394 J. W. Gibhs — Eij[ailihrium of Heterogeneous ISubstances. 



0)1 the Exper'miental Determination of Fundamental Equations for 

 Surfaces of Discontinuity. 



When all the substances which are found at a surface of discon- 

 tinuity are components of one or the other of the homogeneous 

 masses, the potentials u^, //g^ *^tc., as well as the temperature, may 

 be determined from these homogeneous masses.* The tension o' may 

 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' -zzp" (which 

 is equivalent to an equation between ^, yUj, yWg, 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 equa- 

 tion 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., /<j, //2, etc., which satisfy 

 the equation />'=/>", but not as sufiicient to establish the rate of 

 change in the value of a for variations of ^, /<j, //g, etc., which are 

 inconsistent with the equation p' =z p!' . 



To show this more distinctly, let <, //„, ?»3, etc. remain constant, 

 then by (508) and (98) 



da = — I\ dpi , , 

 dp' = y^' djj^, 

 dp" = ri" (^Mi, 



771/ 77}/ 



;// and y i" denoting the densities — p and — ^. Hence, 



dp' - dp" = (ri' - r/') (^Mi, 

 and r, d{p' ^p") = {y," - y,') dff. 



But by (500) 



(c 1 + C2) dff -f (T c?(Ci + C2) = (l{p' — p")- 

 Therefore, 



I\ (c, + c^) dff + r, ffd{c, + Cs) = {y," - r/) dff, 



or JKi" — r,' - ^\ (c, + C2) \dff = r^ ff d{c, + Cg). 



* It is here supposed that the thermodynamic properties of the homogeneous 

 masses have already been investigated, and that the fundamental equations of these 

 masses may be regarded as know^n. 



