On Machines in General, 313 



Theorem. 

 XXII. In the shock of li(D-d todies, whether this shock le 

 immediate, or whether it he made lij means of amj machine 

 jvithont spring, it is clear that in respect io> ajiij geometrical 

 7novement, — 



\st. The momentum of the quantity of movement lost ly 

 lite whole system is equal to zero, 



2d, The momentum of the quantity of movement lost ly 

 any pait-of the bodies of the system, is equal to the momen- 

 turn of the quantity of movement gained by the other part, 



3d. The momentum cf the quantity of real movement of 

 the general system, immediately after the shock, is equal (a 

 tlie momentum of the quantity of movement of the same sy- 

 stem, immediately before the shock. 



it is clear, from the preceding definition, that these three 

 propositions are radically the same, and are nothing else 

 than the same fundamental equation (F) expressed in dif- 

 ferent ways. 



We may also remark that these propositions bear a great 

 relation to those we extract from the consideration of the 

 Tuomenta relatively to different axes ; but the latter are less 

 general, and are easily inferred from those established 

 in XVII. 



There is, therefore, as we see by the third proposition of 

 this theorem, in every percussion or communication of 

 movement, whether immediate, or caused by the intermedium 

 of a machine, a quantity which is not altered by the shock : 

 this quantity is not, as Descartes thought, the sum of the 

 quantities of movement ; nor is it the sum of the active 

 forces, because the latter is only preserved in the case where 

 the movement changes by insensible degrees, as we shall 

 see lower down, and it always diminishes when there is 

 percussion, as will be proved in the second corollary. 

 When the system is free, the quantity of movement estimated 

 in any ratio, is in truth the same before and after the per- 

 cussion ; but this preservation does not take place if there 

 are obstacles, any more than that of the momenta of quan- 

 tity of movements referred to different axes : all these quan- 

 tities 



