On Improvements of the Microscope. By Prof. E. Abbe. 23 



those errors which, while they have to a certain extent the character of 

 spherical aberration, originate mainly in the unequal behaviour of dif- 

 ferently coloured rays ; in fact the elimination of these errors realizes an 

 achromatism of higher order than has hitherto been attained. The 

 objectives of this system may be therefore distinguished from achromatic 

 lenses in the old sense of the word, by the term apochromatism, and may 

 be called ajpochromatic objectives. 



The practical advantages gained by these improvements are as 

 follows : — 



Firstly, the aperture of the objective can now be utilized to its full 

 extent. In the case of the old objectives of somewhat considerable aper- 

 ture, the inevitable defect in the convergence of the rays has to a great 

 extent prevented a proper combined action of the outermost zone and the 

 central parts of the aperture ; for this reason it has never been possible 

 to realize such a degree of resolving power as is to be expected by theory 

 from a given aperture. In practice, therefore, these objectives perform 

 like ordinary objectives of perceptibly greater aperture. For example, 

 a dry objective of aperture scarcely greater than that of the higher dry 

 systems at present used, gives with central illumination an image of 

 Pleurosigma angulatum, which for clearness and distinctness of definition 

 can scarcely be distinguished from the image obtained with good water- 

 immersion lenses of the existing type. The water-immersion objectives 

 are in the same way shown by corresponding observations to have an 

 optical efficiency at least equal to that of the old homogeneous-immer- 

 sions, if we do not take account of the practical advantage of the latter in 

 dispensing with the cover-glass correction. The advantage is conspicuous 

 with illumination by a broad central cone of light such as is given by a 

 wide diaphragm. 



In the second place, since with the new objectives there are no longer 

 the same obstacles to a considerable increase of magnifying power by the 

 eye-piece, the greatest magnifying power which can be utilized with a 

 given aperture may now be obtained with an objective of relatively greater 

 focal length, and very short focal lengths are rendered unnecessary. 



Former investigations made by the author* have shown that with 

 the best objectives of the old kind and with large apertures, the limits 

 of a completely satisfactory clearness of image, such as is required in 

 difficult observations, are reached when the super-amplification is 4-6 

 fold ; that is to say, when the total magnifying power of the objective 

 and eye-piece together is 4 to 6 times as great as that obtained with the 

 objective when used by itself as a magnifying lens. Under these 

 circumstances, to obtain a magnifying power of 1200 — e. g. with an 

 objective for homogeneous immersion — under satisfactory conditions, it is 

 necessary to use an objective which has by itself a magnifying power of 



200, and consequently a focal length of only ^^-^ = 1-25 mm. On the 



other hand, a number of careful comparisons have shown that with the 

 apochromatic objectives the available super-amplification, even with 



* " On the relation of Aperture and Power," see this Journal, 1883, p. 803. 



