ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



327 



Fig. 65. 



Fig. 66. 



Fig. 67. 



balsam-angle would not of course be similarly " cut do^vn," the air- 

 film having been rej^laced by tbe immersion fluid. 



The problem, therefore, was how to restore the " cut down 

 aperture, so that the dry objective with the balsam-moimted object 

 might be brought back again (as it was supposed) to the 

 condition in which it was when the object was dry, with 

 its " undiminished " aperture bearing upon the object. 



The device hit upon was the convex hemisphere. If 

 Fig. 65 represents the rays radiating from a given point 

 in air, their direction will remain the same (as shown in 

 Fig. 66) if a glass hemisphere is so placed that the radiant point is 

 at its centre. A hemisphere was therefore said to be merely a 

 " radiating lens." 



A small glass hemisphere was placed over the balsam- 

 mounted preparation, and attached to it with balsam. 

 The angle of the radiant pencil (when the dry objective 

 was focussed upon the object through the hemisphere) 

 was now of course as large with the balsam-mounted 

 preparation as it was originally when the object was dry, and a dry 

 objective was therefore, it was supposed, shown to be capable of 

 having as large an aperture with a balsam-mounted object as with 

 a dry one, all that was required being to 

 bring the object under suitable condi- 

 tions ! 



Now, strange to say, the propounders 

 of this problem had actually overlooked 

 the fact that the hemisphere magnified 

 the object li times,f so that the objec- 

 tive was no longer a ^ inch, but had been 

 converted into a ^ inch, utilizing, how- 

 ever, not a smaller but the same back 



t The notion that the hemisphere does not 

 magnify evidently originated from considering 

 only the point at the exact centre. From this 

 poiut all rays pass out radially without refrac- 

 tion. 



If, however, not a jooint but an object of de- 

 finite dimensions is considered, as in Fig. 67, it 

 is seen that the hemisphere magnifies in pro- 

 portion to its refractive index. 



The ray a c is transmitted in a straight line, 

 but a jjarallel ray b d, from an adjoining excen- 

 trical point, is refracted to the principal focus F. 

 In a lens of refractive index » = 1'5 the dis- 

 tance of the principal focus from the vertex c is 

 = 2 r. Therefore the vii'tual point of divergence of the excentrical pencil from h 

 is transferred to b*. As : — 



ah* : ab = "P a'.¥ c 



= 2 r 4- r : 2 ;• 



= 3:2. 



Thus the line a b is seen magnified | times. 



