2 ART. G. — IT. NAGAOKA : THE INDUCTANCE 



for its rapid convergence ; the object of the present communica- 

 tion is to shew that tlie same method may be conveniently em- 

 ployed for expressing the mutual inductance of solenoids of any 

 length. 



For the self-inductance of solenoids, the formula can be put 

 in a form convenient for practical calculation, and by tabulating 

 a certain factor S as a function of the ratio of diameter to length, 

 we can dispense with the rather intricate formula, that has 

 hitherto been employed for the same purpose. 



§ 2. The mutual inductance for two circuits is given by 



Tr C f cos £ ds ds' ,-,. 



^'^=J J r (1) 



where £ is the angle between the elements ds and ds, and r the 



distance between the two. In the case of two coaxal solenoids 



of the radii a and Ä, length 21, 21', placed in such a position 



that the distance between the centres is d, 



r- = (r + A-+dr~2aA cos {<p — <p'), 

 e=(p — <p' ; ds = ad<f, ds' = A dip' . 



For two circles, whose planes are at the distances z, z from the 

 centre of the coil {a) 



M _ f"" n Aacos{<p-f)d<p elf 



Consequently the mutual inductance M of two solenoids with the 

 number of turns per unit length n and n, 



j i)/o dz dz' (3) 



31 



<i-i> -I 



I. Mutual Inductance of Coaxal Circles. 

 § 3. In the paper already cited, I showed that mutual in- 



