262 Prof. Clausius on the Application of the Mechanical 



latter is the quantity consumed in vaporizing the part m, at the 

 temperature Tj. As m^ is but little smaller than M, the last 

 quantity of heat is far greater than the first. 



In order more conveniently to compare the two factors with 

 which these two quantities of heat are multiplied in equation (25), 

 we will alter the form of the one which multiplies Mc(Ti— Tq). 

 If, for brevity, we make 



then 



and 



so that we have 



,p^ , (26) 



To _1-^ 



T,-To 



Z Z^ <2^ 



= —3 + 3:3 + 3:4+ ^''•••- 



Hence the equation (25) or (XI) becomes 



W'=m,...^ + Mc(T.-T„).|(^ +0+6+ ^'=--)(2'^ 



It is easy to see that the value of the infinite series, which 

 distinguishes the factor of the quantity of heat Mc(Tj — Tq) from 

 that of the quantity of heat mj^Tj, varies from \ to 1, as 2" increases 

 from to 1. 



23. In the case last considered, where the vapour by expan- 

 sion cools down to the temperature of the condenser, we can 

 easily obtain the expression for the work done in another man- 

 ner, without considering the several operations which constitute 

 the circular process. 



For in this case every part of the circular process is reversible. 

 We can imagine that the vaporization takes place in the con- 

 denser at the temperature T^, and that the mass M, of which m^ 

 is vaporous and M — Wq liquid, enters the cylinder and raises the 

 piston ; further, that by the descent of the piston the vapour is 

 first compressed until its temperature is raised to T„ and then 

 that it is forced into the boiler ; and lastly, that by means of the 

 small pump the mass M is again conveyed in the liquid form 

 fcom the boiler to the condenser, and allowed to cool there to 



