J. RHEINBERG ON THE BLACK AND WHITE DOT PHENOMENON. 117 



perforations, it appears that circumstances may occur where the 

 surface of the perforation would be white.* It would necessitate 

 certain special relationships between the depth and the breadth 

 of the perforations. I have not worked this matter fully 

 out yet. 



Mr. Nelson pointed out in a paper a few years ago before the 

 Bristol Naturalists' Society (" Proceedings," Vol. VIII., Part II., 

 1896-7) that the visibility of the black and white dot depends on 

 the aperture of the objective, because the greater the aperture 

 the easier it is to obtain a black dot, and that if the aperture is 

 very small indeed only a white dot is obtainable. This admits 

 of explanation on my theory. For as all the rays beyond the 

 " critical angle " for the diatom and the medium in which it lies 

 help to form the black dot, as soon as the aperture of the 

 objective is cut down beyond a certain point, more and more of 

 these rays get cut off, till at last we have the limiting case where 

 the aperture is so small that practically only a parallel beam of 

 light is allowed to pass upwards, and this light simply passes 

 straight through the diatom perforations and the diatom silex, 

 without any chance of reflection from the sides occurring at all, 

 and therefore no black dot can come about. 



It is instructive to note that different effects will be produced 

 according to the diflferent media in which the objects are mounted, 

 since the critical angle for diatom silex and various media varies 

 very greatly. The reason why, for example, P. angulatum with 

 a |-th objective can best be resolved in air, is dependent on this. 



Another thing which helps to prove the theory is that the 

 position which the black and white dots take up are not the same. 

 Careful examination will show that the rows of white dots occupy 

 intermediate positions to those which the black dots previously 

 occupied. The explanation of this involves the action of cones 

 of light on the perforations, and cannot readily be shown by 

 diagrams. 



Finally, T should like to say that it must not be imagined that 

 my explanations pretend to anything else than to give a general 

 idea of the cause of the phenomenon. I am fully aware of their 

 incompleteness. For one thing, I have only dwelt upon the 

 formation of the black dots, and not shown how by the super- 



* This refers to ordinary iHumination, and not to the special case 

 mentioned below. 



