30 



Mr. W. H. M. Christie on the 



[Mar. \ 3 



convenience in delineating the prominences, a cylindrical eyepiece or a 

 train of half-prisms magnifying (between the eye-lens and the eye) must 

 be used. 



Such a combination is also suitable for spectrum-analysis, where a 

 bright-line spectrum has to be distinguished from a continuous spectrum 

 forming the background. Thus with this arrangement the sodium lines 

 in the flame of an ordinary paraffin candle are seen with great brilliancy. 



In general, however, a combination of wide separation, purity, and 

 brightness is required ; and here we must take the values for b 2 and b 3 

 given above in terms of b v 



(1) and (2) give the same purity % 



(3) gives the purity 2p 



m — 1 m n b 1 

 1 A 



6, 



If we take the same number of half -prisms in the three cases, 2p = n ; 

 and (3) is superior in this respect to (1) and (2), the purity being pro- 

 portional to 1 + 1 + 1+.. to n terms and to 1 + — + — + . . to n terms 



m m n 



in the two cases respectively. 



But as the practical question is how to get the best result out of a 

 given quantity of glass, we should divide the purity by the quantity of 

 glass, and thus we get the ratio for what may be called the efficiency, 



and 



b 



"L+l . h A £or (!) and ( 2 ), 

 1 m n + l m n \ w v ' 



1 



Hence 



E 3 m M + l m n + l 



which shows the advantage of the half -prism train, m being greater than 1. 



On the other hand, there is a small additional loss of light at the per- 

 pendicular faces in the half -prism train amounting to 6 or 7 per cent, 

 for each half -prism ; but as not more than three, or at the most four, are 

 ever likely to be required, even for the sun, this loss is hardly sensible. 



As regards the thickness of glass, the ratio of purity to thickness of 

 glass is the same in all three cases, viz. : — 



j_ A 1 

 m n ' b t 



"We may consider one other point, viz. the effect of error in the 

 surfaces and of unequal density in the glass, though the question is a 

 very obscure one. An error in the surface being equivalent to a slight 

 deviation in the incident ray, its effect will vary as the magnif ying-power ; 

 and thus with the train of half -prisms magnifying, the errors of the half- 

 prisms are magnified in proportion to their distance from the end of the 



