IX. On the self-inductance of circular coils of rectangular section

As an approximate formula for the calculation of the self-inductance of a coil of rectangular section, L = 4πan2 {log 8a/r -2} was first given by Maxwell, where a is the mean radius and r the geometric mean distance of the section of the coil from itself, the current being supposed to be uniformly distributed over the section. In the following paper it w ill be shown that the same formula will give the self-inductance to any order of accuracy when in it are substituted for a and r the mean radius and the G. M. D. respectively, each suitably modified by small quantities which depend on a and on the section of the coil, provided, of course, that the series for L is convergent.