160 PKOCEEDINGS OF THE SOCIETY. 



on the cover of the Journal is erroneous and misleading, and should 

 at once be discontinued. 



" Addendum. — Since writing the preceding I have had occasion to 

 refer to the number of the Journal for Dec. 1879, vol. ii. No. 7, and while 

 turning over the leaves I to-day (3rd January 1881) stumbled over 

 the original communication of our treasurer, Mr. Stephenson, which 

 appears to throw some light on the so-called ' numerical aperture.' 

 The article to which I allude appears at p. 839. 



" I have no doubt I read it at the time of publication, as I distinctly 

 remember some of the other articles in the same number ; but evi- 

 dently it did not arrest my attention, and indeed had it done so it is 

 not probable that I should have gone out of my way to have opposed it 

 as it then appeared, that is, as the simple expression of Mr. Stephenson's 

 opinion, which of course he was fully within his rights in publishing, 

 and had it so remained I should probably never have taken any notice 

 of it, for, naturally, I do not feel called upon to record my dissent 

 from every proposition with which I may happen to disagree ; but the 

 persistent way in which the expression 'numerical aperture' has 

 been of late thrust forward in the Journal, and the repeated publica- 

 tion of the ' table,' which I now perceive has been extracted from this 

 paper, on the cover, culminating in an impossible explanation of a 

 non-existent phenomenon, ostensibly on editorial authority, have up- 

 set my equanimity, and I find it high time to protest against the 

 appearance of this error having been adopted by the Eoyal Micro- 

 scoj)ical Society or its authorities as an article of faith. 



" I have again twice perused the article with careful attention, and 

 I am more than ever discontented with the term ' numerical aperture ' 

 and the assumptions which follow as being altogether erroneous and 

 misleading, for I now find, as I had already conjectured, that the 

 mysterious ' numerical aperture ' is not an aperture at all, but a mere 

 product of an arbitrary calculation ; and the best of the joke is, that 

 it is actually based upon the much-maligned ' angular aperture ' — 

 the vaunted ' numerical aperture ' being the product of the sine of 

 half the angle of aperture multiplied by the index of refraction for 

 the medium in contact with the objective. How our friend Mr. Wilson 

 can make this agree with his statement (quotation A) that it * has 

 ' nothing to do loith angle ' I must leave to him to reconcile. Hitherto 

 I have been taught that the ' sine ' has everything to do with its 

 angle. 



" It is alleged by Mr. Stephenson that the ' theoretical resolving 

 power ' is indicated by the calculation above described. Certainly it 

 may be so, and 1 frankly admit that, as at present informed, I am un- 

 able to disprove it ; but I look upon the statement not only with 

 doubt and suspicion, but with a conviction that it will be very difficult 

 to establish such a conclusion, and that at any rate it remains as yet 

 in the category of things not proven. 



* [It will be seen, on referring to the original at p. 1091, that Mr. Shadbolt 

 has (unintentionally we are sure) misquoted Mr. Wilson, who made no such 

 statement. One of the factors in tlie expression of niunerical aperture is the sine 

 of half the anijlc of aperture. — Ed. J. R. M. S.] 



