12 Mr. W. H, M. Christie on the [Mar. 1, 



Taking these three cases respectively, we have 



i. ty = 0; A=mA' + A",n=??i'(n' + n"). 



ii. ty'=— 3^ = 0; .-. o^ = A' = m'n', fy = A" = wi"n", and £D= A' + A" 



==m'n'+m"n". 



iii. £0=0 ; .*. S0= - angle through which the prism is turned = 0. 



Then 0= m " A ' + m ' A " _ ^A' + A" _ A _ m n 

 m" — m' m — 1 m — 1 m — 1 



In the second and third cases the scales of the dispersion and purity 

 are variable, and are given by (i) for the part of the spectrum under 

 examination on substituting the corresponding values of <p, 0', xp, \p' in 

 m'j m", A', A". 



The three forms of simple prism which we have specially to consider 

 are : — I. Half-prism magnifying ; II. Half-prism diminishing ; III. Iso- 

 sceles prism. 



I. Half-prism magnifying. 



1. Magnifying-power . . ???.,== — = ^*fr , since and </>' = and m'=p. 



2. Dispersion A, = A"=^tan \p=m l ty tan ty, since A=0. 



3. Purity II, = fyz tan xp'. 



II. Half-prism diminishing. 



Keeping <j> and </>' as the angles at the perpendicular face, which is now 

 that of emergence, and taking m n , A ;/ , and II „ as the values of the magni- 

 fying-power, dispersion, and purity in this case, we have : — 



1. Magnifying-power m n =— = — — on and m" being interchangec 



2. Dispersion A, = — A" + A'=— = — . ^ta,n\L=du tan \b\ 



r m t m t **m t jj, ' T 



since A' =0. 



A, 



3. Purity II /; = — = A,= m t U= ^ tan \p=mfafa% ^ . 



m, 



III. Isosceles prism. 



1. Magnifying-power . . m iu =l, since and m'=m". 



2. Dispersion A,„= A' + A"=2 ^ tan \p=2m' Bp tan 



3. Purity n //y =A /// =2A / . 



