156 PROCEEDmGS OF THE SOCIETY, 



rical aperture ' convey no such meaning, nor indeed to ray mind any 

 meaning at all. If the ' angular aperture ' of a lens be correctly 

 gauged, it forms a very exact measure of the proportion of the radiant 

 pencil of (say) 180° that the said lens will admit, and I am therefore 

 constrained to meet with a very decided negative the statement in 

 quotation B relative to this point. Angular aperture means now just 

 as much and just as little as it ever did. 



" Of course mere aperture is not a fair measure of comparison 

 between two or more lenses any more than mere achromatism, or 

 mere correction for spherical aberration ; but 

 cceteris paribus, it is a very important element in 

 the comparison, and ' angular aperture,' as above 

 defined, has exactly the same value whether in a 

 dry or an immersion lens, neither more nor 

 less. 



" I am really almost ashamed to give a dia- 

 gram to illustrate so elementary a matter as the 

 angle of aperture ; but in the face of the con- 

 tention which has been advanced, it seems needed 

 for the completion of my argument — to convince 

 those at least who have not studied the pheno- 

 mena of optics. 



" Let E (Fig. 31) be a radiant point, and 

 ah c d efg rays proceeding therefrom, it is clear that an aperture of 

 ^\ of an inch in diameter placed at x admits the whole of the rays 

 depicted, while the aperture of i inch diameter at y admits only three 

 of them. The ' angular aperture ' of the small diameter is aB,g, 

 while that of the larger one is only c R e. 



" It is therefore clear that ' numerical aperture ' cannot be equiva- 

 lent to absolute aperture : it is alleged to have nothing to do with 

 ' angular aperture,' but to be something ' quite different.' Then 

 what is it? I want to see it, or at least to have a diagram of its 

 supposed form ', in fact, any information about it will be thankfully 

 received. 



" Mr. Wilson says ' the original note ' and my letter relate to tivo 

 distinct matters, as if they were in no way comparable with one another 

 — such, for instance, as the time of day with the length of a man's 

 nose. Well, I don't object, only why do Mr. Wilson and others con- 

 stantly persist in comparing the ' angular aperture ' of an impossible 

 lens with this mysterious ' numerical aperture,' of which we have 

 no definition ? 



" If it were possible practically to employ an angular aperture 

 of 180° in lenses, whether dry or immersion, the ivhole of the rays 

 emitted from a radiant point would be admitted by both lenses 

 if the object under inspection were immersed in air, and by the 

 immersion lens, in a suitable liquid, if the object were mounted in 

 balsam ; it is, therefore, simply absurd to talk about an ' aperture ' 

 which admits more than the whole of that which has to be admitted. 



" To speak of a lens of 180° angular aperture in air (or anything 

 else) admitting only a pencil of 81° 58' is a contradiction. A lens 



