JOURNAL OP THE COLLEGE OP SCIENCE, IMPERIAL UNIVERSITY, 

 TOKYO, JAPAN. 



VOL. XVI., ARTICLE 15. 



Note on the Potential and the Lines of Force of 

 a Circular Current. 



By 

 H. NAGAOKA, Professor of Physics. 



§ 1. The potential of a circular electric current or of a vortex 

 ring of small section, has been investigated by Lord Kelvin,'^ MaxwelP^ 

 Hicks,^^ and Minchin."*^ They all express the solid angle subtended 

 by the circle by means of elliptic integrals or in terms of zonal 

 spherical harmonics. The lines of force of a circular current are 

 usually obtained from the expression for the mutual potential energy 

 (denoted by M) of two coaxial circular coils. By using F. 

 Neumann's formula, M may be expressed by means of elliptic 

 integrals, or developed in terms of zonal harmonics, which is some- 

 times advantageous for calculating the action between thick coils. 

 Maxwell has also given a table of the coefHcients of mutual induction, 

 when the coils are near each other. In these calculations we are 

 always in need of Legendre's tables. It is very curious that so 



1) Lord Kelvin, Trans. R. S. E., 1869. 



2) Maxwell, Treatise on Electricity and Magnetism II. Chap. 14. 



3) Hicks, Phil. Trans, for 1881, p. 628. 



4) Minchin, Phil. Mag. vol. 35, 1893. 



