786 Mr. F. Twyman on an Interferometer 



(a) Spherical aberration. 



" The marginal rays, or rays which pass through the outer 

 zones of the lens, do not meet the axis in the same point as 

 the paraxial rays/" 

 ib) Coma. 



" The linear magnification of a very small object, 'situated 

 on the axis of the instrument, is different when different zones 

 oil the instrument are used to form the image." Obviously 

 only a small angular field is here considered ; however, in the 

 case of photographic leuses, highly corrected as they are over 

 large angular fields, essentially the same definition obtains. 



(c) Astigmatism. 



"A thin pencil which is not homocentric, but diverges 

 from (or converges to) two focal lines is said to be astigmatic." 

 Here, similarly , one has in the case of photographic lenses 

 to deal with image-forming beams of large angular extent. 



(d) Curvature of Field. 



"In order that a plane object may give a plane image the 

 condition for flatness of field must be satisfied." Otherwise 

 the focal surface is said to have curvature. 



(e) Distortion. 



" The image is said to be affected by distortion when the 

 object (supposed te be a plane figure at right angles to the 

 axis of the lens) gives rise to an image which is not geome- 

 trically similar to itself." 



This classification of aberrations, established by the mathe- 

 matical investigations of von Seidel, Petzval, Abbe, and 

 Helmholtz, finds complete acceptance with practical opticians. 

 That such should be the case is a little surprising, for all 

 these investigations have been carried out on the assumption 

 that terms of orders higher than the third in the angular 

 aperture and field of view are negligible* — an assumption 

 which is certainly not justifiable in the case of camera lenses. 

 Furthermore, they have, of course, been arrived at by 

 the methods of geometrical optics, and on that account break 

 down entirely in cases where one is concerned with details 

 of definition approaching the^ ideal resolving power of an 

 optical system. 



Nevertheless, it seems that, broadly speaking, all observed 

 aberrations may be grouped for descriptive purposes in this 



* It is true that the sine condition has been derived by Clausius and 

 Helmholtz from more general considerations, based on the laws of 

 thermodynamics ; but we are here concerned, not with the conditions 

 necessary to secure freedom from aberrations, but witli the nature of the 

 defects of the image resulting from non-compliance with those conditions. 



