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XLI. On Induction in a Rotating Conductor. 

 By E. Jochmann*. 



THE equations (26) and (27) of my memoir " On the Elec- 

 tric Currents induced by a Magnet in a Rotating Con- 

 ductor'^ can be easily integrated, by means of a development in 

 series according to spherical functions, in the special case of a 

 conducting sphere rotating around one of its diameters. The 

 results, on account of their remarkable simplicity, shall be 

 here given. 



Let 



s = ^a? + b 2 + c 2 



be the distance of an inducing pole from the centre of the sphere, 

 and X denote the angle between the directions of s and r, where 



r=vV + 2/ 2 + **; 



then if p represent, as before, the distance of the point (x, y, z), 

 within the conductor, from the inducing pole, so that 



p 2 - = r 2 + s 2 — 2rs cos X, 

 we shall have 



tt n ,v Her— ss cos X) 

 r sp(p + s—rcosX) 



where the summation is to be extended to all the existing mag- 

 netic poles. If, further, we put 



Y=2nkJ&r , f* ~ ay w 

 psyp + s—r cos X) 



the components of the current- density at the point (x, y, z) 

 will be 



oW oW 



U=V^r Z 5T — i 



y oz oy 



d¥ 0^ 



Ox dz 



oV oV 



w=x ~ y-^—' 



oy J ox 



From the form of these expressions it is manifest that the radial 

 components of the current at each point within the sphere 

 vanish, — in other words, that all the currents flow on concen- 



* From the Journal fur die reine und anqewandte Mathematik, vol. xxxvi. 

 p. 329. 



f Phil. Mag. S. 4. vol. xxvii.p.522. 



2 A2 



