Investigating Aberrations of Symmetrical Optical System. 509 



content myself with stating that for a central stop an axial 

 distance k in front of the first surface, the astigmatic 

 separation, i. e. the distance between primary and secondary 

 foci, is 



UDR-JFj + Z^DS-JQ-FR + LPj-A^FS-LQ)}/^^ 2 . 



(iii.) Distortion and curvature of field. 



If now the previous aberrations have been corrected and 

 the conditions D=0=F=J=L thus satisfied, the optical 

 system is point-to-point perfect for parallel light, i. e. an 

 infinite point source will produce a definite point image. 



The coordinates of this image are now given by 



f=-S/Q + n 2 (BS-QH)/2Q*, 

 r'=-rc/ZQ+n 3 B/2Q 2 , 



where n denotes the direction of the infinite object. 



For a flat field the ^-coordinate of the image must be the 

 same for every source at infinity, i. e. f must be independent 

 of n. 



The condition for this is BS — QH = 0. 



On the other hand, for absence of distortion we require 

 that the distance from the axis of the image-point be pro- 

 portional to the tangent of the inclination to the axis of the 

 infinitely-distant source, i. e. that f be proportional to n/l 

 for every infinite source. This requires that B = 0. 



The system is corrected for both curvature of field and 

 distortion if we have B = = H. 



In the uncorrected system Newton's form for the curvature 

 of the field gives 



2(r-?o')/r 2 = KBS-QH)n 2 /Q 2 }/{^ 2 // 2 Q 2 } = BS-QH. 



The distortion can be measured by (f — f ' ) /(n/l) = Bn 2 /2Q 2 

 to lowest order. 



For an optical system completely corrected for parallel 

 light the conditions are B = = D = F = H = J = L. 



These six conditions in virtue of the last identity in (18) 

 contain only five independent conditions, tallying of course 

 with Seklel's five conditions. 



The foregoing analysis makes attempt at no more than 

 outlining the method ; I hope to have subsequent occasion 

 to show its application, on the one hand to such theoretical 

 questions as discussions of the form of an uncorrected image, 

 and on the other to practical questions of optical instrument 

 design. 



Phil Mag. S. 6. Vol. 34. No. 204. Dec. 1917. 2 



