222 OPERATIONS SUBSIDIARY TO INDUCTION. 



define Accelerating Force was immediately followed by the 

 doctrine that accelerating forces may be compounded : the 

 process of defining Momentum was connected with the prin- 

 ciple that momenta gained and lost are equal : naturalists 

 would have given in vain the definition of Species which we 

 have quoted, if they had not also given the characters of 



species so separated Definition may be the best 



mode of explaining our conception, but that which alone 

 makes it worth while to explain it in any mode, is the oppor- 

 tunity of using it in the expression of truth. When a defini- 

 tion is propounded to us as a useful step in knowledge, we 

 are always entitled to ask what principle it serves to enun- 

 ciate." 



In giving, then, an exact connotation to the phrase, 

 " an uniform force," the condition was understood, that the 

 phrase should continue to denote gravity. The discussion, 

 therefore, respecting the definition, resolved itself into this 

 question, What is there of an uniform nature in the motions 

 produced by gravity ? By observations and comparisons, it 

 was found, that what was uniform in those motions was the 

 ratio of the velocity acquired to the time elapsed ; equal velo- 

 cities being added in equal times. An uniform force, there- 

 fore, was defined, a force which adds equal velocities in equal 

 times. So, again, in defining momentum. It was already a 

 received doctrine, that when two objects impinge upon one 

 another, the momentum lost by the one is equal to that 

 gained by the other. This proportion it was deemed necessary 

 to preserve, not from the motive (which operates in many 

 other cases) that it was firmly fixed in popular belief; for the 

 proposition in question had never been heard of by any but 

 the scientifically instructed. But it was felt to contain a 

 truth : even a superficial observation of the phenomena left no 

 doubt that in the propagation of motion from one body to 

 another, there was something of which the one body gained 

 precisely what the other lost ; and the word momentum had 

 been invented to express this unknown something. The 

 settlement, therefore, of the definition of momentum, in- 

 volved the determination of the question, What is that of 



