( M4 ) 



((l-.t-)' a, + 2 .. (l-.r) g,, -4- ^c.^ a,) h- 2 ((l-.iQ a, + ■^' a,,)((l-.^^) K + ■'• ^) 



or: 



- a, {{1-wy b, + 2 .; (1-..0 Z.,) - 2 «,, .6-'' ^>, + «. .t-' ^>, 



which we may also write as 



?>i "^ b, b' 



We therefore tinally and approximately obtain : 



(I, = - /.r (%, T-i) - ET {iorj{i\-h^) - 1) + [(.',)„- roij J - 



when we call 



«1 ^^' — 2 «12 ^1 l>^ \ K^ ^'i' = A. 



The corresponding expression for n^ evidently becomes : 



ft, = - k,T{log T-1) - RT{log{V-b,) - 1) + [{e,\-TMo] - 



a, A a — .cY 



h h ^" 



As (omitting p) it follows from the equation of condition, lliat 



RTV^ RTb' 



V-b^ = , 



Rb,' 

 and that, therefore, lo<i (V^ — b^) ^= lo<j \- lotj T, we may write in 



general : 



f/, = e, - c,T- {k, + it-) Tlor, T+a, — ^ + RTlog (1 - ..) 



.(2) 

 (i^ =:e^ — c,T— (A-, -f R) T log T + «, — + RT log x 



(1 +''■•'•) ! 



In this equation then 



b^ A, 



^•i == (>ix)u - KK + R)-\-Rlog^-^\ c,z={,iX-{t+E)i-lUog^, 

 whilst 



.1 .4 



— = (( and ■ = «, 



6/ ' 6„6' 



and also 



