IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 367 
are realized, I select a series of fifteen experiments published in 
vol. xv. of the Mémoires de ? Académie, page 208 ; it comprises 
the observations of as many different tartaric solutions, in which 
the ponderable proportions of water varied from e=0°40399 to 
e=0'95083. The mean temperature at which all these solu- 
tions were observed was + 12°68, with slight variations near 
this value, as may be seen at page 205, where the temperature of 
each observation is given. All the values thus obtained for [a] 
were connected by the rectilinear form 
[~] = (A) + (B) e, 
and, on determining the coefficients (A), (B), by the condition 
of satisfying the two extreme observations alone, I found 
(A) = 1:17987 ; (B) = + 14:3154; 
which consequently gives for any value of e, 
[a] = — 117987 + 14:3154. e. 
Then, on calculating the values of [a] by this formula, accord- 
ing to the value of e proper to each experiment, and comparing 
them with the observed values, the agreement was such, that I 
could not answer for the small differences which occasionally 
occurred, as may be seen at page 208 already cited. 
55. At present, to submit these same results to the hyper- 
bolic relation, I first take the two same extreme data; and, as it 
is necessary to add a third, since we have three coefficients to 
determine, I chose for this purpose a mean between the simul- 
taneously observed values of [«] and of e, which corresponded 
to the mean of the entire series, which had not entered into the 
primitive calculation of the coefficients (A), (B) of the rectilinear 
relation. Operating thus, I found 
A= —1°55526; B= + 2263727; C= + 14-4455; 
and consequently 
B 1 
G= + 15°67075 ; G = 0069225 ; 
whence is generally deduced 
[a] = — 1555264 2263727 e_ f 
e + 14°44555’ 
or again, 
15°67075 e 
[#] =—155526 +7 9.969995" 
