216 ON THE THEORY OP THE MICROSCOPE. 



image outside the central portion of the field, and in particular 

 that peculiar kind of chromatic fault which, although it has 

 nothing to do with the chromasy due to focal differences, has 

 been hitherto interpreted as an indication of it. 



This class of anomalies affects exclusively the constitution of 

 the image outside the centre of the field. The perfection with 

 which the rays unite in the central region, and therewith the 

 maximum capacity of performance, depends on the contrary 

 -entirely on the real aberration spherical and chromatic, as 

 commonly understood. A closer analysis of these yields the 

 following results. 



(i.) Chromatic aberrations, as they shew themselves where a 

 large angular aperture is used, do not depend alone on those 

 ■differences of focus which affect the image-forming beams as a 

 whole (in accordance with the phenomena of dispersion of colours 

 and their un-uniform course through crown or flint glass) ; but also 

 quite as much in an unavoidable inequality of coincidence 

 of colours of variously inclined pencils of rays within the angle 

 of aperture, which manifests itself in this, that an objective which 

 is perfectly achromatic when direct illumination is used must be 

 more or less over corrected for use with oblique illumination. 

 Although the first mentioned ordinary form of colour dispersion 

 (primary and secondary) may be entirely removed or rendered 

 scarcely noticeable, the last named source of chromatism cannot 

 be counteracted or removed by any known material or any known 

 technical treatment. Its influence is such, moreover, as to set 

 limits to the attainment of perfect action (at least in objectives of 

 middle and moderately high power) before their action would be 

 affected by other unavoidable sources of error. According to 

 Professor Abbe's experiences the actual performance of objectives 

 whose focus ranges from 6 mm to 3 mm (Jth to |th) falls in 

 consequence of this defect far below what might be attained so 

 far as the possibility of correcting spherical aberration by 

 appropriate technical means is concerned. 



(ii.) Spherical aberration on a stricter examination of its causes 



