236 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



The same physical relations may of course be deduced without 

 giving up the use of the surface of tension as a dividing surface, but 

 the formulae which express them will be less simple. If we make 

 t, /z 3 , // 4 , etc., constant, we have by (98) and (508) 



where we may suppose I\ and F 2 to be determined with reference 

 to the surface of tension. Then, if dp' dp", 



and 



t rr 



Ct/OT == 1. i - 7 ~/, CvlLn *~ JL nC(/Un* 



yi-yi 

 That is, 



(-) =-r 2 + r i 4^X;. (515) 



\afJ. 2 / p ' - p " t t, M3 , M4> etc. Vi Vi 



p 

 The reader will observe that -, - represents the distance between 



7i -Vi a 

 the surface of tension and that dividing surface which would make 



I\ = ; the second number of the last equation is therefore equivalent 



to -r 2(1) . 



If any component substance has the same density in the two homo- 

 geneous masses separated by a plane surface of discontinuity, the 

 value of the superficial density for that component is independent 

 of the position of the dividing surface. In this case alone we may 

 derive the value of the superficial density of a component with 

 reference to the surface of tension from the fundamental equation for 

 plane surfaces alone. Thus in the last equation, when y 2 ' = y 2 ", the 

 second member will reduce to F 2 . It will be observed that to 



in mass, will be equal to the sum of the superficial tensions of mercury in contact with 

 water and of water in contact with its own vapor. This will be, according to the same 

 authority, 42*58 + 8 "25, or 50 '83 grammes per meter, if we neglect the difference of the 

 tensions of water with its vapor and water with air. As p 2 , therefore, increases from 

 zero to 236400 grammes per square meter (when water begins to be condensed in mass), 

 <r diminishes from about 55*03 to about 50*83 grammes per linear meter. If the general 

 course of the values of a for intermediate values of p 2 were determined by experiment, we 

 could easily form an approximate estimate of the values of the superficial density F 

 for different pressures less than that of saturated vapor. It will be observed that the 

 determination of the superficial density does not by any means depend upon inap- 

 preciable differences of superficial tension. The greatest difficulty in the determination 

 would doubtless be that of distinguishing between the diminution of superficial tension 

 due to the water and that due to other substances which might accidentally be present. 

 Such determinations are of considerable practical importance on account of the use of 

 mercury in measurements of the specific gravity of vapors. 



