OMEN 
VAN DER WAALS, another maximum at DY and a minimum at C have 
now made their appearance. To A as vapour phase corresponds the 
coexisting solid phase A’. To P' as solid phase the coexisting liquid 
phase P". [ef. also the p-7-diagram of fig. 4(D, where the line SM 
runs. back in consequence of the fact that 46 is negative, which 
implies that also Av is negative for the transition solid-liquid (P'P"). 
By approximation the quantity Av is namely = (@;— 8;) Ad, in 
which 8u, is always >> Boud). The pressure of coexistence at PE 
will always be much greater than that at 44”, when the temperature 
is considerably lower than that of the triple point S (see fig. 4). 
For not too low values of 7’ we may also have a metastable coexist- 
ence gas-liquid QQ" (ef. figs. 1 and 4). If the temperature is very 
low (as in the following calculation), 3 will draw near to 1 only 
for exceedingly high values of v, whereas for all values of v between 
A and D the value of 3 is practically =O (association is complete), 
as will appear from the following calculation. The minimum value 
of 8, which was mentioned in § 2, then lies in the immediate neigh- 
bourhood of 0. Only between the points D and £ does 3 increase 
rapidly from @=(+)0 to §=(+)1, and this in consequence of 
the rapid decrease from v—=(+)b, to v—=(+)2b,. From £ to the 
highest pressures 8 remains then in the immediate neighbourhood 
of 1, and becomes exactly =1 for p= o \v = 26,). It is self-evident 
that for higher values of 7’ the values of 8 for P' and P" will 
approach each other more. 
At the temperature of the triple point S the three transitions 
AA’, QQ" (metastable), and PP" will coincide. There is only one 
pressure of coexistence (three-phase-pressure). 
For temperatures above that of S (comp. fig. 2 and fig. 4 (ID) 
the coexistence QQ", which was first metastable, has become stable, 
whereas AA' has now become metastable, just as P’P". (These last 
transitions, of course, at not too high values of 7’). Now only a 
liquid phase coexists with the vapour phase. 
For higher temperatures the minimum at C and the maximum at 
D will draw nearer to each other, and they will finally coincide in 
an horizontal point of inflection C‚,D (comp. fig. 3 and fig. 4 (IID). 
From this moment we have, therefore, the original isotherm of 
VAN DER WaaLrs with the simple coexistence gas-liquid. 
At last at still higher temperature (the critical temperature in K) 
also the last maximum (4) and minimum (/) will coincide. 
How all this is modified when Ab is positive, and so the line SM 
runs to the right in fig. 4, will be easily seen by the reader. We 
shall revert to this in a following paper, and mention now only that 
