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XIX. The Inductance of Tivo Parallel Wires. By J. W. 

 Nicholson, D.Sc, B.A., Isaac Newton Student in the 

 University of Cambridge *. 



WHEN direct and return currents flow in two wires of 

 great length, and the alternation is not rapid, the 

 effective self-induction L per unit length of the system may- 

 be calculated readily by the method of geometric mean dis- 

 tances f or by simple integration ±. If the wires have radii 

 (a, b) and permeabilities (/a 1? /x 2 ), and if c be the distance 

 between their axes, 



L = 21og^ + J-0, 1 + M2 ) (1) 



But this formula ceases to be of any practical utility in many 

 cases when the frequency of alternation is several thousands 

 per second. Such frequencies are of constant use in practical 

 work. For example, in the measurement of small inductances 

 by Mr. Albert Campbell's method §, it is necessary to employ 

 long leads in order to keep them at some considerable dis- 

 tance from bridge and other circuits. The self-induction of 

 these leads must be small, and a calculation of its value is 

 very desirable. It was therefore suggested to me that I 

 should attack this problem. The general case presents ap- 

 parently insuperable mathematical difficulty, but the solutions 

 given below appear to include all cases of practical im- 

 portance. A short statement of these results was given by 

 the author in 'Nature/ Jan. 30th, 1908, but the limitations 

 were not emphasized. 



Let the axis of z be chosen parallel to those of the two 

 wires. Any point in a section defined by a constant value 

 of z may be conveniently specified by means of polar co- 

 ordinates in two ways. Let these coordinates be (r, 6) and 

 (p, </>), where (r, p) are the distances of the point, from the 

 two axes respectively, and (0, o) its orientations measured 

 from a line perpendicular to both axes. 



In the figure A and 13 are the projections of the axes of 

 the two wires, and AB = c. A and B will be referred to as the 



* Communicated by the Physical Society : read June 12, 1908. 

 t Maxwell, ' Electricity and Magnetism.' 

 X Russell, Alt. Currents, i. p. 50. 

 § Phil. Mag. Jan. 1908. 



