Longitudinal Component in Light. 267 



tion subject to the equation 



so that we can write 



, TT r T Ifi flrfj « 2 /d 2 J lrfJ.Nl i 



By means of the differential equation we may of course express 



all the differentials of J in terms of J and — — . We may, how- 



p dp^ 



ever, simplify matters very much in the ordinary case of light 



by observing that q is generally a very large number, so that 



terms involving its powers are large. Keeping to these we 



d 2 J d n J 



see that -r-o = — g 2 J. and that the hio-hest term in -r— is 

 dp 1 7 ; ° dp n 



I "— \ J. Using these terms only we get 



py 



^M b -T^{fh-) 



8111 sine 



= 4H J. ?-=m jb. 



9 

 Without going into the question as to the best series to ex- 

 press J by it is evident from its integral form and from the 

 dynamics from which it is derived that it must represent a 

 wave propagation. In fact by integrating by parts it could 

 be expanded in the form 



J = Jj cos (pt — qp) + J 2 sin (pt — qp)* 



In any case we can see that for any constant value of p H 

 passes through a series of values giving the alternate lights 

 and darks on a screen illuminated by a narrow slit. 



Considering now the magnetic force we have 



dR Q dR n 



