96 
MR. S. BUTTER-WORTH ON EDDY-CURRENT LOSSES 
The shorter wave-length assumes n — 3 • 3 and the longer wave-length assumes n — 1 • 1 . 
If we introduce a third system with n — 2-2 for the mid-regions, a choice of one or 
other of these systems will enable the time-constant (89) to be secured to within 10 
per cent, throughout the range of the table. The table shows clearly the transference 
of the applicability of the results to the regions of lower frequency as the stranding 
becomes finer. The observed inferiority of stranded wire coils at short wave-lengths 
is thus due to lack of internal spacing at these wave-lengths. 
(24) Comparison of Stranded Wire Coils with Solid Wire Coils. —Assuming both coils 
to have the same length of wire, the same total copper section and wound to give the 
best time constants, the ratio of the time-constants is by (81 a) and (89), 
t'It = l'llly {z)/sy (s*z), . (90) 
since sS 2 = d 2 and 2 is proportional to d. 
In (90) r = R'/L for the stranded wire coil and T that for the solid wire. Now, the 
ratio y(z)/y(sh) lies between 1 and 2 l for all possible values of 2 and s, so that the 
formula 
t'/t = 1-2/s 1 .(91) 
may be taken as comparing the two cases. 
For the 3-system we have therefore 
s = 3 9 27 81 
t'/t = 0-91 0-69 0-53 0-40 
when the same length of wire is used in both coils. 
If coils of equal inductance are compared, the conditions are different, as the spacing 
for stranded wire coils is not the same as that for solid wire coils. In fact, throughout 
the range for which spacing is advantageous, 
I) = 2d 
for the solid wire coils, and for stranded wire coils on the 3-system having the same 
copper section, 
D = (1-244 ) p nd. 
For coils of the same shape and of radius a, the inductance L is proportional to 
a 3 /D 2 and the length of wire l is proportional to a 2 /D. Hence, to keep the inductance 
constant, l 3 /D must be constant. We have then 
l oc D. 3 , a cc D' 1 , 
and from (89) 
R'/L oc D-A 
