J 5$ On Machines in General, 



eient; or else geometry is sufficient; and in this case it 

 is a defect in the principle, not to make known the geonij^^ 

 trical conditions to which this movement is subjected. 



VI. The two laws mentioned are confined to the case of 

 equilibrium. We pass easily from this case to that of the 

 movement by M. D'Alembert's principle in dynamics. But 

 we have found several others which are immediately applied 

 to the case of movement ] such as that of the preservation 

 of living powers under the shock of perfectly elastic bodies 5 

 which is so much the more gener^^l, as it extends even to the 

 case of the movement passing rapidly from one state to the 

 other: but it would seem that people have little dreamed of 

 the use that might be made of it in the theory of machines 

 properly so called. It is, however, evident, that this law 

 should have its analogy in the shock of hard bodies : and as we 

 generally take the latter to use it as a term of conjparison, 

 this principle, transferred to hard bodies with the modiii- 

 catipn which the difference of their nature requires, cannot 

 fail to be more useful than the preservation in question. We 

 shall show, in fact, that we may dedilce from it several 

 capital truths with the greatest facility, and particularly the 

 preservation of living powers in a system of hard bodies, the 

 movement of which changes by insensible degrees ; a prin- 

 ciple of well-known utility in the theory of machines. We 

 shall thereby see, at the same time, an intimate relation 

 between these two preservations of living powers; — we draw 

 from it also the principle of DeiScartes ; and even, by gene- 

 ralizing it, the law of equilibrium in machines with weights 

 above mentioned. This principle, in short, after having given 

 to it the extension of \vhich it is susceptible, appeared to us 

 to contain all the laws of equilibrium and of movement: and 

 >vp have not found a better for the basis of our theory. 



VII. This essay will be dividc(J into two parts: In the 

 first we shall treat of the general principles of equilibrium 

 and of movement in machines; and in the second we shall 

 examine the properties of machines properly so caHed, 

 without ever stopping at any particular machine. 



PART 



