( 13V ) 
dp A E 
15. We now proceed to consider the expression for — = 
more closely. 
The general equation for A F may. be found from 
A7=®-«' = (6-JH [(» — *) “ (»' — & ')]- 
In this b = b 1 -\- 0A b, b' = b x + 0'A b, hence b—b' =(£— P') &b, 
so that we get : 
■ ( 17 > 
Now as p — p’ is always positive (we indicated the phase with the 
slightest value of p, i.e. the solid phase, by accented quantities), 
while — A b is supposed to be positive, — AF will have its greatest 
positive value at T=0, viz. — A b. For then P—p has its maximum 
1_|_£ 1 + 0 * 
value 1 — 0, and the term with RT, in which p _^ a j~ 
will be as small as possible. *) 
For A E we may write (see (12) on p. 36 of II): 
A E = ((S-f?) (q, + y RT) + (? + 5) AF ’ 
or after substitution of the value of AF found: 
A E = {$-?) yJ IT + W-P) [«. “ (p + £i) Ai >] + 
Now we saw above that q 0 —^ (-A5), i* e * ^o - 
when p 0 is the pressure of coexistence at T= 0, and v 0 is the 
“third” volume on the part 'ED (cf. also II, p. 35—36), is of the order 
— (.RTlog X — (y -f 1) RT log T), 
i.e. of the order 
A6), 
aT+pTlogT, 
so that the above expression for A E must be of the order 
„’T + p T log T =z T {a 1 + plog T) 
in the neighbourhood of T= 0. So it follows from this that for 
T= 0 also AE=0; that for ^>0 A E becomes at first negative 
i ) For in practice v and v f will differ very little, whereas & will mostly be 
considerably greater than & (cf. also II* p. 39 footnote, where we demonstrated 
on the same ground that v — b is always > V — b'). 
10 
Proceedings Royal Acad. Amsterdam. Vol. XII. 
