332 SUMMARY OF CURRENT RESEARCHES RELATING TO 



(c) Finally, the angular aperturist says that all he meant to convey 

 was that the cover-glass of the balsam-mounted object prevented rays 

 of light passing out into air, while when a suitable immersion fluid is 

 used they can pass out freely by reason of the critical angle having 

 been abolished. 



Of course the whole question between dry and immersion objectives 

 depends upon the critical angle ; and equally of course, both parties 

 admit that the air above the cover-glass in Fig. 62 stops rays from 

 reaching the objective. But the crucial question is, of what " ivhole " 

 is a portion stopped oif ? The angular aperturist contended, a portion 

 of that " whole" which is emitted in air when the object is uncovered. 

 In fact, however, it is of that " whole " which is emitted in balsam, and 

 as the balsam " whole " is much greater than the air " whole " (a fact 

 which he denied), the fractional portion of the former which is emitted 

 is not necessarily less than the " whole " of the latter. 



By all methods, therefore, we come back to the demonstration of the 

 essential fallacy of the angular aperturist, viz. that equal angles in 

 different media are the same. 



(3) Power of the Plane Surface of a Lens. — Another fallacy is 

 that the plane surface of the front lens of an objective exercises power, 

 so that when in a homogeneous-immersion lens the action of this plane 

 surface is abolished by the use of the immersion fluid, the back 

 spherical surfaces have to be increased in power by way of com- 

 pensation. Or, to put it in another way, that in dry objectives 

 the refraction at the plane surface atones for less refraction at the 

 spherical ! 



This fallacy so continually crops up when diagrams are attempted 

 to be drawn to illustrate the possibility of a dry lens equalling a 

 wide-angled immersion lens in aperture, and in various other forms 

 in discussions on the difference between the two kinds of objectives, 

 that we think it will be useful to dispose of it once for all. 



Dealing with experiment first, there is a very simple way of 

 demonstrating the fallacy experimentally. 



Take a homogeneous-immersion lens. Here the spherical surfaces 

 are supposed to have been increased in power to replace the action 

 of the plane sm'face which has been abolished by the immersion 

 fluid. If, then, there was loss of power when the plane surface was 

 abolished, there must be gain of power when the plane surface is 

 restored. Restore the plane surface, therefore, by using the objective 

 on a dry-mounted object. According to the view propounded, the 

 objective must now magnify more than it did on the balsam-mounted 

 object. Let any one who believes in it try the experiment and 

 record the result ! 



If theory is preferred to experiment, is it not obvious that a plane 

 surface can have no power, the loss of which requires to be replaced 

 by an increase of the power of the spherical surfaces ? — that a plane 

 surface is the optical zero as regards power (the hemisphere being the 

 optical 1 or unit giving an amplification of an object at its centre in 

 proportion only to the refractive index of the substance of which it is 



