92^ 



In consequence of this we liave: 

 ha — bi- 



hi) — 



h— b^^ '" f{vk) 



from which follows for the relation {b,, — hi) -. {hk — /;„) 



bk 



b'l 



.tH) 



bk — b, \-b'u{—f\vk)y:f"{vk) 

 The equation (/;), written in the form : 



{d) 



bk) 



b'l 





l-è'A-(-/Wr:/'H) 



('■) 



b-bk = {h„ 



then becomes : 



h — bk = {bk — b,) 

 in which b'k in given by (24). 

 First Example. 



/(.) = . -'7/3. 



Then f\v) = d/[v : ^) : d{v: ^) = — e—"lf, , and ƒ " {v)=e—^'|^^ , so 

 that we obtain : 



b'k ' .-'■^//5_ ,— "A? 



h — bk = {bk-b,) 



1 — b'l. 



■vklii 



as {—f{vk)y:f\vi) = ^—^kl^ 

 Hence we get : 



b - bk = (bk - b,) 



b'k 



1 



Vk — V 



.bk — b„ 



(1 - b'k) 



(25) 



1 - b'k 

 as /? according to (c) = (bk — b„} : [1 -- b'k)- 



But the equation (25) — which in the neighbourhood of the criti- 

 cal point of course perfectly accurately satislies the conditions : 1) 

 that at z; = 00 the value of b becomes properly brj in connection 

 with {(i), and 2) that the equation at vk for b'k and b"k gives tlie 

 values determined by (24) — is quite deficient in the neighbourhood 

 0Ï Vg. It has, namely, also to satisfy there for ó'7?i«// values of è^- — /;„, 

 when y is near Ya (ideal substances). Now in this case with b'k = 

 =^{l^k — luy -.bkVk (see (24)), and in regard of the circumstance that in 

 consequence of b'k becoming ^0, unity may be written for 1 — b'k, 

 for V =iv^, b =2 ba we get : 



Vk — v„ 



bk-b, {bk-b,y bj^b, 



-e 



bk — ^0 



hkvk 



