408 Transactions of the Society. 



sides determined numerically ; the solution for A and (3 then 

 becomes a very simple matter. Examples of this will probably 

 occur in a future paper which I hope to bring forward later on. 



The cases of interference which are of the most frequent 

 occurrence, and which are of the greatest importance, are those 

 which lead to so-called diffraction-phenomena ; and a few words on 

 problems of this kind may save many digressions hereafter, besides 

 shedding some light on cases already dealt with in this Journal. 



These cases may be stated thus : — 



Light from a luminous point passes through certain apertures 

 — wanted, the intensity and phase of the light at any point beyond 

 those apertures. 



The solution is obtained by applying the Huyghenian principle 

 and its extension by Fresnel. 



According to the former, we obtain the light-effect at any point 

 beyond a given wave-front by considering each point in the wave- 

 front as a new source of light, but so that all of these points are at 

 any moment in the same phase and state of vibration, and by 

 combining the disturbances reaching the given point from all 

 these points of the wave-surface, according to the universal rule 

 stated above. Fresnel extended this principle to any surface con- 

 taining the diffraction apertures, whether this surface coincide with 

 the wave-fronts or not, by stipulating that the fictitious luminous 

 points in that surface must have assigned to them the relative 

 phases of the direct light reaching those points, and that the 

 combined effect at any point beyond the surface must be deduced 

 with due regard to these phase-relations. 



I will not attempt to deal with the difficulties in connection 

 with both these principles which have been raised on theoretical 

 grounds, nor with the way in which they have been overcome ; 

 those who are interested in that are strongly recommended to look 

 the subject up in Drude's " Theoretical Optics." * Suffice it to state, 

 that these investigations justify the applications of those principles 

 which are here dealth with. 



The application of these principles which is of most interest 

 in the theory of microscopical vision is that which leads to the 

 explanation of the peculiar effects produced by gratings and other 

 regular structures. 



As I have dealt with this very fully from the mathematical 

 point of view in my paper of November 1904, and in the reply to 

 the " discussion " of that paper, I need not repeat the mathematical 

 treatment. But it may be once more insisted upon that in all 

 these cases the result of the interference-phenomena is completely 

 characterised by the resulting amplitude, i.e. the maximum dis- 



* Drude. "Theory of Optics." translated by G. R. Mann and R. A. Milliken- 

 Longmans, Green and Co., 1902. 



