of one of the spheres, or their common center of gravity, will of necessity be the focus of the conic section described. He shows, furthermore (Princip. i. 1.), that, in every case, the angular velocity with which the line joining their centers moves, must be inversely proportional to the square of their mutual distance, and that equal areas of the curves described will be swept over by their line of junction in equal times.

(378.) All this is in conformity with what we have stated of the solar and lunar movements. Their orbits are ellipses, but of different degrees of eccentricity; and this circumstance already indicates the general applicability of the principles in question.

(379.) But here we have already, by a natural and ready implication (such is always the progress of generalisation), taken a further and most important step, almost unperceived. We have extended the action of gravity to the case of the earth and sun, to a distance immensely greater than that of the moon, and to a body apparently quite of a different nature from either. Are we justified in this? or, at all events, are there no modifications introduced by the change of data, if not into the general expression, at least into the particular interpretation, of the law of gravitation? Now, the moment we come to numbers, an obvious incongruity strikes us. When we calculate, as above, from the known distance of the sun (art. 304.), and from the period in which the earth circulates about it (art. 327.), what must be the centrifugal force of the latter by which the sun's attraction is balanced, (and which, therefore, becomes an exact measure of the sun's attractive

energy as exerted on the earth,) we find it to be immensely greater than would suffice to counteract the earth's attraction on an equal body at that distance— greater in the high proportion of 354936 to 1. It is clear, then, that if the earth be retained in its orbit about the sun by solar attraction, conformable in its rate of diminution with the general law, this force must be no less than 354936 times more intense than what the earth would be capable of exerting, cæteris paribus, at an equal distance.

(380.) What, then, are we to understand from this result? Simply this, that the sun attracts as a collection of 354936 earths occupying its place would do, or, in other words, that the sun contains 354936 times the mass or quantity of ponderable matter that the earth consists of. Nor let this conclusion startle us. We have only to recall what has been already shown in art. 305. of the gigantic dimensions of this magnificent body, to perceive that, in assigning to it so vast a mass, we are not outstepping a reasonable proportion. In fact, when we come to compare its mass with its bulk, we find its density* to be less than that of the earth, being no more than 0.2543. So that it must

consist, in reality, of far lighter materials, especially when we consider the force under which its central parts must be condensed. This consideration renders it highly probable that an intense heat prevails in its interior, by which its elasticity is reinforced, and rendered capable of resisting this almost inconceivable pressure without collapsing into smaller dimensions.

(381.) This will be more distinctly appreciated, if we estimate, as we are now prepared to do, the intensity of gravity at the sun's surface.

The attraction of a sphere being the same (art. 376.) as if its whole mass were collected in its center, will, of course, be proportional to the mass directly, and the

* The density of a material body is as the mass directly, and the volume inversely: hence density of: density of :: 102543: 1.

354936 1384472

square of the distance inversely; and, in this case, the distance is the radius of the sphere. Hence we conclude*, that the intensities of solar and terrestrial gravity at the surfaces of the two globes are in the proportions of 27.9 to 1. A pound of terrestrial matter at the sun's surface, then, would exert a pressure equal to what 27.9 such pounds would do at the earth's. An ordinary man, for example, would not only be unable to sustain his own weight on the sun, but would literally be crushed to atoms under the load. t

(382.) Henceforward, then, we must consent to dismiss all idea of the earth's immobility, and transfer that attribute to the sun, whose ponderous mass is calculated to exhaust the feeble attractions of such comparative atoms as the earth and moon, without being perceptibly dragged from its place. Their center of gravity lies, as we have already hinted, almost close to the center of the solar globe, at an interval quite imperceptible from our distance; and whether we regard the earth's orbit as being performed about the one or the other center makes no appreciable difference in any one phenomenon of astronomy.

(383.) It is in consequence of the mutual gravitation of all the several parts of matter, which the Newtonian law supposes, that the earth and moon, while in the act of revolving, monthly, in their mutual orbits about their common center of gravity, yet continue to circulate, without parting company, in a greater annual orbit round the sun. We may conceive this motion by connecting two unequal balls by a stick, which, at their center of gravity, is tied by a long string, and whirled round. Their joint systems will circulate as one body about the common center to which the string is attached, while yet they may go on circulating round each other in subordinate gyrations, as if the stick were quite free

1

Solar gravity: terrestrial: 354936 2 : -2 279 1; [the re

(440000)

(4000)

spective radii of the sun and earth being 440000, and 4000 miles.

A mass weighing 12 stone or 170 lbs. on the earth, would produce a pressure of 4600 lbs. on the sun.

from any such tie, and merely hurled through the air. If the earth alone, and not the moon, gravitated to the sun, it would be dragged away, and leave the moon behind and vice versa; but, acting on both, they continue together under its attraction, just as the loose parts of the earth's surface continue to rest upon it. It is, then, in strictness, not the earth or the moon which describes an ellipse around the sun, but their common center of gravity. The effect is to produce a small, but very perceptible, monthly equation in the sun's apparent motion as seen from the earth, which is always taken into account in calculating the sun's place.

(384.) And here, i. e. in the attraction of the sun, we have the key to all those différences from an exact elliptic movement of the moon in her monthly orbit, which we have already noticed (arts. 344. 360.), viz. to the retrograde revolution of her nodes; to the direct circulation of the axis of her ellipse; and to all the other deviations from the laws of elliptic motion at which we have further hinted. If the moon simply revolved about the earth under the influence of its gravity, none of these phenomena would take place. Its orbit would be a perfect ellipse, returning into itself, and always lying in one and the same plane: that it is not so, is a proof that some cause disturbs it, and interferes with the earth's attraction; and this cause is no other than the sun's attraction or rather, that part of it which is not equally exerted on the earth.

(385.) Suppose two stones, side by side, or otherwise situated with respect to each other, to be let fall together; then, as gravity accelerates them equally, they will retain their relative positions, and fall together as if they formed one mass. But suppose

gravity to be rather more intensely exerted on one than the other; then would that one be rather more accelerated in its fall, and would gradually leave the other; and thus a relative motion between them would arise from the difference of action, however slight.

R

(386.) The sun is about 400 times more remote than the moon; and, in consequence, while the moon describes her monthly orbit round the earth, her distance from the sun is alternately th part greater and as much less than the earth's. Small as this is, it is yet sufficient to produce a perceptible excess of attractive tendency of the moon towards the sun, above that of

NOM

the earth when in the nearer point of her orbit, M, and a corresponding defect on the opposite part, N; and, in the intermediate positions, not only will a difference of forces subsist, but a difference of directions also; since, however small the lunar orbit MN, it is not a point, and, therefore, the lines drawn from the sun S to its several parts cannot be regarded as strictly parallel. If, as we have already seen, the force of the sun were equally exerted, and in parallel directions on both, no disturbance of their relative situations would take place; but from the non-verification of these conditions arises a disturbing force, oblique to the line joining the moon and earth, which in some situations acts to accelerate, in others to retard, her elliptic orbitual motion; in some to draw the earth from the moon, in others the moon from the earth. Again, the lunar orbit, though very nearly, is yet not quite coincident with the plane of the ecliptic; and hence the action of the sun, which is very nearly parallel to the last-mentioned plane, tends to draw her somewhat out of the plane of her orbit, and does actually do so-producing the revolution of her nodes, and other phenomena less striking. We are not yet prepared to go into the subject of these perturbations, as they are called; but they are introduced to the reader's notice as early as possible, for the purpose of re-assuring his mind, should doubts have arisen