ZOOLOGY AND BOTANY, MICBOSCOPY, ETC. 305 



That, in fact, a radiant pencil has exactly the same value, for 

 equal angles, whatever the refractive index of the medium in which it 

 may be. 



The essential feature of the second theory is that it does not 

 regard the angle only, but takes account of fundamental optical phe- 

 nomena actually existing in nature, which the old theory entirely 

 overlooked, whereby it is shown that even when the medium is the 

 same, apertures cannot be compared by the angles only of the radiant 

 pencils, but by their sines ; whilst when the media are different, the 

 refractive indices of those media must also be considered. An angle 

 of 180° in air is therefore equal in aperture to one of 96° in water or 

 82° in oil, and represents consequently not a maximum, but much 

 less than the aperture which is represented by the same angular 

 extension in water or oil. 



A radiant pencil has therefore an entirely different value for equal 

 angles in media of various refractive indices. 



It will be seen that the points of distinction between the two 

 theories are by no means differences of nomenclature only,* but turn 

 upon fundamental physical and optical principles the very existence 

 of which is wholly denied by the " angular " theory ; the point of 

 essentially practical importance to the microscopist, who may require 

 for his observations large aperture, being that, contrary to the angular 

 view, immersion objectives have apertures in excess of the maximum 

 attainable with a dry objective, that is, exceeding 180° angular in 

 air. 



The " aperture question " will ever hold a most prominent place 

 in the history of the Microscope, representing as extraordinary a 

 series of mistakes as were ever committed in any branch of science, 

 and in which (down to comparatively recent times) both the leaders 

 and the rank and file were equally involved. " Aperture " may be 

 said to have been the " Haschisch " of the microscopist ; when that 

 has formed the subject of consideration, the simplest and oldest 

 established optical principles have not been disregarded merely, 

 but their very converse tacitly assumed, as if the great optical 

 physicists of this and the previous century had never lived, or had 

 written nothing that was worthy of consideration ! 



(2) "Dry" and "Immersion" Objectives. — To understand the 

 question of aperture, it is of course necessary in the first j)lace to have 

 a clear idea of the essential difference between a " Dry " and an 

 " Immersion " objective. Some misapprehension exists on this point, 

 as we have been assured that we must be entirely wrong in asserting 

 that a dry lens can never have as large an aperture as a wide-angled 

 immersion objective,! for said our critic, " 1 can show you that if 



* We deal hereafter more in detail (see II. " Angular- Aperture Fallacies," 

 No. 7) with the notion that the difierence between the two views is " only a 

 question of nomenclature " ! 



t By " wide-angled immersion objective " is always meant one whose angular 

 aperture exceeds twice the critical angle of the medium used for immersion, i. e. 

 > 96° for water and > 82° for balsam or oil. 



