2W Dr. J. W. Nicholson on the 



of h 2 c 2 . Tables of the Bessel functions of the second kind 

 must then be employed. L is the real part of 



and becomes 



t ov // \ a fi ha , \ . ^ber^ber'^-fbei^bei^ 

 L = 2Y (/,c)-4|log T +yj + - - (ber ^ + (be i^ (U) 



where x has its previous value, and Y represents the function 

 introduced by Hankel. Tables of this function are given in 

 Gray and Matthews' Treatise. 



If ^— is the frequency, 



li = ^ . 10- 10 (73) 



A general idea of the range of frequency with which these 

 formulas may be used, can be obtained at once. The neglected 

 terms are of order h 2 a 2 in comparison with those retained. 

 The radius of a wire is rarely greater than two millimetres, 

 and thus with a frequency of a hundred million per second, 

 h 2 a 2 becomes 1*6 . 10 -5 , which may be neglected at once in 

 comparison with unity. Most frequencies dealt with in 

 practice are therefore within the scope of these formulae, 

 when the wires are not of large cross-section. But another 

 source of error is present, owing to the neglect of terms 

 depending on orientation. Upon examination, the error is 

 found to be of relative order a 2 /c 2 . Even if c = 5a, the 

 formulas are sufficiently accurate for most applications. The 

 error is about ten per cent, if c = 3a, which is the limiting 

 closeness for the majority of practical purposes. More 

 accurate results suited to this case are obtained in the next 

 section. 



Higher Approximation. 



The terms depending on orientation in the vector potential 

 do not contribute to the total current across any section of a 

 wire, which is proportional to a line integral round the 

 boundary. In considering the supposed waves of potential, 

 it is therefore only necessary to calculate the successive 

 coefficients of the Bessel functions of zero order. 



