Aberration of the Concave Grating. 131 



For the lateral images S± to the right and left of the 

 central ones we have 



For B 



B S, 



^1 



15° 



30° 



60° 



e=K=-\- 5° 



±5° 



+ 5° 



+ 5° 



For Case D we must have 



sin i^ + sin 5° = sin ic + [sin (i^ + /c) = sin ( — ^d) ] , 

 from which we get for ^d to be used in (8a) 



s^ s^ s'^ s;; 



«D = 2c = 2^30' 7° 26' 14° 29' 25° 40' 



«+=^+D= 2° 30' -(2° 25'), -(9° 22'), -(31° 21'). 

 For the lateral images of Case E we must have 

 sin 2^ + sin 5° = sin (0 -}- /^') = sin ^e? 

 and therefore for e^ to be used in (8a) 



S' S'' W" S^" 



for e^=- 0° 9° 53' 24° 23' 51° 9' 



10° 2' 20° 15' 35° 58' 72° 24' 



i^=- 0° 0° 0° 0° 



The values of S^ and S^ are likewise the values of the 

 aberration at the centre and edges of a 10° field for Case F, 

 which therefore requires no separate consideration. 



Finally, for Case H we have a number of identical 



fields, S' S^^, each corresponding to a particular value 



of i^. Only one set of these is considered, i. e. the set S' for 

 which i — b°. The centres of these will lie at points Q^ de- 

 fined by the relation 



sin 5° = sin % — sin Q^. 



Hence for /h = 5° 15° 30° 60° 



0^=0° 9° 53' 24° 23' 51° 9' 



Also the two edges of this set S' will lie at points 



^H = sin"^(sin zh — sin 5° + sin 5°), 



for i^= 5° 



15° 



30° 



60° 



^+H= 5° 



15° 



30° 



60° 



6/-H=-5° 



-H 4° 51' 

 K 2 



19° r 



43° 46' 



