2 Prof. A. Schuster's Electrical Notes. 



magnetic effects of a moving charge all these investigations 

 have led to the same result, but there is a remarkable 

 discrepancy in the expression for the force which acts on the 

 charge if it is moving in a magnetic field. In his first paper 

 J. J. Thomson calculates that force to be ^fiepH, where p, is 

 the magnetic permeability, e the charge, p the velocity, and 

 H the field, the motion being supposed to take place at right 

 angles to the lines of force. Heaviside omits the factor ^. 

 In his later researches J. J. Thomson calculates the force to 

 be i/jLepH, and I believe he still takes this expression to be 

 the correct one, applying it to some of his experiments on 

 gas discharges. There are also some other discrepancies 

 between J. J. Thomson's first paper and Heaviside's, which 

 are exhibited in a tabular form as follows :*— 



J. J. Thomson, 1881. 

 T. 2/**y/15a 



X. ifiepH. 



M. 



$fMie 2 pip 2 - 



COS 6 



Heaviside, 1889. 

 fie 2 p 2 /Sa 



fiepH 



W&P1P2 



J. J. Thomson, 1893. 

 fie 2 p 2 IZa 



&eptt 



(cos e + cos a cos ft) 



Here T represents the energy of the magnetic field pro- 

 duced by a moving sphere of radius a, and M the mutual 

 energy of a pair of spheres carrying charges e ly e 2 , and moving 

 with velocities p^ p 2 . X is the force already referred to 

 which acts in a magnetic field H on the moving particle. 



2. In the " Bakerian Lecture " of 1890, I calculated the 

 effects of a magnetic field on kathode rays, and adopted 

 Heaviside's expression for the foree acting on a moving 

 electrified particle. I may here give the simple reasoning 

 which seemed to me to show its correctness. 



Let ABC (Fig. 1) be a circular ring made up of a large 

 number of rigidly connected but insulated electrified parts. 

 Let e be the electric charge of each of 

 these parts, and let their number per unit 

 length be N. Let this ring be set into 

 rotation about its axis MM', the linear 

 velocity being p, and let the two following 

 assumptions be made : — 



(1) The magnetic field produced by the 

 convection of the electrified ring is the 

 same as that of a current of strength Nep 

 circulating round a conductor coinci- 

 dent with the ring. 



(2) The magnetic action of the revolving ring on a magnet 



