AND DISPERSION IN ICELAND SPAR. 
433 
Then by substitution in the formula 
sin PML = 
sin PL 
sin PM 
(5) 
we obtain P M L. 
If we call P M §, and the angle P M L y, we have for the four prisms respectively 
Table VIII. 
Prism I. 
II. 
III. 
IV. 
s 
22° 53' 23" 
14° 23' 11" 
25° 23' 36" 
13° 26' 29" 
X 
0° 13' 35" 
0° 29' 41-7" 
0° 7 31" 
0° 9' 57" 
We shall now prove that in the case of prisms I., III., and IV. we may neglect the 
inclination of the plane of the prism to the plane z x. For S being the optic axis, N 
the point in which any wave normal meets the sphere, M the intersection of P Q and 
z O x. 
Let 
NS=(9 NM=i fj 
SM=X SMN= X 
we have 
cos 0= cos X cos xfj-\- sin X sin xjj cos y 
y 
= cos (X — xjj) — 2 sin X sin i jj sin 2 ~ 
Li 
— cos (X —r jj)—x say 
cos 2 0= cos 2 (X — \fj) — 2x cos (X — xf/j 
neglecting x 2 
This we may do, for x z is <(’004) 4 
1 
2 
cos 2 6 
sin 2 6 
0 
/V 
cos 2 (X— xp)-\-2x 
cos (X —i fj) 
In neglecting the mutual inclination of these planes, i.e., in putting y = 0, we omit 
1 
