particularly as given by French Writers. SI 



proves that the velocities are proportional to the forces, (pres- 

 sures) by observing that it is an liypothesis, (Art. 193,) and 

 that the agreement of its results with experience shows it to be 

 the law of nature. 



It will appear from a careful consideration of these proofs, 

 that, first, it is taken for granted that any velocity waz/ be 

 produced by an instantaneous force : That 2 J, it is proved 

 from experiment that this force is as the velocity : That 3<7, 

 it is taken for granted that we may, at our choice, at any in- 

 stant, consider the body either as possessing the velocity, or as 

 acted upon by the force which would produce it : And that ^th^ 

 it is also taken for granted that these instantaneous forces acting 

 together may be compounded according to the laws of statics. 



But I shall endeavour to show that there are steps in these 

 reasonings, (and I believe that the considerations generally 

 employed by French writers in the elementary portions of me- 

 chanics cannot be resolved into any more satisfactory than 

 these,) which are on several accounts liable to objections. 



I. In the first place, I would object to the supposing all 

 velocities in bodies to be produced by forces acting instanta- 

 neously, that is, acting at a single indivisible and uncontinued 

 moment of time. For the fact really is, that there are no 

 such forces in nature, and that forces of impulse and impact, 

 which appear at first sight to operate in this manner, seem to 

 do so only in consequence of a vague and imperfect mode of 

 conceiving them, and do in reality produce their effects by a 

 continued pressure acting for a short but finite portion of time. 

 And this is the case with all forces which ever come under our 

 observation; insomuch that we cannot in •strictness suppose 

 any such process as a body at rest acquiring at once a finite 

 velocity without going through the intermediate degrees of 

 velocity. And even if we allow that we can conceive such 

 an operation taking place, yet it must, it would seem, also be 

 granted, that the process would be different in kind from any 

 of the real actions of bodies one upon another, and therefore 

 it may deserve serious consideration whether it can, in sound 

 reasoning, be made the foundation of deductions which are 

 to be applied to cases of continual pressure. 



This is a step in the mode of obtaining the first principles. 



