72 NOTES ON THE RESOLVING POWER OF 



proceeds only slowly at first, as the diaphragm is further reduced, 

 and it is not until about one millimetre diameter that very con- 

 siderable deterioration is noticed. The eye is itself an optical 

 instrument. The radius on the retina of the first dark ring of a 

 point source is about 0.01 mm. when the diameter of the effective 

 pupil is 1 mm. This is about eight times the diameter of a retinal 

 cone. But the total magnification 



T V 

 M=:MiM2=TT. J nearly 



V diam. back lens of obj. 



F. diam. bright spot ; 



or taking V = 25 cms. and 2 mm. as the diameter of the bright 



spot, the magnification becomes 



diam. back lens obiective 

 M = 125 p ^— 



For the case F = 0.2 cms., back lens = 0.6 cms. diam. 



M = 375 diameters. 

 If we suppose a reduction of the bright spot to 0.1 cm. diam. to 

 be permissible M = 750 diameters. 



These results are of the same order as before. 



In the case of photomicrography, as we have seen, the per- 

 missible magnification is the same whether an eye-piece is used or 

 not. There is the added advantage that the photographic image 

 can be examined with the eye at best ajperture. On the other 

 hand, there is deterioration in the image due to the grain in the 

 plate, by an amount varying much for different plates. Where the 

 finest representation is required, it should not be forgotten that 

 the old " wet " process could be resorted to; or, failing that, process 

 plates are the next best. 



The attainment of as close an approach as possible to perfect 

 images is limited by the extent of the elimination of all the aberra- 

 tions calculated by methods of geometrical optics. Professor A. E. 

 Conrady emphasises the fact that extension of numerical aperture 

 has surpassed the value warranted by the existing design and con- 

 struction of lenses. The same may be said concerning condensers 

 €ven more emphatically. Pioneer investigations on waves of non- 

 spherical form were made by Lord Rayleigh and others. The varia- 

 tion of the intensity in the focal plane of a planoconvex lens has 

 been worked out by L. Silberstein (Phil. Mag., Jan., 1918), who 

 at the same time exhibits the general method by which all such 

 problems can be attacked ; and the same kind of question has been 

 worked out by graphical integration by Professor A. E. Conrady 

 (Monthly Not., R. Astr. Soc, June, 1919). Not only are the 

 aberrations of the " lenses " important. The performance of a 

 condenser is modified by the presence of a slide of very imperfect 

 optical quality. So far as its inequalities in thickness are concerned, 

 the errors arising are much reduced by the immersion medium 

 when used with the condenser; a similar remark holds in regard to 

 the objective and cover glass. 



With biological speciniensi the objective " focusses " only a thin 

 layer. If this is near the top of the specimen, the light from the 

 condenser is scattered by the layers beneath ; if it is near the bottom 



