316 SUMMARY OP CURRENT RESEARCHES RELATING TO 



can get is the smaller pencil of 80° in balsam (equal, according to the 

 angular ajierture view, to 80° in air), and it is therefore supposed to 

 be placed in circumstances in which its full jiowers cannot have play, 

 in consequence of the object being in fault. The immersion objective 

 now steps in, and by virtue of the immersion fluid above the cover- 

 glass restores the old condition of things when there was no question 

 of critical angles, and so is able ultimately to take up a pencil equal 

 to, but not exceeding, that which the dry lens took up when the object 

 was uncovered. The mistake of the numerical aperturist is (it is 

 imagined) clear. He has treated the 80° in Fig. 62 as if it were 

 precisely the same thing as the 170° of Fig. 61, and so is of course 

 able to show something more than that when the immersion lens is 

 used. When ho thought, however, that he had 170°, he had really 

 only 80° ! 



As soon as the non-identity of the whole hemispheres of radiating 

 light is ajjpreciated, the theory built up by the angular aperturist on 

 this aspect of the aperture problem at once tumbles to the ground ; 

 his hemisphere in air is indeed still a whole hemisphere, but not a 

 maximum beyond which there can be nothing more, as it is in fact 

 exceeded by the hemisphere of water, and the latter again by the 

 hemisphere of oil. The notion that the balsam-mounted object in 

 Fig. 62 is guilty of some fault which cuts down the light coming to 

 the dry lens, is proved to be groundless. The quantity of light or 

 number of rays in the air pencil of 170° of Fig. 61 is seen to be not 

 greater than, but only equal to, that in the balsam pencil of 80° of 

 Fig. 62 ; that the balsam 170° of Fig. 62, which had been assumed by 

 the angular aperturist to be the equivalent of the air pencil of 170° 

 of Fig. 61, is in fact much more. 



If, therefore, quantity of light were, as the angular aperturist 

 supposed, a proper, and not an insufficient basis for determining the 

 aperture question, the angles alone cannot be taken for the deter- 

 mination, as the quantity in any given angles in air, water, or 

 balsam must be compared by the values of (n sin m)^, n being the 

 refractive index of the medium and ii the semi-angle of aperture. 

 The numher of rays in the plane angles are compared also by the 

 values of n sin u. In neither case does 180° in air represent a 

 maximum. 



(6) The ''Resolution" Test. — The contention of the angular 

 aperturist here is that the resolving power of an objective must vary 

 in accordance with the angle, and reach a maximum at an air-angle of 

 180°. 



In the case we have just considered, he had no excuse for not 

 recognizing the obvious fact that quantity of light was an entirely 

 insufficient basis on which to discuss aperture, or for not performing 

 the simple experiment ready at his hand, which would have showed 

 at once that the light transmitted from the smaller balsam pencil 

 was not in fact, as he had assumed it to be, less than that trans- 

 mitted by the larger air pencil. In the case, however, of the resolving 

 power of objectives, there is somewhat more excuse, for whilst it is 

 seen that the resolving power increases with increasing angles in the 



