434 Prof. Rowland on Spherical Waves of Light 



*'=-W V5i "*{ [1+cosS] [ 1 -rp]-4'} 6 "' s< " v " A ' 



1 = — ; — 5- sin I 



And for the magnetic induction, 



36'X'y 

 2VKp 



£ sin * { [1 + cos 0] [l - 1] - ^ } e-«CP-vo<fc, 



$ 



P" = i***^ sin sin A { 1- "£■ } r*0>-™>(h. 



In these v is the thickness of the disturbed stratum, so that 

 vds=dv. The electric displacement within the stratum is 



When bp is very large, the disturbance is in the spherical 

 surface; and indeed it only requires a fraction of an inch from 

 the origin to be able to omit the terms in bp, and also P' 

 and P". The equations then become very simple, as follows. 

 The electric displacement, 



r r. 



©' = —7 cos 0(1 + cos 0)e- ib b-vt>d8, 



<&' = -^^ sin 0(1 + cos e)e' ib( P- Y Ods; 

 and the magnetic induction, 



0" = j^jr? sin 0(1 + cos 6)e-^-v*)ds, 



q 7 2 "V / 



P" = lyj-cos 0(1 + cos 0)e-^-yOds. 



From either of these expressions or the more exact ones 

 we see that the distribution of the magnetic induction is 

 exactly the same, but turned around the axis of Z 90°, as the 

 electric displacement. As this result would also apply to the 

 elastic-solid theory, we conclude that diffraction gives no means 

 of determining the relation between the displacement and plane 



