132 DR. HAROLD A. WILSON ON THE ELECTRIC EFFECT OF 



(4.) Comparison of the Results Obtained until the Theory. 



In section (1) we obtained an expression for the electromotive force (E) in the 

 ebonite, which was E = V (C -f- C')/C. Now V (C + C') is the quantity of electricity 

 required to produce a deflection equal to that due to E, so that, supposing that Q is 

 all produced by E, we get, theoretically, Q = EC. 



Now E = (1 K" 1 ) TraH (r 2 2 rj 2 ), so that E should be proportional to n and H ; 

 and H is proportional to C, so that, theoretically, Q should vary as Cn in agreement 

 with the results obtained. 



The direction of E should be theoretically the same as the induced electromotive 

 force in a conductor moving in a magnetic field. It was verified repeatedly when 

 doing the experiments that the sign of the charge indicated by the observed 

 deflections was the same as would have been obtained if the rotating cylinder had 

 been a conductor. The results obtained are therefore in complete agreement with 

 the theory, as regards the direction of the effect and its variation with the magnetic 

 field and rate of revolution. 



To complete the comparison of the results with the theory, it is necessary to 

 calculate the magnitude of the effect which ought to be obtained according to the 

 theory with the apparatus used. The simple formula E = TTH (1 K" 1 ) H (r 2 2 r^} 

 cannot be used for this purpose, because in the actual apparatus H was not uniform, 

 owing to the finite length of the solenoid. Further, the induced electromotive forces 

 in the conducting coatings of the cylinder have to be calculated, and the small effects 

 due to them added to the effect due to the electromotive force in the ebonite to 

 obtain the full theoretical value of the observed effect. The quantities to be 

 determined are therefore : (l) the capacity C of the ebonite cylinder; (2) the specific 

 inductive capacity of the ebonite ; and (3) the distribution of the magnetic field due 

 to the solenoid in the region occupied by the cylinder. The determination of (1) and 

 (2) will first be described. 



To determine the capacity between the inside and outside coatings of the cylinder, 

 the inside coating was connected through a commutator to a potentiometer, so that 

 it could be charged up when required to a known potential. The outside coating was 

 first connected to earth and then the inside coating charged up. The outside coating 

 was then insulated and the inside coating put to earth. The resulting deflection of 

 the electrometer gave the charge induced on the outside coating in terms of the 

 electrometer sensibility, as determined by means of the small guard-ring condenser. 

 The deflection due to charging the inside coating to 0'400 volt on one occasion was 

 185 millims. The electrometer sensibility was then - 000184 electrostatic unit per 

 millimetre, so that the capacity required is 300 X 185 X 0'000184 -=- 0'400 = 25'5 

 centims. The mean of several determinations done during the course of the experi- 

 ments was 2 5 '4 centims. 



To determine the specific inductive capacity of the ebonite, the outside coating was 



