18 ART. 0. — II. NAGAOKA : TUE INDUCTANCE 



and 



h^{v)- ^,,;=r^ [/|;-^l + 4îV^>^-l(l-r/(2?>-l)}] (13 



in wliicli tlie term involving r/ is generally negligibly small, and 

 the whole expression is nearly equal to '' g- in most practical cases. 



Although the expressions (12) and (13) appear somewhat 

 abstruse for numerical calculation, the calculation is not so labori- 

 ous as in dealing with a formula involving incomplete elliptic 

 integrals, even when Legendre's table is accessible. Taking the 

 case d=o, 2^=200, 2Z'=20, ^=15, a = 10, 1 found ili=4T/m'x G213.51/i> 

 which coincides with the value deduced from Roiti's formula. 



It is evident without proof that the formula given by Viriamu 

 Jones for a helix and a circle, and the formula arrived at by 

 Kussell for the mutual inductance of a cylindrical current sheet 

 and a coaxal helix can be deduced in a similar manner, and 

 expressed in terms of jj-functions. 



III. Self-inductance of Solenoids. 



§ 11. For the self-inductance of solenoids, several formulae 

 have been deduced by different physicists. They generally assume 

 different forms according as the solenoid is short or long. Most 

 of them are, however, complicated and not suitable for the use of 

 experimental physicists and engineers. In the following I propose 

 to show that the self-inductance of a solenoid can be easily cal- 

 culated by tabulating a certain coefficient % Evidently the self- 

 inductance of a very long solenoid is given by 



(1) For numerical calculation, see Proc. Tokyo Math. Pliys. Soc, 4, 284, 1908. 



