The Abbe Diffraction Theory. By J. W. Gordon. 361 



lines of the secondary diffraction system must be quite independent 

 of the position of the grating on the stage of the instrument, and that 

 coincidence between them and the bright lines of the real image of 

 the grating, if it existed in any given case, would be a matter 

 of chance liable to be destroyed by the least displacement either of 

 the source of light or of the object, and so unlikely to recur as a 

 matter of probability that it may be regarded as practically an 

 impossible contingency — in this respect like most other coincidences. 

 Here again is a crucial test under which the theory breaks down. 



There is still a third point to be considered, the simplest and most 

 obvious of all objections to the Abbe theory. We are told that these 

 minute striations, seen in the microscopic image of a Zeiss' Diffrac- 

 tions Platte, are really diffraction images — images, therefore, of the 

 narrow slit which serves as the source of light. That is perhaps 

 conceivable. The slit which lies under the sub-stage condenser is 

 long and narrow and bright ; it is arranged so that its axis is parallel 

 to the common axis of the ruled lines in the grating ; it bears, there- 

 fore, a strong resemblance to these lines ; and if we suppose its image 

 to be repeated a proper number of times and to be duly disposed in 

 space, it is quite easy to suppose that we might mistake its repeti- 

 tions for a picture of the ruled grating. But, now, suppose that this 

 Abbe stop is removed, and a candle substituted as the source of light. 

 On looking down the tube of the instrument at the new diffraction 

 system, you see, of course, spectra in the shape of candle flames; but on 

 replacing the ocular and looking once more at the image of the 

 Diffractions Platte, you do not see a grating ruled with candle flames. 

 You see exactly what you saw before, a grating ruled with straight 

 lines — that is to say, with lines prevailingly and approximately 

 straight. But here and there a broken line or a wavy line will betray 

 a tremor in the ruling instrument. Now if all these are interference 

 images of the candle flame, why are they not all exactly alike, in the 

 first place ? why do they not all bear at least a general resemblance 

 to a candle flame, in the second place ? and why do they not change 

 in appearance when a broad source of light is substituted for a narrow 

 source, in the third place ? To these questions again there can be 

 no answer, except that the Abbe theory is wholly at variance with 

 the facts. 



These observations may suffice upon this line of criticism. It is 

 desirable to come to closer quarters with the Abbe theory by examining 

 the line of argument by which it is supposed to be supported. And 

 naturally, in the first place, one turns to the argument already 

 referred to in Naegeli and Schwendener's book. The mere mathematics 

 of that argument may be taken to be correctly worked out ; but it is 

 necessary to examine with some care the physical basis of the ex- 

 position. It proceeds, as will be obvious from a glance at the diagram 

 (fig. 68), to deduce from the relative positions of a, a' and a" — the 

 three diffraction images of the source of light which enter into the 



