846 Prof. Clausius on the Application of the Mechanical 

 If in the equation (1), which was 

 Q=A.W, 



we substitute the values of Q and W thus found, and then bring 

 the terms involving m^ to one side of the equation, we have 



m^[r^ + Au^(p'i-'Pi)'] =miri + Mc(Ti-T2) +/Xoro-/Ac(T5-To) 

 + Aii,ono(p'i-Po)'^AMa{p,^p',) (XIII) 



By means of this equation the magnitude m^ is expressed in 

 terms of other magnitudes, all of which are supposed to be given. 



35. If the mean pressure ^j were considerably greater than 

 the final pressure p^, it might happen that the value of m^ would 

 be less than nti + fiQ, which would denote that a part of the vapour 

 originally present had become condensed. This would be the 

 case, for instance, if we were to suppose that, during the time 

 the vapour was entering the cylinder, the pressure there was 

 nearly equal to that in the boiler, and that by the expansion of 

 this vapour already in the cylinder, the pressure ultimately sunk 

 to the smaller value jo^. On the contrary, if jo'j were but a little 

 greater, or indeed smaller than j[?2> ^^^^ ^^^ ^2 ^^ should find a 

 value greater than mj + /Zq. The latter ought to be considered 

 as the rule in steam-engines, and amongst others it holds for the 

 special case oipf^-=p^ assumed by Pambour. 



We have thus arrived at results which differ essentially from 

 Pambour's views. Whilst he assumes that the two different 

 kinds of expansion which successively take place in the steam- 

 engine are governed by one and the same law, according to which 

 the original quantity of vapour is neither increased nor diminished, 

 but always remains exactly at its maximum density, we have found 

 two different equations which point to different deportments. By 

 the equation (XIII), fresh vapour must be produced by the first 

 expansion during the entrance of the steam ; and according to 

 the equation (VII), a part of the then existing vapour must 

 become condensed when the further expansion takes place, after 

 disconnecting the cylinder and boiler, during which time the 

 work done by the vapour corresponds to its full expansive force. 



As these two opposite actions, consisting of an increase and a 

 diminution of vapour, which must also exercise opposite influ- 

 ences on the work performed by the machine, partially cancel 

 one another, the ultimate result may, under certain circumstances, 

 be approximately the same as that to which Pambour's simpler 

 assumption leads. We must not, however, on this account ne- 

 glect to consider this difference when once established, especially 

 if we wish to ascertain in what manner a change in the construc- 

 tion or driving of the steam-engine will affect the magnitude of 

 its work. 



