in Conducting Sheets and Solid Bodies. 7 



When the oscillations are produced by sound, as in the tele- 

 phone, we find, on taking the number of vibrations as 350 

 per second, and n=2 to roughly represent the case, that the 

 values of p and k are equal for a thickness of -^ centim. and a 

 radius of 3 centim. In this case half the original field is sup- 

 pressed inside the shell, and a new field of the same intensity 

 as this half is added whose phase of oscillation is increased by 

 a quarter period. By increasing the radius or the thickness, we 

 soon make k the most important term; but if the area of the 

 original magnetic disturbance remain the same, n=2 will not 

 represent the circumstances when the radius is very large. 

 At any rate, if the number of vibrations per second or trie 

 thickness of the sheet is increased, say fourfold, we have now 

 #=4p, \^ of the original field will be suppressed, and a new 

 field of ^f of the original with phase augmented by a quarter 

 period will be introduced. 



In the Phil. Mag. for 1882 Lord Eayleigh describes an ex- 

 periment in which a coil conveying a current with a micro- 

 phone-clock in circuit was placed close to another coil con- 

 nected with a telephone, and the insertion of a thick plate of 

 copper between the coils very considerably diminished the 

 inductive effect in the telephone. 



IV. For the case of a solid sphere or a shell of considerable 

 thickness, the very remarkable conclusion holds that no ex- 

 ternal magnetic disturbance whatever can induce currents 

 which do not circulate in concentric shells. In fact, it 

 appears that no difference would be produced if the sphere 

 consisted of concentric layers separated by infinitely thin non- 

 conducting partitions. For, assuming such a distribution, and 

 replacing it for the instant by its corresponding lamellar 

 magnet of strength <1> at the point considered, we have for 



outside space a corresponding magnetic potential H = — (Pr), 



where P is the potential due to a distribution of matter whose 



density is throughout the shell. The components of the 



outside vector potential are, as before, 0, - — tttt? ~~ -ttt- 

 r ; ' sin 6 dcf> dd 



Inside the shell 12 clearly denotes the potential of the magnetic 

 induction of this equivalent lamellar magnet, from which the 

 vector potential is derived as before. We have V 2 P equal to 



— — — inside the shell, and equal to zero outside, by Laplace's 

 equation. 



