ON THE LAWS OF GRAVITATION. 411 



the centre, abound so much in bright stars as the opposite hemisphere. If 

 Sirius is a million times as far from the sun as the earth, and if he should 

 descend towards the sun by means of their mutual gravitation only, he 

 would move, on a rough estimate, but about 40 feet in the first year, and 

 in 1000 years only 8000 miles. It has been conjectured that the mutual 

 ?. -ravitatioii of the stars of a nebula is sometimes the cause of the peculiar 

 form of the aggregate, which somewhat resembles that of a drop of a liquid 

 ,ield together by its cohesion ; but unless the form of the nebula was ori- 

 gii.ftlly spherical, it could scarcely have acquired that form from the opera- 

 tioiitof gravity, since the spherical form of a drop is owing as much to the 

 elasticity as to the attractive force of the particles of water, and it would 

 be necessary, in order to preserve the analogy, that the stars should also 

 be floating in an incompressible fluid. 



The sun's change of place, dependent on the relative situation of the 

 planets, is so inconsiderable, that it escaped observation until its existence 

 had been deduced from theory. Not but that this change would be suffi- 

 ciently conspicuous if we had any means of detecting it, since it may 

 amount in the whole to a distance equal to twice the sun's diameter, or 

 seven times the distance of the moon from the earth ; and this change is 

 readily deducible from the general and unquestionable law of mechanics, 

 that the place of the centre of inertia of a system cannot be changed by any 

 reciprocal or mutual action of the bodies composing it, the action of gra- 

 vity being found to be perfectly reciprocal. But the earth accompanies the 

 sun in great measure in this aberration, and the other planets are also more 

 or less affected by similar motions ; so that the relative situations are much 

 less disturbed than if the sun described this irregular orbit by the ope- 

 ration of a cause foreign to the rest of the system. 



The simple revolution of a body, in a given plane, indicates, at first 

 sight, the existence of an attractive force directed to some point within the 

 orbit ; and the Keplerian law of the equality of the areas described in equal 

 times, by a line drawn from each planet to the sun, agrees precisely with 

 what is demonstrable of the effects of central forces, and points at once 

 to the sun as the centre of attraction of the system. And since the orbits 

 of the planets are elliptical, and the sun is placed in one of the foci of 

 each, it may be mathematically proved that the force directed to the sun 

 must increase in proportion as the square of the distance decreases. 



The times of the revolutions of the planets are also in perfect con- 

 formity with the laws of gravitation, that is, the squares of the times are 

 proportional to the cubes of the distances from the sun. It was easy to 

 infer, from what Huygens had already demonstrated of centrifugal forces, 

 that this Keplerian law must be true of bodies revolving in circles by the 

 force of gravitation ; but Newton first demonstrated the same proportion 

 with respect to elliptic orbits, and shewed that the time of revolution in an 

 ellipsis is equal to the time of revolution in a circle, of which the diameter 

 is equal to the greater axis of the ellipsis, or the semidiameter to the mean 

 distance of the planet. 



The universality of the laws of gravitation, as applied to the different 

 planets, shews also that the matter, of which they are composed, is equally 



