The self and mutual-inductance of linear conductors . Fig. 25. where r^ is the g. m. d. of a single conductor ( = , p being itsradius) and r^g is the distance between centers of the conductors iand 2, etc. If a is the radius of the circle on which the conductorsare distributed C. E. Guye, Comptes Rendus, 118, p. 1329; 1894. j^osa.] hiductance of Linear Conductors. 335 log 7?= log {r^na~^^ or R = (r^ na-y ^^^) . The proof of this, as given by Guye, depends on the followingtheorem: If the circumference of a circle is divided into n equal parts bythe points A, B, C, . . and M be any point
The self and mutual-inductance of linear conductors . Fig. 25. where r^ is the g. m. d. of a single conductor ( = , p being itsradius) and r^g is the distance between centers of the conductors iand 2, etc. If a is the radius of the circle on which the conductorsare distributed C. E. Guye, Comptes Rendus, 118, p. 1329; 1894. j^osa.] hiductance of Linear Conductors. 335 log 7?= log {r^na~^^ or R = (r^ na-y ^^^) . The proof of this, as given by Guye, depends on the followingtheorem: If the circumference of a circle is divided into n equal parts bythe points A, B, C, . . and M be any point on the line throughOA (inside or outside the circle), then putting OM — x X—a = MKMB . . MN (Cotess theorem).Dividing by MA = .r — ^, x- + ax-^ . . d-^^MB • MC . . MNMaking M coincide with x\, and hence x^a^ 7td- = AB ? AC . . AN 12 ^13 • • • • (^\-n which substituted in (61) gives (62). Since the self-inductance of a length / of the multiple system isequal to L^2l \ 2/ (63) we see that the calculation for any case i
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