﻿Motion of Constant Electromagnetic Systems. 1125 



Jochmann * and Larmor t have both worked out the 

 general form of the solution £01* the case in which the system 

 is a conducting solid of revolution and the magnetic induction 

 symmetrical about the axis of rotation, and have given the 

 details for the case in which the solid is a sphere and the 

 induction uniform. 



The potential at a point distant r=(>a) from the centre 

 of the sphere and with co-latitude is 



n a 1 a 5 / 3 . „ A lcoBa* 



i/r = C .rtwB— 1—- sin- 01+ *< , 



cr 6 cr 6 \ 2 J 6 cr 



where co is the angular velocity and C is a constant. When 

 the sphere remains insulated from the initiation of the motion, 



Q= — t and only the middle term of yjr remains. 



o 



When the pole is earthed, = J. The sphere is uniformly 



charged within, the volume density being — - — § . Still 



further details are given by Jochmann. 



§14. If the rotating body is magnetic, it is electrically 

 polarized by the motion, the polarization at any point where 



the intensity of magnetization is I being P= - [(W)!]. On 



account of the conductivity of the body, however, ^an equal 

 and opposite polarization is produced by electric induction, 

 and no gross effect of the polarization appears. The ex- 

 istence of this polarization, but with the wrong sign, together 

 with its neutralization by conduction, has been pointed out 

 by JSwann (/. c. ante). 



§15. Experiments by the author §, by E. H. Kennard || r 

 and by G. B. Pegramlf, in which a screened cylindrical 

 condenser was placed coaxially in the field of the rotating 

 system of § 13, short-circuited, and tested for charge when 

 at rest and when rotating with the electromagnetic system, 



* E. Jochmann, Crelle's Journal, xxxvi. p. 329 (1863) ; also Phil. Mag* 

 xxviii. p. 347 (1864). 



t J- Larmor, Phil. Mag. xvii. p. 1, Jan. 1884. See also, J. Larmor, 

 Roy. Soc. Phil. Trans. A. 186, p. 695 (1895). 



X Recently the above results for the sphere have been published by 

 Swann, /. c. ante, who does not refer to previous investigators. 



§ S. J. Barnett, Phys. Rev. xxxv. p. 323 (1912). 



|| E. H. Kennard, Phil. Mag. xxxiii. p. 179 (1917) ; see also, for a 

 related experiment, Phil. Mag. xxiii. p. 937 (1912). 



11 G. B. Pegram, Phys. Rev. x. p. 595 (1917). 



