16 



Mr. W. H, M. Christie on the 



[Mar. 1, 



Thus the two forms of compound prism may be considered together ; 

 but there is this important distinction, that the refraction at the outer 

 surface of the crown corrects irrationality of dispersion in the direct- 

 vision prism, since the angle of refraction is greater for the red rays, 

 whilst in the ordinary compound prism the irrationality is greatly 

 increased. At the same time the refraction at the outer surface of the 

 crown slightly decreases the dispersion for the whole spectrum in the 

 direct-vision prism, and slightly increases it in the other form ; but this 

 effect is produced in the latter case by spreading out the violet rays, and 

 in the former by bringing them closer together, the dispersion for the red 

 rays being about the same for the same angles of refraction in the two 

 forms, as will be seen more clearly when an actual case is taken. Thus 

 the apparent superiority of the ordinary compound prism turns out to be 

 illusory, being gained by inequality in the scale ; and this is aggravated 

 by corresponding loss of light for the violet rays, as the deviation at both 

 refractions is greater than for the red rays. On the other hand, both the 

 scale and the loss of light are equalized throughout the spectrum in a 

 properly constructed direct-vision prism, which is therefore, indepen- 

 dently of its practical convenience, the best form of compound prism for 

 general use. 



Compound Prism. — "We have here 



sin (j> = fx sin ; ll sin \p=Li sin \p' ; sin x — A 6 ' sul X > 



f + f = a; f+x'«0; D = 0- x -a+/3; 

 the deviation D being considered positive when the pencil is bent from 

 the refracting edge of the flint prism. 



1. Magnifying-jpoiver. ll, ll being constant, 



m= *X - ¥ , W m H \ h' t h CQt j x ^ i x CQt f x _ lx cot X 

 <ty ' ty' ' ty' ' cty ' ^x' c °t 0' c °t $ c °t x 



_ cos <f> cos \p' cos x ,J Ll m "m'" 

 cos (f>' ' cos \p ' cos x m> ' 



where 



/ COtd)' COS (b' n cotxb' LL COS \L' n, cotx' »cosv' 

 COt (j) COS (p cot \f/ Ll cos \p cot x cos x 



2. Dispersion. — Taking logarithms and differentiating, ll and ll being 

 now variable, 



to« *± tan a + 52^4 V; ^Ytan++ 



1 LL T COt</> \it p J QOt^ 



01 s 



where 



X Li X ^COfc X X ' 



fy^A'+m'fy'; ^-A"4-^'^'; tx sss *'"+* n '"h't 

 A'=Mtan'f A'' = (^-^W, A'"-^tan x , 



