242 
Proceedings of the Royal Society 
Let us first find the conditions of a flat spectrum 8 = o. 
When 8 = o, v x = v 2 , and we obtain the conditions 
1_1 = 1 _1_^1 j _l^(l + COSa) 2 (l-l^ 2 (l“COSa))_^l j _l^ ^ 
° A ? 2 ~ b ~\ a+b ) 4 (/n — l) 2 (ju. + 1) sin 2 a \ a + 6 / 
from which f x and / 2 may be found in terms of known quantities. 
1 1 n ^ 1 
/ = a (1 " c) “ b C 
1 1 ,1 
? = 7 (1 + c ) H — c 
/* h a 
When a, the angle of the prism, is 60°, then 
3(4-V) 
c = 
16 (/*- 1) 2 0* + l) 
If we now make fi = 1*5 we find c = -5025, and 
i - ‘4975 -5025 
f x a 
1 _ 1-5025 
/, " & 
5 
•5025 
a 
19 
If a = — 6, the first lens may be dispensed with, and the second 
A 1 
lens will correct the defects of the prism. 
If a is greater in proportion to 5, a concave lens must be placed 
in front of the prism. The most convenient arrangement will be 
that in which the prism is placed in the position of least deviation, 
and the lens placed between the prism and the screen, while the 
distance from the slit to the prism is to that between the prism 
and the screen as 1 - c is to c. For quartz, in which ^=1*584 
for the ordinary ray, - = 2*53, so that the best arrangement is 
a = 1*53 6, or the lens should be placed on the side next the screen, 
and the distance from the slit which admits the light to the prism 
should be about one and a half times the distance from the prism 
to the screen. 
The following Gentlemen were admitted Fellows of the 
Society: — 
Rev. David Aitken, D.D. 
Robert M. Ferguson, Ph.D. 
