[ 156 ] 



VIII. Mr. Lewis Wright's Criticism of Theories of 



Microscopic Vision . 



To the Editors of the Philosophical Magazine. 



Gentlemen, 



IN the June Number of the Philosophical Magazine there 

 appear what purport to be criticisms by Mr. Lewis 

 Wright upon papers on Microscopic Vision by Professor Abbe, 

 Lord Rayleigh, and myself. Unfortunately, when writing 

 these criticisms he had formed an erroneous conception of that 

 method of resolving light upon which he chiefly comments. 



The present letter is an attempt to substitute a correct pre- 

 sentment of this method of resolving light, and deals necessarily 

 with the parts of Mr.Wright's paper of which I find it incumbent 

 on me to take notice on account of their having appeared in the 

 pages of the Philosophical Magazine. It is not to be inferred 

 from my silence in regard to the other parts of Mr. Wright's 

 paper, either that I agree with them, or that I am not sensible 

 of several observations of value which they contain. 



On p. 481 Mr. Wright explains that he is not qualified to 

 deal with the theoretical bearings of the subject; and that this 

 is so is made plain by a mistake which goes to the root of 

 the matter, and to which he gives expression on p. 484. He 

 there says "Ask these functions [t. e. circular functions] to 

 express a given disturbance and many surrounding replicas, 

 and they will do it. But ask them next to express a limited 

 disturbance resolved in this manner, and no more, and they 

 fail ; their edge at present is not sharp enough to do that." 

 Mr. Wright must be unaware that Fourier proved, some 

 eighty years ago, that their edge is sharp enough to do it. 

 And, by a very curious coincidence, it so happens that an 

 example of their accomplishing this feat is worked out in 

 detail in the very number of the Philosophical Magazine in 

 which Mr. Wright's opinion is published. (See the June 

 number of the Phil. Mag. pp. 534 and 535.) 



In 1896, when I wrote my papers on Microscopic Vision 

 (see Phil. Mag. for October, November, and December of 

 that year) I assumed that any reader who would take the 

 trouble to follow the proof of my fundamental proposition 

 would be aware that a theorem when proved for any spacing 

 of equidistant points is thereby proved to be true of the 

 limiting case when the spacing is infinite, and that this proves 

 it true for a single point unaccompanied by others. As 

 Mr. Wright experiences difficulty in understanding a proof 

 by the mathematical contrivance of introducing replicas, he 



