540 RICE 



ART. L 



enables us to express jui in terms of /, /X2, ms, etc. If this expres- 

 sion for /xi is substituted in the original function expressing a, 

 say f{t, Hi, /i2, . . . ) we obtain an entirely different function 

 say x(^ M2, M3, . • .). No doubt 



but certainly a//aAi2 is not equal to 6x79^2, etc. The differential 

 coefficients dx/dfii, 9x/9m3, etc., are the new values of the 

 surface concentrations (with reversed sign); there is of course 

 no dx/dfJ-i at all, in consequence of the fact that we have elim- 

 inated Ti; it has no existence. To be still more explicit the 

 equation p' = p" is by means of [93] equivalent to 



ev' — t-qv' — MiTi' — M2T2' — . . . 



= tv" - iw" - MiTi" - m2" - . . . (14) 

 Hence 



ey' - ey" - tinv'- nv") - M2(72^- 72^0 - M3(73^- 73^0 - ■ . . 



Ml = —, -T, . 



71 ~" 71 



Inserting this value of mi in fit, ni, H2, . . . ) we obtain 

 x{i, M2, M3, . . •). We can then derive dx/dfx^ by observing that 



dx df df dm 



dn2 dfii dni dn2 



and obtaining 9mi/9m2 in this result from (14). Thus 

 dx 9/ 9/ 72' - 72" 



80 that 



dm dm dni ji — 7i" 



— ^2 — ii / _ „ 



dm 71 — 7i 



which is equation [515], obtained by Gibbs in another way. 

 We observe in passing that if the dividing surface is considered 

 to be moved a distance X toward the side to which the double 



