20 ART. G. — II. NAGAOKA : THE INDUCTANCE 



where A' and E are complete elliptic iutegnil« of the first mid 

 second kinds resp., we find that 



Consequently 



/v = 4;r/r-| j-/7?+F {r-K+ {a--l')E)- cÀ , (15) 



which is identical with the formula obtained by Lorenz^^' and 



Cohen/^) 



or l^ 



Remembering that ^'^^'=—2x72 ? ^^'^—'^,^1^ > ^^'^ ^^^^^ 



The self inductance of the solenoid is thus 



L = i7TH\ Ttcc. 2f.^ -p~\lf {E-E)-¥E-h \ (IG) 



Putting S = A _1^ 1^ (7^- E)^-E~l,)^, ( L7) 



we get Z=47rM"xArea of Cross Section x Length x 8 



Area of Cross Section „ , ^ 



Length ^ ^ 



where N is the total number of windings. 



ah 

 Putting h = sina, tga = j-=jj-, we see that a is equivalent 



to a semiangular aperture of the solenoid at the centre. Thus 



8 can be generally expressed as a function of angular aperture. 



In practice, it will be convenient to tabulate 8 as a function 



1 Lorenz, Wied. Ann., 7, p. 170. 1879 ; Oeuvres, 2, p. 196. 



2 L. Cohen, Bull. Bur. Stand., 3, J^- 303, 190. 



