224 On Machines in General. 



even prove (XXV), that the conservation of the active forces 

 takes place in incompressible fluids, the movement of which 

 changes by insensible degrees; and in short, generally every 

 thing which we have proved of a system of hard bodies is 

 equally true with respect to a mass of incompressible fluid. 



Scholium. 



XLVIII. This scholium is destined for the development 

 of the principle laid down in the fifth corollary : this propo- 

 sition, in fact, contains the principal part of the theory of 

 machines in a state of motion, because most of them are 

 moved by agents which can only exercise dead forces, or 

 those of pressure : of this description are all animals, springs, 

 weights, &c., which is the cause why the machine gene- 

 rally changes its state by insensible degrees. It also most 

 frequently happens, that this machine passes very quickly 

 to uniformity of motion, for the following reason : 



The agents which move this machine being at first a little 

 above tlie resisting forces, give rise to a small movement 

 which is afterwards gradually accelerated ; but, whether as 

 a necessary consequence of this acceleration, the soliciting 

 force diminishes, whether the resistance increases, or, lastly, 

 if there happens any variation in the directions, it almost al- 

 ways happens that the relation of the two forces is brought 

 nearer and nearer to that in virtue of which they could mu- 

 tually form equilibrium : these two forces are then destroyed, 

 and the machine is no longer moved, except in virtue of the 

 acquired movement, which, on account of the inertness of 

 the matter, generally remains uniform. 



XLIX. Li order to understand still better how this hap- 

 pens, it is only necessary to attend to the motion of a ship 

 which has the wind directly on her poop : this is a kind of 

 machine animated by two contrary forces, which are the im- 

 pulse of the wind, and the resistance of the fiuid upon which 

 it swims : if the first of these two forces, which may be rcji 

 garded as soliciting, is greatest, the movement of the ship 

 will be accelerated : but this acceleration necessarily has 

 limits, for two reasons ; because, the more the movement of 

 the vessel is accelerated, 1st, the more is it subtracted from 



the 



