60 DISSERTATION SECOND. [part u. 



to propositions that were true only in particular cases, to 

 which indeed the ambiguity and vagueness of the word force 

 materially contributed. It does not appear, however, that 

 any good would now accrue from changing the language of 

 dynamics. If, as has been already said, to the question, How 

 are we to measure the force of a moving body ? be added 

 the nature of the effect which is to be produced, all ambigui- 

 ty will be avoided. 



It is, I think, only farther necessary to observe, that, when 

 the resistance opposed to the moving body is not uniform but 

 variable, according to any law, it is not simply either the 

 time or the space which is proportional to the velocity or to 

 the square of the velocity, but functions of those quantities. 

 These functions are obtained from the integration of certain 

 fluxionary expressions, in which the measures above describ- 

 ed are applied, the resistance being regarded as uniform for 

 an infinitely small portion of the time or of the space. 



Many years after the period I am now treating of, the con- 

 troversy about the vis viva seemed to revive in England, on 

 the occasion of an Essay on Mechanical Force, by the late 

 Mr. Smeaton, an able engineer, who, to great practical skill, 

 and much experience, added no inconsiderable knowledge of 

 the mathematics. 1 



The reality of the vis viva, then, under certain conditions, 

 is to be considered as a matter completely established. 

 Another inquiry concerning the nature of this force, which 

 also gave rise to considerable debate, was, whether, in the 

 communication of motion, and in the various changes through 

 which moving bodies pass, the quantity of the vis viva re- 

 mains always the same ? It had been observed, in the colli- 

 sion of elastic bodies, that the vis viva, or the -6um made up 

 by multiplying each body into the square of its velocity, and 



1 Note E, at the end. 



