Inductances of coils in polygonal form are not yet treated except in the case of rectangle.
(1) In this paper the triangular, the hexagonal and the octagonal cases are treated with some calculations of the mutual inductances between two linear conductors in general, assuming the permeability of the medium to be always unity throughout the space. The chief merit of the formulae consist in their accuracy even in the case of small number of turns and considerable length of pitch.
Contents of each section are as follows:
1. The mutual inductance between any two straight linear conductors not parallel to each other is calculated in general form by means of the Neumann's formula _??_, the result of which is identical with that of the F. F. Martens's _??_Equation (1)_??_.
2. The mutual inductance between two parallel straight conductors are treated _?_Equation(2)_??_.
3-5. The self inductances of cylindrical coils of rectangular polygonal sections (triangular, hexagonal and octagonal) are treated after the manner of Dr. A. Esau. _??_Equation (4), (5) and (6)_??_. A coil is considered to be made up of separate folygons, so that the self inductance of the coil may be equal to the sum of the self inductances of the separate turns plus the sum of the mutual inductances between each turns.
6-8. The self-inductances of plane coils having the same forms are given. _??_Equation (7), (8) and (9)_??_.
9. Some remarks are made concerning the inductance of the coil as a function of the number of sides, the relation between the cylindrical coils and the plane coils, and the available limits of the formulae.
Readers are warmly recommended to refer to the papers published by Prof. F. F. Martens
(2) and Dr. A. Esau.
(1)
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