of a Mass of Ma t ter . 9 5 



the external work consists onlyin overcoming an external pressure, 

 he gives the equation 



U= \pdv } 



%) 

 whence follows 



*=$%*> (10) 



The integrals which here occur are to be taken from a given 

 initial volume to the actually existing volume, the temperature 

 being supposed constant. Introducing this value of F into 

 equation (8), he writes it in the following form : — 



^Q=^ + AT^^ 2 ^)^T + AT^^. . (11) 



t. :c 



His reason for taking an infinitely large volume as the initial 

 volume is not stated, although the choice of the initial volume 

 is evidently not indifferent. 



It is easy to see that this manner of modifying equation (6) is 

 very different from my development ; the results are also discord- 

 ant; for the quantity F is not identical with the corresponding — Z 



XX 



in my equations, but only coincides with it in that part which 

 could be deduced from data already known ; that is to say, the 

 last member of equation (6) gives the differential coefficient v for 

 the magnitude which has to be introduced, since, to get the 

 correct value of this member, we must in any case put 



dJ_lc!Z_dp 



dv ~A dv ~ dT [ } 



Rankine has, however, as may be seen from equation (10), 

 formed the magnitude F by simply integrating according to v 

 the expression given for the differential coefficient according to 



v. In order to see in wdiat way the magnitude — Z differs from 



A. 



this, we will modify somewhat the expression for Z given in the 



preceding section. 



According to equation (2), 



T 



-r dZ = dJj. 

 A 



dh denotes here the internal and external work, taken together, 

 which is performed when the body undergoes an infinitely slight 

 change of condition. We will denote the internal work by d\ ; 

 and since, when the condition of the body is determined by its 

 temperature T and its volume v, I must be a function of these 



