380 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
sponding to the pure tartaric solution, can ever be obtained. 
Nevertheless, this length of are enables us to establish indu- 
bitably, either graphically or by numbers, its curvature, as is 
proved in figs. 6, 7 and 8, Plate V., and in the tables relating to 
it at the end of this memoir, which present under the same 
form the results of three different series, made at temperatures 
scarcely different, with very dissimilar proportions of water, from 
the weakest values of 6 up to the greatest which the solubility 
of the boracic acid allowed of employing in each series without 
precipitation. The numerical coefficients of the three hyperbolas 
thus obtained are expressed in the following table, with the indi- 
cation of the general circumstances proper to each series of ob- 
servations which they represent. 
Relation of the Mean 
weight of water Numerical coefficients of the equilateral temperature 
to that of the hyperbola. of the 
tartaric acid in observations of 
all the solutions each series. 
of each series. 
n. A. B. Cc. . 
1036666 | 72661 | 143-44690 | 0-28093240 423-8 
3°000000 95830 7032000 0:07538665 +23°4 
5-000000 10°3336 51°88556 0:034308553 +215 
65. The chance of the season, rather than an intentional fore- 
sight, admitted of these three series being effected at tempera- 
tures slightly different; and, fortunately, this phase of tempera- 
tures is precisely that in which the proper power of the tartaric 
acid is scarcely influenced by the variations of that element. 
The differences manifested in the coefficient A result from the 
changes which this power experiences according to the various 
proportions of water associated with that acid in the pure tartaric 
solutions, and they are there reproduced such as the immediate 
observation of these solutions had previously shown them to be, 
which proves the continuity of the results. With respect to 
the two other coefficients B and C, which depend on the reci- 
procal action exercised between each tartaric solution and the 
boracic acid introduced, it is immediately seen that their nume- 
rical values increase in proportion as the quantity of water  asso- 
ciated with the tartaric acid diminishes ; but Iam not acquainted 
with the precise law of these variations. Only it is evident, 
from the graphical delineation as well as from the numbers, 
that the realizable portion of the hyperbola is curved in propor- 
tion as the constant amount of water was greater in comparison 
