PEOCEEDINGS OF THE SOCIETY. 129 



the sum of n single components to substitute the sum of one half of n 

 pairs of components, in that case this common factor will become 2c. 



Yet once again, if for the phase angle ^' l 2 ir, we write the arbitrary 



A 



symbol /?„ , the above equation will become 



A a + o + , . . n) = s (2 c cos /?„) 



Now, turning to page (HO of the last volume of the Society's 

 Journal, I find a table incorporated in Mr. Conrady's paper there 

 printed on "Theories of Microscopic Vision," and in column : J > of that 

 table I find the successive values of this expression 2 (2 c cos/? ?( ), 

 tabulated for a series of values of the angle fi„ , and put forward as 

 being the compound amplitude A^i + 2 + . . +«> 



Mr. Conrady in the paper to which I am referring makes all the 

 assumptions above enumerated, together with a further assumption 

 which involves, as an item in his equation, an additional factor, sin a. 

 This sin a causes great embarrassment to Mr. Conrady, and eventually 

 he disburdens himself of it by arbitrarily treating sin a as being = 1. 

 Whether in the circumstances in which he found himself that was a 

 legitimate way of eliminating a troublesome factor is a question which 

 it is not here necessary to discuss, but column 3 of the table referred 

 to shows conclusively that the equation which Mr. Conrady now attacks 

 with so much warmth is not a thing of my devising. 



With reference to one other point upon which Mr. Conrady has dealt 

 with a matter of fact, I desire to point out that he has fallen into an error. 

 It is not correct to say that Lord Rayleigh's results apply only to one, 

 and that an exceptional, case. Lord Rayleigh dealt with three cases, one 

 of them being a case in which there was no determinate phase relation 

 between the overlapping antipoints. Even in that case the black bar 

 limit of resolution is ^ of a wave-length, not a half wave-length, as 

 previously supposed. Where the phase relation is favourable, this 

 limit comes down to ^ °f a wave-length, and where specially favourable 

 the limit is evanescent. This is quite accurately stated in my paper. 



I do not propose to follow Mr. Conrady in detail through his criti- 

 cism, since a controversy on those lines would not only be tedious but 

 would fall much below the level of scientific discussion. I will notice 

 oidy one other point, and that because it is barbed by a charge of dis- 

 ingennousness which Mr. Conrady thinks fit to bring forward. This 

 relates to Professor Abbe's disclaimer of the Abbe theory. In a passage 

 now well known, and which appears in Carpenter's book on the Micro- 

 scope, Professor Abbe wrote : " I no longer maintain in principle the 

 distinction between the absorption image [or direct dioptrical image] 

 and the diffraction image, nor do I hold that the microscopical image 

 of an object consists of two superimposed images of different origin or 

 different mode of production. 



"This distinction, which in fact I made in my first paper of 1873, 

 arose from the limited experimental character of my first researches, 

 and the want of a more exhaustive theoretical consideration at that 

 period," etc. 



Feb. 15th, 1005 k 



