



1 





k 



a x 





n 



+ 



W ' 



CLz 



— 



w 



+ 



w ' 



142 Dr. H. Bateman on the 



and make use of the relations 



X + A = 2£', fJL + ii Q =2v F , v + Vo = 2?, o- + <7 = 2M, . (29) 

 we obtain the field specified by the potentials 



m m 



t . Y- • (30) 

 , 1 1 I 

 <t> ~ + — • 



r IV Wq J 



The properties of this type of electromagnetic field have 

 been discussed in a previous paper *. 



When w, Wq, cr, o-q are defined by equations (19) the 

 electromagnetic field specified by the potentials 



•a — Lz 1° °L ;a -—- m ° a 



1 x ~ M w ~ M w ' y ~Mw~ M wi ' 



h- (31) 

 _ n o- no 5 •*-£ °: 2»* 



has singularities at points for which cr is zero and the 

 electric charge associated with the point (f, rj, f, t) is zero. 

 If in addition equations (26) are satisfied and we add to the 

 potentials (31), the corresponding ones in which o- is replaced 

 by cr , we obtain the potentials 



ia ~--^ 



??i m 



?z n ^ 





ia,, = — , 



ia z = 5? 



W Wq ' 



itf 2t' 



10 Wq 1 





1 1 



| 







1 



J 



(32) 



These specify an electromagnetic field in which both the 

 electric and magnetic forces at (&*, y, z, t) are perpendicular 

 to the radius from f, tj, f, t. The field has singularities at 

 points where w and w , and consequently a or cr , are zero. 

 The moving point f , 77, J", t may be described as a gun which 

 fires out magnetic doublets in directions for which a and a 

 vanish respectively. If we write 



and treat a, /3, 7 as constants, the components of the electric 

 * Phil. Mag. Oct. 1913. 



