86 
MR. S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
Even when z is as small as 3, a is therefore less than \($z. For most purposes it is suffi¬ 
ciently accurate to take 
R' = (3z .(67) 
From the relation z 2 = 4 W /R 0 we may write 
2 = 0-0479 s/fjW, = 830/v/RVv,.(68) 
in which / is the frequency in cycles per second, X the wave-length in metres, P' 0 the 
resistance of the wire of the coil in ohms per 1,000 yards. 
Hence (67) becomes 
R' = A/v4 = AV/,.(69) 
where A and A' are given by 
A - 146-7 (: 2+u n d 2 /D 2 ) R/\/R' 0 1 
A' = 8 • 47 x 10- 3 (2+u n d 2 /D 2 ) R/VW, j 
(16) Comparison of Formula (69) with Experimental Observations. — Lindemann 
and Huter* have measured the effective resistances of a series of single layer coils over 
a range of wave-lengths to which formula (69) is applicable. 
Their method was to bring the coil into resonance with an air condenser at the required 
wave-length and to measure the effective resistance in this condition by adding a known 
non-inductive resistance and observing the reduction in current. The method measures 
the resistance of the whole circuit of which the coil is a part, so that the resistance of the 
coil may be deduced if the resistances of the non-inductive portions of the circuit are 
known, and the condenser is assumed to be free from loss. 
Their results included four solenoidal coils wound with thick solid wire, and for these 
coils they found that the effective resistance could be expressed in the form 
Pd = A/VX + B/X 2 .(71) 
The data given by Lindemann and Hu ter for these coils enable the value of A in formula 
(70) to be calculated. The results are given in the following Table, which includes also 
three other coils measured by a similar method at the National Physical Laboratory. 
It is seen that the value of A as calculated from formula (70) is in good agreement 
with the value of A determined experimentally. In the calculation, the value of u n 
taken has been the value given in the short table for solenoidal coils in Section 14. 
These values have been deduced upon the assumption of a large number of turns. 
Calculations based on the value of u n , as deduced from a straight system containing 
the same number of wires as there were turns in the coil, were found to give a value 
of A which in every case was lower than the value deduced from observations. 
* ‘ Verb. Deutsch. Phys. Gesellschaft,’ vol. 15, 1913, p. 219. 
