30 Transactions of the Societi/. 



ahrupthj hroJcen off" at the limit of tlie aperture-cone (the intensity 

 of the deflected hght suddenly cut down to zero at a definite 

 obliquity). Theory shows, that a thread-shaped object which could 

 yield such a particular diffraction eff'ect, must (other difierences not 

 considered) be at all events greater in breadth than another one 

 yielding the full continuous dissipation of light.f 



(4) As long as all distinct elements of a structure are 

 measured by large multiples of the wave-length of light, all 

 diffracted rays of perceptible intensity will travel within a 

 narrow cone around the direction of the incident beam from 

 which they originate. In such a case any narrow aperture- 

 angle will be sufficient to admit the whole. The images of 

 such coarse objects (or of their coarser parts) will therefore be 

 always perfectly similar to the object, i. e. will be true enlarged 

 projections. 



(5) When the diameters of the elements of a structure (or 

 of some of the elements in it) are reduced to smaller and 

 smaller multiples of the wave-length which corresponds to the 

 medium in which the object is, the difi'raction pencil originating 

 from an incident beam has a wider and wider angular expan- 

 sion (or in other words the diffracted rays are further apart) ; 

 and when this diameter is reduced to a few wave-lengths, not 

 even the hemisphere can embrace the whole diffraction effect 

 which appertains to the structure. In this case the ivhole 

 can only be obtained by shortening the wave-length, i. e. by 

 increasing the refractive index of the surrounding medium in 

 such a degree that the linear dimensions of the elements of the 

 object become a large multiple of the reduced wave-length. 

 With very minute structures, the diffraction fan which can be 

 admitted in air, and even in water or balsam, is only a greater 

 or less central portion of the whole possible diffraction fan cor- 

 responding to those structures and which could be obtained if 

 they were in a medium of much shorter wave-length. Under 

 these circumstances no Microscope, however wide may be its 

 balsam-angle, can yield a com^plete or strictly similar image. 



These propositions relate to structures of all kinds, whatever 

 may be then' physical and geometrical composition — isolated ele- 

 ments of any shape not excluded ; they embrace the totality of the 

 objects of microscopical research. 



t The theory of diffraction if developed on a more general basis shows that a 

 structure may always exist which is competent to originate as tlie whole of its 

 diffraction effect any given, even discontinuous or abruptly broken off, diffraction 

 spectra, for instance that portion of the actual diffraction spsctra of another struc- 

 ture which remains after excluding a certain other portion. Such discontinuous 

 spectra are not obtained with structures (as an ordinary grating) whose diffrac- 

 tion effect is solely based upon interception of the rays by varying absorption. 

 They are, however, obtained with structures which occasion at the same time 

 varying retardation of the transmitted waves owing to unequal thickness or 

 unequal refractive index of the transparent elements. 



