222 On Machines in General. 



In a weight machine, the movement of ivhkh is vnifor'fn, 

 the centre of gravity of the system remains constantly at the 

 same height. 



XLin. Since 4- MW^ orM^H is (XXXII) the mo- 

 mentum of activity produced by a weight M g, which we 

 make to ascend to the height H, it to] lows evidently 

 that 



IVhntever method we take to raise a certain weight to a 

 given height, the forces employed to produce this effect con- 

 sume a momentum of adivity equal to the produce of this 

 weight, ly the height to which we should raise it. 



XLIV^. In the same manner since (XLT) the momen- 

 timi of activity produced in a given time by the I'is inertia; 

 of any body is equal to the half of the quantity by which 

 its active force augments during this time, we may con- 

 clude also, that 



In order to make any given movement arise ly insensible 

 degrees in a system of bodies, or to change that which has 

 arisen, it must folloiv that the poners destined to this effect 

 do consume a momentum of activity equal to the half of 

 the quantity by luhich the sum of the active forces of the sy- 

 stem will have been augmented by this change. 



XLV. It follows evidently from tliese two last proposi- 

 tions, that in order to elevate a v/cight Mg" to a height H, 

 and make it assume at the same time a velocity V, it must 

 happen, supposing this body in repose at the lir^t instant, 

 that the forces employed to j-sroduce this effect consume 

 of themselves a momentum of activity equal to M^H -f- 



XLVI. We have supposed in all that has been said, as 

 the title of this corollary announces, that the movement 

 changes by insensible degrees; but if, when proceeding, any 

 ftudden shock or change happens in the system, what we 

 have mentioned would not take place. Let us suppose, for 

 instance, that at the moment of this shock the centre of 

 gravity of the system has descended from the height A; that 

 at this same instant the sum of the active forces is X im- 

 mediately before the shock, and Y immediately after the 

 shock: let us call O the momentum of activity, which 



the 



