320 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
Let 8 be the actual density of the system, J the length of the tube 
through which the observation is made; and let us call 
falys Lede’ du siale 
the deviations which would be produced on the type ray through 
the unit of thickness, by as many diaphanous systems composed 
solely of a same kind of these complex groups, under a same 
imaginary density equal to 1, at the temperature at which the 
experiment is made. Returning then to the proposed system, 
since all these groups are there uniformly diffused in an excess 
of the liquid supposed to have no longer any modifying action 
on them, the observed deviation « should be equal to the sum 
of all the partial deviations which they might individually pro- 
duce, in the ratio of their proportions by weight in the mixed sy- 
stem, that is to say, we shall have 
[w],¢,28 + [a],e,18....4+ [eliali=a; 
on substituting in this equation for ¢,,¢,....¢ their above- 
formed he a we shall readily have 
(m) +1) fa] E+ (a4 1) [o]ag? + oon m1) [oii 2 EB). a) 
The relations = fe = are individually constant in all the 
systems of the same nature which are supersaturated, or only 
saturated with the inactive liquid, since the weight P of the 
active substance will always be distributed between all the con- 
binations in the same relations, in virtue of the stability attri- 
buted to them. The powers [«],, [«].,.... [Ji will also be 
constant, from the individual identity of their composition; and 
the multiples ”,, .,..., mi will be equally so, since they ex- 
press the fixed proportions of the inactive liquids which enter 
into each of the groups. The first member of the equation 
(4.) will thus be constant in all similar systems in which E is in 
excess, and the same holds good with the second member, which 
is equal to it. Therefore, if the numerical value of the function 
= a 2 be calculated according to the observable elements 
which compose it, we should find it the same in all the systems 
of like nature in fixed combinations, which will be derived one 
from another by successive additions of the inactive liquid, 
when the quantity of this liquid employed shall surpass or equal 
that necessary to complete these combinations. The optical 
