IN CYLINDRICAL CONDUCTORS, ETC. 
95 
because of twisting and the need for symmetrical distribution. Tlius if three wires 
each of diameter S are arranged so that their centres form an equilateral triangle, the 
diameter of the cylinder in which these wires can be twisted is 
(l + 2\/3) nS = 2155 nS, 
in which n is a factor greater than unity, introduced to allow for insulation between 
contiguous wires. Denoting D 2 /sS 2 by /a 2 the value of /a for the three-wire system is 
l-244w. If three three-wire systems are twisted, then, assuming rigidity, the over-all 
diameter of the resulting nine-wire system is (2-155) 2 nS, and the value of /a is 
(1 • 244) 2 n. 
Generally, if the operation is repeated p times, the result is a ?> p system for which 
D = (2‘155) p nS, M = (U244) p n. 
Applying this result to (88), it is seen that, as G/(l -f- F) increases with frequency, there 
is a lower limit of frequency below which the conditions may not be satisfied. If we 
depart from the condition of best internal space the resulting increase in R//L follows 
a law similar to that for solid wire. If we allow a 10 per cent, variation, the actual value 
of /a may range between 0‘63 p 0 and 1 -75 p, 0 where /a 0 is the ideal value of p, and this 
may be used to extend the lower limit of the range of application. At the higher 
frequencies, although G/l -|- F tends to the finite value 1/2, the spacing required is so 
large as to give unpractical coils. 
If we set as practical limits to n the values 1-1 and 3-3, and allow a 10 per cent, 
variation, the wave-length limits for copper wire of the usual gauges used in stranding 
are given in the following table :— 
Table giving Limits of Application of Formulae (87), (88), (89). 
A = Wave-length in metres. 
Wire No. S.W.G. 
42 
40 
38 
36 
No. of strands : 
fA = 
0 
0 
0 
0 
3 < 
\x = 
430 
630 
960 
1570 
fA = 
10 
10 
20 
30 
9 i 
U = 
600 
850 
1330 
2150 
fA = 
80 
120 
180 
290 
27 1 
\a = 
900 
1290 
2030 
3200 
fA = 
140 
200 
300 
500 
81 1 
\a = 
1270 
1800 
2800 
4500 
