734 PROCEEDINGS OF THE SOCIETY. 



the problem, and had thus been led to a different solution which is, as 

 a matter of fact, impossible, because devoid of physical meaning, as I 

 shall show presently. I therefore wrote privately to Mr. Gordon, point- 

 ing this out, and repeating the essential parts of my argument ; but as 

 he does not, apparently, accept my explanation, and maintains his 

 objection, it becomes necessary to publish my answer to his indictment. 



A repetition of my proof of the theorem in question, carried out 

 with more minute care as to definitions, will probably be the quickest 

 way of stating my case, which is a very simple example of the applica- 

 tion of Huyghens' principle. 



The latter teaches us that the whole disturbance caused by coherent 

 light from any given aperture at any point beyond that aperture is 

 determined by the sum (or integral) of all the elementary disturbances 

 produced by light from the component elements of the given area. 



Referring to fig. 95 accompanying my paper, the wave-motion pro- 

 duced in the sufficiently distant reference-plane C D by the undulations 

 from an element of surface, or strip, in the centre of the slit A of a 

 grating was expressed by the formula 



(1) x A = c . sin a ; 



and I took great pains to clearly point out a as an angle uniformly in- 

 creasing by 360° for every complete vibration or wave. I used the 

 simple symbol a for this ever-increasing angle for the sake of brevity, 

 as in the whole of this proof its sine only appears as a common factor 



of all the terms. Its value is mathematically to be stated as 2 ir - t ; 



A 



where i? has the usual meaning, A. is the wave-length of the light under 

 consideration, v the velocity of light, and / the time reckoned from the 

 instant when the first undulation is assumed to have reached the plane 

 C D. And it must of course be borne in mind that this meaning is 

 to be permanently connected with my angle a, as otherwise the physical 

 meaning of the various equations would be lost, owing to their no 

 longer expressing light- vibrations. 



I next considered two elementary strips of the slit, E and F, equi- 

 distant from the central strip A, and designated the constant difference 

 of phase between the light reaching C D from those elements and that 

 from A by an angle /?, which, consequently, is independent of time. 

 The wave-motion which light from E and F would produce in the 

 plane C D contemporaneously with the light from A according to (1) 

 would then be 



(2) x F = c sin (a — /?) 



(3) x r = c sin (a -f- /?). 



I next added these two disturbances together by solving the sines, 

 and obtained 



II. x s -f x F = 2 c cos /? sin a ; 



and I tabulated the value of the amplitude : 2 c . cos /3 in column 2 of 

 Table I. 



Corresponding pairs of elementary strips are to be formed so as to 

 cover the entire width of the slit. Let the number of pairs be n with 



