812 Tramaetio7is of the Society. 



XXXVII. — On Neiv Methods for Improving Si^lierical Correction, 



aj)plied to the Construction of Wide-angled Object-glasses. 



By Professor E. Abbe, of Jena, Hon. F.R.M.S.* 



(Bead llfh Jane, 1879). 



The correction of spherical aberration, in dioptric systems of all 

 kinds, is based on the much-applied principle of compensating one 

 deviation by an opposite deviation of the same kind. The positive 

 aberration of the collective (convex) lenses of any system is balanced 

 by the negative aberration of dispersive (concave) lenses. Besides 

 this method there can be no other, as long as practical optics is 

 confined to spherical surfaces. 



Though this principle might be applied in various ways, one 

 only has hitherto been adopted, which may be called the method of 

 allied corrections. Spherical correction is always effected by con- 

 cave lenses of the higher dispersive material (flint-glass), which 

 are used for getting rid of the chromatic dispersion of the positive 

 (crown-glass) lenses. The combmation of a concave flint-lens 

 with a convex crown-lens (generally cemented together) is the 

 means of effecting both corrections at the same time, without being 

 obliged to treat each separately. But of course it is not at all 

 necessary that those binary lenses should be corrected, even ap- 

 proximately, in themselves. In the case of compound systems, as 

 microscopic objectives generally are, one part of the system may be 

 considerably under-corrected in each respect, provided it is balanced 

 by an opposite deviation in the other part of the system. 



The circumstance mentioned here — the possibility of correcting 

 both aberrations by the same elements, appears to be a great advan- 

 tage in the construction of objectives ; and from one point of view 

 it is in fact so, as it saves the unavoidable complication of separate 

 concave lenses for spherical correction, in addition to those which 

 are necessary for achromatism. But, on the other hand, this com- 

 bination of the two corrections is the origin of a very serious defect, 

 which becomes especially obvious in wide-angled systems. The 

 amount of spherical aberration which is introduced by a lens of 

 definite curvatures depends on its refractive index. Now the re- 

 fractive index varies with the colour of the rays in both kinds of 

 lenses, but in the flint the increase of this index, say, from red to 

 blue, is much greater than in the crown, which is of course necessary 

 for chromatic correction. In consequence of this the negative 

 aberration in any optical system increases more rapidly from. red to 

 blue than the positive, and it is therefore impossible to obtain 

 simultaneously the correct balance for different colours, _ If the 

 compensation is got for the red rays, the negative spherical aber- 



* The original paper is written by Professor Abbe in English. 



