: 
j 
4 
( 323 ) 
terms in powers of the small quantities y—1 and ¢—1. According 
to Van Der Waats’ method ') I wrote this new equation: 
0) 0°9 
NE (psf) A Parag yf 
2 Op Op y 
where the co-efficients ae aoa. ete. can be immediately derived from 
those of the above mentioned empirical reduced equation of state. 
1. The p,v, T diagram for a simple substance in the neighbourhood 
of the critical point. 
In order to limit the number of the continually re-occurring factors 
as much as possible, I shall not write the equation of state of the 
pure substance in a reduced form, but thus: 
p =k, +k, (oon) +k, (ov)? + &, oor)? +.... =f). . (2) 
where 4, /,, 4, ete. are temperature functions which can be developed 
in powers of 7—7%,; as for instance: 
k=, +k, (TT) + ks (LT) +. (2) 
and it is evident that £,,—= pz while k,, and k,, are zero. 
We might clearly find the equations of several curves in this 
diagram, such as: the border curve, the curve of the maximum or 
minimum pressures, the curve of the points of inflection ete. I shall 
derive the former only, chiefly in order to apply to a simple case 
the method of calculation to be used afterwards for finding the 
pressure, volume and composition of the co-existing phases with 
mixtures. 
If v, and v, represent the molecular volumes of the vapour and of 
the liquid, co-existing at the temperature 7’ under the pressure p,, 
then these 3 unknown quantities will be determined by the equations: 
pi A7 Pe AEN Ses he oe 
and by Maxws.’s criterium 
neef POR STe ate: A eee 
Vi 
The two unknown quantities v, and v, I shall, however, replace by the 
i 1 
two infinitely small quantities >(v,-+-v,)—x=# and zji P 
is therefore the abscissa of the diameter of the border curve for 
chords parallel with the v-axis, and g is the half chord. 
1) Zeitschr. f. physik. Chem., 13, 694, 1894. 
