472 On Eliminating Errors of Adjustment, SfC [Feb. 24, 



middle of the slit. Let be the angle of incidence, which will be 

 half the angle of the prism, and the complement of either angle 

 A or B, 0' the angle of refraction, jx the index of refraction, b the 



base AB, I the length of path, LM + MN, of the ray within the glass, 

 p=JjN. In spectroscopic work it is the focns of rays in the primary 

 plane that we have to deal with ; and we get for the shortening (s) of 

 the focus, or, in other words, the distance by which the slit is virtually 

 brought nearer to the collimating lens, 



7 COS 5 



s=jp — L 



/jl COS 2 



But since MBL = 9O°-0 and MLC 9O°-0' we have 

 ^_^cos^0 _ also = Z cos (0—0') ; 



COS0' 



whence s=bl cos (0-0') ._^?_± \ ={ 



I COS JUL COS° J V fl/ 



where t is the thickness of a compensating plate which shall produce 

 the same shortening of focus. In the figure, the part of the prism 

 which is out of use is represented as cut away, to make the instru- 

 ment more compact, and EFGrH represents the compensating plate. 

 The faces CD of the truncated prism, and EF, HGr, of the plate, 

 of course need not be polished, and had better perhaps be blackened. 



In the figure I have taken 80° for the angle of the prism, and sup- 

 posed fL to be 1*52, which data give £=1 "22-55, nearly. A blunter 

 angle would have made the instrument a little more compact in the 

 direction AB, but I wished to avoid needless loss of light by the two 

 reflections that accompany the refractions. The size of the prism and 

 compensating plate must depend upon its distance from the slit, and 



