IN CYLINDRICAL CONDUCTORS, ETC. 
99 
which gives 
6m 2 + I = (l+F )/Gu n {nd/b) 2 .(96) 
Assuming the condition such as to make m large, 
6 ( mndjb ) 2 = (i + F)/w„G,.(97) 
an expression determining the total number of turns (N = m X n). With this value 
of N we obtain from 
L = 4ttN 2 «X(^), l = 2-7raN, 
the relation 
L 2 = - X 2 f 
irCi CC \oU n \jr/ 
for the inductance of the coil, and this leads to the same value for ajb as for single* 
layer coils, viz.:— 
a/b = 1-6, u n = 3’87 .(98) 
When both conditions are satisfied 
R'/L = 1'187y ( 2 ) \/fpjld .(99) 
When 2 > 1, condition (97) with u n — 3-87 shows that (mnd/b) 3 < 3; and since ndjb 
is of the order unity, m will not exceed 2. Many-layered coils are therefore only of 
advantage when z < 1. When this is the case, G = z 4 /(34: and F is negligible. 
Condition (97) may then be written, when ajb = 1*6, 
N dfb - 1-66/z 2 ; 
or, expressing z in terms of wave-length and diameter, and assuming the wire to be of 
copper of resistivity 1600 C.G.S. units, 
N = 2'8 x 10~ 4 Xa/<7 3 ,.(100) 
A being the wave-length in metres, a the coil radius in centimetres, and d the diameter 
of the wire in millimetres. 
For stranded wire coils of the same total copper section the conditions are 
ajb — 1*6 
N = 2’8x10- 4 A a\/7/d 3 , .(101) 
while 
R'/L = ri87y (z)\/fp/lsS, .(102) 
d being the diameter of the equivalent solid copper, S the diameter of one strand, 
s the number of strands, and z is calculated from the diameter of a single strand. 
