150 Transactions of the Society. 



pencil, which was supposed to have a special virtue of itself, in the 

 delineation of ohjects. Naturally, therefore, the same angles, whether 

 in air or any immersion fluid, were considered to produce an equal 

 effect, and the advantage of immersion objectives was rested on 

 minor points. 



An estimation of the emergent beam, however, must obviously 

 give the same result as one of the incident beam (assuming them 

 both to be correctly made), it being of course impossible for any- 

 thing to emerge that has not first been admitted. But to quote 

 Mr. Crisp : — " The great and obvious advantage in dealing vdth the 

 emergent pencU is that it is always in air, and so the perplexities 

 are eliminated which have enveloped the consideration of the 

 admitted pencil, which may be in air, water, oil, or other substances 

 of various refractive indices." * 



The subject of aperture is not, in reality, a difficult one, and any 

 intricacy in which it may seem to be involved will be found to arise 

 from the necessity of clearing away some of the old entanglements, 

 such as the curious mistake involved in the " hemisphere puzzle " 

 and similar matters. Looked at de novo, there are two simple 

 stages in the aperture question. 



(1) To appreciate that, in using the term " aperture," we use it 

 not in any artificial sense, but as meaning opening and nothing 

 else, — defining, simply, the capacity of an objective for receiving rays 

 from the object and transmitting them to the image. 



(2) That the aperture (as so defined) of an objective is determined 

 by the ratio between the diameter of the emergent beam and the 

 focal length of the objective. According as this ratio is greater or 

 less, so the objective will receive and transmit a larger or smaller 

 portion of the total quantity of rays presented to it. 



The emergent beam of an air objective of 180^ angle cannot 

 exceed in diameter twice the focal length ; that of a similar water- 

 immersion objective may be one-third larger, and of an oil-immer- 

 sion half as large again, and the relative capacities of such objectives 

 (with equal angles) to receive and transmit rays will always be as 

 1, 1^ and 1^. 



It cannot be too carefuUy borne in mind that it is not a question 

 of this or that theory, but the ordinary laws of geometrical optics 

 which determine that, aU other things being equal, one objective 

 will receive and transmit a greater quantity of light than another, 



* As pointed out by Mr. J. Mayall, jun., at the commencement of the dis- 

 cussion, if 180° in air is equivalent to 82° in glass, the 140° in glass of the 

 immersion lens must represent something more. This fact is, however, bo con- 

 stantly misinterpreted, owing to the supposition that when the immersion fluid is 

 introduced the effect is only that the 82° is no longer compressed by the action of 

 the plane surface of the lens, but is allowed to expand to 140°. This is one 

 only of the apparent difficulties that obscure the proper estimation of the incident 

 pencil, and which are avoided by dealing with the emergent beam. 



