28 Transactions of the Society. 



developed in another paper. t In order, however, to give here a 

 summarized idea of the benefit attendant upon increased aperture, 

 and to indicate ivhat it means for the general interest of micro- 

 scopical vision : difference of the diffracted light which is utilized 

 for the image — I briefly point out here some propositions which 

 are established by theory and experiment in that paper : — 



(1) Perfect similarity between the microscopical image 

 and the object, or a true enlarged projection of the object 

 by the Microscope, always depends on the admission to and 

 utilization by the objective, of the ivhole of the diffracted 

 rays which the structure is competent to emit. 



(2) Whenever a portion of the total diffraction fan apper- 

 taining to a given structure is lost, the image will be more 

 or less incomjylete and dissimilar from the object; and in 

 general, the dissimilarity will be the greater the smaller 

 the fraction of light admitted. In the case of periodic struc- 

 tures, the exclusion of all diffracted rays, except the central 

 (direct) beam of the diffraction fan, will entirely obliterate the 

 details of the image. With structures of every kind (periodic 

 and irregular) the image will lose more and more the indica- 

 tions of the minuter details, as the peripheral (more deflected) 

 rays of the diffraction spectrum or diffraction pencil are more 

 and more excluded. 



For example : When a striation, a grating, or a diatom is close 

 to the limit of the delineating power of a given aperture (i. e. when 



the distance of the hues is not much greater than ^ ) the image is 



always depicted by two diffraction beams only (if with bright field, 

 by the direct, undeflected ray, and one spectral ray). In this 

 case the striation always appears as if the darker and brighter 

 interspaces composing the striation were very approximately of 

 equal breadth, although the inspection of a more complete image of 

 the same structure, obtained by means of a much greater aperture, 

 should show the proportions of the alternate striae to be very 

 different. 



Another example : The diffraction fan of isolated corpuscules or 

 threads (say bacteria or cilia), in a clear field, must be exactly identical 

 to that of equal-sized holes or slits of equal shape in a dark back- 

 ground, and there must be (as theory shows) a continuous and nearly 

 uniform dissipation of diffracted light over the whole hemisphere, 

 provided the diameter of the object is very small (a fraction of X) ; 

 and this would be so even in a medium of highest known refractive 

 index. Such objects can be seen, however minute they may be ; 



t ' Die Grenzen der geometrischen Optik in der Theorie des Sehens und der 

 optischen Instrumente.' (The limits of Geometrical Optics in the Theory of 

 Vision and Optical lustrumeuts.) 8vo. Jena, 1881. (In the press.) 



