22 Transactions of the Society. 



the spherical aberration can be ehminated, that is to say, the spherical 

 aberration can be completely corrected for two different colours of the 

 spectrum at once (and therefore practically so for all colours). 



The latter object has hitherto been attained in certain kinds only of 

 telescope objectives, for which it was originally formulated by Gauss, 

 without however — for want of a simultaneous correction of the secondary 

 dispersion — any decided advantage being gained. 



The fulfilment of the first condition depends upon the employment 

 of pairs of glasses in which the so-called relative dispersion, the 



quotient 1-, differs considerably, while the ratio between the partial 



dispersions at different parts of the spectrum is at least approximately 

 constant, or in which on the other hand the quotient is constant while 

 the latter ratio is different. Now this is entirely a matter of the 

 chemical composition of the glass ; the experimental researches men- 

 tioned at the outset, have established the fact that in the series of silica 

 glasses this requirement cannot be satisfied, but it is so when phos- 

 phates and borates are used in combination, the former as a substitute 

 for crown, the latter for flint glass. The circular of the Glastechnisches 

 Laboratorium gives the results of the spectrometric measurements of a 

 number of such glasses, and thus supphes the requisite data for their 

 application to the purpose in question by means of the usual methods of 

 calculating the colour dispersion in optical systems. 



The second requirement, which refers to spherical aberration, involves 

 in the case of systems of so great an ajjerture as are used with the 

 Microscope, the consideration of very complicated relations between the 

 separate elements of the system which have not yet been expressed in a 

 general form in the theory of dioptrics. So far as the author can at 

 present see, the correction of these aberration differences depends upon a 

 very pronounced accumulation of spherical deviations in one part of the 

 system, which are compensated for by equal and opposite deviations in 

 another part. If these purposely produced accumulations are to be 

 correctly compensated, the possibility of varying the index of refraction 

 independently of the dispersion, as may be done with the new glasses, 

 will be an indispensable aid. 



It was made clear from the theoretical consideration of the con- 

 ditions of delineation, and it was practically proved by the objectives 

 which have since been produced, that by the simultaneous fulfilment of 

 both these requirements the concentration of the rays in the images 

 formed by these objectives is essentially more perfect. Apart from the 

 unusual purity of colour in the images, which is almost as perfect with 

 oblique as with central illumination, the better or more complete con- 

 centration of the rays is evinced by the fact that the images may be 

 further magnified by very high eye-pieces without appearing indistinct, 

 and without producing the impression of insufficient light, provided only 

 that the mechanical construction has been improved proportionately with 

 the optical action. 



As has been said above, the condition by which these properties are 

 obtained in the new objectives, and the characteristic which distinguishes 

 them from the dioptrical point of view, depends upon the elimination of 



