Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/330

The inductive action of the eight nearest round wires on the wire under consideration is less than that of the corresponding eight square wires on the square wire in the middle by 2 × (.01971).

The corrections for the wires at a greater distance may be neglected, and the total correction may be written

$2(\log _{\epsilon }{\frac {D}{d}}+0.11835)$.

The final value of the self-induction is therefore

$L=n^{2}M+2l(\log _{\epsilon }{\frac {D}{d}}+0.11835)$,

where $n$ is the number of windings, and $l$ the length of the wire, $M$ the mutual induction of two circuits of the form of the mean wire of the coil placed at a distance $R$ from each other, where $R$ is the mean geometric distance between pairs of points of the section. $D$ is the distance between consecutive wires, and $d$ the diameter of the wire.