39tj J. W. Glbhs — Eipiilihriutn of Heterogeneous iSuhstances. 



and the quantities of the component substances in the vicinity of the 

 surface of discontinuity. 



These results can be exhibited in a more simple form, if we deviate 

 to a certain extent from the method which we have been following. 

 The particular position ado])ted for the dividing surface (which 

 determines the superficial densities) was chosen in order to make the 

 term i ( 6\-f" ^2) ^ (^'1 + ^2) i" (494) vanish. But when the curvature 

 of the surface is not supposed to vary, such a position of the divid- 

 ing surface is not necessary for the simplification of the formula. It 

 is evident that equation (501) will hold true for plane surfaces (siip- 

 posed to remain such) without reference to the position of the divid- 

 ing surfaces, except that it shall be parallel to the surface of discon- 

 tinuity. We are therefore at liberty to choose such a position for 

 the dividing surface as may for any purpose be convenient. 



None of the equations (5 02) -(5 13), which are either derived from 

 (501), or serve to define new symbols, will be affected by such a 

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

 f^, if, )n\, m%, etc., as also fg, //g, F^, 7^2? etc. and i/:^, will of course 

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

 The qiTantity ff, 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 A measured normally and toward the side to which v" relates, 

 the qiiantities 



^sj '^S) ^15 ^25 etc., 

 will evidently receive the respective increments 



X{e/-e,'), A (7/v" - //v'), ^(rx"-ri'), A(K2"-r2'), etc., 

 ^v', fv", f/\', 'h" denoting the der.sities of energy and entropy in the 

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

 the increment 



A(£/-6/)-a(//v"-//v')-/'i^(ri"-ri')-/^2^(r3"-r2')-etc. 



But by (93) 



- p" = €y" - 1 7/v" -- /<! Ki" - /'2 rs" - etc., 



- p' = fv' - t fh' - Ml Vi - M-z y% - etc. 



Therefore, since jo'=y, the increment in the value of o' is zero. 

 The value of o' is therefore independent of the position of the divid- 

 ino- surface, when this surface is plane. But when we call this quan- 

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



