370 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
pression of [«], which is given by experiment, there will result 
— (ay 4 B)# 
whence we shall have 
(A) = — 117987 ; (B) = + 143154, 
Now, if we take z or = as the abscissa, [«] will be the ordinate, 
not of a right line, but of an equilateral hyperbola, having its 
asymptotes parallel to the axes of the rectangular co-ordinates 
of [a] and z, as represented in fig. 3, where the letter O desig- 
nates the common origin of these co-ordinates. The centre C 
of this hyperbola is placed at the point whose abscissa O X is 
x = — 1, and the ordinate C X, [«] = (A) + (B). Its summit 
S, consequently its most curved portion, corresponds to the ab- 
scissa O H, whose value is x = — 1 + (B), which gives, for 
the ordinate H S, [«] = (A) + (B) — “(B). We have therefore 
at this summit, 7 +1= 7 (B), consequently «= ran which 
determines the ponderable proportion of acid answering to it, 
which being only a function of the single coefficient (B), is, like 
it, independent of the temperature. By substituting for (B) the 
number 14°3154, which is its value in the rectilinear expression 
of [«], calculated for 100 millimetres, we deduce « = 0°2643, a 
value proveable by experiment. For this reason, having adopted 
this length to express [a] relative to the red ray which I have 
taken as type, I multiplied the experiments between the values 
of «, 0°20 and 0°34, in order to confirm the curvature of the 
hyperbola with full certainty. In fact, the values of [a] obtained 
in this interval being constructed graphically, manifest this curve 
in so decided a manner, that it is impossible to mistake it. And 
the course of the numerical values of [«] moreover proves this 
result with greater strictness; for, agreeing with the rectilinear 
relation, of which e or 
Pp = E is the abscissa, with an accuracy 
equal to that of the observations themselves, they are conse- 
quently incompatible with a similar relation, in which the ab- 
scissa is. The uninterrupted continuity of their variations, 
P 
conformably to the rectilinear or hyperbolic law, of which the 
it et it 
