The Abbe Diffraction Theory. By J. W. Gordon. 359 



diffraction images of the source of light in the upper focal plane of the 

 instrument will correspond with the number and distance from centre 

 to centre of the bright lines of the grating in any given portion of 

 the field occupied by the microscopic image of the grating. It leaves 

 much unexplained ; for instance, it does not disclose any agreement 

 between the total number of images in the interference pattern and 

 the total number of lines in the grating ; it does not show why the 

 bright images of the supposed diffraction pattern should be super- 

 posed upon the bright lines of the real image of the grating instead of 

 being intercalated between them ; and it does not explain why these 

 repeated images of the source of light should assume the shape as 

 well as the position of lines in the diffraction grating. 



A " theory " which rests upon such slight foundations and leaves so 

 much to be explained can hardly be regarded as an elaborated theory ; 

 but in fact, the importance of these omissions is by no means to be 

 measured by the mere gaps which they leave in the doctrine itself. 

 The attempt to supply any one of them reveals at once the unsound- 

 ness of the entire hypothesis. To take them briefly in their order. 

 First there is the question of total number. You place your Diffrac- 

 tions Platte, supplied by Zeiss of Jena for the purpose of demon- 

 strating the Abbe theory to the eye, upon the stage of your Micro- 

 scope, illuminate it by a narrow beam of parallel light, and observe it 

 through an a a objective. You count the number of stria? in the image ; 

 thirty-one in the coarser ruling, sixty-one in the finer. You read in 

 Naegeli and Schwendener's book that these are not really produced 

 by the refraction of light from the corresponding strife in the grating, 

 but are images of the slit through which the light enters the Micro- 

 scope placed by Abbe's law exactly where the images of the striae, if 

 produced by refraction, ought to fall. You inquire why they are 

 exactly the same in number as the strife in the grating. There is no 

 numerical relation between the number of lines in a diffraction 

 grating and the number of images of the source of light which it 

 will yield. Why then should these particular interference images 

 agree in number exactly with the markings on the object ? To this 

 there can be no answer. The number of repetitions in a diffraction 

 pattern when the whole is in view must depend upon the brightness 

 of the incident light. If this be increased, the old images will show 

 with enhanced brilliancy, and new images will come into view beyond 

 them. If, on the other hand, the light be diminished, the number of 

 visible diffraction images will diminish also by the fading out of those 

 that are least luminous. Hence the number of spectra which a given 

 grating will yield is quite indeterminate, and the proposition that a 

 definite number of line images, thirty-one in one part, sixty-one in 

 another part of the field, may be generated in this way, will not bear 

 stating. 



The theory is equally at fault if you examine it to ascertain why 

 the bright diffraction lines should be superposed upon the bright lines 



