IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 357 
of acid, in the unity of weight, expressed in hundredths; 2 the 
excess of the resulting density above unity, expressed in thou- 
sandths, this density being taken comparatively to that of di- 
stilled water at the same temperature. The relation of « to y is 
Kae hes 
z= pa 
a and 6 are two constants which, at the temperature of 6°°8 C., 
have the following numerical values :-— 
a = — 1380°875, b= + 302°7003 ; 
both these values increase, preserving their proper sign, in pro- 
portion as the temperature rises. 
To reduce this statement to the notations which we have 
adopted in the course of the present memoir, let 8 be the abso- 
lute density of the system, that of water being 1, and « the pro- 
portion by weight of acid existing in each unit of weight of the 
solution. According to the definitions above given of x and of 
y, we evidently have 
x = 1000 (§— 1), y = 100; 
introducing then these expressions instead of x and y into the 
preceding algebraic relation, we shall derive from it 
t1iqe 
10 
aan 100—-— 6 
Thus, making, for the sake of abbreviation, 
a! = 5 a = — 138-0875, 6 = + 302°7003, 
we have, at the temperature of 6°8, which I take for example, 
ale 
Bares 100¢ — b’ 
as this law is maintained without discontinuity in all the pro- 
portions in which the solutions may be observed in the liquid 
state, we may extend it even to the case where the proportion 
of water is null, which would suppose « = 1. Then the result- 
ing density, which I shall call ¢,, would be that of the acid un- 
crystallized alone, in the molecular state of disaggregation. 
We should thus have 
a’ 
By giving to the constants a! and } their proper numerical va- 
