22 Trait surf ions of the Society. 



Very interesting results emerge if we consider what will happen 

 if some part of the conical wave-front be blotted out. For 

 example, we may suppose the apex to be cut off by an opaque 



X7 



\ 



V 



/ 



/ \ / 



1 V I \ 



' V / V 



fc T-P S 



Fig. 17. Fig. 18. 



object introduced into that part of the field, as in fig. 18. In that 

 case it is plain that we shall not have a bright dot at the level of 

 p 2 , but a projection, having reduced diameter, of the opaque object 

 surrounded by a nebula of diminished breadth. This will sud- 

 denly change into a bright dot when the plane p 5 is passed, to be 

 again reversed into a black dot as before at the level of j) x . 



The microscopist will recognise in these descriptions a close 

 resemblance to certain phenomena very familiar in high power 

 microscopy, where objects come into view having dimensions com- 

 mensurable with the dimensions of the antipoint, but for practical 

 application the theory must be so extended as to include the 

 common case in which we have to deal with sources of illumination 

 of finite extent and in which the individual antipoint is merged^ 

 and the boundaries between light and dark areas are traced by 

 diffraction fringes. The great problem then may be formulated 

 thus : What is the structure of a diffraction fringe if we assume 

 that the antipoint, instead of being monophasal, has the phase 

 structure of fig. 11, in which successive zones exhibit successive 

 phases in a regular series ? 



The mathematical solution of this problem is too intricate to 

 be developed here, and therefore my own contribution to it is 

 embodied in a note. The result of the note is a rough approxima- 

 tion only to the desired solution. It may even be that the problem 

 is not susceptible of a complete solution, but if it be I must leave 

 the task of solving it to other and abler hands. For immediate 

 purposes the broad result suffices that in a diffraction fringe, as in 

 the antipoint, we have a polyphasal surface which may be divided 

 into zones parallel to the true boundary, and when so divided will 

 exhibit the successive phases in due serial order. A typical diffrac- 

 tion fringe is represented diagrammatically in fig. 19, and it will be 

 observed that the fringe extends for a distance equal to the radius 



