348 M. E, Jochmann on Induction in a Rotating Conductor. 



trie spherical surfaces. It likewise follows therefrom that the 

 results are also immediately applicable to the case of a shell 

 bounded by two concentric spherical surfaces. In this case, 

 however, we must also assume a distribution of free electricity 

 on the inner surface of the hollow sphere, of such a nature that, 

 in virtue of its presence together with that of the electricity 

 within the conductor and on its external surface, the potential 

 V may acquire the above value. The form of the current- 

 curves within the conductor is determined by the equations 



r= const., W = const. 



The components of the action of the system of induced currents 

 upon an external magnetic pole m are 



dQ dQ dQ 



~ m W ~ m W ~ m "5T 



where f, 77, f are the coordinates of the pole, and 



Q= ^(^'^dx'dy' dz' + A ( V'^drfdy'dJ+^V'jdrfdy'dz', 



in w r hich expression M/ 7 denotes what \P" becomes when x, y, z are 

 changed into x\ y' } z', and, for brevity, we have put 



The integration can easily be effected when it is required to 

 calculate the reaction of the system of induced currents upon a 

 single inducing pole, or when, after differentiation, £, 77, f are 

 made equal to a, b, c respectively, and consequently V to p. For 

 then, putting for simplicity 6 = 0, we have in the case of a solid 

 sphere of radius R, 



nkKira^VSRs 2 — 7R 3 9s 2 -R 2 , s-R 



y= _ + 



l0 * *TrJ ' 



2s 2 L s 2 -R 2 ' 2s ° s + R. 



and in the case of a hollow sphere with internal and external 

 radii equal to R l3 R 2 , respectively, 



nkK'rraii 9 r9rs 9 — 7r a 9s 2 -r 2 s-rl^ 



Y= 2^~ h^ ^-^s-^sTrl^' 



whilst in both cases 



x=o, z=o. 



The relation between these results and those obtained in the 

 former memoir for the case of a plane disk is manifest. 



The result takes a remarkably simple form under the hypo- 

 thesis of a sphere rotating under the influence of a constant 

 magnetic force, such as that of the earth. The coordinate plane 

 y = may now be made to coincide with the plane of the axis of 

 rotation and the direction of magnetic force, or, as we may call 



