1877.] 



Magnifying -power of the Half-prism. 



27 



and 



If we make/ 2 =— f so as to equalize the two cylindrical lenses, we 

 have M' = _(m' - 1) 2 . ?, Thus if 



M'= 9|; mW^nd/^-/^/; 



M'=25|, m' = 6, and f=-f 2 =&f 



Taking 1 inch as the equivalent focal length of an ordinary eyepiece, 

 we should get in the perpendicular direction magnifying-powers 9 and 25 

 times as great with cylindrical lenses of | and ^ inch respectively. 

 There would probably be no difficulty in applying such lenses. 



We shall see, however, that one or more small half-prisms placed be- 

 tween the eye-lens and the eye would answer the same purpose, with the 

 advantage of increasing the dispersion ; and this arrangement appears to be 

 decidedly superior to a cylindrical^eyepiece. 



We may now find expressions for the angular breadth of the lines, the 

 dispersion and the purity of the spectrum in the different cases, as well as 

 the quantity of glass used for the train of prisms and its total thickness. 



Let p= number of whole prisms. 



n= number of half -prisms. 

 m— magnifying-power of each. 

 2A= dispersion of each whole prism. 

 Q= quantity of glass in the smallest half -prism 

 of the train. 



t= thickness of glass in the smallest half -prism 

 of the train. 

 b v 6 2 , and b 3 = breadth of slit in the three cases. 



1 — g— coefficient of absorption per unit of thickness. 

 l — 7c 1 and 1 —^ 2 = proportion lost by reflexion in passing through 

 one half -prism of the light polarized in and 

 perpendicular to plane of incidence. 

 1 — Tc x and 1— k 2 = similar quantities for a whole prism. 



1. Half-prisms magnifying. 



By what precedes it will be clear that each half -prism in the train 

 will magnify the angular separation of two pencils falling on it, whether 

 coming from the two edges of the slit, or corresponding to two lines in 

 the spectrum (such as the two D lines). Thus the breadths of the two 

 D lines will be magnified in the same ratio as their separation, due to the 

 dispersion of the preceding prisms, and to this will be added the disper- 

 sion proper (as distinct from the magnifying-power) of the half -prism 

 itself. 



