304 J. RHEINBERG ON BLACK AND WHITE DOT PHENOMENON. 



are employed, whilst the black and white dot effect is most 

 marked with wdde cones of light. 



So that I think we may dismiss spherical aberration as the 

 primary and direct cause, and regard the changes in the image 

 which tube length, etc., cause as subsidiary. 



(2) With regard to pin-hole effects, it is only necessary to 

 observe that pin-hole images have no fixed focus, and the images 

 do not alternate in light and dark. If the object be a bright 

 point the image will always be bright. 



(3) We have to examine whether bands caused by diffraction 

 are the direct cause, and I think I can show you by simple 

 geometry that this is not the case. 



Mr. Nelson finds that the distance between the black and 

 white dot in dry-mounted specimens of Pleurosigma angulatum is 

 pretty constant at 3 A, with which my own measurements agree. 

 We also know that the perforations of P. angulcUuvi are about 

 1 X apart, and that the angle between the dioptric and first 

 diffracted beams is about 60°. 



We will therefore draw lines diverging 60° from points 

 A. B. C. (fig. 2), and consider the distance A to B or B to C to be 

 1 X. Now the distance between B and B^ would rej^resent the 

 distance between the white and black dot, and it will be seen 

 that it is less than the distance from A to B or 1 X, whereas to 

 accord ^\dth fact it should be about three times as great. 



I have calculated corresponding results in the case of one or 

 two other diatoms. 



We see, therefore, that diffraction cannot be considered as the 

 direct cause of the black and white dots, notwithstanding the 

 part which diffracted light plays in every optical image. 



(4) Failing any other theory we are thrown back upon what, 

 for shortness, I may call my " critical angle " explanation, and 

 we will briefly pass over the pros and cons, beginning with the 

 latter. 



{a) Objection has been taken to my comparison wnth trellis- 

 work. It has been said that, since the position of the dot at the 

 various foci is the same, this is fatal to the argument. 



Let me admit at once that the comparison with trellis-w^ork is 

 probably too loose, seeing that we are not dealing with simple 

 bands of light and darkness crossing in one direction only, but 

 with cone-shaped figures crossing in many directions. And it is 



