ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 369 



alternately light and dark spaces, so do the diatoms when the focus is 

 adjusted to different planes. Mr. Rheinberg prefers the black dot 

 image, and gives full reasons for bis preference, and states also that dif- 

 ferent effects will be produced, according to the different media in which 

 the objects are mounted ; and that the positions which the black and 

 white dots take up are not the same, because careful examination will 

 show that the rows of white dots occupy intermediate positions to those 

 which the black dots previously occupied. 



E. M. Nelson,* in discussing this subject, applied the same lens and 

 illumination to diatoms marked with various degrees of fineness. He 

 considers that Mr. Stokes is right in assigning to spherical aberration 

 an important function, for in those cases where there is a white dot both 

 above and below the black dot, the upper or lower white dot can be 

 made the stronger or weaker, or both made alike, by means of screw- 

 collar or tube-length adjustments. He has also reason for thinking that 

 the upper black dots observed by Mr. Stokes with annular illumination 

 must have been images of the stop at the back of the condenser. The 

 examination of a considerable number of specimens has shown that there 

 is more variety in the association of the blackness and whiteness than is 

 commonly supposed. Thus a balsam-mounted Pleurosigma formosum 

 generally has the white dot below; but Mr. Nelson has met with a 

 reverse example. He finds, so far as he can measure it accurately, that 

 the distance between the two dots is fairly constant at 3 A. 



With regard to Mr. Rheinberg's papers, Mr. Nelson is of opinion, 

 after many careful observations, that the white and black dots are exactly 

 superimposed. This seems to be a fatal objection to the trellis- work 

 theory, notwithstanding its interest and ingenuity. 



In a paper read before the Quekett last March, Mr. Rheinberg 

 returns to the study of the subject and admits that the two dots are 

 superimposed. He then sums up the possible theories as four, viz. : — 



(1) Spherical aberration by reason of the objective acting in zones, 

 each zone having its own focus within certain limits. 



(2) A pinhole effect. 



(3) Crossing of bands arising from diffraction. 



(4) Crossing of bands (or rather cones) formed by reason of the 

 difference of refractive indices of the media, in accordance with the 

 ordinary laws of total reflection beyond the critical angle. 



He gives his reasons why the last should be preferred, and also 

 suggests that " critical angle " rather than " trellis-work " theory is the 

 more suitable short title. It has the following six points in its favour: — 



(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, &c. It can also be shown to harmonise with 

 those changes at different foci caused by diffraction. 



* Tom. cit. (April 1902) pp. 261-5 (5 figs.). 



