IN THE FIELD ROUND A THEORETICAL HF.KTZIAN < >M II.LATOIJ. I r, I 



Hence, 



/, = A,e" 



where A, and A... are constants and 



apr 

 Take only an outgoing wave and write p p, + PtV 1, hence 



t/r= B e-" ( '- r> sinj ! (< ar) ....... (iv) 



where / must he > ar, or \fi = 0. 



2w 

 I/a is clearly the wave velocity v. Take p 2 = v, then 



n, 



if l = e-" (l - r) Bm' 2 (vt-r) ........ (v). 



For typical oscillators 2irpi/p t seems to vary from '3 to '5, hence >i = '3 to ' 

 or we see that if r be small as compared with X, then 



p 



/ = -- e"*' sin p t t. 



Now, if X, Y, Z lie the three components of electric force, we easily find 

 v- .*-(**\ V- ^W Z- - 



dx\dz/' dy\dz]' ' ,/ 



or they are the three components of a " potential function " 



Take B = E/, and we see that V is the potential* due to a " double point " 

 of moment oscillating between + Ele.'*' and E/e""' ; thus the maximum charges 

 rapidly diminish with the time. In fact, we have a system entirely analogous with 

 that of HERTZ, except for this rapid diminution of the maximum charges with the 

 time. It is in this running down of the maximum charges that the damping effect of 

 the oscillator consists. 

 f 



(3.) We shall now proceed to find the forces. 



In the first place let us find the value of p d\ft/dp, which, following HERTZ, we will 

 term Q. Then the components of electric and magnetic force can all be found by 

 simple differentiation of Q, >'.<., 



1 rfQ 1 dQ a dQ 



Z = - , R= , and P = - . . . . ml 



p tip p >/: p >lt 



* To \\afi HERTZ'S language, see ' Electric Wave*,' p. 142, and compare MAXWEU., vol. 1, 129. 

 VOL. CXCIII. A. V 



