Aberration of the Concave Grating, 129 



Making use of the quantities a, a^^ «!, />, ^j, c, e^ and ^j, 

 already computed, and putting the quantity 



,Vpsin^;S = K, 



a constant for any given grating, we may write the expres- 

 sions Zo Zh as follows : — 



Zo=-Kao (11a) 



ZA=+Ka (10a) 



ZB,= -K(a, + sin2,^) (15a) 



ZB = K[-4ai-^^+a(l-6tang2/i;)sec2A:] . (16a) 



Zn = 



ZE=K[-^^^^^+.^ao-M)] (22a) 



rj ^r( Stano/c 2c \ ,^„ . 



\ sm co^^kJ ^ ^ 



Z. 



sin.;8 



=K-^£-^^^) (^^«) 



For Cases D and H, in which we must use the general 

 equation (8), we may write 



r 4 sin 6 cos i cos i-V cos ^ "j 



I _|. — ^ — — - — [cos^i — (cos ^ + 2cos i)^tang'^^] I 



By means o£ the general formulae (8a) ... (27a) and the 

 aid of Table I. we can readily compute the aberration of the 

 concave grating for any form of mounting, and for any given 

 point in the spectral held. In order to compare the efficiency 

 of the same grating mounted in the different ways above 

 discussed, the aberrations Za . . . Zh have been computed for 

 twelve different points in the spectral field for a grating of 

 the semi-angular aperture (/3 = *01) generally used. Four of 

 these points correspond to the images formed on the axis of 

 the grating for i = 5^, i = 15°, z = 30°, and i=:60°, of mount- 

 ing A (or Aq), and are designated by the symbols Sq', Sq", 

 Sq'", and So^^ respectively. Eight others correspond to the 

 spectral images which lie 5° on each side (/c=+5°) of the 



Flul Mag. «. 6. Vol 6. No. 31. July 1903. K 



