NEWTON S PRINCIPIA. 127 



E, the other parallel to the line joining E and G, the 

 former force will only accelerate the motion of M and 

 E round G by an addition to the mutual attraction of M 

 and E ; the latter force will draw the centre G towards S 

 or towards G , the common centre of gravity of the three 

 bodies, and combined with the action of M and E upon 

 their centre G will make G revolve in an ellipse round 

 G , the common centre of the three, round which also, in 

 like manner, S will describe an ellipse, G being the centre 

 of those two ellipses. Thus the bodies M and E will de 

 scribe an ellipse round the centre G, and the centre G 

 and body S will describe ellipses round the centre G , 

 both G and G being the centres of these ellipses ; and 

 so of any greater number of bodies. Moreover, the ab 

 solute amount of the attractive force in each centre will be 

 as the distance of the centre from the bodies or centres of 

 gravity severally, multiplied by the masses of the bodies. 

 So that E and S are attracted to G by a force as (M + E 

 + S) multiplied by their respective distances from G. 

 Lastly, the times in which these ellipses are described by 

 the bodies and the centres, are all equal by what was 

 before proved respecting motion when the force varies as 

 the distances. 



This law of the centripetal force is the only one which 

 preserves the entire ellipticity of the orbits, notwithstand- 

 ing any mutual disturbances; but it produces, at great 

 distances, motions of enormous velocity. Thus we have 

 seen that Saturn would move at the rate of 75,000 miles 

 in a second (or a third of the velocity of light itself), were 

 there no disturbance from the other bodies ; but the dis 

 turbance might greatly accelerate this rapid motion. If 

 the law be the inverse square of the distance, there will be 

 a departure from the elliptical form of the orbits and 

 from the proportion of the areas to the times, indicating 



