J. W. Gibbs — Vapor- Densities, 279 
component gases necessary for the equilibrium of such a mix- 
ture under any given conditions, these substances afford an 
that paper, new determinations of the density have been pub- 
lished in different quarters, which render it possible to compare 
. 
similar comparison of theory and experiment is made with 
respect to each of the other substances which have been men- 
tioned. 
The considerations from which these formuls were deduced 
may be briefly stated as follows. It will be observed that they 
are based rather upon an extension of generally acknowledged 
principles to a new class of cases than upon the introduction of 
any new principle. 
e energy of a gas-mixture may be represented by an ex- 
pression of the form 
m, (¢, t 3.3 E,) 2 m, (c,¢ + E,) LE etc., 
with as many terms as there are different kinds of gas in the 
mixture, m,, ms, etc., denoting the quantities (by weight) of the 
several component gases, ¢, C, etc., their several spec he 
at constant volume, E,, E,, etc., other constants, and ¢ the abso- 
lute temperature. In like manner the entropy of the gas-mix- 
ture is expressed by 
mM. 
a (H, + ¢, logy t — a, logy =) 
m 
So m, (H, + e, logs t— 4, logx sn) +. etc., 
* “On the els eous Substances.” Transactions of the Con- 
indie Aaa a = a Tb The equations referred to are (313), (317), 
(319) and (326), on pages 233 and 234. The applicability of these equations to 
such cases no idering is discussed under the heading “ Gas-mix- 
tures with Convertible Components,” page 234. 
