On Improvements of the Microscope. By Prof. E. Abbe. 21 



of view, introduce considerable changes in the fundamental treatment 

 of dioptrical problems, and are calculated to open up in different 

 directions paths for the deyelopment of optical instruments which haye 

 hitherto remained closed. 



As regards the Microscope, an endeavour has been made to obtain 

 improvements with the help of these materials through the workshops 

 of Zeiss, the author having undertaken the necessary theoretical in- 

 vestigation. The following is a notice of the aims at which this research 

 was directed, and the results to which it has led. 



Objectives. 



By judicious use of the new glass-fluxes, and particularly those 

 which have been produced by the aid of phosphoric and boric acid, 

 together with silicate glass of different compositions, it is possible to 

 remove two important defects in regard to objectives, which have 

 hitherto placed insuperable obstacles in the way of the further perfecting 

 of the Microscope, since they could not be overcome with the means 

 hitherto available. 



Complete achromatism has always been unattainable on account of 

 the great disproportionality of the dispersion at different parts of the 

 spectrum, which is peculiar to the ordinary crown and flint glass. In 

 the best objectives it has not been possible really to unite more than two 

 different colours of the spectrum ; the inevitable deviation of the rest — 

 the so-called secondary spectrum — always left coloured cu-cles of dis- 

 persion of appreciable extent and intensity. Besides this, it has been 

 impossible with the glass hitherto available, at least with types of con- 

 struction which could be used in practice, to correct the spherical 

 aberration for more than one colour. With all objectives, when the 

 spherical aberration has been removed as far as possible for the centre of 

 the spectrum, there has remained a spherical under-correction for the 

 red, and an over-correction for the blue and violet rays, and this defect has 

 made itself felt in practice as a more or less marked inequality between 

 the chromatic corrections for the central and the peripheral zones of the 

 objective. 



Both these defects unite in making the concentration of the rays in 

 the image formed by the objective less complete in proportion as the 

 aperture of the objective increases ; therefore, in objectives of con- 

 siderable aperture, the available magnifying power is reduced to such 

 as can be obtained with relatively low eye-pieces, because with higher 

 eye-piece magnification the imperfections of correction become incon- 

 veniently visible, and necessitate the employment of objectives of very 

 short focal length, if a high magnifying power with an image of 

 satisfactory definition (therefore with a low eye-piece) is to be obtained. 



Both these imperfections in the convergence of the rays in the 

 achromatic objectives hitherto used can now be as good as entirely 

 eliminated by the use of the new glasses. 



In the first place the secondary chromatic deviation is removed and 

 reduced to a practically harmless residue of colour of a tertiary 

 character, and this has not been hitherto even approximately effected in 

 any kind of optical construction. Secondly, the chromatic difference of 



