A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 593 



In the experiments made by the Committee of the British Association for 

 determining a standard of Electrical Resistance, a double coil was used, con- 

 sisting of two nearly equal coils of rectangular section, placed parallel to each 

 other, with a small interval between them. 



The value of L for this coil was "found in the following way. 



The value of L was calculated by the preceding formula for six 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 = I in each case. 



Calling the results L(A), L (B), L(C), &c., 



we calculate the coefficient of mutual induction M(AO) of the two coils thus, 

 2ACM (AC] = (A +B+ C?L(A +B + C)-(A + B}*L 



Then if n, is the number of windings in the coil A and , in the coil C, the 

 coefficient of self-induction of the two coils together is 



L = n?L (A ) + Zr^njtf (AC) + < L ( C) . 



(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 such a uniform 

 current would do. 



The corrections arising from these considerations may be expressed as nu- 

 merical 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 



VOL. I. 75 



