128 Prof. F. L. 0. Wadriwortli on ike 



The t'linctions 



^'^^^'-^o^^e -'[ . , . . (24) 

 /: ((9) =6^ sin (9 =e,J 



which appear in (21) and (22) have l)een computed for the 

 same values of 6 as have ah'eady been used for i in 



/i(0 fS)' The results are oiven in columns 7, 8, and 



*9 of Table I. 



(F) When 6 is very small expressions (21) and {2T) re- 

 duce respectively to 



w.= |cos6', (25) 



and Zp = + p sin^/8 tang 6 



-f ^ sin'yS sec^^^ [1-9 tang26>] . . . (26) 



These expressions may also obtained from (6 a)* and (14) by 

 putting z = 0. It is very nearly the same as (18) for small 

 values of i. When the angle of incidence is nearly normal 

 to the grating Cases B and C may therefore be considered as 

 practically identical ^vith Case F. 



(G) Finally, let 6= -\-i. This is the case of specular re- 

 flexion. The aberration at the central point in the field, i. e. 

 in the undeviated image of the source of light, will be given 

 by the expression 



ZG.= +/osin^^sm6'+^sin'/9(l--9tang^6>)cos6>, . (27) 



which is identical with (10) with the exception of the re- 

 versed sign of the first term. For the special case = i = 

 we have 



Zg=|sm';8=|sin'A .... (28) 



the well-known expression for the aberration at the j^rincipal 

 focus of a spherical mirror. 



(H) When the spectral image is situated at a distance k 

 from the undeviated image the aberration will be found, as 

 in Case D, by substituting in (8) the value 



* See p. 126; footnote. 



