312 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
the mixture thus reduced to the total length /,; and let 8, be — 
likewise its density, which may be established with or without 
modification of the partial volumes. We shall again have 
ee 
These are the circumstances assigned to the experiment. To 
calculate the theoretical result, we must seek the ponderable pro- — 
portion «, of the active substance in the mixed system. Its ex- 
pression is evidently 
ee iiad AGO hee 
ae he ae ea | 
Now, the molecular power of this substance being [«],, its pre- 
sence in the proportion ¢,, in the system whose density is 8, will 
produce, through the thickness /,, the deviation [a], ¢, /, 8; so 
that, if we call this resulting deviation «,, we ought to have 
ay = [a], 1, %. 
Replacing [«], and «, by their above-formed expressions, the 
densities ¢, and 8, disappear, and there remains 
TONS fe 
a= 4) ae A 
But as the volumes V,, V, are both measured in the same cylin- 
drical tube B, in which they occupy respectively the lengths /, 
and /,, they are proportional to those lengths, which gives 
et ae 
Vea : 
consequently 
Bar= (19 
which is precisely the result observed. 
I long ago performed this experiment, by mixing essence of 
turpentine with olive oil bleached by a long exposure to the sun. 
It may be very easily repeated on aqueous solutions of cane- 
sugar, starch-sugar, or dextrine, diluted with water at a constant 
temperature. Nevertheless, when the observation is carefully 
made, a very small inequality is perceived, or rather suspected, 
between «, and «,, when the primitive solution is very concen- 
trated; this arises from a feeble reaction which then takes place 
between the active substance and the water present, as we shall 
hereafter prove in other examples, in which such a reaction is 
indubitable. 
16. The following is another more complex application of the 
formula (2.), which is curious and important from the results” 
which it furnishes. 
