282 J. W. Gibbs — Vapor- Densities. 
in the values given to A’ and C. We may therefore cancel 
this term, and then determine the remaining constants by com- 
parison of the formula with the results of experiment. 
In the case of a mixture of Cl,, PC], and PCl,, equation (8) 
will have three terms distinguished by different suffixes. To 
fix our ideas, we may make these suffixes », , and ,, referring to 
Cl,, PCls and PCI, respectively. Since the constants a, a and 
a, are inversely proportional to the densities of these gases, 
a,dm, = a,dm, = — a, dm, 
i 11 —1 : 
and we may substitute —, —, — for dm,, dm,and dm, in equa- 
tion (8), which is thus reduced to the form 
m,v C 
wh ce oe A ott 7 
log gs A Blogt+-—- (7) 
If we eliminate m, ms, ms by means of the partial pressures, 
Pa Ps; Ps We obtain 
ies 
. PP; 
when A’, B’, like A, B and ©, are constants. If the chlorine 
and the protochloride are in such proportions as arise from t . 
decomposition of the perchloride, p,=p, and 4p ps= (Pats) 
In this case, therefore, we have 
=—A'—B'logt+<, (8) 
=~ A'—B’logt + <. (9) 
applying to the vapor of perchloride of phosp : 
values of the constants are properly determined. This result 
might have been anticipated, but the longer course which we 
have taken has given us the more general equations, (7) and 
(8), which will apply to cases in hick there is an excess of 
chlorine or of the protochloride. 
If the gas-mixture considered, in addition to the components 
capable of chemical action, contains a neutral gas, the expres: 
sions for the energy and entropy of the gas-mixture should 
properly each contain a term relating to this neutral gas. 12 
would make it necessary to add c,m, to the coefficient of dt ™ 
(1), and = to the coefficient of dt in (2), the suffix , being 
