S^Qf, On MacUnes In General. 



vary by in&enslbilip degrees : finally, as fixed points or some 

 obstacles may be met with, let us consider them as they 

 really are,ii^;fi§i,9tj that is to say, as ordinary bodies of them- 

 selves,^ i^ali^ing ,pfirt of the system proposed, but firmly ar- 

 rested iu.the spot where they are placed. 



XV. In order to. attain the solution of this problem, let 

 u^^fi/^t,of3^eurv;e, tlxat, all the parjti^^-oi;' the system being sup- 

 posed perfectly hard, i. e. incompressible and inextensible, 

 we may visibly, whatever it may be, regard it as composed 

 of an infinity of hard corpuscles, separated from each other 

 either by small incompressible rods, or by small inextensible 

 wjres;. for when two bodies strike, push, or tend in gcne- 

 rjj. to approach each- other without being able to doit, on 

 account of their impenetrability, we can conceive between 

 tl)e two a small incompressible rod, and suppose that the 

 njp.Vemj^pt^^ is,trau&miUed From the one to the other accord- 

 ing to this rod : and in the same way, if two bodies tend to 

 separate, we may conceive that the one is attached to the 

 other by a small inextensible wire, according to which the 

 movement is propagated : this being done, let us conjider 

 successively, the action of each of these small corpuscles upon 

 all those which are adjacent to it, i, e. let us examine two by 

 two all these small corpuscles separated from each other by a 

 small incompressible rod, or by a small inextensible wire, 

 and we shall sec what ought to result in the general system 

 of all these corpuscles. Let us name for this purpose, 



77/ and m" The masses of the adjacent corpuscles. 



V and V' The velocities they ought to have the follow-^ 

 ing instant. 



F' The action of m^^ upon m\ that is to say, the force or 

 quantity of movement which the first of these cor- 

 puscles imprt-sses upon the other. 



F'' The reaciion of ?»' upon ni\ 



q[ and q' The angles formed by the directions of V and 

 F and by thJse of V' and F^'. 



This being done, the real velocity of m' being V, this 

 velocity estimated in the direction of F will be \' cosine q*; 

 in the same manner the velocity of tt^' estimated in the 

 direction of V will be W^ cosine g". Therefore, since by 



the 



