IN CYLINDRICAL CONDUCTORS, ETC. 
77 
Table V.—Spacing = 0-03 cm. 
6° 0. ... 
21-1 
21- 
4 
21 
5 
21 
5 
21 
2 
21 
0 
20 
9 
21 
0 
21- 
1 
/ 
60 
236 
740 
1000 
1473 
2038 
3058 
3918 
5170 
R s /R ... 
1 -005 
1 
068 
1 
464 
1 
658 
1 
995 
2 
31 
2 
74 
3 
06 
3 
46 
Calculated < 
Rp/R. 
0-015 
0 
165 
0 
759 
1 
00 
1 
37 
1 
83 
2 
56 
3 
09 
3 
72 
Lr'/r. 
1-020 
1 
243 
2 
223 
2 
66 
3 
37 
4 
14 
5 
30 
6 
15 
7 
18 
Observed 
R'/R. 
1-017 
1 
244 
2 
231 
2 
688 
3 
460 
4 
272 
5 
522 
6 
449 
7 
512 
Difference per cent. 
+0-3 
-0 
1 
-0 
4 
-1 
1 
—3 
2 
-3 
•5 
-4 
3 
-5 
0 
-4 
5 
The calculated values are in general too low, but with so small a spacing R/ is varying 
rapidly. The formula gives the following values of R//R when the wires touch - 
R'/R. 
1-021 
1-253 
2-288 
2-75 
3-52 
4-35 
5-64 
6-57 
7-71 
Difference per cent. 
+0-4 
+0-7 
+2-6 
+2-2 
+1-7 
+ 1-4 
+1-8 
+ 1-6 
+2-7 
In Tables I. and II. the skin effect is the only one of importance and very good agree¬ 
ment is obtained. These tables really check the experimental observations as the skin 
effect formula is well established. Tables IV. and V. form the real test of the proximity 
effect. It is seen that the small discrepancies are sufficiently accounted for by a slight 
adjustment (0-5 mm. at most) in the spacing. In Table III. the skin effect is pre¬ 
dominant, but there is a rather large discrepancy. It is noteworthy that this group 
also shows a discrepancy on the resistance-temperature diagram, and that both the 
discrepancies are removed if we assume the measured values of R' and R to be both 
in error by 0 • 04 R. 
(C) Losses in Parallel Wire Systems and in Short Coils. 
(10) When the field acting upon the cylinder is uniform and has magnitude H, then 
by (18) the eddy-current losses per unit of length are given by 
W = \wo? Hh/n ( z ), 
or eliminating w by <o = z 2 R 0 /4, and putting z 2 \]s l = G {.z ), 2 a = d, 
W = 1R 0 d 2 G (z) I-P,. (49) 
€) 
Consider a system of parallel wires each of diameter d and occupying a square space 
of side D. Let these wires carry equal currents I in the same direction. Then, if the 
spacing is not too close, the currents may be supposed to be concentrated on the axes 
and producing uniform fields acting on the other wires, The field acting upon any wire 
s may be written H s = 2lkJD where k s is a numerical quantity depending upon the 
distribution of the wires and the position of the wire s in the system. By (49) the eddy- 
current loss in the wire s due to the field of the neighbouring wires is 
■W=PW^G(*)F.(50) 
per unit of length. 
