of Edinburgh^ Sessio7i 1863 - 64 . 253 
in terms of the optical constants;* but if the optic axes lie in the 
plane ca, we have also, 
tan '^ 0 ) = 
{a - hf (a 
(b - cf (b 
7)v/3)V 
Cx/3)V 
- b'‘^ 
(a — by (a — bV dfd {b - cf (b - cV ‘dfd^ ’ 
which is a relation between the optical and crystallographic con- 
stants. 
Similarly, if the optic axes lie in the plane ab, and b'cd be in 
descending order of magnitude, 
(b - cj (b - cs/^fa? (c - ay (c - as/^y¥ ’ 
and if the optic axes lie in the plane be, and cab' be in descend- 
ing order of magnitude, 
(c - ay (c - adSyb^~ (a - by (a - bs/lyd ' 
27. A serious objection may be made to formula such as the 
above, expressing relations between a' , b' , c, and a, b,c. 
In the formula 
(a-by(a-bs/Syd 
_ ^,2 - 
for instance, the left side of the equation is a function of the wave- 
length. 
But since a, b, c depend only on the angles between the faces of 
crystals, which are of course invariable, the right side of the equa- 
tion is independent of the wave length. 
The only way of overcoming this difficulty appears to be by sup- 
posing that the apparent angles between the faces of crystals of 
the prismatic system, as determined by the reflective goniometer, 
may vary with the kind of light employed. Some experiments 
The measurements of Kirchhotf {Ibid.) have shown that this formula 
agrees closely with observation in the case of Aragonite. 
Also, if a'= V the crystal becomes uniaxal, and the optic axes coincide witli 
axis c ' ; hence tan '^co ought to vanish when a'= h' . 
If h'= c' the optic axes coincide with axis a' ; hence tan ought to be- 
come infinite when V— c' . Fresnel’s expression fulfils these conditions. 
