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XL. Essay upon Machines in General. By M. CarnOT, 

 Member of' I he French Institute, &'c. ^c. 



[Continued from p. 144.] 



Fifth Corollary. 



Particular Law concerning Machines, the Movement of 



which changes by insensible Degrees. 



XL. J-X a machine, the movement of which changes ly 

 insensible degrees, the momentum of activity consumed 

 in a given time by the soliciting forces, is equal to the mo- 

 mentum of activity exercised at the same time ly the resist- 

 ing forces. . 



That is to say (XXXIII) that the momentum of activity 

 consumed by all the forces of the system, during the 

 time given, is equal to zero : this will be clear (XXXII) if 

 we prove tiiat tlie momentum of activity consumed at 

 each instant by these forces is null : now F expressing each 

 of these forces, V its velocity, Z the angle comprehended 

 between F and V, and d t the element of lime, the momen' 

 turn of activity consumed by all the forces of the system 

 dunng dt, (XXXIII) 5 FV cosine Zdt; we must there- 

 fore prove that wc have ^FV cosine Z^/=0; oriFV 

 cosine z = : now this is clear by the fundamental the- 

 orem : ergo Sec. 



The particular law here in question is certainly the most 

 important of the whole theory of the movement of machines 

 properly so called : we shall give some peculiar applications 

 when we enter upon the detail of the subject, in the scho- 

 lium which will succeed to the following corollary, and 

 which will conclude this essay. 



XLI. Let us suppose, therefore, for instance, that the 

 powers applied to the machine arc weights : lei us call in 

 the mass of each of these bodies, in the total mass of the 

 system, g the gravity, V the actual velocity of the body m, 

 K its initial velocity, t the time which has gone past since 

 the commencement of the movement, H the height from 

 which the centre of gravity of the system has descended 



during 



