536 RICE ART. L 



or, neglecting quantities of the second order, 



di.^ = tdt]^ -\- r]^dt + ads + sda + nidmi + Widiii + etc. 



But since e^ is equal to a function (^(tj'S, s, rrii^, m-f, ...) of 

 ri^, s, rrii^, m^^, etc., 



d4) d(j> d4> 34) 



de^ = — dr]^ + — ris + - — : drui^ + - — : dnii^ + • • • 

 3?j* ds dmi^ dmf 



= tdrf + ads + /ii c^Wi'^ + jii dm%^ + . . . 



by equation (12) above. Hence by equating these two values 

 of dt^ we obtain 



iq^dt + sda + TUi^dni + mo^dfXi + . . . = , 



which is equation [503] of Gibbs. Equation [508] is just 

 another way of writing it. We have already seen that a can 

 be expressed as a function of the independent variables, t, jUi, 

 H2, etc., and [508] shows that if this function were known so 

 that a = fit, Hi, juo, • • •)> where/ is an ascertained functional 

 form, then 



9/ 9/ 9/ 



Vs = — — ' Ti = - —- , T2 = - — f etc. (13) 



01 Ofil OfJ.2 



Equation [508] is the "adsorption equation" and as we shall see 

 presently the experimental verification of its validity is beset 

 with difficulty and some doubt. One cause of this difficulty 

 can be readily appreciated by considering the form of the equa- 

 tions (13) which constitute another way of expressing the Gibbs 

 law of adsorption. Considering the first component, we see that 

 its excess concentration in the surface (estimated of course per 

 unit area) is given by the negative rate of change of the surface 

 tension with respect to the potential of the first component in 

 the adjacent phases, provided the temperature and the remaining 

 potentials are not varied. Now, quite apart from the trouble 

 involved in measuring with sufficient precision the excess con- 

 centration, it is impracticable to change the amounts of the 

 components in the phases in such a manner that all but one 

 of the potentials shall not vary. 



