(18 ) 
u, and uw’, vanish, the first derivatives of u may be considered to 
be small in this case but the second derivatives on the other hand 
will be decisive for the course. 
In order to determine for this case also the projection of the curves 
of constant pressure we will make use of equation (7): 
P horde y! 
log mla DID ttn neil Td 
“mm 
If we call the values of #; and y,, for which u’, and u’, vanish, 
en and ym and the corresponding pressure pj, then we have: 
Pu 
log BET inl hence also: 
Pp ( vy A y ' ' 
loy DE =logil de (e ™—1)+y,(6 PID He y, Lln Yp Um: 
in 
It appears already from this form of p„ that this pressure of this 
system may be considered as a coincidence pressure, and as this 
system can be realised, it may be considered as an ordinary maxi- 
mum tension. If we now consider w/,, and gu’, to be small, so that 
' 
JA ) 
"Tbe ; 
we may put ¢ “—1=—w’, and ¢ “—1=yp’,, and 
' ! ' 1 ' 
log tl Ar 4, Ur, 5 u mj er ae u n° 
then we find for mixtures, whose composition does not differ much 
from en and Yy : 
Pp 
log Pm — Ux — En 
m 
If we write: 
Ene ee] 9 . , " j " 
Urn = En + 4 (em) u Bei 2 (a io ie) (4, — Ym) UW xmym 1 (y, —Yn)* Le zond 
’ 
we may write the last equation: 
P 4 € \ " 2 ' 
log ——— 4 {(a, Ei) ed + 2 (wv, —2£») (7, — Ym) {t mjm En (y, —Yn)* fl ‘yom . 
Pm 
If we only inquire into the mathematical consequences of this last 
equation, without trying to answer the question, if the suppositions 
as to the values, which we have ascribed to Wom, (rym ANT U jn, MAY 
be found in nature, we may only say, that if wom and gyn vanish, 
the curves of equal pressure in the immediate neighbourhood of 
this singular point will be conic sections. In order that p, may be 
really a maximum pressure, the first member must be negative for 
all real values of z,n and y,—ym and this requires, that gom and 
yn are both negative and that (& omm)" SW em "ym. Then the curves 
of equal pressure are ellipses whose centre is the singular point. 
For a binary mixture the quantity mw’, has always appeared to be 
negative in accordance with this theory, when the components were 
