82 
MR. S. BUTTERWORTH OX EDDY-CURREXT LOSSES 
Hence if H r is the whole field acting on r, and H r , that portion of the field contributed 
by the wire s, the resistance to be added to the wire s to imitate the eddy losses in the 
remainder of the system is 
Remembering that 
(58) may be written 
fr = s -1 r=n 'l 
= 2 H„-H,+ Z H„-H„ 
r L r = 1 r = s+1 J 
21 H = 2I/1_, , 1 N 
1 (r-s)D’ r D \r * n + r, 
ftp. = u n R ^ G (z), . . . 
(58) 
(59) 
where u ns is a numerical quantity depending on the number of wires and the position 
of s. 
The general distribution of resistance is sufficiently illustrated by the case of a 16- 
wire system The values of u ns for this system are found by the above method to be 
f 1 2345678 
16 15 14 13 12 11 10 9 
u ns = —0-19 +0-08 0-17 0-22 0-25 0-27 0-28 0-29 
The values of u ns when added should give the value of u n for the whole system. Thus 
i = 16 
2 u ns = 2-74, and this agrees with the tabulated value of u n for the 16-wire system. 
s = 1 
As regards the negative value of for the extreme wires, it must be remembered 
that the equivalent resistances for each wire are such as to imitate the potential differences 
produced by the eddy losses in the wires, and it is quite possible that the phase relations 
may produce a rise in potential in phase with the current in part of a system. The 
only condition that is essential is that the value of u n for the whole system shall be 
positive. Curves A and B of fig. 6 (p. 79) show the distribution of proximity resistance 
and of loss respectively for a 16-wire system. 
(D). Single Layer Solid Wire Coils. 
(14) Single Layer Coils. Effect of radius of curvature of Coils. —A single layer circular 
coil, whose width of winding is small compared with the radius of the coil, differs only 
slightly from a straight parallel wire system, so that formula (53) will hold for a coil of 
this kind as a first approximation. The slight differences which occur, due to helicity 
of winding and owing to the fact that the wire (regarded as a cylinder under the 
action of a transverse field) is curved, are probably too small to be measurable and . 
the mathematical difficulties too great to make a theoretical treatment possible. 
A more important difference is the modification of the transverse field acting on the 
