( 626 ) 
is the case in the plaitpoints, but also in the other points, in which 
a phase coexisting with an other, passes through the spinodal curve. 
In fig. 5 there must therefore be maxima or minima at P, Q, BW, 
BE, D, C, R. If from the differential equation we calculate the 
2 
dp 
value of Ee for the points B'E' and BE, it appears, that for the 
at, 
two branches which meet, this value is the same there. If we 
differentiate equation (a), we get: 
dp dp d(v,,) ( | 025 dv dp 05 dz, z,) 
ne en (Ei. — , 
Dn deden de 6 : (0x,*p7 de’, de, Òz oT de, 
dp eS . REMI 4: 
—— and being O, this equation is simplified to: 
da, Oz 3 
dp ) 0% 
Var == (Li? 
de? (5 : Ors? PT 
5 
The quantities v,,, (w‚—,) and Gel are the same for the 
mi pT 
Pp . f 
two branches, and so also ——~,. In fig. 5 this has not been fulfilled 
Uk, 
in the tracing of the branches in the neighbourhood of the points 
Bi. Better in the neighbourhood of the points BE. Also in the 
eusps an inaccuracy in the proper curvature of the branches may 
be detected here and there. But the figs. should be considered as 
only schematical. The properties that the two curves in fig. 2 which 
touch have the same curvature, and that this is also the case with 
the two eurves which touch in fig. 5, are of course closely allied. 
dp Op Op dv 
Pelt) 
da 0a Jor Ov Je pdx 
d*p 0*p 
dp dv dp dv\? Op do 
pach pat (elen ln) tan 
da? Òm?.r Ow Ov \ da Ov? \ da Ove 7 da 
follows for two curves, passing through the same point, and for 
adhere fared ee ek andi en | whiel 
which, therefore, - —, ze and — is the same, and which 
"Ox? Ox Ov Ov? Ov ay 
From 
and 
; 
dr d 
touch in that point, and for which also (=) is therefore the same, that 
at 
: ae. f ‚dp : 
the equality of EE involves also the equality of — and vice versa. 
ax at 
Kortrwne’s thesis, which has also been proved by Krvyver, might 
therefore also be proved by the method followed here. 
