384 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT ~ 
from the want of solubility of the boracic acid. In fact, the cal- 
culation thus carried out gives 
For n = 1:03666, B = 030431 ; 
n = 3'0000, p= 19172; 
n = 5:0000, 6 = 013688. 
Now the greatest values of 8, which I have been able to realize, 
are for the first series 0°094, for the second 0°0492, and for the 
third 0:0695,—all vaiues very inferior to the preceding. In 
truth, I do not now recollect with certainty whether, in the second, 
I carried the experiments as far as the limit of precipitation of 
the boracic acid, and it is presumable that I did not. Accord- 
ing to the values of 6 given by the formula, that is to say by the 
numerical law of the phenomenon, it is seen that the maximum 
of optical action of the complex group corresponds to a ponde- 
rable amount of boracic acid less, in proportion as the system con- 
tains more water, and consequently less tartaric acid, in the unit 
of weight. But probably this peculiarity depends on the tem- 
perature. 
If these results be compared with those which we have already 
found for the simple aqueous solutions of tartaric acid, it will be 
perceived that the double mode of mutability noticed here is only 
an extension of that which we have there observed, and which is 
attributable to the greater complication of the ternary system 
considered. And we only find in it a simultaneous reaction 
of the three bodies presented to each other, producing in the 
whole mass of the system uniform chemical groups, perpetually 
varying in their material constitution as well as in their optical 
properties. The numerous experiments which I have related in 
vol. xvi. of the Mémoires de l’ Académie on the liquid systems 
formed by tartaric acid and water with the earths and fixed alka- 
lies, already led to this result ; but I was not then able to follow 
so far the phases of their variations, nor to establish so precisely 
their physical laws as I have done here. 
68. It remains for me to give some directions as to the course 
which should be followed to determine easily the constants A, 
B, C, which characterize the hyperbolic law proper to each series 
in which the relation n of the water to the tartaric acid has the 
same value. Representing then, as previously, by [a] the 
function i which is the ordinate of the hyperbola correspond- 
