dn Machines in General. S2 3 



the moving Forces will have to consume cliiring the whole 

 time of the movement, and g that which ihey will have to 

 consume tiom the commencement to the epoch of the 

 percussion : let us suppose finally, for the sake of more 

 simplicity, that the system is at rest at the first instant, and 

 at the last, it is clear (XLV) that we shall have q — M. gli 

 + -i-X; and that, by the same ratio, the momentum of ac- 

 tivity to consume by the forces moving after the shock, 

 i.e. Q, — q, will be M g (H - //) — \Y -, therefore Q — 

 MgH + J-X -.1 Y: now (XXIII), it is clear that X > Y: 

 thus the momentum of activity to consume in order to 

 raise in this case M to the height H, is necessarily greater 

 than if there had been no shock, since in this case we should 

 have simply had Q = M ^ H (XLIII). 



Hence it follows, that without consuming a greater 

 momentum of activity, the movina, forces may, by avoiding 

 all shock, raise the same weight to a greater height H, for 



then we shall have (XLV) O = M ij H, or H = -~- , 



' -^ ^ Mg 



It-, 1 r-r O - i (X - Y) 



while m the present case we have H = ^==^ — -: 



^ Mg 



whence we see, that X being greater than Y, we must neces- 

 sarily have also H' > H, 



Sixth Cokollarv. 

 Of Hydraulic Machines. 

 XLV 11. We may regard a fluid as an a5senibI;!oc of at> 

 infinity of solid corpuscles detachcil froin each other; we 

 may therefore applv to hvdraulic machines all that wc have 

 said of other machines : thus, for example, from the ftrst 

 corollary (XXXV) we may conclude, that if a fluid mass 

 without gravity, be enclosed completely in a vessel, and, 

 that, having made two equal apertures in this vessel, we ap- 

 ply pistons to it; the forces which will act upon the fluid 

 mass on pushing these pistons must be equal, if they mu- 

 tually form an equilibrium ; /. e. that in a fluid iTiass the 

 pressure spreads equally in every direction : this is the fun- 

 damental principle of the equilibrium of fluids, which we 

 generally regard as a truth purely txperimculal. We shall 



even 



