( 607 ) 
passing through the point «= .w2,, v =O, appear to be the liquid 
branch and the branch v < 6, which has no physical signification. 
These two branches touch the line vy = 4% in the point mentioned as 
appears from the fact, that the product of these two roots is in the 
neighbourhood of this point 4’, and the sum of these roots 20d. 
Besides we can also prove this directly from the direction of the 
tangent. For: 
9 da 
dp  2MRT dd da 
dv dode ais (v—b)? de v3 
DP OM RT Ga. 
2 dv* (v—b)? oy! 
If we substitute in this equation the value for (v—d) from the 
dp 
equation for aa = (0, we get: 
) 
MRT\?/: 
eS vile 
db 2a 
2MRT — 2 
dv x v? 
BEAP bs HORTA 
En ba vile 
i 2a 
2MRT — —— 
vt 
When we approach v == 0 the second members disappear in 
numerator and denominator, so that we keep: 
dv = db 
| dx a =“ da: b=—=0 
ae did) 
d, 
So for 2 little greater than «,, - = 0 will have greater volume 
av 
dy 
than st for the same wv. If, however, there should occur a 
Vv 
minimum critical temperature in the system, and we shall see later 
on that this is very possible, there will be a point of intersection of 
d d 
“P —0 and = = 0, which will, of course, constitute a fundamental 
Vv 
point for the diagram of isobars. 
Before proceeding to a discussion of the shape of the isobars them- 
selves, we shall have to indicate for a complete elucidation of the 
problem discussed in the beginning, which gave rise to this inves- 
