On.Machines in General. ' 13 



TI. Among the principles more or less general which 

 have been hitherto proposed, we shall only mention two 

 very celebrated ones, and upon which we shall have some 

 observations to offer. 



Tiic first is that which assigns for -the general law of 

 equilibrium in weighing machines, that the centre of gravity 

 of the system is then at the lowest possible point ; but al- 

 though this antient principle be very simple and gt-neral, it 

 does not seem that all the attention it deserves has been paid 

 to it : it is certainly, first, because it is subject to some ex*- 

 pressions, like all these where a maximum and iQ,inimum is 

 mentioned : second, because it has no relation except to a 

 particular species of force, which is gravity : thirdly and 

 lastly, because it appears difficult to give a general and rigo- 

 rous demonstration of it. But first, we shall show that by 

 a small change in the display of this principle, we may make 

 of it a very precise, geometrical, and true proposition, 

 without any exception whatever. Secondly, although it 

 has no relation except to giavity, yet it is easy to apply it 

 to all imaginable cases : for this purpose it is only re- 

 quisite to substitute a weight in the place of each of the 

 powers which are of a different genus ; this is very easy by 

 means of a line passing upon a return pulley, in such a 

 manner that there now remains no other defect to this prin- 

 ciple than that of being indirect. Thirdly and lastly, al- 

 though we cannot demonstrate it rigorously without ascend- 

 ing to the first principles of mechanism, it is, however, 

 easy to account for it so as to remove every doubt, if we 

 had even no other proofs, as we shall show when we come 

 to the exact demonstration which we shall endeavour to give 

 of it in ihe course of this Essay. 



Let us imagine therefore a machine to which there are no 

 other forces except weights applied ; I suppose it, besides, to 

 be of any arbitrary form, but that no movement has been 

 given to it; this being done, whatever be the disposition of 

 the bodies of the system, it is clear that if there be equili- 

 brium, the sum of the resistances of the fixed points or any. 

 obstacles, estimated in the vertical direction, contrary to the 

 gravity, will be equal to the total weight of the system ; 

 2 hi\% 



