293 COSMIC PHILOSOPHY. [pt. n. 



phery. What now will be the result ? The direction of a's 

 motion, instead of remaining unaltered, will be at each 

 instant deflected from a straight line in such a way that A 

 will continually approach nearer and nearer to a point some- 

 where in advance of b, upon the line in which B is moving : 

 instead of a straight line we shall have a curve of which the 

 coordinates will bear to each other a ratio equal to the ratio 

 between a's momentum and b's tractive force. The velocity of 

 A will also cease to be uniform. For as soon as A has passed 

 on beyond B, a portion of its momentum will be at each in- 

 stant consumed in neutralizing b's tractive force, so that the 

 velocity due to the remaining momentum, will be at each 

 instant diminished. Now, unless a's momentum be infinite, 

 this process cannot go on for ever. By the time that a has 

 arrived at the point directly in advance of B, so much 

 momentum will have been lost that b's attraction will 

 begin to overbalance it, and the curve in which A is moving 

 will begin to turn back toward B. But now b's tractive 

 force begins to augment at each instant the velocity of a, 

 until, by the time that A has reached a position alongside 

 of B, its momentum is considerably in excess of b's attrac- 

 tion, and it is consequently carried on toward a point in the 

 rear of B. The same rhythmical decrease and increase in 

 A's momentum continues until the curve is completed, and 

 A has reached the position from which it started. Thus our 

 attracted body, instead of moving in a straight line, moves 

 in a closed curve of which one of the foci must coincide in 

 position with the common centre of gravity of the attracted 

 and attracting bodies. The result which we have here 

 obtained by supposing A to be so much smaller than B that 

 its reciprocal influence upon b's motion might be left un- 

 considered, is not altered if we suppose a and B to be equal 

 in size. In this case the common centre of gravity lies mid- 

 way between the two bodies, and is the common focus of the 

 two closed curves respectively described by them. 



