764 On the Resolving Power of a Spectroscope. 
the dispersion is not nearly so great. This latter is the case 
in which very wide slits may advantageously be used. 
The corresponding equations in the case of a prism are : — 
A6 _ cos r' cos <b __ B 
A0 
8/ju 
cos r cos 
sin a 
cos 6 cos r 
A = 
Sill a 
~B' 
d/Jb 
V dfi 
B oVk 
cos r' cos <£ dX 
where //, is the refractive index and the other data are 
explained by the accompanying figure. 
Occasionally the question of purity may not be the most 
important one. It is notorious that the focal length of the 
telescopes usually furnished with spectroscopes is almost 
alw<ays much less than it advantageously might be. In a 
particular single-prism spectroscope which I have in mind, 
the sodium lines (DiD 2 ) are only just separable when the 
prism is in the position of minimum deviation. This is simply 
not owing to a lack of purity, but because the ultimate images 
are so close together that it would be impossible to detect 
intermediate images (with the telescope provided), if such 
existed, because the separation is below the minimum visible. 
By turning the prism so as to increase the angle of emergence, 
the dispersion becomes so great that in spite of the simul- 
taneous increase in he breadth of each line one would easily 
detect several intermediate lines. 
