EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 217 



all the conditions which we have obtained for ordinary solids, and 

 which are expressed by the formulae (364), (374), (380), (382)-(384). 

 The quantities I\', F 2 ', etc., in the last two formulae include of 

 course those which have just been represented by T a ', F b ', etc., and 

 which relate to the fluid components of the body, as well as the 

 corresponding quantities relating to its solid components. Again, 

 if we suppose the solid matter of the body to remain without 

 variation in quantity or position, it will easily appear that the 

 potentials for the substances which form the fluid components of the 

 solid body must satisfy the same conditions in the solid body and in 

 the fluids in contact with it, as in the case of entirely fluid masses. 

 See eqs. (22). 



The above conditions must however be slightly modified in order to 

 make them sufficient for equilibrium. It is evident that if the solid 

 is dissolved at its surface, the fluid components which are set free may 

 be absorbed by the solid as well as by the fluid mass, and in like 

 manner if the quantity of the solid is increased, the fluid components 

 of the new portion may be taken from the previously existing solid 

 mass. Hence, whenever the solid components of the solid body are 

 actual components of the fluid mass, (whether the case is the same 

 with the fluid components of the solid body or not,) an equation of 

 the form (383) must be satisfied, in which the potentials [jL a , fjL b , etc., 

 contained implicitly in the second member of the equation are deter- 

 mined from the solid body. Also if the solid components of the 

 solid body are all possible but not all actual components of the fluid 

 mass, a condition of the form (384) must be satisfied, the values of the 

 potentials in the second member being determined as in the preceding 

 case. 



The quantities 



t, X K ,, ...Zz, fji a) yu 6 , etc., (469) 



being differential coefficients of e V ' with respect to the variables 



(470) 



will of course satisfy the necessary relations 



dt 



, etc. (471) 



. 



dx 



This result may be generalized as follows. Not only is the second 

 member of equation (468) a complete differential in its present form, 

 but it will remain such if we transfer the sign of differentiation (d) 

 from one factor to the other of any term (the sum indicated by the 



