44 OUTLINES OF NATURAL PHILOSOPHY. 



It has been disputed, whether this expression of the 

 force be a necessary truth, or one known only from 

 experience. D'ALEMBERT, Elemens de Phil. Mdan- 

 geS) torn. 4. p. 197. It seems, however, to be in fact 

 a definition, rather than a theorem. We have 

 no distinct idea attached to the word FORCE, 

 which we can compare with that conveyed by the 



formula -, in order to see whether there is a 

 t 



necessary agreement between them or not. But 



as the quantity ^ is of great importance, and fre^- 

 t 



quent recurrence in mechanical investigations, it is 

 convenient to have a term to denote it. Though 

 any term might be employed for this purpose; 

 yet as the thing called FORCE, is conceived 

 to be always greater, the greater the change 

 of velocity which it produces in a given time, 



or to increase and diminish just as does, we may, 



without diverting the word Force from its usual sig- 

 nification, employ it to denote the quantity _, or the 



t 



momentary increment of the velocity divided by 

 the correspondent increment of the time. FORCE, 

 in dynamics, has, in reality, no other signification 

 than this; the one expression may be everywhere 

 substituted for the other, and thus an entire treatise 



of 



