Shielding of Concentric Spherical Shells. 105 



The true values of the unshielded forces are 



-2f /a! 3 and 2^o/(2aO 3 = O25^ M 3 . 

 The above series gives 



-l-994^ /«i 3 and 0248^/^ 



which proves that the number of terms taken gives results 

 sufficiently approximate for the purpose of illustration. 

 The corresponding values of the shielded forces are 



-0294-^o/a! 3 and 0-081f 0/ V. 



These conclusions may be summed up as follows : — 



Let A and B be the two external points, and let A be that 



towards which the magnet is moved. Then we get the results 



given in the following table : 



Position of Magnet. 



Centre 



Halfway between centre 

 and outer boundary of 

 shell. 



Numbers proportional 

 to force when 



Unshielded. I Shielded. 



0*593 at 

 A&B 



2 at A 



0-25 at B 



0-137 



0-294 



0081 



Eatio. 



0-23 



015 



0-33 



Case of Two or Three Concentric Shells of the same 

 Permeability separated by Air- Gaps. 



In the case of three shells there are twelve simultaneous 

 equations, and we finally get : — 



M* [gniya! — ZcL^a^Ui — a 5 )(a 2 -oc s ) ^ 



+ %V {V a 2 — ?«3) a 2«<t( a — «i) («4 - a g) 



+ %v(v*5— £*i)<x2 a z( a o— «i)(«2— «s) y. . . (3) 



= ^|r a a 1 a 2 a 3 a 4 (N + 1) G /J?, J 



where f =(N]x + l)(N + ^) and v = N{fj,-l) 2 . 



This reduces to the case of two shells if we put any two 



