EFFECT OF GROUM) PERMEABILITY 



475 



At" 



1 ! cos 26 



+ 



1 Y 



5! cos 60 



9! cos 100- + 



Q = 



M L 



cos Q .- , .. cos 30 



(^) 



+ 3(12^2 - 8m^ - 3) 



cos 50 



x2 - 1 \2 



3 ! cos 40 



- W 



I ! cos 



+ ( ^^^— r^ V 1 1 ! cos 120 - + 



It is worth noticing that when /- is so large that only the leading 

 terms in P are of importance 



P = [m + (//i + //,..) V27rXaJAt]47rXco[.v- + (V/i + //,.)-; 



At power frequencies (Jii + Ji2)\2wXo:iJ. is small in comparison with fx. 

 When /i — 1 is small a series in powers of /x — 1 is a convenient 

 torm of solution. This is readih- arrived at bv writing 



1 + MT 



I -I 7 L 



The expansion is absolutely convergent for all values of r if 

 e = M - 1 < 2. 



■)^ 



l.XVr^ + 1 + M^) = (Vr- + 1 - r) - er(\r- + 1 



+ eV2(Vr-^ + 1 - r)-^ - + 

 e3(8r' 



= \72 + 1[1 + e272 + 62(4r^ + t2) + e3(8r6 + 4r^) 



+ e^(16r8 + 12t6 + r^) + ^^ilr^^ + 327^ + 676) 

 + t«(64ri2 + 8O7IO + 2478 + 76) 

 + e7(1287" + 1927^2 ^ 807'o + 878) + • • •] 

 - [r + €(27^ + 7) + e-(47^ + Zt'^) 



+ 6^(877 + 8t5 + 7^) + 6^1679 + 207^ + 57S) 

 + 6^(32711 + 487^ + 18t7 + 7^) + • • •]• 



