358 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT ’ 
lues at the temperature of 6°8, I found in the memoir cited that — 
the density 8,, thus calculated for the state of disaggregation, is 
lower than that of the solid crystallized acid only in the relation 
of 57 to 59. 
Whatever it may be, as it is one of the terms of the hyper- 
bolic law, it may be taken numerically as a starting-point, and 
all the other densities derived from it according to the corre- 
sponding values of «. With this view I take the expression of 
the constant a! in function of 8, by the preceding relation, and 
substitute it in the general expression of the density 8, which I 
shall henceforth call 8,, in order to call to mind that it is calcu- 
lated in the hyperbolic law. I thus find 
Ol + ey OA) 
7><76D ef os" ee Cee (a.) 
Now, I take the expression of the density § by deducing it from 
8, by the law of simple mixtures, and represent it by 2,,, in order 
to distinguish it from the preceding. The equation (2.) of § 39 
being applied to this case, with §, = 1 gives, as we have already 
seen in § 42, 5 
8 
&= 8, 4+ 
— 1 e 
sara, wea 
thence we easily derive 
jo ES) Ge) 
Sin = OF ea 1 — aa ° * . . (d.) 
On subtracting this expression from that of $,, the result is 
b 8, 
oe et) sf HS LAT (l— xa} 
and on reducing to a common denominator the factor included 
within the parentheses, 
(1 — «)e (8, — 1) [6 + (100 — 4)3,] 
(100, — 8) [e + (1 — «) 8, ] : 
Now, the equation which determines 8, gives 
(100 — 4)8, = 100 —b +d’, 
a, —s Om == 
whence 
b + (100 — 4)8, = 100 +a’; 
consequently 
ra (1 —«)e (8, —1) [100 + @] 
=~ (008 2) [s + (1 — 2) oma (¢.) 
From the nature of the physical problem, the ponderable pro- 
