626 



Transactions of the Society. 



to the fact, which has been pointed out before now, and I believe 

 by various writers, that the diffraction-image under the conditions 

 which I have here assumed, and which have always been assumed 

 in explaining the Abbe theory, has no focus — viz;, whilst in ordinary 

 microscopical observations we cannot be in doubt as to the position 

 of the image which is sharp and thus inspires confidence, the 

 result, when we carry out the experiment suggested by the theo- 

 retical investigation, is that either the image remains continuously 

 sharp through quite a long range of focal adjustment, or else that 

 we get a regular succession of sharp images all equally good. 

 Hence the need of my stipulation, at the beginning of this section 

 of my paper, that I intended discussing the diffraction effects 

 produced in the plane of the geometrical image. I shall now have 

 to show how that plane is to be found, or rather, whether and in 

 what manner the image can be caused to be sharp in that plane 

 only, so as to be readily picked out simply by focussing. This is 

 the second point for the elucidation of which I am inclined to 

 claim credit. 



Let me first recall the reason for this want of focus in a simple 

 diffraction-image. 



Fig. 97. 



In fig. 97 the case is shown where only the direct light and 

 first diffraction-wave of one side enters the objective. The two 

 waves are brought to a focus * in the upper principal focal plane 

 of the objective, and thence spread out again, coming into complete 



* As the focussing of these waves by the objective is another of the points in 

 connection with the Abbe theory which Mr. Gordon has attacked, it may be worth 

 while to point out that we need not deal with waves filling the entire aperture of the 

 objective, iu which case the objection that there must be heavy spherical aberration 

 would be justified. We have only to consider small wave-segments corresponding 

 to a small number of structural elements, and therefore of very small angular extent ; 

 and for such the assumed focal properties of the points Pand P' can be shown to 

 he rigorously correct ; a reversal of Hockin's proof of the optical sine law (which 

 latter can be proved by other methods) is perhaps the most direct and the mo.-t 

 satisfactory. 



