JOURNAL OF THE COLLEGE OF SCIENCE, IMPERIAL UNIVERSITY, 

 TOKYO, JAPAN, 



VOL. XXVII., ARTICLE 6. 



The Inductance Coefficients of Solenoids. 



By 

 H. Nagaoka, liigahiJmJcusM. 



rrofesaor of Physics, Sei. Coll., Tokyo. 



§ 1. The practical importance of having an accurate stand- 

 ard of inductance has lately been felt in electrical measurements 

 relating to alternate currents and electric waves, and different 

 formulae have been deduced for expressing the inductance coeffi^ 

 cients of solenoids. Among the numerous expressions which have 

 from time to time been given by different i:)liysicists for calculat- 

 ing the mutual inductance of coaxal circles or coils, we may 

 mention those bearing the names of Maxwell, Weinstein, Heavi- 

 side, Roiti, Searle and Airey, Himstedt, Jones, Lorenz, Gray, 

 Cohen, Russell, and Rosa. These formulae can be conveniently 

 divided into two classes ; the first makes use of Legendre's tables 

 of elliptic integrals, while the second utilizes the expansion in 

 series, which takes different forms according to the method of 

 expansion. They have been examined and criticised by Rosa^^^ 

 and Cohen in the Bulletin of the Bureau of Standards, 

 Washington. 



A few years ago, I gave a simple series for calculating the 

 mutual inductance of two coaxal circles,^"^ which is remarkable 



(1) Rosa, Bull. Bur. Standards, 4, r,01,1907 ; Eosa and Cohen, 5, 1, 1908. 



(2) IT. Nagaoka, Journ. Coll. Sei., 16, Art. 15, 1903; Phil. Mag., [G] 6, p. 19,190-i. 



