372 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
[a] = 3 ande+e=1, 
there results 
a 
Ce 13(1—e)’ 
substituting then this expression of [«] in the first member of 
our rectilinear equation, and deducing the relation = we have 
l 
Fy = (A) + [(B) — (Ae — B) 4, 
a relation in which e represents the proportion of water asso- 
ciated with the acid, as previously. When e = 0, the second 
member is reduced to (A), that is to say to the proper power of 
the acid, without addition of water, at the temperature at which 
the experiment is made. When e = 1, it becomes null, because 
the solution is only pure water. It becomes null again when e 
(A), 
(B)’ 
alizable at temperatures lower than 23°, at which (A) is negative ; 
because if (A) were positive, it would suppose that water were 
removed from the acid instead of pov added to it. Between 
is equal to — but this second value is only physically re- 
these extreme limits of e, the values of 7 are the ordinates of a 
parabola of the second degree, of which e is the abscissa, and 
which is represented in fig. 4, in the supposition of (A) being 
positive. The axis S H of this —. is parallel to the right 
line O Y, on which the ordinates ~ are measured from the origin 
13 
O; and it is distant from this right line by a quantity O H 
equal to 6B) (By The proportion of water e equal to this 
2(B) 
value is therefore that which, for each temperature, gives to the 
groups of water and acid the most energetic rotatory power, 
2 
whose expression is ion But it is easy to perceive 
that this relation does not correspond to a constant number of 
chemical equivalents supposed invariable. For the proportion 
(B) + (A), 1g B)— 
2(B) ° (B) + (A) 
of water which it gives being 
portion of acid is is the relation by 
