146 THE THEORY OF GRAVITATION. 



all the atoms are directed toward the center of the earth would have 

 required that each new shower of atoms must seek it in a different 

 direction from that followed by the shower next preceding, a condition 

 not in accord with the predilection of the sect of the Epicureans for 

 the operations of chance, nor with their antipathy for occult qualities 



In order to extricate themselves from this difficulty the atomists 

 would necessarily have rejoined that there was no place in the heavens, 

 equal in dimension to the earth, toward which there did not advance 

 in a given time quite as many atoms as our planet encounters in the 

 same portion of time, and that these other atoms were in motion exactly 

 like those encountered by the earth. Not that there was any particular 

 relation between places and the streams setting toward them, but, since 

 it was essentially a confused movement, equal areas must naturally 

 intercept, one equally as much as another, the paths of the atoms 

 which blindly traverse space; and in consequence they must be equally 

 exposed to their visits. 



XL 



When once the Epicureans were thus come to explain the matter so 

 neatly, the most thoughtful and curious among them would certainly 

 have followed out the consequences which could be easily deduced from 

 this hypothesis, and they would necessarily have arrived at the follow- 

 ing propositions : 



1. The atoms which pass to one side of any central body contribute 

 nothing to the force of gravitation which it exercises toward other 

 bodies, for such atoms are exactly counterbalanced by direct antagonists. 

 Gravitation would be due solely to those atoms which are fortuitously 

 directed toward the central body. As we have seen, the resultant 

 action of these atoms is everywhere directed toward the central body, 

 like the rays of light converging toward a focus when assembled by a 

 convex lens or a concave mirror. Hence, it is proper to apply to them 

 what has been proven in Paragraph IV touching the terrestrial gravi- 

 tation; that is to say, their gravitational effect is inversely propor- 

 tional to the square of the distance of the attracted body from the 

 central body. 



2. The gravitational atoms are directed not only toward the centers 

 of the greater bodies, but toward each of their particles as well, since 

 they move indiscriminately in all directions in space. The atoms, 

 moreover, act effectively in those directions in which their antagonists 

 are intercepted; that is to say, in all directions in which there are 

 particles of matter. Therefore they tend to move the heavy masses 

 which they encounter not toward the heavenly bodies in gross, but 

 toward each of their particles in detail. Hence the gravitation of 

 masses toward the center of a celestial body is nothing but the result- 



