ON THE LAWS OF GRAVITATION. 517 



unless the form of the nebula was originally spherical, it could scarcely have 

 acquired that form from the operation of gravity, since the spherical form of 

 a drop is owing as much to the elasticity as to the attractive force of the par- 

 ticles 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 pla- 

 nets, is so inconsiderable, that it escaped observation until its existence had 

 been deduced from theory. Not but that this change would be suihciently 

 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 dis- 

 tance of the moon from the earth ; and this change is readily deducible from 

 the general and unquestionable law of mechanics, tliat the place of the cen- 

 tre of inertia of a system cannot be changed by any reciprocal or mutual ac- 

 tion of the bodies composing it, the action of gravity being found to be per- 

 fectly reciprocal. But the earth accompanies the sun in great measure in this 

 aberration, and the other planets are also more or less aff'ected by similar 

 motions ; so that the relative situations are much less disturbed than if the 

 sun described this irregular orbit by the operation 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 ma- 

 thematically pfoved that the force directed to the sun must increase in pro- 

 portion as the square of the distance decreases. 



The times of the revolutions of the planets are also in perfect conformity 

 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 ; 



