164 THE WORLD-ENERGY 



meet the greater body will have traversed but one 

 thousandth of the originally intervening space, while 

 the remaining nine hundred and ninety-nine thou- 

 sandths will have been traversed by the smaller 

 body. 



In short, the greater the difference between the masses 

 of the two bodies, the less significant relatively becomes 

 the velocity of the greater body, so far as the mere ques- 

 tion of quantity of space traversed in the approach be- 

 tween the two is concerned; though it is never to be 

 forgotten that the total quantity of motion of the one 

 body is precisely the same as that of the other, and that 

 in this sense the "fall" of the greater body toward the 

 less is exactly equal to the "fall" of the less toward the 

 greater. 



But, let us repeat, the attractions are between the 

 ultimate force-centers and between them alone. Through 

 the same distance, therefore, the attraction between any 

 two such force-centers must ever be the same; and since 

 the total quantity of motion is proportional to the im- 

 pressed force, it is evident that any two force-centers 

 must, so far as their mutual attraction is not masked by 

 external forces, traverse any given space between them in 

 precisely the same time, whether they act singly or in 

 groups. For, suppose a group of ten particles or force- 

 centers on one side, and a group of five on the other. 

 Each of the ten particles in the one group will attract 

 and be attracted by each of the five particles in the other 

 group precisely in the same way and precisely with the 

 same result as if each particle on either side were com- 

 pletely dissociated from the other particles of its group. 

 In other words, the fall together of two bodies through 



