122 



Prof. F. L. 0. Wadsworth 071 the 



in the primary plane are shown in fig. 1, in whicli i = the 

 anole pac =the anole of incidence; ^ = an<>le cao^ = ano\e of 



iiff'racti 



on: ?/ 



ao'= focal distance from grating to primary 



Ficr. 1. 



f 



image; p = ca = radius of curvature of the spherical surface, 

 and y3 = angle ?)ca = semi -angular aperture of surface at the 

 centre of curvature. 



In investigating the aberration at the primary focal point 

 0' we shall follow, with some slight modifications, the method 

 adopted by Lord Rayleigh in his paper " Aberration of 

 Lenses " *, and also followed by Glazebrook in the paper 

 already referred to. Let ah, h'Ji be instantaneous sections 

 of the plane wave-front incident at the central point «, and 

 the extreme left-hand edge of the grating aperture. Then 

 the relative retardations of the central with reference to the 

 extreme edge rays at the focal point wdll be 



Zi = u — (Iw' -\-bh) for the right-hand half, 

 Z2 = H-(&V-aA0 ,, left „ 



From the geometry of the triangles hao'j hah, and hac we 

 find for ho' and hh 



V 



ho' 



= ,.y/?^2 + 4^2 sii,2| „4^,,sii,|gii,|^| ^0J 



{u—p sin/3sin^)^-psin^/3cos 6{u — p cos 6) + ^sin*/S(/3 — ?/ cos 6), (1) 

 * Phil. Mag. vol. ix. p. 40, .Tan. 1880. 



