12 AKT. ü. — II. NAGAOKA : THE INDUCTANCE 



/ can bü written 



/ 



-r- 



sin^(p d(p 



■y/ A' + er + c'- — 2 Aa cos (p 



+ c 



1 



sh-^ip d(p 



(/P + a'—'2Aa cos (p) -y/A^ + a^ + c^ — 2Aa cos <p 



.(S'O 



Puttino; cos </> = as + ß 



^ = Uc^ 



2 \i 

 Aa 



_ 2/3 



ß= 



A' + à-+c^ 



e..- 



6Aa 

 1-/5 ._ 1 + /9 



so that Cl + ('2 + 63=0 and ("i—Cz'- 



cy( ■', .'^ ..X 4(1+3^9') 



(^) 



j/3 = 4 Ci e. G., 



.8/9 (/3-1) 



a' 



we have 



sin <p i/^-+«Hc^— 2 ^4a cos <p = -/'4(s— ej) (s— 63) («—63) 



Let 



=/ 



* fZs 



f V^ 



SO that s=jJio , 



1 1 , A- + a-—2 Aa i-i 2 (A^ + a-)— c- 



and let i>v = ^ç—. '~=- ^ ,., ^ 



2 Aa a b Aaa 



then 



^jv-c, = --^-r--{c,-c,) = --, 



pv-e.,= 



4:Aa 

 (A-af 



2Aa a ' 



4:Aa ^' ^'^~ 2 Aaa ' 



(A + af , , M + aY- 



4^a 

 whence c^ — C3 = ^^ ' 



2 Aaa ' 



4yia 



-(^2-^3) 



(10) 



