ROTATING A DIKI.K(Ti;lC IN A MAUNKTIC FIKLD. 128 



I 'iigth measured axially across a concentric cylinder of radius r, is the same for all 

 values of r ; it is equal to Q, the charge per unit length with changed sign on 

 the inner face of the outside coating of the cylindrical condenser. Moreover, F" is 

 here dV /dr, where V is the potential of the electrostatic distribution because it is 

 a steady one. Thus, ft being the number of revolutions per second in the axial 

 magnetic field H, 



_ Q = * ["- 27rr rf . V + (\ - 

 47T |_ ar 







Integrating this equation from r = /-, to / = r t we get 



- log = - (V, - V,) + l - H (r/ - r,'). 



Let C lie the capacity, Iwtween the two coatings, of unit length of the cylinder, also 

 let V 2 V, = V, and E = (1 K~') irH(r 8 * r, 2 ) ; then this equation becomes 



- Q/C =: - V + E. 



Now, if the capacity of the connected apparatus, consisting of the outside surface 

 of the outside coating together with the connecting wires and electrometer, is C', and 

 if we now let Q and C each apply to the whole length of the actual cylinder, we 

 have Q/C = V + E ; and V = Q/C', as the total charge of the system is zero ; 

 so that, eliminating Q. we get E = V (C 4- C^C. 



This equation will l>e true for the actual cylinder of finite length if C is taken to 

 be the actual capacity between the outside and inside coatings, which of course will 



K/ 



be a little greater than - , where / is the length of the cylinder. 



2 log rj/r, 



Suppose now that a quantity of electricity, q, given to the whole insulated system 

 produces a rise of potential ?',.so that v = q/(C 4- C'), then multiplying the equation 

 E = V (C + C')/C by this, we get E = V/r . q/C. If the electrometer deflection due 

 to V is D, and that due to v is d, this equation may be written E = D/d . ///C. 



Thus E can be determined in terms of the two deflections of the electrometer, the 

 known charge, and the capacity between the outside and inside coatings of the 

 cylinder. It has been assumed in the above discussion of the theory of the 

 experiment that the magnetic force is everywhere parallel to the axis of the rotating 

 cylinder. In the actual experiments this was only approximately the case. The 

 necessary corrections on this account are considered in Section 4. 



(2.) Description of Apparatits. 



A Government Grant from the Royal Society of 36 was obtained in 1903 to cover 

 the cost of apparatus for the experiment. The apparatus used was originally made by 

 W. G. PYE & Co., of Cambridge, but it was afterwards modified in detail by the 

 mechanics of the Cavendish Lalmratory workshop. 



K 2 



