IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 319 
tion (3.), the multiple » + 1 disappears, and there remains for 
this particuliar case ra] 
1 
The expression of [«], coincides then with that of [«] given by 
the equation (1.) of § 8, for active liquids chemically homogene- 
ous. This should be the case, since the mixed system being 
then composed solely of new-formed groups, which are all iden- 
tical, it becomes chemically homogeneous, as is supposed in 
equation (1.). 
If, no longer limiting E, the primitive groups of the active 
substance are supposed not to combine with any, or only with 
an insensible proportion of the inactive liquid, m becomes null, 
or may be neglected; and the expression (3.) of [«], is reduced 
to 
ee ai _a(P+E). 
[ali =7-33 or [e],= P1d > 
it is then found to be identical with that of [a] given by the 
equation (2.) of § 14, for the case in which the active substance 
is diffused in the inactive liquid by simple mixture, which ac- 
cords in fact with the identity of the circumstances thus intro- 
duced into the equation (3.). 
21. I now consider the general case in which the total weight 
P of the active substance is divided spontaneously into any num- 
ber of partial weights P,, P,, P3,.... Pi, which would form as 
many fixed, but different, combinations with proportions in 
weight of the inactive liquid designated by n, P,, m, P.,.-.. 
ni Pi; admitting always that the total weight E of this liquid 
surpasses or equals the sum 2, P, + 2, P,+...+ 2: Pi, in 
order that there may be supersaturation, or exact saturation, in 
all the systems thus composed. The condition of partition of P 
will require first that we have 
ee ee a ae) bas 
then the absolute weights of the partial combinations will be re- 
spectively 
(nm; + 1) Py, (mo + 1) Pa, «(mi + 1) Pi 
and designating their ponderable proportions in the mixed sy- 
stem, by the letter < successively affected by the same signs, we 
have 
= Ht1)P, , _ (m+1)P,  — Ut DP 
1 P+E Th P+E preeey ae 6 Tee 
Zz 2 
