Conducting Sphere on Magnetic Induction. 179 



and p large compared with /, we have, considering only 

 maximum values, for a point on the axis 



b,= 6j V h ■• T <= ' • • • • (28) 



and for a point a considerable distance from the axis 



_ 9TT 7f J,f 2 d ^ 



kl p ... (29) 



*«=»(**+ ^)?J 



It appears from these equations that when the primary 

 circuit is near the surface of the plate the normal magnetic 

 induction at a point just outside the plate is small, but that 

 the tangential magnetic induction at a point some distance 

 from the axis is not necessarily small ; hence for the purpose 

 of " Induction Telegraphy" the receiving-circuit should be 

 vertical rather than hoiizontal. 



Let /? = 1885, which makes the frequency 300 ; then for a 

 plate in which /*=1, <r = 2 . 10 13 , which are about the values 

 for sea-water according to Mr. S. Evershed's experiments, 



& 1= = -00077; 

 for yu = l, o-=1600, which are about the values for copper, 



7^=2-72; 

 for /a = 1000, cr=10 4 , which are about the values for iron. 



k x = 34-4; 



for a sphere the size of the earth a =637 x 10 6 cms. ; so that 

 in all these cases k-fi is large ; hence for a sea-water plate the 

 magnetic induction normal to the surface is 44 times as great 

 as it would be were the plate of iron, and more than 3000 

 times as great as it would be were the plate of copper. 

 Let (J J be the current in the sphere along the curve s' 



U * - a 



when Aa is large 



_ /42n + 1)j? n n 

 W " ~ (n + l)k& /(/ra)' 



