106 
1 M, 6 
== — e ° e e . 
1 Mi M, + Mi : ( ) 
M, 
and 
Mi 
Tae 
M,+ My 
so really a hyperbola. 
Also the second above mentioned peculiarity of the eines that 
the quantity 5 in the equation of the hyperbola becomes much 
smaller than is usually the case, is found confirmed here. For 
Mie 
— is found for this quantity. 
M, 
The heat of mixing. Mr. Katz has already pointed out’), that the 
hyperbola found by him is in accordance with a formula given by 
VAN Der Waats in the Théorie Moléculaire. But this formula was 
derived on the supposition of linear dependence of b on « (h,-+-b,=20,,) 
and we saw already that both the experimental vapour pressure and 
volume contraction lines and the theory exclude this supposition in 
our case. If we, however, again assume the supposition, on which 
the said formula of vaN DER WaAALs is also founded, that viz. the 
; ; : Ay me 
potential energy of a mixture may be represented by — ee find 
"3 
for the increase of the potential energy or the absorbed quantity of 
heat when M,« gr. of dry substance is mixed with MZ, (1—2) er. 
of water : 
sle) bs b, a, a, c 
A =———— (2a, — 4+ a, ure Vas, U = (6, +b, | (7) 
Between A and the quantity W used by Mr. Karz the relation 
A 
M, 
So it appears that we do not get a hyperbola for W, but a curve 
of higher degree than the second. 
In how far this involves a deviation from the experimental data, 
we shall examine presently; first we must see what conclusion may 
AE exists again, and of course, equation (6) holds again. 
U 
C . 
be derived from the limiting ratio = for very small values of 2 
De. p. 970. 
