132 Prof. F. L. 0. Wadsworth on the 



Each of these fields lies to the left of the geometrical 

 (undeviated) image of the source which always corresponds 

 to S+. The first of these, S', for i^. = 5° evidently corresponds 

 exactly to the corresponding one for Case A-B. For each 

 field lying to the left there is a corresponding field lying to 

 the right, which it is also of interest to consider in this special 

 case. The centres of these right-hand fields lie also at points 

 defined by the relation 



or for iH= 5° 15° 30° 60° 



(right) 0H=1O°2' 20° 15' 35° 58' 72° 24' 



The edges of the right-hand fields similarly lie at points 



0H = sin~^ (sin i^ + sin 5° + sin 5°) , 



or for different values of ig- 



(right) 0+H= 4° 15° 30° 60° 



0_2=15° 10' 25° 40' 42° 24^ — 



For 0+B. the aberrations may be computed by (27a) ; for 

 all other points they must be computed by the general 

 formula (8). 



The values of the relative aberrations Za/K Zh/K for a 



grating of semi-angular aperture /3 = "01, and for the dif- 

 ferent fields S' S\^ above considered, are tabulated in 



Table II. For each point there are in general two values of 

 Z, Zi, and Zg, as already defined, which are tabulated sepa- 

 rately, although in most cases we are concerned only with 

 the maximum (numerical) values of Z, which for positive 

 values of /3 (right hand of grating) is always Z^ except for a 

 few cases which may be noted in the table. 



Comparing the relative aberrations in any field for these 

 different cases we see that the most advantageous type of 

 mounting for an objective concave-grating spectroscope is 

 A, for w^hich ^=0 for Sq, the centre of the field. This form 

 is particularly advantageous for large values of Nm\, i, e. for 

 large angles of diffraction, because, as shown clearly both by 

 (10) and (16) and by the table, the aberration both at the 

 centre of the field and at the edges decreases with increasing 

 values of i. With all of the other mountings, and wdth the 

 Rowland mounting as well, the aberration increases with 

 increasing values of i. 



Comparing the aberrations of the concave grating when 

 used as an objective spectroscope with the aberrations of the 



