On the Estimation of Aperture. Bij Prof. E. Able. 35 



Fig. 3. 



would at all events show less than any one of the partial images 

 could have exhibited. The single fact that we obtain distinct and 

 well-defined vision by means of wide apertures, and that for the 

 observation of very minute structures such wide apertures are 

 required, at once disproves the notion that their effects depend on 

 such circumstances as solid vision with the naked eye or with the 

 binocular Microscope. Whenever we have the advantage of solid 

 vision, owing to a different perspective projection of different 

 images, in the Microscope or otherwise, this is solely because 

 these different images are seen by different eyes. 



There is, however, still another point of view under which 

 the essential difference between wide-angle vision in the Microscope 

 and variety of perspectives in ordinary vision becomes very evident. 

 Suppose for a moment that there did exist a different perspective 

 of a microscopical image by axial and by oblique rays, similar to 

 that in ordinary vision; and suppose 

 a minute cubical prominence ah e 

 (Fig. 3) on an object to be observed 

 by a wide-angled objective allowing an 

 obliquity up to 60°. If it were true 

 that the oblique beams project both 

 faces a h and & c of the cube, whilst 

 direct beams depict ah only, it must 

 certainly be just as true that the face 

 a h must be seen shortened by the 

 oblique rays in the proportion of 1 : 2, 

 as it of course is in ordinary vision. But 

 what is true for the small facets of a minute ridge must also be true 

 for any larger portion of the field. Under the above assumption, any 

 larger object, as a Pleurosigma scale, ought to appear shortened, 

 and the markings closer together by 1:2, in the direction of 

 incidence of a pencil of 60° obliquity ; or, in other terms, the ob- 

 jective ought to yield only half its anijolification in that direction. 

 No microscopist has ever yet observed such a thing ; and if it 

 did exist, microscopical vision even with very moderate apertures 

 would be entirely destroyed. In point of fact, the identity of 

 power or amplification with all obliquities embraced by the aper- 

 ture-angle is the essential criterion of an aplanatic system; and 

 the law of convergence of the rays at conjugate aplanatic foci 

 which was applied for the determination of the aperture-equivalent, 

 is, as has been deduced by the author, the necessary and sufficient 

 condition of identical amjplification in wide-angled systems, without 

 which no image could be dehneated by such systems. 



This consideration shows that the diverse obliquities of the rays 

 in a wide-angled system cannot give rise to anything like all-round 

 vision, because in the Microscope there is no difference oi projection 

 connected with different obliquities. 



