Methods for Imp'oving Spherical Correction. By Prof. Ahhe. 813 



ration of the flint lenses will be in excess for the blue ; and if it is 

 got for the blue rays, this negative aberration will be in defect for 

 the red. The system, therefore, will be either spherically over- 

 corrected for the blue or under-corrected for the red. Binary lenses 

 especially increase this discrepancy to a great extent, the negative 

 aberration in this case arising from the concave surface in which flint 

 and crown meet together. This negative aberration therefore depends 

 on the small difierence of the refractive indices of flint and crown, 

 which difierence must of course vary from red to blue to a much 

 greater extent than the refractive indices themselves, relatively. 



The residual aberration considered here — "chromatic difierence 

 of spherical aberration" would be the correct name — is readily 

 observed in any kind of dioptric system, Telescopes or Microscopes. 

 The visible result of which must be (as may be easily demonstrated), 

 a characteristic discordance of achromatism for the various zones of 

 the aperture of any objective ; if the central part of the aperture is 

 well corrected chromatically, the peripheral zone must be over- 

 corrected, and if the marginal rays afibrd the best possible achroma- 

 tism the central rays must be under-corrected. This derivative 

 defect of colour-correction must rapidly increase with increasing 

 aperture, as it owes its origin to spherical aberrations (which vary 

 with the square of the angles), and therefore becomes especially 

 visible in such wide-angled systems as are used with the Microscope. 

 Every attentive microscopist and optician will be familiar with 

 its appearance in microscopic objectives, which always reveal a 

 considerable difi'erence of achromatism, in their performance with 

 central and with obHque illumination. If an objective has the best 

 possible colour-correction in the central part of its aperture (direct 

 light yielding the secondary colours only), obhque light will show 

 broad borders of yellow and blue on the outlines of the objects — the 

 indication of chromatic over-correction of the marginal zone; and 

 if the primary colours have been obhterated for the marginal pencils 

 (rose or violet and green remaining only with oblique light), central 

 illumination will give deep tints of red and blue on sensitive pre- 

 parations such as organic tissues or the thick ribs of diatoms.* 



These results of residual spherical aberration are of great prac- 

 tical importance. As they cannot be eliminated by the means 

 hitherto appUed, they represent an universal defect in microscopic 

 objectives. Owing to this defect the performance of the best 

 glasses is not equally satisfactory for every kind of work. An 

 objective which has been corrected chromatically for central hght 

 will sometimes afibrd a well-defined and colourless image on 



* This description will hold good for the central part of the field of vision 

 only ; for outside the axis the phenomena in question may be totally concealed by 

 the much coarser chromatic effects arising from difference of amplification for 

 different colours, which is never absent in wide-angled objectives. 



