156 THOMSON ON CARNOT'S 



during the first and third operations may at once 

 be determined by means of Mariotte's law, since 

 in them the temperature remains constant. Thus, 

 if, at the commencement of the cycle, the volume 

 and pressure be v and p, they will have become 

 v -f- dv and pv/(v -f- civ) at the end of the first 

 operation. Hence the diminution of pressure 

 during the first operation is p pv/(v -f- dv) or 

 pdv/(v + dv) and therefore, if we neglect infinitely 

 small quantities of the second order, we hswepdv/v 

 for the diminution of pressure during the first 

 operation ; which to the same degree of approxima- 

 tion, will be equal to the increase of pressure during 

 the third. If t + T and t be taken to denote the 

 superior and inferior limits of temperature, we 

 shall thus have for the volume, the temperature, 

 and the pressure at the commencements of the 

 four successive operations, and at the end of the 

 cycle, the following values respectively: 



(1) v, 



(2) v + dv, 



(3) v + dv+ 



(4) v + 0, t, p - 



(5) v, t + r, p. 



