ROTATING A DIELECTRIC IN A MAGNETIC FIELD. 135 



Tlie mean induction through the outside coating is ir (r., : r.f) 200 = 132, where r, is 

 the radius of the outside coating. Here 2r 3 = 4 '25, 2r., = 4'15 and 2r, = 2'01 centims. 



The quantity which has heen determined experimentally is the charge which, when 

 given to the outside coating, will produce a deflection equal to that observed on 

 reversing the magnetic field. Now, if l>oth the brushes were connected to earth, the 

 charge induced on the outside contiu^ would In? equal and opposite to this charge which 

 has been determined. This follows at once from the equation EC = V (C -f- ('') Q, 

 l>ecausi i when lx>th surfaces of the cylinder are at zero potential the induced charge 

 is evidently EC, E heing understood just now to include the induced electromotive 

 forces in the coatings as well as the induced electromotive force in the ehonite. 



The brush on the outside surface was at the centre of the cylinder, where the 

 Held strength is 206. Consequently the outside surface of the cylinder had a 

 mean potential, Cn (206 200) TIT.,- = -f- 85 Cn electromagnetic units below that of 

 the brush. The mean potential of the inside surface of the outside coating was 

 therefore -{- (132 -f 85) On = +217 Cn electromagnetic units below the brash. The 

 field at the brush on the inside coating was 196, so that the mean potential of the 

 inside coating was Cn (199'4 196)flT, 2 =ll Cn electromagnetic units above that of the 

 brush. The capacity between the inside and outside surfaces was 25 '4 centims., and 

 that l)etween the outside sxirface and the surrounding tube 24 centims. Consequently 

 the charges induced on the outside coating, when both brushes were earthed, were 



' Q'" = Cn (217 + 1 1) 25-4/3 X 10 10 electrostatic units 

 on the inside surface, due to the electromotive forces in the coatings. 



Q" = Cn (+ 85) 24/3 X 10 l electrostatic units 



on the outside surface, due to the electromotive force in the outside coating, and 

 Q' = (1 -- K- 1 ) Cn (2067 X 25'4)/3 X 10 l electrostatic units 



on the inside surface, due to the electromotive force in the ebonite. These equations 

 give, since K = 3 '54, 



Q'= 12-58 X 10~ 7 Cn, Q"=0'68 X 10~ 7 Cn, Q'"= 1 '93 X 10~ 7 Cn electrostatic unit. 



Thus the total charge on the outside coating was 15'19 X 10~ 7 Cn, and this should 

 be equal to Q, which was found experimentally to be 15'35 X 10~ 7 Cn electrostatic 

 unit. It thus appears that the charge, as calculated by the theory, agrees with 

 that found within the limits of experimental error. The difference between the 

 effect calculated and the mean effect found is only 1 per cent. Subtracting Q" and Q'" 

 from the effect found we get 1274 X 10~ 7 Cn electrostatic unit, which may be 

 regarded as the experimental value of the effect due to the etanite alone. The 

 corrections Q" and Q'" though somewhat large are not open to any doubt, because 



