850 Prof. Clausius on the Application of the Mechanical 



work occasioned by incomplete expansion. To do so it would 

 only be necessary to calculate the uncompensated transformation 

 produced in the passage of the vapour from the cylinder to the 

 condenser, and to include the same in N. By this calculation, 

 which need not here be executed, we obtain precisely the expres- 

 sion for the work which is given in (XIV). 



40. In order next to be able to apply the equations (XIV) to 

 a numerical calculation, it will be necessary first to determine 

 the magnitudes pf^y p'q, and jo"q more precisely. 



"With respect to the manner in which the pressure in the 

 cylinder varies during the entrance of the steam, no general law 

 can be instituted, because the entrance canal is opened and closed 

 in such a variety of ways in different machines. Hence no defi- 

 nite universal value can be found for the relation between the 

 mean pressure />',, and the final pressure p^, as long as the latter 

 is strictly interpreted. Nevertheless this will be possible if the 

 signification of ^^^ be slightly changed. 



The cylinder and boiler cannot of course be instantaneously 

 disconnected ; more or less time is always required to move the 

 necessary valves or slides, and during this interval the vapour in 

 the cylinder expands a little, because, the orifice being diminished, 

 the steam which enters is less than that which corresponds to 

 the velocity of the piston. In general, therefore, we may assume 

 that at the end of this time the pressure is already somewhat 

 smaller than the mean pressure y,. 



But if, in calculation, instead of restricting ourselves to the 

 end of the time necessary for closing the entrance canal, we allow 

 ourselves a little freedom in fixing the time of disconnexion, we 

 shall be able to obtain other values for p^. We can imagine the 

 point of time so chosen, that if, previously to the same, the whole 

 mass M had entered, the pressure at that moment would have 

 been precisely equal to the mean pressure calculated up to the 

 same time. By thus substituting the more definite momentary 

 disconnexion in place of the actual gradual one, we incur but an 

 insignificant error, as far as the amount of work is concerned. 

 We may therefore adopt this modification of Pambour's assump- 

 tion, and set p'l =Pq, reserving, however, for special consideration 

 in each particular case the proper determination, according to 

 the existing circumstances, of the moment of disconnexion. 



41. With respect to the reaction p'q at the return of the piston, 

 •'it is evident that, under otherwise equal circumstances, tne dif- 

 ference^Q— j9q will be smaller the smaller Pq is. In machines 

 ,with a condenser, therefore, it will be smaller than in machinegj 

 without a condenser, where p^ is equal to one atmosphere. In 

 locomotives, the most important machines without condensers, 

 there is usually a particular circumstance tending to magnify 



