386 J. W. Gibbs — Vapor- Densities. 
theoretical value) is counterbalanced by the excess of densi 
of the protochloride. When z> 400, the effect of the deficiency 
in the density of the possible perchloride distinctly preponder- 
ates; when z <250, the effect of the excess of density in the 
protochloride distinctly preponderates. But the magnitude of 
the differences concerned is not such as to invalidate the general 
conclusion established by the experiments of M. Wurtz, that 
the dissociation of the perchloride may be prevented (at least 
penly) by mixing it with a large quantity of the proto- 
chloride. 
Table for Jacilitating caleulation.—The numerical solution of 
equations (10), (11), (12) and (18) for given values of ¢ and p 
may be facilitated by the use of a table. If we set 
D 
<< 17 
4=5> (17) 
1 
1000 D, (D—D,) 1000 (4—1) 
re 1 or pete gaer SH ass 20 18 
= 8 —Gp —Dy Mee a 
we have for peroxide of nitrogen, 
ae pee i 9-451; (19) 
Tigge- G78 2 ee , 
for formic acid, 
3800 
Pe ee a —9 : 20 
= prpoyy t loge —9e4 ; (20) 
for acetic acid, 
3520 
a | Oe 21) 
=F o75 t logp—ssso; ( 
and for perchloride of phosphorus, 
5441 
2 Be re 22 
= e278 + log p— 11353. (22) 
By these as the values of L are easily calculated. The 
values of 4 may t 
value of D may be obtained by multi lying by D,, viz, by 
1589 for peroxide of nitrog: , 2 
pe 
of the number of the 
the more complex type to the whole number of molecules. Thus, 
i nitrogen there are 20 molecules of the typ? 
