312 SUMMARY OF CURRENT RESEARCHES RELATING TO 



whole, it is absurd, he conteuds, to speak of a water-immersion 

 receiving more, and still more absurd to speak of an oil-immersion 

 receiving more than that still. The numerical aperture notation, 

 therefore, which gives a maximum of (1 • 0)^ for the dry objective, 

 (1*33)^ for the water immersion, and (1'5)^ for the oil immersion, is, 

 he thinks, not only manifestly erroneous but misleading on a vital 

 point. 



The simple answer to this view is that the angular aperturist has 

 overlooked a fundamental optical principle, which lies at the root of 

 any such a photometrical question, viz. that the radiation of light 

 from an object in air, water, or oil is not identical,* but that the 

 whole hemisphere of radiation in air is to the whole hemisphere of 

 radiation in water or oil as the squares of the refractive indices of 

 the media, i.e. as 1 to (1-33- =) 1*77 and as 1 to (1*5^ =) 2-25. 

 The quantity of light in pencils of different angles must be com- 

 pared therefore not simply (as in the case of the same medium) by 

 the squares of the sines of the semi-angles (sin tt)-, but by the squares 

 of the sines multiplied by the refractive indices, i. e. (« sin m)^.| 



We have dealt with this photometrical suggestion as propounded,! 

 but at the same time it must be obvious that mere quantity of light 

 alone cannot be a sufficient basis on which to rest aperture. If it 

 were, it could be very readily disposed of on either view of the 

 aperture question. If the angular aperturist pointed out that when 

 the object is in balsam and air above the cover-glass a portion of 

 the light from the object (which is admitted when it is in air) 

 is lost by internal reflection at the cover-glass (see Figs. 61 and 

 62), it would only be necessary to increase the source of light 

 and the lost amount would at once be recovered. If, on the other 

 hand, it was the numerical aperturist who rested the advantage of 

 the immersion objective as regards aperture simply on the increased 

 quantity of light which he obtained by the use of oil (say 2j times 

 as great as with air), all that his oj)ponent would have to do would 

 be to take care and use a lamp three times as bright with his dry 

 objective, and he would then have beaten the immersion objective ! 

 Or, if he used an electric light, his dry objective would of course (on 

 the view supposed) have an "aperture" enormously exceeding that 

 of the immersion objective with only an ordinary lamj) ! No increase 

 in the amount of the illumination, however, can make a dry lens 

 equal in performance (as regards the special function of aperture) a 



* See further on this subject, III., No. 2, " Increase of Eadiation in Glass, 

 Oil," &c. 



t As will be seen inf,-a, p. 321, n sin !« is the expression for "numerical 

 aperture." 



X See this Journal, ante, p. 150: "If they had a radiant point, whether it were 

 " immersed in air or balsam, or any other medium, the quantity of rays from such 

 " radiant point must be the same identically whatever the medium was ; " and 

 p. 155 : " It is presumed no one will be found hardy enough to contend that the 

 " total amount of light emitted from a radiant point under a given fixed illumina- 

 " tion would be greater if the said radiant point were in oil or any other dense 

 " transparent medium, tlian if it were in air. In point of fact we may regard 

 " this total amount of radiant light as a fixed quantity, while the illumination of 

 " the object remains unaltered." 



