1 i On Machines in General. 



but if a movement is given^ a part oF the gravity will be 

 employed to produce it, and it is only with the surplus that 

 the fixed points will be charged ; thus, in this case the sum 

 of the vertical resistances of the fixed points will be less at 

 the first instant than the total weight of the system : thus 

 from these two forces combined (the gravity of the system 

 and the vertical charge of the fixed points) there will result 

 from it a single force equal to their difference, and which 

 will push the system from top to bottom as if it were free: 

 thus the centre of gravity will descend necessarily with a 

 velocity equal to this difference divided by the total mass of 

 the system. Again, if the centre of gravity of the system 

 docs noi descend, there will necessarily be an equilibrium. 

 In general therefore — For ascei'taining that several Lueights 

 applied to any given mackine should make a mutual equili^ 

 Iriinn, it is sufficient to prove that if' we abandon this ma- 

 chine to itself) the centre , of gravity of the system luitlnoi 

 descend. 



III. The immediate consequence of this principle, which 

 is true without exception, is, that if the centre of gravity 

 of the system is at the lowest possible point, there will ne- 

 cessarily be an equilibrium ; for, according to this proposi- 

 tion, it is sufficient, in order to prove it, to shov/ that the 

 centre of gravity will not descend : Now, how could it de- 

 scend, when upon this hypothesis it is at the lowest point 

 possible ? 



IV. In order to give another application of this principle, 

 I suppose tbat it Ts required to find the general law of equili- 

 brium between two weights, A and B, applied to a given 

 machine : I say then, that in consequence of the preceding 

 principle, there will be an equilibrium between these two 

 weio:;hts A and B, if by supposing that one of the two has. 

 to bear it, and the machine has to take a small movement, 

 it would happen that one of these bodies would ascend while 

 the other descended ; and that at the same time these 

 weights were in the reciprocal rates of their estimated velo- 

 cities in the vertical direction : in fact, if we suppose that 

 A then descends with the vertical velocity V, while the ve-. 

 loclty of B, also estimated in the vertical direction would be 



8 u, we 



