77 
crystallized bodies on homogeneous light. 
would appear to an eye immersed in the medium, a plate may 
be conceived cut in such a direction as to make their apparent 
centres coincide, in which case the tints immediately about 
the poles will coincide with Newtok’s scale, and the extra- 
ordinary image will totally disappear in the pole at an azi- 
muth 45 °. This condition gives 9 = o, 9 — l a + l <p =±= o, 
whence ( supposing R, R 7 the indices of refraction for extreme 
red and violet rays and £R = R 7 — R) we find 
la=l<p = — tan <p 
The angle <p however becomes imaginary, and this method, in 
consequence, inapplicable when the separation of the extreme 
axes (7 a) is greater than the maximum dispersion of the co- 
lours of an intromitted white ray, that is, when 
* tR 
d a > — 
RVR 1 -! 
Let us resume our equation (b), and supposing the form of 
the function \J/, and the constants a , k, k\ R and d'R ascer- 
tained, let the angle 9, at which the coincidence takes place 
be observed, and the value of la will then become known. 
If we suppose it small, which it is in the generality of crys- 
tals, we get 
la 
k — k' 
k' 
.4/— S in<p.4/ + ji + li} 
d 4 dj, 
d9‘ d 9 
( C ) 
(4/ being put for 4/ (9, 6') for the sake of brevity). At inci- 
dences nearly perpendicular, l<p may be neglected, and the 
expression reduces itself to 
(d) 
l a = 
k — k' 
d 4” £? -vp 
d 9' 
d 9 
The comparison of these formulae with observation, which 
