RESIDUO-CAPILLARY ATTRACTION. 211 



If then we have a second mixture of the same two original fluids, 

 we shall have 



— + -^ = 1 



and r-i + p-i = p , 



where rj and p-i are the two partial densities, and p the total density of 

 this second mixture. These equations serve in like manner to express 

 r-i and p-i in terms of p, {r) and {p). 



11. Let us now endeavour to express the mutual capillary affinities 

 which exist between the two mixtures just mentioned, and a third 

 material (as that of a membrane or tube), in terms of the densities 

 of these mixtures and the mutual capillary affinities between this same 

 material and the unmixed fluids. 



Let the former affinities be denoted by H, K, L, M, N, namely, 

 H between the tube and the first mixture, 

 K between the tube and the second mixture, 

 L between the first mixture and the second, 

 M between the first mixture and its like, 

 N between the second mixture and its like; 



and let the latter affinities be denoted by {H), {K), (L), {M), (A^), 



namely, 



{H) between the tube and the fluid of density (r), 

 (K) between the tube and the fluid of density (p), 

 {L) between the fluids of densities (r) and {p), 

 {M) between the fluid of density (/•) and its like, 

 (iV) between the fluid of density (p) and its like. 



The attraction ^cH of No. (9) will be the sum of two partial 

 attractions, namely, that of the tube upon two coexistent cylinders of 

 the opposite fluids, whose densities are those of the original unmixed 

 fluids diminished in the ratios r^ : (r) and p^ : (p). Hence by the latter 

 part of that No., 



ic^=ic(^)^ + ic(^).^; 



