AND ITS SELF-CONSERVATION. 165 



any given space will take place in precisely the same time, 

 whatever the masses of those bodies may be. 



This may be regarded as the second universal law of 

 falling bodies. And it will be noticed that it develops 

 directly from the second law of motion. 



It is evidently a necessary inference from this that 

 velocity, properly speaking, is the rate of approach of two 

 bodies toward each other, and that it is only when the 

 mass of the one body becomes infinitesimal, as compared 

 with the mass of the other, that it is even approximately 

 correct to refer the velocity solely to the smaller body. 



But, again, as the distance between the approaching 

 bodies grows less, the force of attraction between them 

 becomes greater. It is evident, therefore, that, since the 

 force not only acts continuously, but also with continu- 

 ously increasing intensity, the increase in the rate of 

 approach of any two bodies, due to their own mutual 

 attraction, will be by a ratio whose value must constantly 

 increase, and must at any given moment be equal to that 

 which would have resulted from the action of a constant 

 force, through the given time, compounded with that pro- 

 duced by the increased action of the force for the same 

 time. 



From the fundamental conditions of motion, it appears 

 then that, in the^zrs^ place, the mutual attraction of any 

 two bodies results in each acquiring in any given time 

 precisely the same quantity of motion as the other, 

 regardless of mass ; secondly, that the meeting of any 

 two bodies through any given distance, in consequence 

 of their mutual attraction, will take place in precisely 

 the same time, regardless of mass, though the portion of 

 the total distance at first separating them traversed by 



