The Belation of Ajoerture and Power. By Prof. E. Abbe. 803 



power of the objective, only two small portions of the aperture are 

 simultaneously utilized, one by the direct beam, the other at the 

 opposite edge of the opening by the diffracted beam, as may be 

 ascertained by a glance at the objective's clear aperture. All 

 defects and aberrations of the system which inhere in the inactive 

 portions, do not exist for the image in that case, whilst they will 

 at once become effective when those objects of a very complicated 

 and irregular structure, which produce a continuous and widely 

 spread out diffraction-pencil, are observed. This consideration will 

 show that the ordinary test-objects of the Microscope — particularly 

 lined objects, and in a somewhat less degree all kinds of diatom 

 markings — are the most unsuitable preparations for a proper 

 judgment of the performance of the instrument in regard to the 

 general conditions of scientific work inasmuch as the latter are 

 always much less favourable than those of diatom observations. 



3. In the face of the many intricate circumstances hinted at in 

 the foregoing discussions, a numerical estimation of the super- 

 amplification which is favourable or even admissible with various 

 kinds of objectives, must be a very difficult if not impossible task. 

 It would rarely be possible to assign any measure which would 

 receive the general assent of microscopists, because so many 

 elements are concerned in the question which cannot be estimated 

 apart from the individual opinions of the observers. 



One particular difficulty in observations for this purpose is to 

 decide whether a given objective is really up to date or is 

 afflicted with accidental defects, which might be avoided by more 

 accomplished workmanship, and must therefore be disregarded. 

 Another drawback to an accurate estimation arises from the before- 

 mentioned very different sensibility of the image to difference of 

 structure ; and not the least of all is the large amount of personal 

 equation which is always met with, when a judgment as to dif- 

 ference of quality has to be formed in regard to microscopic images. 

 Moreover, every one who estimates the value of the element in 

 question must be conscious of its provisional character. For 

 whilst the amount of super-amplification which a system is able 

 to bear with a certain degree of perfection of the image is the true 

 standard of the progress of microscopical optics, the determination 

 of the said element cannot claim anything more than a temporary 

 value : those figures of v which may very well conform to the 

 present conditions will not be true for the Microscopes of a 

 former period, and will perhaps be upset within a few years by 

 the further progress of optical science and art. 



I have now made observations for the purpose in question 

 during many years — studying the performance of a large number 

 of objectives of various kinds and various origins, upon very dif- 



