368 SUMMARY OF CURRENT RESEARCHES RELATING TO 



Lord Eayleigh suggested that in his case the drop would be just 

 distinguishable when the maximum of intensity due to the second curve 

 was superposed on the first minimum due to the first, and experiment 

 has borne this out. In this case the two halves of the aperture send 

 light in opposite phases to the first minimum, and the angular deflection 

 of the minimum is the angle subtended by the wave-length of light at 

 the distance of the breadth of the aperture. Two lines which subtend 

 a greater angle than this can be resolved. 



Similar methods were applied by Lord Rayleigh in 1896 to the 

 Microscope, and additional results have been given in his recent com- 

 munication to the Royal Microscopical Society, which follows Mr. 

 Gordon's interesting paper on Helmholtz's theory of resolving power in 

 the Journal of the Society. In his paper Mr. Gordon discusses in detail 

 Helmholtz's theory, and points out how far it is from fully explaining 

 all the difficulties of Microscopic vision. 



In Lord Rayleigh's earlier paper he deals with (1) two independent 

 linear sources viewed through a Microscope, and shows that they can be 

 resolved if the distance between them is half that given by Abbe's 

 theory ; (2) two sources which are always in the same phase ; in this 

 case resolution is impossible if the distance is that given by the theory. 



If, instead of having two sources, either cophasal or independent, we 

 have a long series, the problem is more complex, but the method is the 

 same. An expression is found for the variations of intensity in the 

 view plane, and the question is considered whether or no these varia- 

 tions are sufficient to be noticed by the eye. 



In the paper the question of the visibility of a dark bar on a uniform 

 field is dealt with, and here again a distinction must be drawn between 

 the case in which the field is self-luminous and that in which it is due 

 to a distant source. In the latter case it appears that the image of the 

 bar would be marked by a perceptible darkening across the field, even 

 when the breadth of the bar was but ^ of that given by Abbe's theory, 

 though the breadth of this shadow would not be a measure of that of 

 the bar ; in the former case the fall in intensity over the geometrical 

 image is only one-half of what it is in the latter. Moreover, we are 

 certain to arrive at erroneous consequences if we apply results obtained 

 from the case of a grating of a large number of parallel slits to a case 

 such as that of a single small aperture through which light is coming or 

 a single small obstacle obstructing the light ; the diffraction pattern due 

 to such an obstacle is entirely different from that due to a grating, and 

 the conditions of resolution will be different also. 



It appears, then, that while Abbe's theory of Microscopic vision is 

 undoubtedly correct in that a small object or objects on the stage pro- 

 duce diffraction patterns in the focal plane of the object glass, and the 

 illumination in the view plane can be inferred from these diffraction 

 images, still this method of regarding the question is not the only 

 possible one, neither is it necessary to go back to the original source if 

 we know the distribution in the object plane. By proceeding, however, 

 in the way indicated by Lord Rayleigh, we can evaluate the distribution 

 of intensity in the view plane, at any rate in certain cases, and obtain 

 thus a numerical estimate of the resolvability. 



