280 J. W. Gibbs — Vapor- Densities. 
where v denotes the volume, and Hy, a;, Hy, aa, etc., denote 
constants relating to the component gases, aj, a2, etc., being in- 
The condition that the energy does not vary, gives 
(m,¢, + m,¢, + etc.) dt + (c,t + E,) dm, 
+ (c,¢+ E,) dm, + etc. = 0. (1) 
The condition that the entropy is a maximum implies that its 
variation vanishes, when the energy and volume are constant: 
this gives 
¢, +m, c, + ete. 
t 
dt + (H, — a, +e, logy t — a, logy =) dm, 
2 (4, ah a, + ec, logy t 46 a, logy =) dm, + etc. = 0. (2) 
Eliminating di, we have 
(H, ~d,—¢,— = +c, logy t — a, logy =) dm, 
© (H, on ee =! + ¢, logy t — a, logs =) dm, + etc. = 0. (8) 
_ If the case is like that of the peroxide of nitrogen, this ease 
tion will have two terms, of which the second may refer to the 
denser component of the gas-mixture. We shall then so f 
@ = 2a,, and dm, = — dma, and the equation will reduce to the , 
form 
m,v C 4 
log M7 = — A Bloge +5, (4) 
where common logarithms have been substituted for Neapera 
and A, B and C are constants. If, in place of the quantities 3 
_ the components, we introduce the partial pressures, Pr» . 
to these components, and measured in millimeters of mercury, 
by means of the relations 
* For certain @ priori considerations which give a degree of probability 1 
these assumptions, the reader is referred to the paper already cited. 
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