particularly as given hy French Writers. S3 



reflected that the meanmgs of our words in science are the crea- 

 tions of our definitions, and that we cannot assume any thing re- 

 specting the things meant, which is not either implied in the de- 

 finition, or deduced from observation. Thus they perhaps con- 

 sidered the wordyorc<? to represent aquaUty connected with the 

 velocity, but necessarily of such a nature that it was subject to 

 all the same laws which apply to statical force. * If such an 

 opinion were adopted, it might manifestly become the founda- 

 tion of error ; for the correspondence between the laws of sta- 

 tics and dynamics, instead of being complete, as it is thus as- 

 sumed to be, might have been partial only. It might, for in- 

 stance, have been true that two forces acting in the same di- 

 rection produced the same dynamical effect as their resultant^ 

 though it had not been true that when they acted obliquely to 

 each other the dynamical effbct was that of their resultant. -j* 

 In this case the velocity could have been as the force, when 

 the force acted in the direction of the motion, but not neces- 

 sarily in other positions. It does not appear, therefore, that 

 we can a priori say generally either the force in dynamics is 

 proportional to the force in statics, or that it is not. So far as 

 the demonstration is concerned, it might have been so in some 

 cases, and otherwise in others. And this perhaps may ex- 

 plain the oversight which I wish to point out. There is no 

 question as to what is the truth in these cases ; but there may 

 be some who consider it a! matter of philosophical importance 

 whether this truth is deduced from assumption or from obser- 

 vation, and it is to those that this examination is addressed. 



III.^ But the most important question is the one concerning 

 the satisfactoriness of the next step in the reasoning. After 

 supposing it shown that a velocity AB results from a force AB, 

 it is taken for granted that when a body moving with a velo- 

 city AB is acted on by a force BD, we may suppose that, in- 

 stead of the body having the velocity AB, it is at that instant 

 undergoing the action of the force AB^ so that the two forces 



* See Note C, p. 38. 



t Suppose, for instance, that two forces, a, Z>, acting at an angle 9, pro- 

 duced a velocity proportional not to ^^(as + Z>^ + 2 a Z> cos. fl,) but to 

 tj (a^ + Z>2 + ^b (cos. 6 + sin. 6)). In this case, as well as in the other, 

 when 6=0, the result is a + Z», and when = sr, the result is o — /&. 



VOL. VIII. NO. I. JAN. 1828. c 



