PROCEEDINGS OF THE SOCIETY. 443 



marked diffraction puttern, there arc extniordinary difficulties of inter- 

 pretation unless one knows beforehand from what grating formation 

 the pattern has been derived. For example, an ai)erture having the 

 form of an equilateral triangle yields a diffraction pattern which is only 

 distinguishable by very refined details from the diffraction pattern of Jin 

 hexagonal aperture — details so refined thut they escaped the notice of 

 Schwerd — ^and it would be easy to design a structure consisting of 

 triangular openings which would give a pattern wholly indistinguishable 

 from one consisting of hexagonal openings. This is only a particular 

 instance. A more general illustration of the difficulty is att'orded by 

 taking the case of a grating structure which consists of groups of small 

 slot apertures. It is possible by arranging slots in different ways upon 

 a field to simulate almost any conceivable diffraction pattern. Unless, 

 therefore, we have the means of determining independently of the 

 diffraction pattern what is the nature of the grating structure, it is (in 

 any case presenting more than a very small complication) impossible 

 to determine the nature of the structure from which that pattern is 

 derived. 



I should like, if Mr. Hartridge will not think me presumptuous, to 

 offer the suggestion that one or two little changes in notation would 

 render his paper very much easier to read. Thus, for example, on page 

 8 of the proof of the diatom structure paper I find the symbol (d) used 

 at the top of the page to signify the distance between neighbouring 

 structure elements, and lower down upon the page the same symbol is 

 used to signify the angle of the diffracted light. In the last mentioned 

 place a second symbol (D) is introduced to signify what (d) signifies at 

 the top of the page. A further difficulty which, no doubt owing to my 

 own stupidity, gave me much trouble in reading the paper, crops up in 



connexion with the formula c:r = sin i + sin {d - i). Mr. Hartridge 



defines the angle d as being the angle which the diffracted pencil makes 

 with a normal to the grating surface. This appears to be a correct 

 definition in relation to the actual pencils with which he works, for I 

 gather that he so arranges the incident light that the angle of incidence 

 \i) shall always be equal to zero. But on the other hand, his formula 

 looks like a generalized expression, and if we give to the angle {i) any 

 finite value, it is necessary to understand that the angle {d) is the angle 

 which the diffracted pencil makes, not with the normal to the grating, 

 but with the. directly transmitted beam. It is easy to see that this last 

 is the angle which Mr. Hartridge really has in mind, because a little 

 lower down upon the page he speaks of measuring that particular angle 

 and obtaining his ratio of sin fZ/sin d at once by division. Unfortun- 

 ately for me, I tried to understand the equation just referred to where 

 it stands in the text, and without reading ahead, and had an hour's hard 

 work before I found out its meaning. 



I am, dear Sirs, 



Yours faithfully, 



J. W. Gordon. 



