Oil Machines in General, 1 55 



being mutual, will put the machine in motion. It is 

 therefore evident that what renders the principle of Des- 

 cartes incomplete is, that by determining the reference of the 

 powers, as to their values or intensities, he does not express 

 that these powers should make opposite efforts, nor in what 

 consists this opposition of efforts: it is clear, in fact, that 

 for an equilibrium one of the forces must resist while the 

 other solicits : now, this is not what happens in the ca^e of 

 the' example of the axletrce; — But what is it in general that 

 distinguishes soliciting from resisting forces ? This in my 

 opinion has not yet been determined. We shall see in this 

 essay that the characteristic difference of these forces consists 

 in the angle they form with the directions of their velocities, 

 so that the one form always acute angles with their velocl-^ 

 ties, while the others form obtuse ones with theirs. 



Lastly. One fault with which we may reproach the princi- 

 ple of Descartes, as well as all those where we are discuss- 

 ing the small movement which would arise in the system if 

 the equilibrium was disturbed, is, that they do not indicate 

 the method of determining this small movement. Now, if 

 for this purpose we must have recourse to some new me- 

 chanical principle, the former is not sufficient ; and if we 

 can determine it by pure geometry, What is the method of 

 doing so ? This is what the principle does not say : and let 

 us not say that the proportion indicated by the principle al- 

 ways takes place whatever the movement is, provided it is 

 possible, i,e. compatible with the impenetrability of bodies; 

 for this would be an error: and we shall by and by show 

 that these movements are subjected to certain conditions, int 

 consequence of which I think it right to give them the nami 

 of geometrical movements. 



We may make the same remark upon all the principles 

 upon v/hich we propose to consider a machine in' two 

 states infinitelv near each other; for, in order to detctiTirne 

 what arc those two states ; i. e. what movement the machine 

 should take in ordqr to pass frbn^ the 'one to the'odiifr,'\ve 

 inust either employ new mechatiical principles tonjiinctlv 

 with that proposed, which would render the latter insuffi- 

 cient ; 



