538 RICE 



ART. L 



liquid rising through another Hquid. Clearly such surfaces are 

 not plane and yet in the argument it is generally implied that 

 the conditions for a plane surface exist. Actually Gibbs has 

 anticipated this point in his discussion on pages 231-233. The 

 crucial point in this is reached on page 232 where he says "Now 

 TiCci + C2) will generally be very small compared to 7/' — 71'." 

 In general where adsorption is very marked Ti/f , which is the 

 average volume concentration in the region of discontinuity, is 

 greater than 7/ or 7 1 , the volume concentrations in the homo- 

 geneous masses; but ri(ci + C2) is of the same order of mag- 

 nitude as Vi/R, where 22 is a radius of curvature of any curve in 

 which a normal plane cuts the surface, and so ri(c] + d) has the 

 same order of magnitude as Fi/f multiplied by ^/R. If the 

 thickness of the film is very small compared to R, the factor 

 ^/R may easily be less than the factor by which one would 

 multiply 7/ or 7/' to obtain Ti/f ; so that Ti (ci + C2) is negligible 

 compared to 7/ or 7/' and therefore to their difference except 

 in the rare cases where 71' and 7/' are extremely near to each 

 other in value. Now even for small bubbles R must be much 

 greater than f , and the conditions postulated would appear to 

 be practically satisfied in the actual experiments. So that, 

 although Gibbs says that "we cannot in general expect to 

 determine the superficial density Ti from its value — {d(r/dfJLi)t.^ 

 by measurements of superficial tensions," the conditions which 

 render this feasible in particular circumstances seem to be 

 satisfied in the usual experiments, and we must look in other 

 directions for the source of the discrepancies which undoubtedly 

 exist. Of course, the first sentence of the next paragraph on 

 page 233 which refers to the practical impossibility of measuring 

 such small quantities as Ti, r2, etc. has no application at present, 

 as the skill of the experimenter has actually surmounted the 

 difficulties. 



17. Importance of the Functional Form of a in the Variables 



We have already pointed out that it is impracticable to obtain 

 da/dfii directly by arranging to vary ni while keeping the other 

 potentials constant. Hence has arisen the device, actually 

 suggested by Gibbs himself, of altering the position of the 



