MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 191 



electric type. Those depending on odd order harmonics are damped harmonic waves, 

 while those depending on even order harmonics are a mixture of exponential and 

 damped harmonic waves. 



Similarly, changes of rotary motion of a charged sphere give rise to disturbances 

 of magnetic type. Those depending on even order harmonics are damped harmonic 

 waves, while those depending on odd order harmonics are a mixture of exponential 

 and damped harmonic waves. That depending on the first order harmonic is, 

 however, a purely exponential wave. 



13. Induced Electrification and Electric Vibration* on a Conducting Sphere 

 moving with Uniform Speed. When a fixed spherical conductor is under the 

 influence of an electrical field, the problem of finding the induced potential is, as is 

 well known, a comparatively simple matter, an inducing potential involving the 

 same spherical harmonic and no other. 



If, however, a spherical conductor is constrained to move uniformly in a straight 

 line in a specified electrical field, the problem is more difficult. An inducing normal 

 force involving a given spherical harmonic no longer gives rise to an induced surface 

 density involving only the same spherical harmonic, hut terms involving other 

 spherical harmonics may also arise. 



The form of solution for a given inducing field depends on what we take as the 

 proper boundary condition. As has been shown, we may take the condition (l) that 

 the tangential component of electric force (X, Y, Z) should vanish at the surface of 

 the sphere, or the condition (2) that the tangential component of (X', Y', Z') should 

 vanish at the surface of the sphere. 



I propose now to give the solutions for the case of a spherical conductor constrained 

 to move in the direction of x with a uniform velocity /(,! in a field of uniform 

 force F, which is parallel to the direction of motion. With condition (2) the problem 

 may be stated as follows : 



Determine a function, r/>, which satisfies 



O.JT Vlf CZ~ 



so that the tangential component of 





a// ' BZ I 



at r a shall be equal to the tangential component of 



(l-P)F(- 1,0,0). 



If, as before, 



- - 



i y ~ ; r~ 



coslr -n sinlr 



