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



connected through sliding contacts to a quadrant electrometer. On reversing the 

 direction of the magnetic field, a deflection of the electrometer needle is obtained. 

 showing that an electric displacement has been produced in the cylinder. 



The inside and outside surfaces of the cylinder are provided with thin metal 

 coatings, and a sliding contact on the outside coating is connected to one pair of 

 quadrants of the electrometer, while the inside coating is connected to the other pair 

 of quadrants and to earth. Let r. 2 be the radius of the outside surface of the 

 cylinder, and r } that of the inside surface. Let the number of revolutions per 

 second be 11, and the magnetic force parallel to the axis of the cylinder be H. Then, 

 if the cylinder were a conductor, the difference of potential V between the two 

 surfaces would be given by the equation 



V = nw (r 2 2 - r, 2 ) H, 



since V would be equal to the electromotive force induced in the cylinder. When 

 the cylinder is composed of a dielectric of specific inductive capacity K, then, 

 according to the electrodynamic theory of LORKNTZ and LARMOR, the electromotive 

 force E induced in the cylinder will be given by the equation 



Suppose that the two coatings of the cylinder are initially at zero potential, and that 

 it is then set rotating in a magnetic field parallel to its axis. Let V be the resulting 

 potential of the outside coating, the inside being permanently connected to earth. 

 The electromotive force E will produce a charge on the inner surface of the outside 

 coating, and an equal and opposite free* charge on the outside surface of the coating, 

 which will distribute itself over the connecting wire and- insulated pair of quadrants 

 of the electrometer. 



We have now to consider the electrostatic induction across the dielectric mass 

 moving through the ether, say, with velocity (f, 77, ) in a magnetic field (a, /6, y). 



By FARADAY'S principles the motion leads to electric force (rjy g/S, g-y, f/3 rja) 

 in addition to that arising from electrostatic distribution ; as the distribution of 

 current is here steady, it does not contribute. 



On the principle of the theory of electrons, this part of the force, depending on 

 the velocity of motion, acts on the electrons of the moving dielectric only, thus 

 contributing to its polarisation (/', g', h'), but does not contribute to the ethereal 

 electric displacement (/, g, h}. Thus, with electrostatic units, 



^ _ W)> whe re /= F, 



with two other similar equations. We may take these equations to represent the radial 

 components, here the only ones. Now the total electric displacement of MAXWELL, 

 represented here by / + ./', is circuital, so that (/+/') 2irr, its amount per unit 



