different cases in which the rectangular section considered has always the same breadth, while the depth was A, B, C, A + B, B + C, A + B + C and n = 1 in each case Calling the results L(A) L(B) L(C) &c we calculate the coefficient of mutual induction M(AC) of the <s>extreme<\s> two coils thus 2AC M(AC) = (A + B + C)<sup>2<\sup>L(A + B + C)  (A + B)<sup>2<\sup>L(A + B)  (B + C) <sup>2<\sup>L(B + C) + B<sup>2<\sup>L(B) Then if n<sub>l<\sub> is the number of windings in the coil A and n<sub>2<\sub> in the coil B the coefficient of self induction of the two coils together is L = n<sub>1<\sub><sup>2<\sup>L(A) + 2n<sub>1<\sub>n<sub>2<\sub>L(AC) + n<sub>2<\sub><sup>2<\sup>L(B) (114) These values of L are calculated on the supposition that the windings of the wire are evenly distributed so as to fill up exactly the whole section. This however is not the case, as the wire is generally circular and covered with insulating material. Hence the current in the wire is more concentrated than it would have been if it had been distributed uniformly over the section, and the currents in the neighbouring wires do not act on it exactly as <s>they<\s> such a uniform current would do The corrections arising from these considerations may be expressed as numerical quantities, by which we must multiply the length of the wire and they are the same whatever be the form of the coil Let the distance between each wire and the next, on the supposition that they are arranged in square order be D and let the diameter of the wire be d then the correction for diameter of wire is + 2(log D/d + 4/3 log2 + [pi]/3 = 11/6) The correction for the eight nearest wires is + 0.0236 For the sixteen in the next row + 0.00083
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
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Cite as
J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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