IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 369 
systems. In the first place, the mere fact of the continuous varia- 
tion of [«] for any values whatever of e, that is to say for any 
proportions of water, shows us that, whatever be the amount of 
this liquid, the acid is never completely saturated or supersatu- 
rated with it, so as to form with it fixed groups which a subse- 
quent addition of water would not further modify. We have 
noticed this in § 46, in discussing the mode of variation of the 
densities offered by mixed systems thus constituted. Consider- 
ing therefore the state of non-saturation doubly manifested by 
these experiments, I assert that the mode of variation of the 
function [«], here realized by the experiment, excludes the sup- 
position of the division of the active substance into two portions, 
-one of which is completely saturated and the other free. For, in 
this case, the second of those which we have enumerated in § 27 
as belonging to the general phase of non-saturation, we have 
established that the function [«] should vary as the ordinate of 
a right line, of which the relation = would be the abscissa. 
Now, such a mode of variability is incompatible with the actual 
mode of variation which we have proved by observation. 
57. To demonstrate this fact, it will suffice to employ the 
simplest of the equivalent expressions which we have obtained 
of [a], that is to say the rectilinear, the hyperbolic leading ex- 
actly to the same conclusion, as may be easily proved. Taking, 
therefore, the simple expression 
‘ [~] = (A) + (B)e, 
it is seen that the abscissa of the real right angle is e, or ee 
instead of = a very different result. To show the incompati- 
bility of these two forms under the conditions of exactitude re- 
quired by the experiments, let us make 
= =z, whence EK = Paz, 
we thence deduce 
EER LOL Cap P 1 
ep hg fy? 
then, substituting this expression of e in the rectilinear ex- 
