The Followers of Maxwell. 361 



is approximately a plane wave, the opposite sides of the ring 

 representing the two phases of the wave. When one of these 

 rings has become detached from the radiator, the energy con- 

 tained may subsequently be regarded as travelling outwards 

 with it. 



To discuss the problem analytically* we take the axis of 

 the radiator as axis of z, and the centre of the spark-gap as 

 origin. The field may be regarded as due to an electric doublet 

 formed of a positive and an equal negative charge, displaced 

 from each other along the axis of the vibrator, and of 



moment 



Ae~ p ^ sin (2irct/\), 



the factor e~ p ^ being inserted to represent the damping. 



The simplest method of proceeding, which was suggested by 

 Fitz Gerald,f is to form the retarded potentials < and a of 

 L. Lorenz.J These are determined in terms of the charges and 

 their velocities by the equations 



I. * = a <^, o.-s^, 



whence it is readily shown that in the present case 



4> = - dF/dz, a = (0, 0, 

 where 



Ae'KC-'P , 2;r . , 

 F = sin (ct - r). 



T A* 



The electric and magnetic forces are then determined by the 

 equations 



E = c 2 grad < - a, H = curl a. 



It is found that the electric force may be regarded as com- 

 pounded of a force < 2 , parallel to the axis of the vibrator and 

 depending at any instant only on the distance from the vibrator, 

 together with a force fa sin acting in the meridian plane 



* Cf. Karl Pearson and A. Lee, Phil. Trans, cxciii (1899), p. 165. 

 + Brit. Assoc. Rep., Leeds (1890), p. 755. 



J Cf. p. 298. The use of retarded potentials was also recommended in the 

 following year by Poincare, Comptes Rendus, cxiii (1891), p. 515. 



