with Special Reference to the Microscope. lo9 



preceded that of Helmholtz, similar conclusions were reached; 

 but the demonstrations were deferred, and, indeed, they do 

 not appear ever to have been set forth in a systematic manner. 

 Although some of the positions then taken up, as for example 

 that the larger features and the finer structure of a micro- 

 scopic object are delineated by different processes, have since 

 had to be abandoned *, the publication of this paper marks a 

 great advance, and has contributed powerfully to the modern 

 development of the microscope f . In Prof. Abbe's method 

 of treating the matter the typical object is not a luminous 

 point, but a grating illuminated by plane waves. Thence arise 

 the well-known diffraction spectra, which are focussed near the 

 back of the object-glass in its principal focal plane. If the 

 light be homogeneous, the spectra are reduced to points, and 

 the final image may be regarded as due to the simultaneous 

 action of these points acting as secondary centres of light. 

 It is argued that the complete representation of the object 

 requires the co-operation of all the spectra. When only a 

 few are present, the representation is imperfect ; and when 

 there is only one — for this purpose the central image counts 

 as a spectrum — the representation wholly fails. 



That this point of view offers great advantages, at least 

 when the object under consideration is really a grating, is at 

 once evident. More especially is this the case in respect of 

 the question of the limit of resolution. It is certain that if 

 one spectrum only be operative, the image must consist of a 

 uniform field of light, and that no sign can appear of the 

 real periodic structure of the object. From this considera- 

 tion the resolving-power is readily deduced, and it may be 

 convenient to recapitulate the argument for the case of 

 perpendicular incidence. In fig. 1 AB represents the axis, 

 A being in the plane of the object (grating) and B in the 

 plane of the image. The various diffraction spectra are 

 focussed by the lens LL' in the principal focal plane, S repre- 

 senting the central image due to rays which issue normally 

 from the grating. After passing S the rays diverge in a 



* Dallenger's edition of Carpenter's ' Microscope/ p. C4, 1891. 



f It would seem that the present subject, like many others, has 

 suffered from over specialization, much that is familiar to the micro- 

 scopist being almost unknown to physicists, and vice versa. For myself 

 I must confess that it is only recently, in consequence of a discussion 

 between Mr. L. Wright and Dr. G. J. Stoney in the ' English Mechanic ' 

 (Sept., Oct., Nov., 1894; Nov. 8, Dec. 13, 1895; Jan. 17, 1896), that I 

 have become acquainted with the distinguishing features of Prof. Abbe's 

 work, and have learned that it was conducted upon different lines to that 

 of Helmholtz. I am also indebted to Dr. Stoney for a demonstration of 

 some of Abbe's experiments. 



