72 
MR. S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
when the currents are similarly directed, and 
ld-3/x 2 +10/D 
when the currents are oppositely directed; while, if distortion is neglected, its value is 
1 +/r-f-p. 4 
by (32). Thus the effects of distortion and of non-uniformity of field are equally 
important. When the currents are similarly directed the distortion is such as to tend 
to reduce the losses, and when the currents are oppositely directed the losses are 
increased. 
The term involving /D will contribute less than 1 per cent, at high frequencies if 
D > 2-5d with the currents oppositely directed, and if D > 2 d with the currents 
similarly directed. 
To this accuracy we may write for any frequency 
in which 
W = pi, jl + F(z) + G(z) 
(46) 
If we assume the remaining terms to be in geometrical progression (46) may be 
written 
W 
2 X V> 
l + F (2) + 
G(z) 
i-|h( z ) f 
(47) 
At low frequencies this formula gives 1 • 043 as the correction for non-uniformity 
when the cylinders touch, and will certainly hold to 1 per cent, up to D = 2d at 
extremely high frequencies. 
H (2) is plotted in fig. 4, up to z — 5, the curve I holding when the currents are 
oppositely directed, and II when the currents are similarly directed. 
Since the effective resistance R/ of a coil system is such that 
W - ART 2 , 
the.effective resistance (apart from electrostatic capacities) per unit length of a pair of 
parallel wires is given by the formula* 
IV = R 0 
|l+F(2) + 
1- 
G(zj 
H (z) 
in which d is the diameter of either wire D the distance of their centres, and F, G, H 
are functions of 2 { = 2 v 7 eo/R 0 } drawn in fig. 3 and 4, and tabulated below. 
* At extremely high frequencies it may be shown that ratio of the resistance of a go-and-return system 
to the skin resistance is given by D/ jD-—d 2 . Formula (48) is then 3 per cent, in error when d = 0-8D. 
