IN STUDYING QUESTIONS OF CHEMICAL MECHANICS, 317 
pletely the active substance which it contains in the state of 
combination, single or multiple, to which it has spontaneously 
arrived. In these three supposable cases, when the first or the 
second is realized, the new chemical groups formed by the ac- 
tive substance will be complete, and an ulterior addition of the 
inactive liquid will not change them. In the last case, on the 
contrary, it will change them. These two phases of stability 
and of instability will cause distinct optical effects, which I 
shall proceed to characterize successively by corresponding 
formule. 
20. In the first, that of supersaturation or of exact saturation, 
I suppose first that the active substance forms with the inactive 
liquid one sole kind of combination, in which each of its parti- 
cles is united with a certain fixed proportion of this liquid. The 
rest therefore of this liquid which shall not have been absorbed 
will offer a free space in which the combined groups may diffuse 
themselves uniformly with the permanent constitution they have 
acquired. ‘To express this result, let P be the total weight of 
the active substance employed, and n P the weight of the inac- 
tive liquid necessary to saturate P in the uniform mode of com- 
bination which we suppose to be effected. The multiple x, 
whether it be entire or fractional, will have a constant value in 
the case of fixity of composition of the groups which we suppose. 
Designating then by E the total weight of the inactive liquid 
employed, every similar system will contain the weight P + n P, 
or (x + 1) P, of combined groups, and the weight E — nP of 
free inactive liquid; this last quantity being necessarily always 
positive or null, but never negative for the systems here consi- 
dered. This being assumed, I make, for abbreviation, 
se Pt: ty etl? tnd) e 
ae eae de Sey 
whence results 
é, = (n+ 1). 
2 will represent, as before, the proportion by weight of the ac- 
tive substance contained in each unit of weight of the system, 
and «, the proportion by weight of the new combined groups in 
it. Let be the actual density of this system, / the length of 
the tube through which it is observed, « the deviation which it 
then produces on the type ray. Since the new combined groups 
may exert on polarized light an action generally different from 
VOL. IV. PART XIV. Z 
