Mr maxwell, ON FARADAY'S LINES OF FORCE. 



81 



XII. Spherical shell revolving in magnetic field. 



Let us next take the case of a revolving shell of conducting matter under the influence 

 of a uniform field of magnetic force. The phenomena are explained by Faraday in his 

 Experimental Researches, Series II., and references are there given to previous experiments. 



Let the axis of z be the axis of revolution, and let the angular velocity be w. Let 

 the magnetism of the field be represented in quantity by /, inclined at an angle 9 to the 

 direction of z, in the plane of zx. 



Let R be the radius of the spherical shell, and T the thickness. Let the quantities 

 Oo, /3o, 7o» l>6 t^^ electro-tonic functions at any point of space; a^, b„ c,, Oj, jS,, 71 symbols 

 of magnetic quantity and intensity; a^, b^, c^, a^, /Sj, 72 of electric quantity and intensity. 

 Let Pa be the electric tension at any point, 



dpi 

 dx 



/3. = |^ + A62 ^ 0) 



7,= -+*C3 



da^ db^ dc^ 



dx dy dz 



2 dfi^ dy^ 



+ + ■ 



dx dy dz 



da. 



=V> 



(2); 



The expressions for a^, /3o, 70 ^^^ to the magnetism of the field are 



ao = -^0 + ~ y cos 6, 



(if, =' Ba + - (z sin 6 - X cos 6), 



^ I • ^ 



yo= Co--y sm 9, 



Aq, Bg, C(, being constants; and the velocities of the particles of the revolving sphere are 



dx 



dy 

 dt 



= wx. 



dz 

 di 



= 0. 



We have therefore for the electro-motive forces 



1 doo I I 

 a^— — = cos y o)X, 



^.= - 



72 = - 



47r dt 



47r dt 



— hi.. 

 47r dt 



4>7r 2 



cos 9wy, 



47r 2 ^ 



sin 9a)X. 



47r2 



Vol. X. Paet L 



11 



