88 
MR, S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
Coil No. 3 was of bare wire and supported by eight pieces of ebonite upon which equi¬ 
distant grooves had been cut to keep the wires in position, these ebonite pieces being 
spaced equally round an octagonal wooden frame. The arrangement involved no metal 
except the wire of the coil. Coil 3 approximately imitates Coil 6, except that the insula¬ 
tion had been removed and the spacing increased. Coil No. 7 was wound on a wooden 
frame with D.S.C. wire and no wax. It is included in the table to increase the range 
of inductance and to put a severe test on the curvature correction for u n . 
In regard to the second term in formula (71), it is interesting to notice that if B is 
divided by L 2 , the result is of the same order of magnitude for all the coils tested although 
the inductance increases nine fold. Thus :•— 
Coil No. : 1 2 3 4 5 6 7 
B/L 2 = 16-3 11-6 8-5 10-9 9-9 7-2 16-7 
A leakage of conductance G would contribute a term « 2 L 2 G to the expression for the 
effective resistance. In terms of wave-length this becomes 3-56 L 2 G/a 2 if A is in 
metres, L in microhenries, and G in micromhos. In order to imitate the resistance 
B/\ 2 by such a leakage the value of 1 /G must range from 0 • 2 to 0-4 megohm to give the 
values observed for B. 
As to whether leakage is the cause of the second term in Lindemann’s equation, and 
as to whether it lies in the coil or the remainder of the circuit is a matter which requires 
further investigation. There is no doubt, however, that the first term of Lindemann’s 
equations may be closely predicted by formula (69). 
(17) Conditions for Minimum Eddy-Current Losses in Single Layer Coils. —The 
inductance of a single layer solenoidal coil of radius a and length 6 may be written 
L = 4tt«6 2 X/D 2 ,. (72) 
in which D is the distance apart of two consecutive turns and X is a function of a/b. 
The effective resistance of the coil is by (53) 
R’ = R {l + F + u v Gd 2 /D 2 ) . (73) 
where F, G depend on the frequency and diameter of wire only, while u n is a function of 
a/6. The values of X and u n for the range of a/b 1 - 0 to 2-4 are given below, the latter 
being obtained by interpolation from the table of Section 14, and the former from 
Rayleigh’s formula 
X = log, 8a/b— l/2 + 6 2 /32a 2 (log, 8«/6—£).(74) 
ajb = 1-0 1-2 1*4 1-6 1-8 2-0 2-2 2-4 
u n = 4-29 4-10 3-98 3-87 3-80 3-73 3-69 3-65 
X = 1-651 1-816 1-958 2-084 2-195 2-296 2-388 2-466 
