28 Transactions of the Society. 



"When this critical value of the super-amplification has been deter- 

 mined for any class of objectives, it fixes the focal length which must be 

 given to an objective in order that the previously determined useful 

 magnifying power corresponding to the aperture may be realised under 

 satisfactory conditions, that is, so that the defects of the image do not 

 make themselves felt. The admissible value of the eye-piece magnifi- 

 cation (as defined above) may be represented by a number v, while the 

 total magnifying power which will be required for complete use of the 

 aperture may be indicated by N ; the proper magnifying power n of the 



N V 



objective should then be — , and the focal length therefore 250 :j^ (mm.), 



when the numbers representing the magnifying powers are referred to 

 the usual distance of vision of 250 mm. The estimation of the eye-piece 

 magnification v which is admissible with objectives of a given type, is 

 Ibeiefore the factor which leads to a rational accommodation of focal 

 tength to aperture. 



The determination of this figure is essentially a matter of experiment 

 and practice, since it is not of general application, but can only be 

 given with reference to a definite type of correction and a definite 

 degree of mechanical perfection in the objective. Every advance in the 

 direction of a more complete removal of spherical and chromatic aberra- 

 tion must naturally diminish the circles of dispersion in the objective 

 image, and make itself perceptible through a higher value of the 

 admissible eye-piece magnifying power, provided that at the same time 

 the perfection of the workmanship satisfies the correspondingly increased 

 requirements for the correction of errors of form and centering in the 

 lenses. 



As has been mentioned, objectives made of the new kinds of glass, 

 corrected in accordance with the above-established conditions, and con- 

 structed with all possible skill, admit, as the author's observations show, 

 of an eye-piece magnification (super-magnification) of at least 12-15, 

 even with the greatest possible aperture, without rendering defects in 

 the collection of the rays visible in the image. With the smaller 

 apertures, such as are employed with the weaker dry systems, the 

 admissible eye-piece magnification reaches much higher figures still. 

 Consequently, in accordance with the rule given above, the highest 

 useful magnifying power to be obtained by homogeneous immersion can 

 be secured with an objective magnifying power of 80-100, and therefore 

 with a focal length of about 3 mm., without loss in the perfection of the 

 image. With the largest aperture of water-immersions, the focal length 

 is about the same, and with the greatest aperture of a dry system 

 about 4 mm. 



That in future with objectives of this kind of correction focal lengths 

 substantially less than 3 mm. will be in general superfluous, will be 

 recognized, from what was said in the beginning, as a practical gain ; 

 and there appears, therefore, no reason why this consequence should 

 not be practically realized. With dry systems, however, of considerably 

 smaller apertures than 0*9, this theoretical determination of the focal 

 length leads in some cases to such high values, that its practical appli- 

 cation is inadvisable, since, especially with Microscopes of the Continental 



