1090 PROCEEDINGS OF THE SOCIETY. 



confusion has arisen from not getting beyond the simple and obvious 

 fact — aboiit which there can be no dispute, that no lens, dry or immer- 

 sion, can possibly have an aperture of 180°. 



I presume that no one will dispute the fact, that two contiguous 

 points in any object must be in a straight line, and that three points 

 contiguous to one another lie in a plane, consequently that if the 

 bundle of light-rays radiant from each point reached 180° — one of 

 such rays at least must pass clean through the adjacent point ; and this 

 is equally true, whether the object is in air, or immersed in water, oil, 

 balsam, or any other transparent medium. The difference is infini- 

 tesimal ; but less than 180° it must be. Again, I presume that no one 

 will contend that it is possible to collect from any given point a 

 larger number of light-rays than are actually emitted from that point, 

 and if so, my contention is established. 



But I am by no means content to leave the matter here. A lens 

 must have a surface of some kind, and it is quite impossible to bring 

 the surface of a lens in close contact with the whole of even so small a 

 part of the object as we wish to examine ; and unless we can do this — 

 nay, even if we could do this — we must leave out a further portion of 

 the supposed pencil of 180° of radiant light ; because, as the extreme 

 rays would be paralell to the front surface of the lens, there would be 

 no refraction, 



I may add further, that were such a lens constructed that it could 

 refract the largest possible portions of the 180° of radiant light, it 

 would be practically useless, as there would be no working distance 

 and no possible adjustment to suit varying sights. I state as a matter 

 of opinion only, that I very much doubt whether we can hope to see 

 any lens constructed to include practically, that is, efficiently, more 

 than 170° of aperture. Let us suppose such a dry lens to have been 

 constructed and placed in position to examine some transparent object 

 simply laid upon a slip of glass, which object is illuminated from 

 below ; the lens would now receive and refract from each luminous 

 point a pencil of 170° ; but if that object were mounted in balsam, or 

 other dense medium, and protected as usual with a thin covering of 

 glass, the same dry objective could no longer refract the 170° radiant 

 pencil of light, because certain of the rays of that pencil would, in 

 their passage towards the lens, fall on the upper surface of the covering- 

 glass, at and beyond the critical angle, and would therefore find no 

 exit ; the angular aperture of each pencil of rays proceeding from the 

 object, would therefore be limited to an angle equal to double the 

 critical angle for the covering-glass employed, I may remark, in 

 passing, that this would not be the case were the object mounted dry 

 and the two surfaces of the covering-glass parallel. 



It now becomes apparent why an immersion objective can in suit- 

 able cases perform better than dry ones. With an appropriate fluid 

 interposed the critical angle for glass becomes obliterated ; and the 

 pencil of rays, whatever its aperture, can pass direct to the posterior 

 surface of the front lens, and there become refracted for effective use 

 in forming an image ; and this is where the immersion lens has the 

 advantage ; it can include as large a portion of the radiant pencils of 



