360 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
n evidently represents the multiple of water associated with the — 
acid. Thus its value should always be positive like those of © 
1—eand of «. Eliminating therefore the latter by its expres- _ 
sion in », the function considered becomes . 
AE LT DN a DN a NR He 
[100 — b(n + 1)] [1 + 28,]’ 
or, on developing the denominator, 
n 
100 — b + [(100 — 4)8, — d] n — 50, n™ 
On differentiating it in this form, relatively to », we find, as 
the condition of its maximum, | 
0 = 100 — 8 + 58, n2, 
whence 
6 —100, 
b8a37 
and as, by the hyperbolic relation, we have 
n=-+ 
i 
ATi jeg oe 
there finally results, 
ieee b — 100 
~ ' Wb[6—100—a']’ 
an expression which contains only the constants of the hyper- 
bolic relation proper to each temperature. 
For the temperature of 6°'8 I found, at page 134 of my me- 
moir, 
a = 55 a= — 138°0875, b= + 302°7003 ; 
these numbers give 
2 = 0°6311), 
consequently 
— = 061318: 
n+1 
The value of ¢ exceeds a little that at which the solution might 
remain liquid at the temperature under consideration, for, at the 
temperature of 8°, I found as the limit of the liquidity -=0°548134, 
as will be seen at page 139 of my memoir. Thus, in all the 
physical phases, in which such a system may preserve the per- 
manent state of liquidity, the action of the acid to contract the 
water added to it, decreases in proportion as the relative quan- 
