IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 383 
BB 
nn 
a = So a &. 
("= [A+ a+ a | 
But the three quantities «, 6, e, are connected by the general 
relation 
e+B+e=1, 
which, for the systems which we unite in one series, becomes 
(nm Ae 1) e+6=1, 
whence 
This value of ¢ being substituted in the expression of [«]", there 
finally results 
ra BB (1 —8) 
(+1) [aJ"= A —p) += BC 
Thus, in each series of systems in which v is given, when the 
coefficients A, B, C of the hyperbolic relation proper to this 
series are known, we obtain by this formula the molecular power 
[a]" of the mixed group, composed of tartaric acid, water and 
boracic acid, which is realized for each ponderable proportion 
of this latter acid, expressed by the corresponding value attri- 
buted to 8. The optical power of this group will vary therefore 
continuously in each series with this proportion; and it will 
moreover vary continuously from one series to another for one 
and the same value of 8, according to the proportion of water 
associated with the tartaric acid, which is expressed by the num- 
ber 7, without these changes having other limits than the possi- 
bility of each system existing in the liquid state with the ele- 
_ ments which constitute it. 
From the general expression of (x + 1) [«]!', we find that, in 
each series in which 7 is constant, the optical action of the com- 
plex group formed of tartaric acid, water and boracic acid, attains 
its maximum of energy when the ponderable proportion of this 
latter acid is such that we have 
BC (1+ C) 
=—CH ———— 
) A rs B 2 
but on substituting in this expression the values of A, B, C 
proper to each of our series, it is seen that the value of 8, corre- 
sponding to the maximum which it indicates, cannot be realized 
