322 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
proved, since the values of this relation are not connected by 
any law of succession which could be theoretically foreseen. 
24. I put now a second case, the inverse of the preceding, 
where the liquid FE is not divided equally among all the consti- 
tuent molecules of P, but is specially absorbed by some which 
form with it a complete and saturated combination, subject to a 
certain fixed proportion, which I designate by the integer or frac- 
tional multiple x. Then, the portion of P which does not enter 
into this combination, is diffused in the system, preserving its 
primitive optical properties. I do not suppose that it dissolves 
in it, uniting by chemical combination with the perfect groups 
already formed, because in this manner the case of the preceding 
paragraph would be reproduced with the same indetermination. 
Let P,, P, be the two portions into which P is separated. P, 
combining with E to saturation in the relation n, and P, remain- 
ing free, the conditions of the phenomenon will be 
PST, Tr te t= wr 
Let us designate as before by [a], the rotatory power peculiar 
to the newly-formed groups, and by [«] the analogous power of 
the active substance observed in the isolated state. Let us call 
8 the density of the mixed system, / the length of the tube 
through which it is observed, and « the total deviation which it 
produces on the type ray under these circumstances. It will be 
easy, by the foregoing principles, to form the theoretical expres- 
sion of « For, first, the total weight of the combined groups 
being P, + » P,, their proportion in weight in the mixed system 
will be HBB, so that having the proper power [«],, the 
whole will produce the partial deviation [«], 12 oo. Then 
the weight of the active substance remaining free being P,, its 
proportion by weight in the system will be pee which will 
produce the partial deviation [a] 73 =—*. PLE =o Since then the sum 
of these two deviations should compose the total deviation « ob- 
served, the condition of this equality will give, on transposing 
to the second member the common factors, 
[2], (P, + aP,) + [4] P, = 2 +) 
The quantities P,, P,, into which the total weight P is decom- 
