EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 329 

 These quantities will satisfy the following general relations : 



d(e B ) = t d(ri B ) + fJL 2 d(T 2 ) + /* 3 d(T 8 ) + etc., (677) 



* = - (n*)dt - (r 2 )^ 2 - (TJdpt = etc. (678) 



In strictness, these relations are subject to the same limitation as 

 (674) and (675). But this limitation may generally be neglected. 

 In fact, the values of ?, (e s ), etc. must in general be much less affected 

 by variations in the state of strain of the surface of the solid than 

 those of or, e s(1 ), etc. 



The quantity 9 evidently represents the tendency to contraction in 

 that portion of the surface of the fluid which is in contact with the 

 solid. It may be called the superficial tension of the fluid in contact 

 with the solid. Its value may be either positive or negative. 



It will be observed for the same solid surface and for the same 

 temperature but for different fluids the values of a- (in all cases to 

 which the definition of this quantity is applicable) will differ from 

 those of 9 by a constant, viz., the value of a- for the solid surface in 

 a vacuum. 



For the condition of equilibrium of two different fluids at a line on 

 the surface of the solid, we may easily obtain 



(7 AB cos a = ? BS ?AS , (679) 



the suffixes, etc., being used as in (672), and the condition being 

 subject to the same modification when the fluids meet at an edge of 

 the solid. 



It must also be regarded as a condition of theoretical equilibrium 

 at the line considered (subject, like (679), to limitation on account of 

 passive resistances to motion), that if there are any foreign substances 

 in the surfaces A-S and B-S, the potentials for these substances shall 

 have the same value on both sides of the line; or, if any such sub- 

 stance is found only on one side of the line, that the potential for 

 that substance must not have a less value on the other side ; and that 

 the potentials for the components of the mass A, for example, must 

 have the same values in the surface B-C as in the mass A, or, if they 

 are not actual components of the surface B-C, a value not less than 

 in A. Hence, we cannot determine the difference of the surface- 

 tensions of two fluids in contact with the same solid, by bringing 

 them together upon the surface of the solid, unless these conditions 

 are satisfied, as well as those which are necessary to prevent the 

 mixing of the fluid masses. 



The investigation on pages 276-282 of the conditions of equilibrium 

 for a fluid system under the influence of gravity may easily be 

 extended to the case in which the system is bounded by or includes 

 solid masses, when these can be treated as rigid and incapable of 



