( 650 ) 



ihougli the variation of pressure is vanisliinglj small. Consequently 

 the system of isothermals satisfies the law of corresponding states, 

 but the border curve does not necessarily do so. Hence we shall 

 see that for the border curve this is only the case to a first and 

 a second approximation. 



The ■^'-surface. 1 shall represent by Xk the composition of the 

 mixture which behaves as a simple substance. In the neighbourhood 

 of the critical point the system of isothermals of this mixture may be 

 represented by the equations (2) and (2') of my paper in these proc. 

 Oct. 25 1902 p. 321; for the rest all the considerations of sections 2 and 

 3 of the same paper are dii-ectly applicable, except that x — Xk must 

 everywhere be substituted for x, and hence also .i'77. — xkiovxjk- Thus 

 we find back, for the system of isothermals of the mixtures at a 

 temperature which differs little from Ti, the equations (18) and (18'), 

 where x — XTk ^^ vanishingly small, but not ,/; and xtl separately ; 



from the circumstance that at the critical point — ^ 0, it also 



follows that ?>?(,i = 0; and because 111^^ =pfc^ — ^„i 71 « we must have: 



''=.,.^=r;-ï)=7.3 (1, 



« Pk \.^-Jfc 



Finally we may remark that whereas in fig. 16 (1. c.) the dotted line 

 which, agreeing with .r <^ 0, had no physical meaning, this line can 

 really exist here, since x <^ x^ may as well be imagined as x > xic. 



The equation of the ip-surface may now be written in this case: 

 111 



^ z=z — m„ (v — VTl:) — - ^1 (v—i-Tk)"— ^^3 (i' — ^Ta)^— - m^ {v — VT/cY - • 



+ RT.Vf:{l-Xk) 



1 {^-.VkY , 2.r;r.-l (.,-^v,) 



1.2 xk'{l-.vky 2.3 .xk'il-xkY 



+ 



"^ 3.4 .vk\l-^^l.Y 



(2) 



where again a linear function of x is omitted, while nig^ = pjk, ^nd 

 further iiio^, m^^ and m^o may be put equal to zero. 



The border curve at a temperature T. In the same way as before^) 

 I find, putting 



Vj i\ x^ x^ representing the molecular volumes and the molecular 

 compositions of the coexisting phases, that 



1) These Proc. V, Oct. 2.-) 1902, p. 330. 



