302 
PHYSICS: A. G. WEBSTER 
Proc. N. a. S. 
- — r<\w\< — \- r 
r r 
for = r, 0<f <1, except when 
w = - ^ e^'^'z 
z 
with a real, the upper and lower bounds of |w| being then reached when 
z = ±^~"V and z = =^ie~"\, respectively. This particular function 
maps |2;|<1 on the w-plane cut along the straight line from w = —2^"* 
to w = 2e''\ 
1 Koebe, GoUingen, Nachr. Ges. Wiss., 1909 (73). 
2 Gronwall, Paris, C. R. Acad. Set., 162, 1916 (249). 
3 Gronwall, Ibid., 162, 1916 (316). 
^ Fricke and Klein, Vorlesungeii iiher die Theorie der automorphen Functionen, II, 
Leipzig, 1912 (497). 
5 Gronwall, Annals Math., Princeton, Ser. 2, 16, 1914 (74). 
ON THE CONNECTION OF THE SPECIFIC HEATS WITH THE 
EQUATION OF STATE OF A GAS"" 
By Arthur Gordon Webster 
Clark University, Worcester, Mass. 
Read before the Academy, April 26, 1920 
One would suppose that this subject was already exhausted, but I am 
disposed to believe that such is not the case. In these Proceedings, 
5, July, 1919 (286-288) I pubhshed a paper "On the Possible Form of 
the Equation of State of Powder Gases." In a private letter from M. 
LeChatelier, in commenting on this paper, he says: "Votre objection 
au sujet de nos chaleurs specifiques nous etait venue a I'esprit, mais nous 
pensions avoir demontre, en partant des principes de la thermodynamique, 
que toutes les fois qu'un fluide obeit a une equation caracteristique de la 
forme 
V = F{P/T) 
les chaleurs specifiques sont independantes de la pression." 
I do not find where, if anywhere, M. LeChatelier has published this 
conclusion. Certainly it is not in the great paper by Mallard and Le- 
Chatelier, Journal de Physique, Ser. 2, 4 (59-84), "Recherches sur la 
Combustion des Melanges Gazeux Bxplosifs," where the matter is not 
mentioned. In a paper published in the Physical Review, 29, No. 3, 
September, 1909, "On the Definition of an Ideal Gas," written by me, 
but suggested by my then colleague Professor Rosanoff, and published 
under our joint names, I have investigated the properties of a gas having 
the equation of state mentioned by M. LeChatelier, but have said nothing 
about the specific heats. Inasmuch as the matter seems to be not quite 
* Contribution from the Ballistic Institute, Clark University, No. 8. 
