234 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



change in the position of the dividing surface. But the expressions 

 e 8 , i/ s , mf, mf, etc., as also e s , ij 8 , T lt F 2 , etc., and \/r s , will of course 

 have different values when the position of that surface is changed. 

 The quantity cr, however, which we may regard as defined by equa- 

 tions (501), or, if we choose, by (502) or (507), will not be affected in 

 value by such a change. For if the dividing surface be moved a 

 distance X measured normally and toward the side to which v" relates, 



the quantities 



e g , j/ s , T 19 F 2 , etc., 



will evidently receive the respective increments 



X(e v "-e v '), x(W-*v), My/'-y/X My 2 "-y 2 ')> etc., 



y'> e v"> tfv'> n\" denoting the densities of energy and entropy in the 

 two homogeneous masses. Hence, by equation (507), <r will receive 

 the increment 



But by (93) 



-p" = e v " - trjy" - fj. l7l " - fryf - etc., 



-p f = e v ' - triv - // iy / - // 2 y 2 ' - etc. 



Therefore, since p'=p", the increment in the value of a- is zero. 

 The value of cr is therefore independent of the position of the dividing 

 surface, when this surface is plane. But when we call this quantity 

 the superficial tension, we must remember that it will not have 

 its characteristic properties as a tension with reference to any arbitrary 

 surface. Considered as a tension, its position is in the surface which 

 we have called the surface of tension, and, strictly speaking, nowhere 

 else. The positions of the dividing surface, however, which we shall 

 consider, will not vary from the surface of tension sufficiently to 

 make this distinction of any practical importance. 



It is generally possible to place the dividing surface so that the 

 total quantity of any desired component in the vicinity of the surface 

 of discontinuity shall be the same as if the density of that component 

 were uniform on each side quite up to the dividing surface. In other 

 words, we may place the dividing surface so as to make any one of 

 the quantities T lt F 2 , etc., vanish. The only exception is with regard 

 to a component which has the same density in the two homogeneous 

 masses. With regard to a component which has very nearly the 

 same density in the two masses such a location of the dividing surface 

 might be objectionable, as the dividing surface might fail to coincide 

 sensibly with the physical surface of discontinuity. Let us suppose 

 that y/ is not equal (nor very nearly equal) to y/', and that the 

 dividing surface is so placed as to make F : = 0. Then equation (508) 



reduces to 



(514) 



