ZOOLOGY AND BOTANY, MICROSCOPY^ ETC, 307 



thinness of the intervening film of air. The appreciation of the fact 

 that it is a dry objective has apparently been obscured by the existence 

 of the immersion fluid between the front lens and the cover-glass. 



A practical advantage of having such a dry lens is that it enables 

 us to consider the question of the surplus aperture of wide-angled 

 immersion lenses (in excess of that of ISO"^ angular in air) with 

 reference to the case of one and the same objective, which in several 

 ways simplifies the consideration both experimentally and otherwise. 

 Without altering the illumination or removing the objective from the 

 Microscope, but simply shifting a slide from that part which contains 

 a dry object to that which has a similar object mounted in balsam, 

 the difference in the aperture of the objective under the two con- 

 ditions is at once made visible. 



(3) Definition of "Aperture." — The first doubt on the mind of 

 an angular aperturist is whether the numerical aperturist is not 

 a person of such confused ideas, or at any rate of such neglected 

 optical education, that it must be a waste of time even to hear 

 what he has to say. This is a perfectly genuine doubt, because 

 the angular aperturist hears his opponent speak of (1) an aperture 

 in excess of that of 180*^ angular in air, and (2) of a balsam-angle of 

 82° being the " optical equivalent " of an air-angle of 180'°, so that he 

 assumes the numerical aperturist not to be aware, 1st, that there can 

 be no angidar aperture beyond 180°, and, 2nd, that a part can never 

 be equal to a whole ! 



When he is satisfied that the numerical aperturist does not dispute 

 either of these propositions, and that he lays stress upon " aperture " 

 as opposed to " angle," his next suspicion is that some double entendre 

 must lie hidden in the word " aperture." 



There is no reason for objecting to the definition of the term 

 " aperture " insisted upon by most angular aperturists, viz. as meaning 

 not resolving-power, but essentially " opening." * In acting upon this 

 definition, however, and attempting to estimate the relative " open- 

 ings " of objectives, only the pencils admitted into the objective from 

 the front have hitherto been considered. The alternative view is now 

 60 obvious, that it seems strange it should not have occurred to any 

 one before Prof. Abbe — notwithstanding the number of minds that 

 have been at work on the aperture question at various times — to 

 regard not the admitted but the emergent pencils (between which he 

 established the existence of a general relation). Whether we take 

 the pencil which emerges from the objective or that which is admitted 

 into the objective, is obviously the same thing as regards the present 

 question, for no one will contend that anything can emerge that 

 has not first been admitted. The great and obvious advantage in 

 dealing with the emergent pencil 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. 



* There are some, however, who treat the idea of " opening " as of secondary 

 importance in regard to aperture, and as giving only greater ilhiuiination, which 

 can of course be obtained otherwise ! 



