The Energy of Segmentation 295 



%vork done over the simultaneous increase of the internal energy of 

 the system; this excess is the energy withdrawn from the system, 

 in accordance with which decrease work is done by it. Now, in the 

 case of such an event taking place isopotentially and under equihb- 

 rium conditions, it is well known that both fF and U (since U = W 

 in accordance with the First Law) are determined simply by the 

 initial and final states. 



In the instance, for example, of the work being done against 

 an outer pressure with an accompanying increase of volume, 



This becomes PF =p {%\ = I'a) with the pressure constant, or, 



dW = dp iyi — v^) 



Substituting this value for dW in equation [8] and p, the intensity, 

 for /, we get, 



fV-r^U.-U,) = E = {y,-v,) p ^/^ = {v,-v,)p==v {p,-p,) 

 or, as is more usual, and since 



dp 



E={v^-v,)T~jj- 



Equation [8] stands, then, in the relation of genus to a certain 

 series of more special energy-laws as species; it, as has been shown, 

 is derivable from them, but only by leaving out their differentia. 

 Conversely, no one of these, in its entirety, can be deduced from 

 it, but, for the discovery of their diflFerentia, empirical investiga- 

 tion is necessary. Yet, in virtue of this relation, it is left quite 

 possible, in fact made quite necessary, that the "differentia" and 

 the "conferentia" should be entirely compatible, entirely capable 

 of being conjoined. That is what is really demonstrated or done in 

 the above substitution. That which is expressed in equation [8] 



*With the volume constant and the pressure changing, W= — I v d p = v (p^ — p2) 



J'*P2 

 Pi 



