1877.] 



Magnifying -power of the Half -prism. 



29 



Dispersion = purity =(m M ~ I 4-m n ~ 2 + 



Total brightness of spectrum.. =h 1 . \(k* n -\-lc* n )c 



5. A train of n half-prisms diminishing followed by a train of n half- 

 prisms magnifying. 



Ereadth of spectrum-lines . . = 1 



Dispersion = purity = ( + — L_ + . . + — + l\w n A 



y m n-i m n-2 m J 



+ (tn,*- 1 + . . +m + l)A 



=2!^. A. 

 m — 1 



n , 



b 2 m t 



Total brightness of spectrum .. i (k^ n -\-'k^ n )c m -i . 



The second train of half-prisms in (4) and (5) may be placed between 

 the eye-lens and the eye, and will then conveniently replace the cylin- 

 drical magnifier. The prisms may in that case be very small ; their 

 dispersion, however, will not be magnified by the eyepiece, and they will 

 therefore add but little to the dispersion or purity. 



In fact if M be the magnifying-power of the vie wing-telescope, the 



dispersion would be (M + 1) m "~^ . and (M + 1) • A, and the pu- 



rity M+l m — 1 ^ , m ~} . a for (4) and (5) respectively. 



J M m — 1 m n M m — 1 V w .r j 



This is on the supposition that the second train has the same magni- 

 fying-power as the first. 



Now for the same brightness of spectrum, neglecting loss of light by 

 reflexion and absorption, we must have b 2 =.m n b l and b 3 = mb v the breadth 

 of the slit being increased to compensate for the decrease in the breadth 

 of the incident pencil. Where this is not practicable (as for star-spectra) 

 the train of "half -prisms magnifying" has the advantage of greater 

 brightness; and, as it gives at the same time wide separation of the lines, 

 it best fulfils the condition (1). 



On the other hand, for viewing the solar prominences, loss of light is 

 of little or no consequence, the important point being to have a strong 

 contrast between the monochromatic image of the slit (filled with the 

 light of the prominence) and the dispersed image due to the light of the 

 sky. Thus the breadth of the slit does not enter into the question, and 

 great purity in the spectrum is the chief desideratum. A train of " half- 

 prisms diminishing " is evidently by far the best arrangement ; but for 



