166 PKOCEEDINGS OF THE SOCIETY. 



" Nor can lie or any one else ever succeed in doing so. It is as 

 much a hopeless task — a demonstrable impossibility — as that of 

 squaring the circle itself, whether looked at from a strictly mathe- 

 matical or experimental point of view. The mathematical has been 

 already given by Professor Abbe,* and the experiments which equally 

 demonstrate it have been shown in this room time after time. 



" The most striking of these is the application of an immersion 

 lens, with ' balsam angle ' exceeding 82°, to a dry-mounted and a 

 balsam-mounted object successively. In the former case the lens 

 acts as a dry lens of an aperture infinitely near 180°, and a bright 

 circle is seen at the back of the objective having a diameter less than 

 that of the posterior lens. With the balsam-mounted object the 

 wJwle diameter of the back lens becomes brightly illuminated, and 

 the surplus aperture of the objective in excess of 180° in air is 

 manifest. If the difference between the diameters of the two bright 

 circles is measured, it will be found to agree with that which should 

 exist on theory. 



" It has been the increased diameter of the back lens — so striking 

 a feature in immersion objectives — that more than anything else 

 has brought practical opticians in England to agree that there must 

 be an actual increase in the ' aperture ' or ' opening ' of this class of 

 objectives. 



" Mr. Shadbolt's Fig. 33. — Mr. Shadbolt's reference to Professor 

 Stokes's paper and the proposition which is illustrated by Fig. 33, is 

 no less insufficient than that which I have dealt with. He cannot 

 have worked out the effect of the diagram, or he would have seen 

 that he had established the very proposition which he had designed 

 the diagram to disprove! The demonstration requires, however, 

 closer attention than can be given to it on an occasion like this, 

 but it shall be priuted in the Journal.f Meantime, however, I 

 may point out that if Mr. Shadbolt will take the diagram to any 

 working optician, he will find it at once pronounced not a practical 

 construction for the purpose for which he proposes it. 



" Numerical v. Angular aperture. — It is the same fundamental 

 fallacy which has led Mr. Shadbolt into approving the sufficiency of 

 the expression of angular aperture. For if it is erroneously assumed 

 that the media have nothing to do with the matter, it does not seem 

 absurd to say that ' angular ajperture gives a very exact idea and 

 measure of the proportion of a pencil of rays that a lens allows to 

 pass ' ; and that it ' has exactly the same value whether in a dry or an 

 immersion lens, neither more nor less.' 



" It must be clear, however, from Mr. Shadbolt's paper itself that 

 the expression angular aperture is erroneous and misleading, in that 



* It is intended to hang up in the library a copy of the diagram which illus- 

 trates the demonstration that no dry objective ccm have an aperture equal to that 

 of an immersion objective with a " balsam angle " exceeding 82°. 



t These Proceedings having run to nearly sixteen pages beyond the usual 

 limit, obliges this to be postponed till the April Journal. It may, however, be 

 stated shortly here, that when worked out, it is found that the Stokes objective 

 and the Shadbolt objective magnify in the proportion of 7 to 5 approximately, so 

 that the latter is « lower pmcer icith the same back combination, and therefore a 

 diminished aperture, the actual figures being 51° instead of 66°. 



