On Mac furies la General. 29 



ments than the latter, there t\ould have been an equilibrium : 

 these destroyed movements are therefore subjected to the 

 same laws, have the same relations to each other, and, lastly, 

 may be determined in the same manner as if the bodies were 

 hard, i.e. by the general equation (F). This equation (F) 

 is not confined therefore to hard bodies, it also belongs to 

 all the bodies in nature, and consequently contains all the 

 laws of equilibrium and of movement, not only for the first, 

 bul even for all the others, w hatever may be their degree of 

 compressibility : but the difference consists in this ; that we 

 may, with respect to hard bodies, suppose u = V ; in such 

 a manner that smV U cosine Z = becomes one of the de- 

 terminate equations of the problem, whereas this does not 

 take place when the bodies are of a different nature : it is 

 therefore this determinate equation, which is the same with 

 the first fundamental equation (E), it is, I say, this deter- 

 minate equation which characterizes hard bodies, and con- 

 sequently it is absolutely necessary to employ it at least im- 

 plicitly in all questions concerning these bodies ; and with 

 respect to any other kind of bodies, we must, besides the de- 

 terminate equations, which we may obtain by ascribing to n 

 in the indeterminate equation (F) difl'erent known values — 

 we must,. I say, also extract from it one which is analogous 

 to the equation (E), and which expresses in some measure 

 the nature of these bodies, in the same way as the latter (E) 

 expresses that of hard bodies. But as this inquiry has but a 

 very indirect relation to n)achines properly so called, we 

 shall at present confine ourselves to examining the case 

 where the degree of elasticity is the same with respect to all 

 bodies, i. e. Let us suppose, that in virtue of elasticity 

 the bodies exercise upon ea-^h other, pressures n times as 

 great as if the bodies were hard, ?i being the same for all 

 the bodies of the system ; let us next suppose that the pres- 

 sure and the restitution are made in an indivisible instant, 

 although in strictness that would be impossible. This being 

 done : 



The reciprocal pressures F becoming n F, will have 

 among them the sanie relations as if the bodies were hard ; 

 therefore their results m U will not have changed their di- 

 rections, 



