852 Prof. Clausius on the Application of the Mechanical 



^^^43. In the^e equations it is assumed that — ^^besides the masses 

 M^ m„ /A, and jaq, of which the first two must be known from 

 direct observation, and the last two may be approximately deter- 

 mined fi'om the magnitude of the vicious space, — the four pres- 

 sures, ^„^;2,jt?g, andjOQ, or what amounts to the same, the four 

 temperatures 1\, T^, Tg, and Tq, are given. In practice, however, 

 this condition is only partially fulfilled/ eo that^n calculaition we 

 must have recourse to other data, i^inm^q xi j^i;q« >in>ni\f .(it 



Of the four pressures, only two, /), and/?Q, can be assumed as 

 known. The first is given immediately by the manometer on 

 the boiler, and the second may at least be approximately deduced 

 from the indications of the manometer attached to the condenser. 

 The two others, p^ and p^, are not given ; but in their place we 

 know the dimensions of the cylinder, and at what position of the 

 piston the cylinder is cut off from the boiler. From these we 

 may deduce the volumes occupied by the steam at the moment 

 of disconnexion and at the end of the expansion, and these two 

 volumes will then serve as data in place of the pressures p^ and j^g. 



We must now bring the equations into such a form that the 

 (lYr calculation may be made by means of these data. 



43. Let v'j as in the explanation of Pambour's theory, again 

 be the whole space, including vicious space, set free during one 

 stroke in the cylinder ; ei/ the space set free up to the time of 

 disconnexion from the boiler ; and ev' the vicious space. Then, 

 according to what was before said, we have the following equa- 

 tions : — , f 

 i 'kiiiQai auujo oiij ill ^^ 'i^-^ta 4'(M + /A)<r=ei/''^^ io Jfigww to nau 



The magnitudes fi and a are both so small that we may at once 



neerlect their product, so that the above become , . ,» 



° ^ 'po 'iff.i yd^TsH 



. . . (45) 

 ft/ T~,T)- 



Further, according to equation (VI),; ., . 



'Where, on account of its subsequent frequent occurrence, a single 



dp 

 letter y is introduced in place of the differential coefficient ^. 



Accordingly, we may replace r^ and r^ by u^ and Ug in the above 

 system of equations ; and then, as the masses m^ and m^ will 

 only occur in the products m^u^ and wigt^, we may substitute the 

 values of the latter as given in the first two equations of (45). 





