265 
if we replace summation with respect to dr by an integration. 
To determine A we derive the total energy, u, 
on 1 n? 
Oh dep 
M= 
Qe sa STE SNEEK) 
in which 
Q= ferro Arran Dern dr RR 
0 
If we now calculate the expression for log, W from (27), allowing 
for (33), (382) and (31), retaining only principal and first order 
terms we get from (8) and (35) for the state of equilibrium 
3 1 n° (4 
s == nkp Inv ——nkp Inh + kp hu —— kp — | — av? — P (37) 
2 2 v\3 
On elimination of h by means of (35) this equation yields what PLanck 
calls the canonical equation of state. And just as in $ 3, noting 
: dP 
that P and Q are related to each other by the equation a 
} 
we now recover equation (12) from (35) and (87), a result to be 
expected and consequently affording a desirable control. 
Introducing the temperature 7’ as defined by (12) and also the 
gas constant A (ef. $ 3) we obtain 
3 RT n (4 
aen gn » (38) 
Vv 
The specific heat at constant volume y, is now found to be 
dependent upon the volume. Putting v = oo in the expression for yo we 
obtain the specific heat at constant volume in the Avocapro state *) 
wa ="), B. 
For the thermal equation of state we obtain 
ee eee) 
with the second virial coefficient 
1 
B=—n 
2 
0 
I 
in which / may be replaced by Er) 
p 
1 — etn EOD eta en Teen 
1) Cf. Suppl. N°. 23, Nr. 394. 
2) This result agrees with that given by ORNSTEIN, Thesis for the Doctorate, p. 73. 
