232 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



be determined by means of the relation (500). But our measure- 

 ments are practically confined to cases in which the difference of the 

 pressures in the homogeneous masses is small; for with increasing 

 differences of pressure the radii of curvature soon become too small 

 for measurement. Therefore, although the equation p' =p" (which 

 is equivalent to an equation between t, fjL v /z 2 , etc., since p' and p" 

 are both functions of these variables) may not be exactly satisfied 

 in cases in which it is convenient to measure the tension, yet this 

 equation is so nearly satisfied in all the measurements of tension 

 which we can make, that we must regard such measurements as 

 simply establishing the values of a- for values of t, fa, /* 2 , etc., which 

 satisfy the equation p' =p' ', but not as sufficient to establish the rate 

 of change in the value of a- for variations of t, JUL I} JUL Z , etc., which are 

 inconsistent with the equation p' =p". 



To show this more distinctly, let t, JUL Z , m 3 , etc., remain constant, 

 then by (508) and (98) 



m ra 



y/ and y/' denoting the densities f and \r> Hence, 



and I\d(y -p") = (y/' - y/) AT. 



But by (500) 



( c i + c z) dor + or d(c : + c 2 ) = d(p' p"). 

 Therefore, 



Afci + c 2 ) da- + IV d(Ci + c 2 ) = (y/' - Vl ') dor, 



or (y" - y/ - F^C! + C 2 )} dor = I> d(c 1 + C 2 ). 



Now ^(Cj+Cg) will generally be very small compared with y/' 

 Neglecting the former term, we have 



dcr _ I\ 7, v 



77 7^\ c i~rC z ). 



<r Vi -Vi 



To integrate this equation, we may regard T lt y/, y/ as constant 

 This will give, as an approximate value, 



1 



Vi "Vi 



o-' denoting the value of o- when the surface is plane. From this it 

 appears that when the radii of curvature have any sensible magni- 

 tude, the value of u will be sensibly the same as when the surface is 

 plane and the temperature and all the potentials except one have 

 the same values, unless the component for which the potential has 



