378 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
Consequently, in order that the first member be positive, it is 
sufficient that n’ should be less than n, that is to say, that the 
tartaric solution should be made with a less proportion of water 
than the ternary systems to be deduced from it, which it is always 
easy to effect. I can state, from numerous experiments, that 
the formation of successive ternary systems is obtained thus 
on the balance with facility and precision, within all the limits 
of the quantities which the solubility of the boracic acid admits 
under the circumstances of the experiment. I have always em- 
ployed it thus, in the state of crystal, in the solutions B which 
I previously formed. 
63. Supposing then a certain number of ternary systems into 
which this acid enters in various ponderable proportions £, 
from the weakest up to the strongest compatible with its ac- 
tual solubility, with the condition that the relation £ is constant 
in all and equal at m, we observe their respective densities 3, as 
well as the deviations « which they produce on a luminous ray 
of fixed refrangibility, for example, on the red ray through known 
thicknesses /, at a constant temperature. Then, in each series 
of systems to which m is common, the deviations a present con- 
stantly the following physical law. 
For the sake of shortness, let 
a 
lal = 753 
we have always 
BB 
[a] = A+ 6+ 
A, B, C are three constant coefficients, proper to each series, 
but which vary with the value of the relation n. In reality, B 
and C are the only ones which it is necessary to derive from the 
observations of each series. For the first A, corresponding to 6 
null, expresses the value of [a], which results for a tartaric so- 
lution free from boracic acid, and constituted in the ponderable 
relation of water expressed by x. Now, this value has been pre- 
viously determined for each temperature, according to the recti- 
linear or hyperbolic laws proper to this class of solutions, when 
their quantities are known. However, in the tables of experi- 
ments which I shall give further on, I have not wished to trust 
to this connexion, and I have preferred deducing the three co- 
efficients A, B, C from observations in which 6 was not nul, 
