452 Intelligence and Miscellaneous Articles. 



angle. This amounts to 90° when self-induction is neglected ; it 

 is more than 90°, reckoned in the direction of the rotation, when 

 the self-induction becomes sensible. The magnitude of this appa- 

 rent rotation depends, when the hollow spheres are thin, in a very 

 simple manner, on the velocity of rotation ; so that thin hollow 

 spheres are especially suited for experimental investigations. With 

 hollow spheres of finite thickness the rotation is different for the 

 different layers: the inner precede the outer; their rotation is 

 bound to no limit, and increases to infinity when the velocity of 

 rotation increases infinitely. The rotation of the outermost layer 

 couverges towards a fixed value. The intensity increases at the 

 commencement with the rotation- velocity, but nowhere so rapidly 

 as the latter ; at greater velocities of rotation it diminishes again in 

 the inner layers. With infinitely increasing rotation-velocities the 

 intensity vanishes in the inner layers, and the entire phenomenon 

 is condensed at the boundary of the sphere. The current that takes 

 place here protects the interior from the external influence, apart 

 from certain limitations. 



The proof and the exact calculation of this course of the pheno- 

 menon forms the body of the investigation, to which are appended 

 the following results : — 



(1) If the self-induction be neglected, the total-current function 

 can be represented in a closed form by the outer potential without 

 any resolution of the latter according to spherical functions being 

 necessary. 



(2) Plane infinite disks are treated as portions of infinite hollow 

 spheres. Tor these, taking account of the self-induction, develop- 

 ments are given which make the solution of the outer potential 

 superfluous. 



(3) The magnetic potential of the induced current, and the heat 

 generated by it, are calculated, from which results the work requi- 

 site for maintaining the rotation, and the moment of rotation which 

 the sphere gives to the external magnets about the rotation-axis. 



(4) The calculation is extended to spheres whose mass is capable 

 of receiving magnetic polarity. 



(o) It is shown how the investigation can be extended to other 

 rotation-bodies if the effect of self-induction be neglected. With' 

 this limitation, the problem is solved for a finite circular disk. 



(6) Dielectric spheres are considered, on the assumption that in 

 them the electrodynamic forces have the same action as equal elec- 

 trostatic forces. 



(7) The formulae are applied to special cases, and the deductions 

 illustrated by drawings. The cases are : — rectilinear motions of a 

 pole over a plane plate at different velocities : an infinite and a 

 finite disk rotating under the influence of rectilinear currents ; very 

 thin hollow spheres, and solid spheres, in a homogeneous magnetic 

 field ; stopping rotating conducting spheres by a suddenly excited 

 electromagnet; damping in a galvanometer with a hollow spherical 

 damper.— Wiedemann's Beiblatter, 1880, No. 8, pp. 622-624. 



