12 Mr. J. J. Thomson on the Magnetic Effects 



So that if the sphere is placed in a magnetic field the force 

 acting upon it is the same as that on a current \ea> cospt. 



When the sphere is moving with a uniform velocity ©, 

 equations (3) become 



1 _„, 2 d 2 F ^ d 2 ty 



whence 



d 2 a d 2 a d 2 a/^ _ ^\_a 

 dx~ 2 + df + d?\ #J ' 



where v is the velocity of propagation of electrodynamic action 

 through the dielectric. If we put 



this equation becomes 



d 2 a d 2 a d 2 a _ ft 

 dx 2 dy 2 dz Y 2 ~ 



With similar equations for b and c, we see that a solution of 

 these equations is 



jd 1 n 



dy V?+7+i? ; 



dx V^ 2 + ?/ 2 + ^ 2 ' 

 c = 0; 



where k is a constant. Since, if fi=l, 



a df __dc db 

 dt dy dz' 



and 



dj___ _ df 

 dt~ m dz' 



we have 



— 4:7TQ)f= — b = k 



dx Vx 2 +y 2 + z? 

 Similarly 



— 4ttg>#= +a = k— - 



and 



dy Vx 2 +y 2 + z x 2 ' 



, dh db da , d? 1 



— 47TO) -7- = — =- = k 



dz dx dy dz x 2 \/ a? + y 2 + z x 2 ' 



