IN CYLINDRICAL CONDUCTORS, ETC. 
67 
In the extreme case in which the wire touches the cylinder, the sum of the series 
becomes 
2 
— -1 = 0-64493. 
6 
Upon the assumption of a uniform field, the first term of the series would be the only 
one employed; and as this is 1 /2, the correction due to non-uniformity of the field is 
a multiplying factor ranging from 1-00 to 1-29. 
If there are two thin parallel wires and the cylinder is situated symmetrically between 
them, the axes of wires and cylinder being coplanar, the alternate terms of the series 
(26) vanish, and the losses become 
4« VI 2 / 1 1 a 4 1 a 8 \ 
1\D 2 \1 2 2 3 2 4 D 4 5 2 6 IF ' ' ’ 
if the currents flow in opposite directions in the two wires, and 
4a>VI 2 / 1 « 2 1 a 6 
mr \¥s D “ 2 4^5 D 6 " 
when the currents flow in the same direction. 
When the wires touch the cylinder, (27) reduces to 
and (28) to 
4m 2 I 2 
K (l 
7T 
- l0ge 2 
x 0-54055 
4w 2 I 2 
V24 
£ 7 +log, 2-1 
A. ,2T2 
X 0-10438. 
_ti 0 
(27) 
(28) 
4 2 I 2 
The uniform field theory would give V—x 0-5000 and zero respectively for these 
cases. 
(6) Eddy-Current Losses at High Frequencies. —At very high frequencies 
\fs n = 2n/v/ 2 z = n\/ R„/2m, 
so that by (18) the energy dissipation is 
W = iVEWS {i (K „r + S (K ,,) 2 a 2 *}.( 29 ) 
The first term is due to a current I = |K 0 distributed symmetrically round the axis 
of the cylinder and flowing in a direction parallel to the axis, and when this is the only 
factor producing the field the energy dissipation is 
w, = iv/iWai 2 . 
This is the formula for the skin effect at high frequencies. 
( 30 ) 
