THE THEORY OF GRAVITATION. 153 



XXI. 



A second difficulty which would have embarrassed the more scrupu- 

 lous atomists, is that the mutual collision of the atoms would retard 

 their motions repeatedly, and diminish, consequently, the gravitational 

 action. Any such effect, nevertheless, has hitherto been imperceptible. 



Now, it would be useless to offer in explanation that the sum of the 

 motions would remain the same, since this is only true when the word 

 sum is used in the sense of geometers, who comprehend by it the differ- 

 ence of contraries. Such a definition is readily seen to offer no assist- 

 ance to the atomist in the case of equality of contrary movements. For 

 the algebraic sum of the motions of the atoms is zero before as after the 

 collision; but before the collision they were capable of effects of which 

 they are incapable afterwards. 



XXII. 



It is apparent that such mutual encounters would be the more rare 

 the smaller the atoms were supposed to be compared with the intervals 

 between them. These intervals can not, however, be assumed very 

 great since gravitation manifests no sensible interruption even in places 

 and times the most adjacent; so that the only conceivable recourse to 

 render the encounter of the gravitational atoms sufficiently rare is to 

 suppose them extremely small. Happily this device is completely suffi- 

 cient. Conceive two balls whose centers trace given courses in different 

 planes. In order that they may never meet it suffices to diminish the 

 sum of their semidiameters till it becomes less than the least distance 

 between their paths. 



But since, with diminishing size, the atoms would be less efficient to 

 produce gravitation, the intensity of which is fixed by phenomena, 1 it 

 is necessary to see if their effectiveness may be maintained by some 

 other properties. I see no recourse of this nature except in the increase 

 of individual density or of velocity. These two recourses appear very 

 natural, and are at the same time the more satisfactory because they 

 were (very probably) in accord with the spirit of the atomists of whom 

 I speak, and would probably have sufficed to close the mouths of their 

 adversaries. 



XXIII. 



Third difficulty: Each celestial body perpetually finds atoms in its 

 path which it necessarily displaces in passing onward. This can not 

 occur without the atoms communicating to the body a part of their 

 motion, and in consequence causing its retardation. Exclusive of all 

 other elements except the. mass displaced, this retardation is propor- 



'A little metaphysical consideration suffices to dispose of this instance; but, as 

 will be seen in a moment, I am able to supplement it by two separate physical 

 conceptions. 



