THE THEORY OF GRAVITATION. 147 



ant of an imperceptible movement of the masses toward all parts of 

 the great body (as, from certain passages of Cicero and Plutarch, it 

 appears had been before supposed by some of the ancients). Conse- 

 quently this gravitatiou would be proportional to the number of the 

 particles ; that is to say, to the mass of the central body. 



Now from these two propositions alone there might have been deduced 

 synthetically the entire theory of universal gravitation without further 

 mention of gravitational atoms. 



XII. 



This is the place to insert a certain proposition which is commonly 

 spoken of as if it were distinct from tbose which teach that gravitation 

 is universal, but which appears to me to be included in that expression. 

 I refer to that which affirms that gravitation is mutual or reciprocal; 

 or, in other words, that it is subject to the ancient law of "mechanics, 

 which states that action and reaction are equal. 



I say that this is the place to consider this proposition, because it can 

 equally well be proved either through the introduction of the agent of 

 gravitation, as I have done in preceding paragraphs, or by considering 

 gravitation abstractly, as I shall do in those which follow. This propo- 

 sition therefore forms, as it were, a gradation between those which I 

 have established by the first method and those which I shall establish 

 by the second. 



First method: Inasmuch as one body is pushed toward another by 

 the atoms which the second body has deprived of direct antagonists, 

 while the latter body is pushed toward the former by these same antag- 

 onists, the two bodies are necessarily pushed toward each other with 

 equal force, whatever be the inequality of their masses or the differences 

 in their forms. 



Second method: Since each particle of one of the two bodies tends 

 toward every particle of the other, the first body is urged toward the 

 second with a force proportional to the number of particles which the 

 second contains, or, in other words, with a force proportional to the mass 

 of the second. Furthermore, since the impetus or momentum of the 

 first body is the summation of the impetus of its separate particles, it 

 is proportional to the total mass of the first body. Thus it follows that 

 the impetus of the first body is proportional to the product of the 

 masses of the two bodies. 



By a similar train of reasoning the impetus of the second body is 

 also proportional to this product. Therefore the usual bodies are urged 

 together with equal forces. 



XIII. 



I am now in a position to examine what other consequences the 

 ancients would probably have drawn from the principle of a mutual 

 gravitation directly proportional to the masses and varying inversely 



