348 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
ceding its return to the state of solidity; whether, in this last 
state, it contains or does not contain water of crystallization which 
would solidify at the same time. Reciprocally, if this value of 
8, was not known, it might be arrived at from the equation itself, 
for each solution in which ¢,, 8,, and the resulting density 6 had 
been observed directly; and we should thus find 8, constant, 
whatever were the amount of the solution on which we had 
founded our conclusion, provided it had always been made at a 
same temperature, and that it had been effected without contrac- 
tion or dilatation, as the formula supposes. I shall adduce here- 
after experiments of this kind. 
41. I shall first apply the formula (1.) to the aqueous solu- 
tions of cane-sugar mentioned at the end of § 34, and the quan- 
tities of which are given in tome xiii. of the Mémoires de l’ Aca- 
démie des Sciences, p. 119. Since they gave for the character- 
istic function a values nearly constant, but yet increas- 
ing a little with the proportion of water, we should expect that 
their densities would not exactly follow the relations proper to 
simple mixtures, but that they would deviate slightly. To these 
three solutions I have added a fourth, the quantities of which 
are given in the Comptes Rendus de Académie des Sciences, 
tome xv. p.625. I have added the indication of the tempera- 
tures at which the densities were measured, and which I found 
registered in my note-book. Although these early experiments 
were made with only the ordinary care and precision which 
ought always to be used, and not with the refinements which 
might be employed for the special object which we propose here, 
I consider them as preferable, because they were not made with 
a view to this object. I shall subsequently relate more recent 
ones, which were made with the greatest care. 
As all the saccharine solutions to be compared may be derived 
from one another by successive additions of distilled water, we 
must make 8,=1 in the equation (2.), and it then becomes 
5 =p t(-4). EP ee 
Here 8 is the density of the mixed system, in which the primi- 
tive solution, whose density is 8,, enters in the proportion ¢,, the 
rest being water added or subtracted. Most frequently this 
proportion ¢, is not given, and we only know the analogous 
proportion of solid sugar entering into the solutions compared. 
3 
