Inductance of Tioo Parallel Wires. 267 



To this order of approximation, the result might have been 

 written down at once. For c/a has already been assumed so 

 great that the distribution may be regarded as made up of 

 cylindrical current sheets. The number of linkages of the 

 lines of force outside the cylinders* is 4 log c/a, and the 

 linkages due to the lines of force wholly in the metal give 

 vise to the second part of (6&) f. 



To the same order the approximation for two wires becomes 



T . c 2 2fM ber x ber' x + bei x bei' x 

 g ^6 + Hi (ber'^) 2 +(bei'#)* 



2j> ber y ber '?/ + bei t/bei'j/) 

 + y~ (ber'</)H(bei'y)* 



(70) 



where 



z ir^n , / irvn , 1X 



and may also be written down at once. 



When the vibration becomes more rapid, even though h^a" 2 

 may be neglected in comparison with unity, the latter cannot 

 itself be neglected in comparison with log (ha). Thus (01) 

 requires modification, and it appears that 



Z*-1 I $uJ ha l±„^ Lir \ 



{log ( ^-f7+T}-^o/^Jo'}, 



and cL is the imaginary part of 

 4* 



or of 



0-<') 



leading to the same value as before. 



But when the wires are different, the new approximation 

 thus calculated differs from the old, and is very cumbrous. 

 It is therefore to be desired that, in practical work involving 

 a knowledge of the inductance of parallel leads, the leads 

 should be of the same size and material. The formula for 

 inductance is then of the same accuracy over a wider range 

 of frequency. 



Cases may arise in practice in which c is so great in com- 

 parison with a that the neglect of h 2 a 2 may not involve that 



* "Russell, Alternating Currents, i. p. 56 et seq. 



t Vide Gray and Matthews, Treatise on Bessel Functions. 



