268 Prof. G. F. FitzGerald on the 



and hence the longitudinal magnetic component 



^H x dK y 



wi= — . -i-'~- 



ay p dx p 



From this it is evident that in every such case m = so far as 

 H is a function of p only. Thus we get 



m 



4-TT T^ #e cose — sine 



t = 4H 



p p e" 



This shows that m does not in general vanish but lias alterna- 

 tions of value like H. The tangential component has for its 

 most important term 



d J sin e 



dp e 



It is evident that this longitudinal displacement is necessary 

 at the edge of the beam in order to prevent any concentration 

 of the magnetic force. So far as our a priori knowledge of 

 pure aether is concerned there seems no sufficient reason for 

 not supposing a concentration of magnetic force just as 

 probable as one of electric force. It would certainly com- 

 plicate our equations very much to suppose both. If both 

 existed we might have two kinds of pressural waves, one a 

 wave of electric condensation and rarefaction, and the other 

 a wave of magnetic condensation and rarefaction. 



It is quite evident from all these cases and from general 

 considerations that the edge of every beam of light is bordered 

 by a region where there are longitudinal vibrations taking 

 place. 



Y. As a final example I take the case of a series of slits 

 forming an optical grating. 



In this case the simplest supposition is to assume that the 

 opacity of the grating varies in a simply periodic manner. 

 This leads to the same sort of equation for H as in the last 

 case except that the intensity in each line is proportional to 



2tt 

 (1 -j-cos ly), where 1= — and s is the interval between the 



lines. s 



This leads to the integral 



where 



H = 2H f " f " (1 + C0S ^ C0S ^'^ dy dz, 



Jo Jo r 



r 2 = V+yo-*/ 2 + ^. 



Now from general considerations it is evident that it must 

 be possible to expand this in terms of cos ly by Fourier's 



