84 
MR. S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
divide the coil into two portions A and B to the left and right of the point in question. 
Then the two components of the field are 
(Ho-H'oMfc-V), H t + H' t 
where the accented letters refer to the field due to the portion B, and the unaccented 
letters to that due to A. H 0 — H' 0 is the normal field for a straight strip, and h — h' 
the correction on the normal field due to curvature, while H T — H' T is the field tangential 
to the layer due to curvature. 
Formulae (64) and (65) give the following values for h and H T :— 
b/2a 
h/2nl 
H t /2wI 
0-1 
0-025 
0-369 
0-2 
0-079 
0-595 
0-3 
0-149 
0-767 
0-4 
0-229 
0-902 
0-5 
0-313 
1-010 
0-6 
0-400 
1-096 
0-7 
0-486 
1-167 
0-8 
0-569 
1-225 
0-9 
0-651 
1-273 
1-0 
0-728 
1-313 
from which the values of h — In' , H T — H' T may be calculated for any point on the surface 
of a coil if b/2a < 1. 
For the eddy loss formula we require the mean square field acting on the coils ; that is, 
denoting H 0 — H' 0 by H, h — h' by H 15 H T -j- H' T by H 3 , we require the mean value of 
(H —H 1 ) 2 +H/ = H 2 —2HH, + H, 2 +H 2 2 
throughout the surface of the coil. 
As regards the integrations required in determining this mean value, the integral of 
H 2 leads to the straight system formula; that of H, 2 and Hy may be carried out by 
approximate methods, since By and f t, 2 are finite throughout the range of integration. 
The integral of H-Hj is obtained as follows. Choose the length of the coil as twice the 
1 +x 
unit of length so that H/2 nl = lo 
1 — x 
at a point on the surface distant x from the 
centre. Suppose H x may be expressed in the form 
H j — cl T f3x T ~yX T OX/ 1 T 
The integrals required are then of the form 
s n 1 + X 7 
x log -- ax. 
-i 
f —x 
