362 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
the values of [«] present a continuous and regular course of 
variation, which is expressed with all the precision of the obser- 
vations themselves, by a rectilinear function of the form 
[2] = (A) + (B)e, 
(A) and (B) being two numerical coefficients independent of e ' 
and «. The coefficient (A) varies regularly with the tempera- — 
ture ; it increases in proportion as that rises, and decreases when _ 
it falls. Its value becomes’ null toward the temperature of 
23° C., and it remains positive above that limit, negative below 
it. The coefficient (B), on the contrary, appeared independent 
of the temperature; and on evaluing [«] for a thickness of 100 
millimetres, I found it equal to 14°3154, relatively to the red 
ray. The collection of experiments, from which these deter- 
minations have been deduced, embraces the interval of tempera- 
ture comprised between —5° and + 26°. After having described 
them in detail in the memoir cited above, I resumed them in a 
subsequent investigation, inserted in vol. xvi. of the Mémoires 
de ? Académie, where they have been confirmed by new applica- 
tions. Although the rectilinear law of the variations of [«] could 
not be proved directly except for the red ray, I have shown, by 
various proofs, that it should be extended to the other simple 
rays, with different values of the coefficients (A) and (B) ; whence 
results the speciality of tints which these solutions produce in 
the images formed by the analysing prism, when the polarized 
beam passed through it is composed of white light. 
49. From what has been established in the first section, § 27, 
the function designated here by [«] is that whose variability or 
constancy characterizes the state of combination, or of non-com- 
bination, of the active substance with the inactive liquid into 
which it has been introduced. Since it is here variable for the 
different proportions of water in which the acid is dissolved, it 
is a certain proof that it is combined, and not in the state of } 
simple mixture. This consequence is, in fact, confirmed by the 
mode of variation of the densities of tartaric solutions formed 
successively with various proportions of water, as we have seen 
in § 46. According to § 27, already cited, the several systems 
of simple or complex combinations, which may most probably 
be effected in similar cases between the two bodies present, 
give rise to certain forms of variability of the function [«] which 
we have there defined, It thus becomes necessary to establish 
with precision, in all its details, that which it assumes in the 
