304 SUMMARY OF CURRENT RESEARCHES RELATING TO 



There are now so many of the Fellows who recognize the errors 

 of the angular aperture view, that we are almost afraid they will be 

 disposed to grudge the space given to these notes. We are, how- 

 ever, obliged to look at the matter a little from our own side of the 

 table. So far as we are aware, there does not exist in print any 

 attempt to deal in a connected form with the old theory of aper- 

 ture, or to point out how it is opposed not merely to optical laws 

 which may be considered to be more or less abstruse, but to those 

 simpler principles which lie at the very threshold of any understand- 

 ing of the Microscope as an optical instrument. Moreover, the true 

 view of the aperture question (first propounded by Professor Abbe) 

 has been disseminated amongst the Fellows almost entirely by verbal 

 or written communications ; and as it is to our lot, as a rule, 

 that it falls to reply by word of mouth or by correspondence to 

 requests for explanations, it will be a great advantage to us, and 

 of corresponding benefit to the Society, that we should be able to 

 refer inquirers to printed statements in the Journal, whereby much 

 time and labour will in future be saved which can be devoted to 

 other matters. 



It will also serve to show what are the points that must be met in 

 any attempts to prove the validity of the " angular " theory of aper- 

 ture ; whilst so far as regards angular aperturists, they can but rejoice 

 on the principle of the invocation, " Oh that mine adversary had 

 written a book ! " 



(1) The two Theories of Aperture. — There have been two con- 

 flicting theories of aperture, the one known as the Angular theory 

 (which formerly had prominent supporters and was recently re- 

 vived by Mr. Shadbolt *), and the other the Numerical (or Abbef) 

 theory. 



The essential feature of the former theory is that it regards the 

 angle only of the radiant pencil, and claims that not only may two 

 a]5ertures be correctly compared by the angles in the case of the same 

 medium, but also when the media are different. An angle of 180° in 

 air is considered to represent therefore a large excess of aperture in 

 comparison with only 96° in water or 82° in oil (or balsam), denoting 

 in reality the maximum aperture of any kind of objective, which cannot 

 consequently be exceeded, but only equalled, by 180° in water or oil. 



* See this Joimial, iii. (1880) pp. 1089-92, and i. (1881) pp. 150 and 154-72, 

 where a full exposition will be found of the old view of aperture and of the action 

 of immersion objectives. See also Engl. Mech., xxxii. (1880) p. 115. 



t This theory is known as the " Abbe " theory of aperture, from its having 

 been first promulgated (some years since) by Dr. E. Abbe, one of the professors 

 at the University of Jena, and an Honorary Fellow of the Society — the first 

 living authority on microscopical optics. We are glad to acknowledge our great 

 indebtedness to him not only for the first exposition of the erroneous view so 

 long held by microscopists on the aperture question, but also for much other 

 instruction in optical matters of the utmost value in connection with the theory 

 of the Microscope. Indeed, tliese notes may be taken to be, as it were, " lecture 

 notes ■' of instruction given by him, the "lectures" not, however, having been 

 oral, but contained in a somewhat voluminous correspondence with ourselves and 

 others extending over several years. 



