484 PROCEEDINGS OF THE SOCIETY. 



image plane seems to me to be extremely ingenious and beautifully 

 simple. The reading of the paper has cleared up in my own mind what 

 has long appeared to me a matter of great difficulty and some obscurity. 



It is, however, worthy of remark that Prof. Everett's propositions 

 relate, and relate only, to a very special optical system, and that that 

 system differs entirely from the system with which we actually work in 

 the Microscope. Furthermore, I may be perhaps allowed to add that 

 it is a system entirely different from that which was the subject of 

 criticism in my paper already referred to and which originally suggested 

 the experiment of moving the grating on the stage of the Microscope. 

 Naegeli and Schwendener who were at that time supposed to have pub- 

 lished an authoritative exposition of the Abbe theory, had laid it down 

 as a fundamental principle upon which their whole argument was based, 

 that there is no phase difference between the different members of the 

 spectrum seen in the upper focal plane of the objective. Their language 

 was " for since these sources of light " (that is to say, the spectra of the 

 various orders) "are point for point the optical images of the same 

 primary source of light, there is no difference of phase between them." 



This was the proposition which I mainly attacked, and Prof. Everett 

 has now shown not only that there is a difference of phase between them 

 but that this difference of phase is calculable, and that by the aid of the 

 very elegant expressions which he has devised it can be calculated with 

 ease. Thus I am entitled to say that, so far as the main controversy 

 goes, I can claim the support of Prof. Everett's paper in my attack upon 

 the Naegeli and Schwendener theory. 



In conducting this attack I endeavoured first to show by a discussion 

 upon geometrical lines that this proposition that there could be no 

 difference of phase between the various members of the spectrum was 

 preposterous, but realising that ocular proof is very much more satis- 

 factory to many people than mathematical- demonstration, I proposed 

 also to test it by the very simple experiment of moving the object grating 

 across the stage of the Microscope. It was obvious that this would 

 make no difference in the position of the spectrum, and if it made no 

 difference to the phase, as Naegeli and Schwendener asserted, then it 

 could make no difference to the interference pattern developed in the 

 image plane of the instrument. This was my argument, and it was to 

 support this argument that the experiment in question was devised. Of 

 course, when the original position is abandoned it is quite natural that 

 the argument directed against that original position should cease to 

 apply, and that is what has happened in the present case. I fully 

 recognise that in the theory put forward by Prof. Everett, and so far as 

 I know put forward for the first time by him and this evening, this 

 particular criterion would no longer serve to distinguish the image 

 formed by diffracted light from the image formed by transmitted light. 



But at this point it will be convenient to pass over to the considera- 

 tion of the difference between the optical system described and analysed 

 by Prof. Everett this evening and the actual system with which we work 

 in the Microscope. The fundamental difference between them is this, 

 that whereas Prof. Everett postulates a single train of plane wave-fronts 

 as the source of illumination, the practical microscopist is most careful 



