Theory of Heat to the Steam-engine, - 439 



symbol denotes, not the whole force, but that part of it which 

 corresponds to a unit of surface of the piston. In this sense let 

 the letter R represent the charge. 



A further distinction must still be made in the case of friction, 

 for it has not a constant yalue in each machine, but increases 

 with the charge. Accordingly Pambour divides it into two 

 parts : that which is already present when the machine moves 

 without charge, and that which the charge itself occasions. 

 With respect to the last, he assumes that it is proportional to 

 the charge. Accordingly, the friction referred to the unit of sur- 

 face is expressed by 



f+S.-R, 



where / and S are magnitudes which, although dependent upon 

 the construction and dimensions of the machine, are, according 

 to Pambour, to be considered as constant in any given machine. 

 We can now refer the work of the machine to these resisting 

 forces instead of, as before, to the driving force of steam ; for the 

 negative work done by the former must be equal to the positive 

 work done by the latter, otherwise an acceleration or retardation 

 of motion would ensue, which would be contradictory to the 

 hypothesis of uniform motion hitherto made. During the time 

 that a unit of weight of vapour enters the cylinder, the surface 

 of the piston describes the space (1 — e)V, hence for the work W 

 we obtain the expression 



W=(1-6)V[(1+8).R+/]. 



On the other hand, the useful part of this work, which for di- 

 stinction from the whole work shall be symbolized by (W), is 

 expressed thus, 



(W) = (l-e)V.R. 



Eliminating R from this equation by means of the former, we 

 have the equation 



(W)^ ^-^/-)^-/ .... (58) 



by means of which, V being known, the useful work (W) can be 

 deduced from the whole work W as soon as the quantities /and 

 8 are given. 



I will not here enter into Pambour^s method of finding the 

 latter quantities, as this determination still rests upon a too in- 

 secure basis, and as friction is altogether foreign to the subject 

 of this memoir. 



