Aberration of the Concave Grating. 151 



view, i. e., from the standpoint of a oiven resolving-power. 

 As th(3 writer has previously shown "^^ the resolving-power of 

 a grating of any form may be stated without reference to the 

 ruling of the surface, in terms only of its aperture and total 

 spectral deviation of the diifracted ray. So expressed, we 

 have 



r=''- (sin«-sin(9), .... (65) 



or for the A type of mounting above considered, 



2W . . 

 r=-^s\m (6e) 



Substituting this in (54) we get 



r. _ V 4 sine _ yi 



V ra tang ^i V r (1 + 



■r--.- (67) 



coszj smz 



The general statement made in the previous paper (Astro- 

 physical Journal, vol. iv. p. 61) is therefore rigorously correct 

 only for certain values of i. It is, however, well within the 

 truth for the maximum values of i and r there mentioned, 

 viz., 2 = 10° and r = 30,000. For these values of i and r we 



get for /3max. 



ySmax= ^^-000387 ^ -073, 



or for the angular aperture at the principal focus o', 



A^2/5^ax.(l + cosi)^^ (for/<15°), 



which is even larger than the limit I3q= -p there imposed^ 



o 



The maximum linear aperture, however, must in this case not 



exceed 95 mm. (Wmax. = 48 mm.), if r is taken as 30,000 for 



X = 5500 tenth-metres, as before. 



Conversely, if we use a maximum angular aperture of 1/5 



at the principal focus, yS ^ "05, and we can, without injury 



to the definition, use a maximum resolving-power o'ja&x equal 



to 



4 



sin^ ^{1 + cos i) sin i 

 3200 

 ~ (1 + cosz) sin^^ 

 or for /=10^, as in the case just considered, 

 r„.ax-93,000, 



* Phil. Mag. vol. xliii. p. 319. 



(68) 

 (68 a) 



