J. RHEINBERG ON BLACK AND WHITE DOT PHENOMENON. 307 



the perforated membranes of diatoms. This shows that another 

 disturbing factor which is often present is not the primary 

 cause. I refer to the fact that in viewing a diatom valve we are 

 frequently looking upon what is practically a double layer, one on 

 top of the other, with perforations facing each other, so that the 

 optical appearance resulting from the lower layer might upset or 

 modify those due to the upper layer. But this objectionable 

 influence is to a great extent done away with, in viewing the 

 perforated membranes within the coarser perforations, since, so far 

 as I am able to ascertain, there is only a single layer of this 

 secondary structure. 



Summing up the points in favour of the critical angle 

 explanation, we fl.nd — 



(a) It will explain the appearances without recourse to other 

 than the most ordinary and generally established optical laws. 



(b) It accounts for the fact that wide-angled objectives will 

 show the results better than narrow-angled ones ; similarly it 

 shows why wide cones are more favourable than narrow ones for 

 the production of the appearances. 



(c) It allows for the alteration of appearances due to spherical 

 aberration, tube length, etc. It can also be shovv^n to harmonise 

 with those changes at different foci caused by diffraction. 



(d) It accounts for the appearances of edges of a transparent 

 object, and of transparent isolated objects, as bacilli, etc.* 



(e) The dimensions of the perforations, particularly the 

 relation of depth to width, account in the simplest way for the 

 fact that sometimes the white dot is seen above and the black 

 belo\v^, sometimes vice versd. It is simply a matter of an extra 

 reflection at the wall. 



(/) Different dimensions of the perforations explain the 

 varying vertical distances between the black and white dots seen 

 in different diatoms on the same slide. 



(</) Lastly, the existence of patches on a diatom showing 

 reverse order of the black and white dot can be accounted for by 

 the difference of refractive index of the gum or other medium in 

 which that portion of the diatom forming the patch is immersed. 



* In non-transparent edges and objects, somewhat similar results may be 

 obtained, more especially with narrow cones, which have their origin 

 entirely in diffraction. In transparent objects and wide cones of light, the 

 change in appearance due to the latter cause is minimised. 



