868 



R. Clausius on the Application of the 



By the addition of these four single quantities of work, we 

 obtain the whole work done during the circular process, namely, 



(35.) W' = mB + log i) -v'(l- e) { b+ Po )-Mo( Pl - Po ). 



31. It is only necessary to divide the foregoing value by m, 

 if we wish finally to refer the work to the unit of weight of 

 steam, instead of to a single stroke of the piston, during which 

 the quantity of steam m is acting. For this purpose, we will 

 M 



denote by J, the fraction — which represents the relation of the 



whole mass which passes into the cylinder, to the portion of it 

 in the form of steam, and which is consequently somewhat 



v' 



greater than 1 ; furthermore bv v the fraction — , that is the 



space which is offered on the whole to the unit of weight of steam 



W 



in the cylinder, and by the fraction — - or the work correspond- 

 ing to the unit of weight of steam. Then we have 



(xii.) W= B + log i) - V(l - 8) (b +p 0 ) -la( Pl - j, 0 ). 



In this equation, there ocurs only one term which depends upon 

 the volume v, and it contains v as a factor. As this term is neg- 

 ative, it follows that the work which we can obtain by means of 

 the unit of weight of steam, under otherwise equal circumstances, 

 is greatest when the volume which is presented to the steam in 

 the cylinder is the least possible. The smallest value of the vol- 

 ume to which, if we can never quite reach it, we can yet approx- 

 imate more and more, is that which we find when we assume 

 that the machine moves so slowly, or that the influx pipe is so 

 wide that the same pressure p , takes place in the cylinder as in 

 the boiler. This case gives thus the maximum work. If the 

 rate of motion be greater with an equal influx of steam, or if 

 with an equal rate of motion, the influx of steam be less, we ob- 

 tain in both cases a smaller work by means of the same quantity 

 of steam. 



33. Before we proceed from this point to consider the same se- 

 ries of processes in their connection, according to the mechanical 

 theory of heat, it will be advantageous to consider beforehand 

 one of them singly, which still requires a special investigation to 

 fix a priori the results relating to it, namely : the influx of the 

 steam into the injurious space, and into the cylinder, when it has 

 here to overcome a pressure less than that with which it is driven 

 from the boiler. I can proceed in this investigation according to 



