On the Estimation of Aperture. By Prof. E. Alibe. 29 



this is merely a question of contrast in the distribution of light, 

 of good definition in the objective, and of sensibility of the 

 retina.f But whenever they are seen, they are seen increased in 

 size, owing to the loss of difiracted light in every medium whose 

 refractive index is not a considerable multiple of the unit. Similar 

 objects of larger diameter — say 10 A. — are dehneated of their exact 

 size, by objectives of perfect definition, because the difiracted light 

 in this case is not, even in a medium like air, subtended far from 

 the direct beam in perceptible intensity, and the whole can be 

 admitted therefore with a moderate aperture. 



(3) When a portion only of the whole diffracted hght from 

 a structure is utihzed, the image is a true enlarged projection 

 of a different structure, namely of one the tvhole of ichose 

 diffracted beams would (if it physically existed) be represented 

 by the utilized diffraction beams of the structure in question. 



For example : If angulatum, either in balsam or adhering 

 to the covering-glass, is illuminated by a direct incident pencil, it 

 is delineated with a ivide-anghd immersion glass by means of the 

 direct undeflected beam and six surrounding spectral beams. The 

 image which is then seen is not a true copy of the real (quite 

 occult) structure of the valve ; but it is a true enlarged projection 

 of that structure which (if it could be produced artificially) would 

 break up by its diffractive power an incident beam into a fan (or 

 more strictly " group ") composed of the direct ray and the said 

 six deflected rays, and these alone. If we illuminate the valve 

 by an obUque incident beam, some of the six spectra are shut-off 

 by the margin of the aperture, and one or two new ones of 

 greater deflection (which remained outside the aperture in the 

 former case) are taken in if the aperture is sufficiently wide. The 

 effective portion of the diffraction group is now very unsymmetrical. 

 The image which is now seen is the true projection of that other 

 structure which would yield this unsymmetrical group as the 

 whole of its diffraction effect, such group being identical both in 

 the number and brightness of its beams to the admitted beams. 



The great variety of aspects which are obtained from one and 

 the same object merely by change of illumination, is fully accounted 

 for and defined by the above proposition. 



Or as another example : A very thin thread — say a minute cilium 

 — only a fraction of \ in diameter, is depicted with considerably 

 increased diameter, even with a very wide aperture. The image is 

 the true copy of another thread (the composition of which can be 

 computed by theory) which would yield a diffraction fan exactly 

 similar to that which is actually admitted by the objective, but 



t In point of fact, neither Professor Helmboltz nor the author have ever 

 spoken (as, however, has so often been supposed) of a limit of " visibility " — only 

 of a limit of visible " separation." 



