348 Prof. Clausius on the Application of the Mechanical 



further compressed, whereas in the latter case it would have time 

 to expand a little more by partially passing into the condenser. 



Lastly, the mass M is conveyed back from the condenser into 

 the boiler, when, as before, the pressure Pq acts favourably, and 

 the pressure jji has to be overcome. 



38. The expressions for the amounts of work done in these 

 processes will be quite similar to those in the simpler case before 

 considered, except that a few simple changes in the indices of 

 the letters will have to be made, and the magnitudes which refer 

 to the vicious space will have to be added. In this manner we 

 obtain the following equations. 



For the time during which vapour passes into the cylinder, we 

 have, according to § 34, 



W, = Kw2 + Mcr-/iXoyu • • • (39) 

 where m"o is simply substituted for Wq. 



By putting M + /i- in place of M, we have, from equation (IX), 

 for the expansion from the pressure p^ to the pressure p^, 



■W« = m^;73-»l2W2;?2-t-T Kr2-.W^g+ (M+/a)c(T2-T3)]. (4^) 

 /^ 0.3 yd 



For the return of the piston, during which time its surface tra- 

 verses the whole space occupied by the mass M + />«, at the pres- 

 sure jOg, diminished by the vicious space /jLQu!'Q + fjLa, we have 



W3=-(m3W3 + Mo— /^ott"o)/o. . . . (41) 



Lastly, for th^ conveyance of the ma^s M back into the boiler, 

 we have );jyolt|^9 t)di mo;i't bjawUU* od bi0oo 



Consequently the whole work is 



W= ^K^2-^3^8+ (M-f7/i)c(T2-T3)] +m2«2(y,-;>2) 1 



^ [. (43) 



The masses mg and wzg which are here involved, are given by 

 the equations (XIII) and (VII), if in the former we put p''^ in 

 the place o( Pq, and change the magnitudes Tq, t-q, and Uq in a 

 similar manner, and in the latter we substitute M + z^forM. 

 Nevertheless, although it is possible to eliminate 7n^ and m^ by 

 means of these equations, I will here merely replace w^ by its 

 value ; it being more convenient in calculation to consider the 

 equation which thus results in connexion with the two before 

 obtained. The following, therefore, is the most general form of 

 the system of equations which serve to determine the work of 

 ,t)ie^^te«^m-engine ; — 



^^ 



