I 



Aherration of the Concave Grating. 137 



readjustment of the focus u in the objective type of mounting, 

 it is interesting to note in passing that since the aberration 

 at the centre of the field (^=0) is of the opposite sign for the 

 regukir Rowland mounting and the A type of O.S. mounting, 

 there is a certain value of ?<, which we will call u' , inter- 

 termediate between the values p (for the Rowland mounting) 

 and the value 



for the A-O.S. mounting, for which the aberration will 

 vanish. We can find this value if we desire by equating 

 the last term of Glazebrook^s general equation (3)* to zero. 

 This together with the second general equation for the focal 

 curve of the grating for this case fj ?. e., 



u'= ^ .... (32) 



1+ cos i— — C0S^2 



gives us tw^o equations from which to determine u' and v, the 

 two conjugate spectral focal distances, so as to satisfy the given 

 condition of zero aberration at the point u' for any given 

 value of I. This solution is not of general, but may become 

 of special interest in some individual cases. 



2nd. Effect of diaphragming a portion of the optical 

 surface or limiting the field of the instrument. 



Several effects may be here discriminated, but they may 

 all be best investigated by considering the character of the 

 aberration in the lateral fields more in detail. This may be 

 most conveniently done by expressing the aberration at a 

 point S+K in terms of the aberration Zq at the centre Sq. For 

 cases A-B and F we see from equations (10), (16), and (17) 



ZB = ZAr-4tang«^ :+ sec^/cri-^tang^/c)"! (33) 



[_ ^ sm/5cos^ ^ ° ^J ^ ^ 



or 



zl=^- 



1 



cosz 



By aid of the Tables already computed for h and 



(Table I.) the values of the ratio R has been determined for 

 seven intermediate points {K = b' to a: = 3°) in each of the 



* Loc. eit. p. 379. 



t See Astrophysical Journal, vol. iii. p. 55. 



