196 CALIFORNIA ACADEMY OF SCIENCES [Proc. 4th Se». 



the point of refraction of this pencil, with the corresponding^ 

 oblique axis to locate the principal points of the image and 

 connecting these principal points produces the distorted shape 

 of the chief image shown in the figure. 



In the same way the comatic and astigmatic image can be 

 located. These two extreme images represent the extreme 

 aberration. The same method would enable one to locate 

 the images produced at any point along the lens surface and 

 they would all be intermediate between the extreme images 

 and the chief image. 



The reasons for designating these two extreme images 

 "comatic" and "astigmatic" is given in "Science", vol. 

 XLVIII, pp. 459-460. 



The distorted shape of the chief image is due not to dis- 

 tortion but to curvature, the former aberration not appearing 

 at all in the simple case of refraction at a single surface. 



Axial aberration can be appreciated by conceiving the legs 

 of the A extending to the optical axis when the corresponding 

 legs of the astigmatic and comatic images will coincide at 

 points considerably further from the lens than the legs of the 

 chief image, the amount of difference being the longitudinal 

 axial aberration. 



