On Machines in General. 1.27 



Q 



*f — — smzi + * -f See. is a maximum ; i. e. greater than 

 q + 1 to 



in any other situation. \ 



It would be easy still to extend these consequences to other 

 hypotheses of attraction ; but this seems useless. I shall 

 therefore confine myself to remarking, that we may, by a 

 principle general to what we have shown, establish that 



Whatever le the nature of the matrix forces applied to d 

 machine, if' we make it move in such a manner that it passes 

 by the position of 'equilibrium, the instant when it shall ar- 

 rive in this situation, will le that at which the momentum of 

 activity consumed during the movement, by these motri& 

 forces, shall be greatest. 



That is to say, the momentum of activity which the pro- 

 posed powers consume during the movement, goes on al- 

 ways increasing until the machine has attained the position. 

 of equilibrium; after which this momentum goes on di- 

 minishing in proportion as the system removes from this 

 position when it has passed it ; whatever, in other respects, 

 may be the route which we make this machine assume in 

 order to bring it to that situation. 



Suppose, for example, that each of the powers applied to 

 a machine are of a given size, and that besides this we know 

 one of the points of direction which it should have in order 

 that there be equilibrium : I say that this situation of equiiU 

 brium is that at which the sum of the products of each of 

 these powers, given by the distance from the point of the 

 machine where we suppose it applied to the -fixed' point 

 given upon its direction, is the least possible*: this is easily 

 deduced from the preceding principle. 



All these things are so easily proved, after what has been 

 said in the course of this second part, that it seems useless. 

 to dwell upon. them. I shall therefore conclude this work 



* It must be remarked, that in all we have said on the subject of a ma- 

 chine considered in different positions-, and of its passage from the one to the 

 other; it must be remarked, 1 say, that these positions are always supposed 

 to be such that we pass from the one to the other hy a movement which is 

 at each instant of those I have called geometrical t otherwise ail these pro- 

 position* would be subject to the same defects with which (in V.) we have 

 thfiught fit to reproach the principle of Descartes^ and of several others. 



2 with 



