64 
ME. S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
Then 
( 2 ) 
\M 2 ) 
2W( Z ) 
2 X(a) 
2 Z(z) 
z X(z)' 
02 
M = 4ZM_ 1 'I 
' 2 V (z) 1 
, M _ 4ff(i) 8 
^0- a y( z ) ^ j 
r • 
The combinations W/X, Z/X, W/V and Z/V are tabulated.* 
In the limiting cases of z very small or very large, it may be shown from the formulae 
already cited that and \Js n assume the following simple forms:— 
z small 
2 large. 
0 ;! = -2z 4 /(2 n) 2 (2n + 2) (2n + 4) 
\Js n = z 2 /2n (2n + 2) 
(21a) 
0. = -1, 'A,, = 2n/\/2z .(21b) 
In regard to the limitations of (21 a), the following table of values of y^ 15 i p- 2 (the 
functions most generally used) has been calculated:— 
z . 
0i- 
02- 
0l/2 2 - 
02 1*- 
0-0 
0-0000 
o-oooo' 
0-1250 
0-04167 
o-5 
0-03119 
0-01041 
0-1248 
0-04164 
1-0 
0-1215 
0-04149 
0-1215 
0-04149 
1-5 
0-2458 
0-0918 
— 
— 
2-0 
0-3448 
0-1563 
0-0862 
0-03908 
2-5 
0-3770 
0-2244 
— 
— 
3-0 
0-3600 
0-2827 
0-0400 
0-03141 
3-5 
0-3257 
0-3212 
— 
— 
4-0 
0-2920 
0-3389 
— 
— 
4-5 
0-2643 
0-3408 
— 
— 
5-0 
0-2416 
0-3337 
— 
— 
For -0-j, (21a) is a good approximation up to 2 = 0-5 and a fair approximation up 
to z = 1. For higher values of n the range of (21a) increases. 
In regard to (21b), its region of application has not been reached at 2 = 5, but if 
we take a second approximation we find, when 2 is large, 
zVi = \/2z-l, 2> 2 = 2\/2 2-6.(21c) 
These formulae give the following values for \/r 15 \ Js . 2 :— 
2 = 2 3 4 5 
x/rj = 0-457 0-360 0-291 0-243 
= — 0-086 0-276 0-332 0-326 
* Savidge, ‘ Phil. Mag.,’ 6, 19, p. 49, 1910. Rosa and Grover, ‘ Bull. Bureau of Stands.,’ p. 226, 1912. 
