( 329 j 
where A, B etc. represent series of the powers of the reduced abso- 
lute temperature ft, with co-eflicients which like 4 are the same for 
all substances, we then put: 
bs p v 
aaa) ) = == en 
Tir Pek Usk 
Tk, por and vj standing for the eritical elements of the mixture 
with molecular composition «, if it remained homogeneous, while 
== 
Tik 
It must therefore also be possible to find expressions for the 
critical quantities of a mixture — these are the elements ppt, Vzph 
Ti of the plaitpoint and ps, var, Tr, of the critical point of 
contact — in which only the co-efficients of the general empirical 
reduced equation of state and further the quantities characteristic of 
the mixture viz. Pir, Prk, Ver, occur, or the co-efficients of the develop- 
ments in series of these quantities in powers of x. In the case of 
mixtures with small values of #, it may, exclusive of exceptional cases, 
suffice, to a first approximation, to introduce the co-efficients: 
— a ata and p = x wa 
Ty div Pk dx 
A first step towards realizing this idea of KAMERLINGH ONNES has 
been made by Kersom *) who took for his basis the general equations 
by which van peR Waats in his Theorie moléculaire and following 
papers has expressed the relation of the critical quantities and the 
composition; he has found what these equations would become for 
infinitely small r-values and has introduced into them the co-efficients 
a 
a and 2 mentioned above, besides others which might be derived from 
the co-efficients of the general empirical equation of state. I have now 
tried to work out this idea in a method which is more closely con- 
nected to the treatment of the y-surface, namely by developing the 
co-efficients of the equation of state and the equation of the 1p-surface in 
the powers of zr. On account of the great complication involved by 
the introduction of the higher co-efficients into the calculation, I have 
confined myself to the lower powers of 2. However, the method 
followed by me can also be used to find the co-efficients of higher 
powers. 
As I have confined myself to states in the neighbourhood of the 
eritical point I could use instead of Kammriincn Onnzs’ empirical 
reduced equation of state the more simple one which it becomes within 
narrow limits of temperature and volume on developing the different 
1) Proc. Royal. Acad., 28 Dec. 1901, p. 293; Comm., n°. 75. 
