[ 326 ] 

 XXXVIII. Intelligence and Miscellaneous Articles. 



ELECTROMAGNETIC INDUCTION IN SPHERES. 

 To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



IN the ' Philosophical Magazine ' for January 1884, Prof. Larmor 

 has published a paper* containing highly interesting researches 

 on the electromagnetic induction in continuous conductors, espe- 

 cially in spherical shells and in spheres. I hope I may be allowed 

 to publish a few lines in order to show that the results of Professor 

 Larmor concerning the induction in spheres have been published 

 some years ago by myself. 



In a paper, " Ueber die Schwingungen eines Magnets unter dem 

 Einfluss einer Kupf erkugel," t I have dealt with the electricity 

 induced in a copper sphere by an oscillating magnet and with the 

 influence of the induced currents on the motion of the magnet. In 

 a second paper, " Einige Versuche liber Induction in korperlichen 

 Leitern,"J I have treated the same problem for a system of 

 magnets. This includes the case of a rotating sphere and magnets 

 at rest, the electromagnetic induction being the same whether the 

 sphere is at rest and the magnet rotates round an axis, or the 

 sphere is rotating round this axis and the magnet is at rest. More- 

 over I have developed the solution of the equations for the case of 

 a sphere rotating in a uniform magnetic field, and for all the cases 

 I have determined the couple of the induced currents on the moving 

 magnets or on the rotating sphere. As Prof. Larmor has given his 

 forruulse expressed in Bessel's functions and in spherical harmonics, 

 they can easily be compared with mine given in terms of the same 

 functions. Indeed the results agree very well. 



At page 21 of his paper Prof. Larmor says : — " It would be very 

 interesting to determine the absolute value of the couple for a 

 copper sphere in a uniform rotating field of known strength, and 

 to determine the log. decrement of its torsional oscillations due to 

 induction in a stationary field, and to deduce thence, by approxima- 

 tion from the general f ormulso, two values for the specific resistance. 



No absolute quantitative experimental verification appears 



to have yet been made for induction-currents in continuous media." 

 I have tested my formula? by experiment, and derived from these 

 experiments values for the specific resistance of copper. Eor a 

 first copper sphere I have found: — Diameter d=92-94 millim. ; 



specific weight s =8-88 ; specific resistance X= 444278 . 1Q n For 



* " Electromagnetic Induction in Conducting Sheets and Solid Bodies." 

 t Inaugural Dissertation, Gbttingen, 1875. Nachrichten der kgl. 



Ges. der Wissenschaften zu Gottingen, 1875, p. 308. 

 \ Wiedemann's Annalen, Bd. xi. p. 812 (1880). Nachrichten der kgl. 



Ges. der Wissenschaften zu Gottingen, 1880, p, 491. 



