( 611 ) 
d : 
= = 0 has split up into two branches. We need not concern ourselves 
v 
; i } ‚dp 
about the righthand branch at least now, for the detaching of = == (0) 
& 
d Re 
and aes For the point with minimum volume of this branch — 
v = . 
which has the well-known shape — lies on the line 
= 0, and so 
avat 
d di 
at greater volume than == 0. The line 2 = 0 can, therefore, inter- 
v LX 
sect this rightside part only in the branch of the two curves where 
dv is oe 
Seas and this intersection does not offer anything noteworthy for 
v 
Et 4 dp 
our present investigation. So we have only to examine how ER 
& 
d; 
intersects the leftside half of al and detaches itself from this 
av 
left side half or the only one that is left at this temperature in the 
case just discussed that A is positive. 
: d, 
7. Now we saw before that in fig. 4 the point where =C 
U 
intersects the line «= v,, lies at a value of wv: 
db\? 
2 MRT (a) 
der dx 
v, ZE Er a e 
dx? 
dp 
At a temperature somewhat but very little lower, == 0 will 
av 
have nearly the same course on the right of «—., as in fig. 4, 
then, very near the valuexv=w,, v=v, it will abruptly turn upwards 
and pass through the point = #,,v —0. This follows also from the 
coefficient of direction, which approaches oo according to formula (3). 
At somewhat higher temperature the first part will remain almost 
unchanged, but the curve, having got very near wv =,v=v, will 
now turn abruptly downward to an asymptote lying somewhat to 
the right of w,. So the question whether for this temperature a 
double intersection of a= 6 and aen Q will exist, which will 
dx dv 
necessarily lead to a contact afterwards, before the curves get quite 
