Longitudinal Component in Light. 269 



theorem, so that 



H = Ii + /*! cos ly + h 2 cos 2ly + h z cos 2tly + . . . 



Observing then that H being a function of x an d */o 01 ^y 

 satisfies the equation 



we get that in general 



so that 



7^ .» = H„ cos ■>/ q 2 — jiH 2 . a, 



so long as nl is < q ; and when nl is > q 



as the value cannot increase to infinity. 

 We thus get the general form for H, 



H = H cos (pt — qx) + H l cos lycos (pt— \/q 2 — l 2 oc) + ... 



+ H n cos nly cos {pt— \/q 2 —n 2 l 2 .x) + ... 



+ H m cos mlye~^ m2L2 -<i Zx cos pt + . . . 



It would appear from this that at the surface of the grating, 

 where x = when £ = 0, 



H = H + H x cos ly + . , . + H n cos nly + . . . 



It would consequently seem that this must in general 

 represent the distribution of opacity at the grating, and that 

 in the case of a simply periodic distribution the general form 

 of H would be 



H = H cos {pt — qx) +B4 cos ly cos {pt— s/q^ — P . x). 



We thus get an interesting form for the double integral for H. 

 The magnetic force to be calculated from this is 



and consequently 



a— — ZHiSin lycos {pt— */q 2 — Z 2 .#), 



J3 = ^H sin {pt — qx) + \/q 2 — l 2 Hi cos ly sin {pt— \/q 2 — l' 2 x). 



In this a. is the longitudinal component of the magnetic 

 force. This represents a series of waves being propagated 

 a way from the grating, together with a series of elliptic 



