ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 313 



wide-angled immersion lens, and difference of light cannot therefore 

 be the root of the difference between the two systems. 



A mode in which " quantity of light " may legitimately come into 

 account in the aperture question is this : — Take a homogeneous- 

 immersion objective of wide aperture, and use it first as a dry lens 

 of large air-angle (say nearly 180"), and then as an immersion lens of 

 smaller balsam-angle (say 134"). On focussing the objective on the 

 object, and observing the emergent beam at the back, a smaller circle 

 will be seen in the former case than in the latter, the two being, 

 however, within a little (the loss by reflection) of the sarae intensity . 

 If the diameter of the smaller circle be taken as 1, that of the larger 

 circle will be equal to 1*4, and the amount of light received by the 

 image in the two cases will be therefore in the ratios of the squares 

 of the diameters, that is, as 1 to 1 ' 96, If, then, we have two objectives 

 of the same focal length, and one is found to take up from the object 

 and transmit to the image a greater quantity of light than the other, 

 the latter being placed in the most favourable circumstances of which 

 it is capable, and the source of light remaining unaltered, it is 

 obvious that the aperture of the former must be larger than that of 

 the latter. 



There is, however, another wiiy in which angular aperturists some- 

 times put the consideration of the hemispheres in different media, 

 which from one point of view is more rational. 



Disregarding mere quantity of light as a criterion, and looking 

 only to the number of rays in the plane angle, it is said that the 

 number in angles of, say, 180^ and 82° in air are equal to those in 

 angles of the same number of degrees in oil. The number, therefore, 

 in the pencil of 80° in Fig. 56 if oil or balsam is above the slide, is 

 supposed to be less than those in the pencil of 170° if air is above. 



This view is, however, as fallacious as the preceding. 



If we take the case of refraction, then one of the most funda- 

 mental of optical principles shows that the same rays which in air 

 occupy the whole hemisphere of 180° are compressed in a medimn of 

 higher refractive index within 



a smaller angle, viz. twice the Yig. 56. 



critical angle. If in Fig. 56 the 

 object is illuminated by an inci- 

 dent cone of rays of nearly 82^ 

 within the slide, and the slide 

 has air above in the first case 

 and oil in the second, it is ob- 

 vious that the same ray which 



is incident on the object at nearly 41° will always emerge in air at an 

 angle of nearly 90° (a), and in oil at nearly 41° (a"), so that the same 

 rays which in air are expanded over the whole hemisphere are com- 

 pressed into 82° in oil, and therefore rays beyond 82° in oil must 

 represent surplus rays in excess of those found in the air hemisphere. 



If, on the other hand, the case of diffraction is considered, then 

 Fraunhofer's law shows that the same diflracted beams which in air 

 occupy the whole hemisphere (Fig. 57), are in oil compressed within 



