242 
and molecular action. This is especially the case with the first 
coefficients A, B and C, as their values can be experimentally 
obtained with pretty high accuracy quite independently of any 
special assumptions which may be made regarding subsequent terms; 
while, from the theoretical point of view, the means are at hand 
for deducing these virial-coefficients from various special assumptions 
regarding the structure and action of the molecules’). 
With regard to the first virial-coefficient A we may remark that 
one may write 
(R is the gas constant, 7 the temperature on the Ketvtn scale) for 
non-associative substances over the whole temperature region hitherto 
investigated. With regard to the question as to whether such sub- 
stances would exhibit another law of dependence upon temperature 
in another region (e.g. at the lowest possible temperatures) we may 
refer the reader to Suppl. N°. 23. 
Both the present and the following paper aim at making a 
beginning with the dednetion of the second virial-coefficient, B, 
from certain special assumptions, having in view its completion in 
subsequent papers by a comparison with results obtained from 
experiment. | 
In his Elementary Principles in Statistical Mechanics Gress deve- 
loped methods which in principle enable us to deal with any mole- 
cular-kinetic problem concerning the equation of state, as long as we 
limit’ ourselves by the assumption that the mutual actions of the 
molecules conform to the Hammronian equations. OrNsTEIN *) adapted 
this method to the deduction of the equation of state and applied it. 
In Suppl. N°. 23 the method indicated by Bourzmann in his Gastheo- 
rie Il $ 61 and based immediately upon the BoLTZMANN entropy 
principle is developed in general terms. This method, too, seems 
suitable for the solution of all problems concerning the equation of 
state of systems in which the mutual actions of the molecules con- 
form to the HamirroNian equations. It has been shown by LORENzz *) 
1) In this connection it must be remembered that, as noticed in § 1 of Comm. 
No. 74, the virial-coefficients in the polynomial (1) differ from those of the corres- 
ponding infinite series in which all the positive powers of vl are present. The 
more attention must be paid to this point, the higher the coefficients concerned; 
it will be quite appreciable with C on account of the absence of the v> term in 
(1), while D in (1) can no longer be regarded as approximating to the coefficient 
of v-—4 in the infinite series (ef. Gomm. N’. 74 § 1). 
2) L. S. ORNSTEIN. Diss. Leiden 1908. 
8) H. A. Lorentz. Physik. Z. S. 11 (1910), p. 1257. 
