IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 325 
mate combination without mutual decomposition, the realization 
of this fact presents two distinct phases. 
1. The weight IE is more than sufficient to saturate P, and to 
bring it to a fixed state, which a further addition of the liquid 
E does not alter. 
2. The weight E is insufficient for this saturation, and a fur- 
ther addition of the liquid E changes the combinations which 
P has formed. The case of an exact saturation is common to 
these two phases, and forms the transition from the one to the 
other. Each of them may, moreover, be realized in imagination 
by several distinct modes, which present different optical cha- 
racters, and which I shall successively enumerate. 
First Poase.—The weight E of the inactive liquid is more than 
sufficient, or just sufficient, to saturate P. 
First Case-—The active substance P takes in combination 
none, or only an insensible portion of the inactive liquid E, 
Then, in virtue of § 14, the characteristic function 
a(P + E) 
Pls 
is constant, whatever be the weight of E, and even whatever be 
the nature of the inactive liquid which composes E, provided the 
condition expressed in the statement be satisfied. The mixed 
system is a simple mixture of P and of E. 
Second Case.—The weight P of the active substance forms 
with the inactive liquid one or more fixed combinations, into 
which this liquid enters in any proportions, n, P), n. P,,... 
n;P;, the surplus of KE. remaining free. 
Then, in virtue of $$ 18, 19, 20 and 21, the characteristic 
function a(P + E) 
Pld 
is again constant for a same inactive liquid, whatever be the 
weight of E. But its absolute value may, and even must gene- 
rally be different for inactive liquids of different nature, asso- 
ciated with the same active substance, for it could only be equal 
by exception. When this diversity of constant values manifests 
itself in changing the inactive liquid, it will show with certainty 
that the state of combination, simple or multiple, takes place in 
some of the mixed systems. 
EA 
