10 ART. r.. — ir. NAGAOKA : THE INDUCTANCE 



§ 6. When two circles are near each other and of nearly 

 equal radii, so that x and ?/ in 



A—a + x , r = // , r-=x- + y- 



are small, the mutnal inductance can be expressed in a series 



r t 2 a Ibrr 32«* ) 



as shown by Maxwell. 



We can easily show that (4') can be so transformed that it 

 coincides with Maxwell's expression. Evidently 



'^•=1T + W+- ' where/.- 



V a 4a- J 

 Consequently 



V 'la 8 a- 48 a' J 



To first approximation 



i)/o = 4-/:ia|l %1. (H-12r/,)-2(H-4ryO | 



and by expansion 



,/3r(l + 12,.) lo,j 4« =„ .0, ««-(l + -^ + ^^-^-^) 



/-^r (1 + 12?,); (^.V'\ {x' + y- x(x' + y'-)\ 



-,/Ä. 2(1 + 4,;,) =-„(2+^-^+^(^) 



