Mechanical Theory of Heat to the Steam Engine. 373 



consider as before the particular portions of the same in succes- 

 sion. 



The mass if flows from the boiler in which the pressure p l is 

 assumed, into the cylinder, the part m , as steam, and the remain- 

 der as liquid. Let the mean pressure acting in the cylinder dur- 

 ing this time be denoted as above hy p[, and the final pressure 



The steam now expands until its pressure has sunk from p 2 to 

 a given value, p 3 and consequently its temperature from T 2 to 

 T z . The cylinder is thereupon put into communication with the 

 condenser in which the pressure p 0 is exerted and the piston 

 makes the whole motion just completed again in the opposite 

 direction. The counter pressure which it thereby undergoes, is 

 during a somewhat more rapid motion greater thanjp 0 , and we 

 will therefore, to distinguish it from this value, denote the mean 

 counter pressure by p\. 



The steam which remains at the end of the motion of the pis- 

 ton in the injurious space, which must be considered for the next 

 stroke, is under a pressure which in like manner need be neither 

 equal to p 0 nor p ' 0 and may therefore be denoted by p" 0 . It 

 may be greater or smaller than p [ according as the cutting off 

 from the condenser takes place somewhat before or after the end 

 of the motion of the piston, inasmuch as the steam in the first 

 place is compressed somewhat further, in the last case, on the 

 contrary, has time to expand somewhat more by the partial influx 

 into the condenser. 



Finally the mass Ji" must be brought back from the condenser 

 into the boiler, whereby as before the pressure p 0 acts to produce 

 the effect and the pressure p , must be overcome. 



38. The quantities of work done in these processes are repre- 

 sented by expressions quite similar to those in the simpler case 

 already considered, only that the indices of the letters are 

 changed in a manner which is easily understood, and the quan- 

 tities which relate to the injurious space must be added. We 

 thus obtain the following equations : 



For the period of influx according to § 34, in which however 

 u" 0 must be written instead of u 0 . 



(39.) W x =(m 2 u 2 +M<J-t* 0 u\)p[. 



For the expansion from the pressure p 2 to the pressure p 2) ac- 

 cording to equation (ix) if M+p is put in the place of M : 



(40.) W 2 =m 3 u 3 p 3 -m 2 u 2 p 2 ^^[m 2 r 2 -m 3 r 3 ^(M+fi)c(T 2 -T 3 )] 



For the return of the piston, in which the space described by 

 the surface of the piston is equal to the whole space occupied by 

 the mass M+p under the pressure p 3 , less the injurious space 

 represented by p 0 u " Q -\-n(j. 



(41.) W pF z-(m a u a +Mo-p 0 u» 0 )p' 0 . 



