80 
MR. S. BUTTERWORTH ON EDDY-CURRENT LOSSES 
Tlie tabulated values of u n when plotted against 1 Jn (fig. 7) enable tlie value of u n 
to be determined for any number of wires. 
(12) Distribution of Losses in Single Layer System. —The energy loss in the wire s, 
due to the fields of the other wires, is proportional to Jcf. From the table for Jcf it is 
seen that this is greatest in the end wires. Thus, in the case of four wires, 93 per 
cent, of this loss takes place in the two outer wires and only 7 per cent, in the two 
inner wires. For a greater number of wires, if the system is divided into four equal 
sections the distribution of loss is still such that approximately 93 per cent, of the loss 
occurs in the two outer sections. This may be of importance in measurements of 
effective resistance based on the determination of the increase in temperature of the 
system, and account should be taken of the possibility of a temperature distribution for 
alternating currents different from that for direct currents. 
(13) Distribution of Resistance in Single Layer System .—Tlie distribution of eddy-current 
losses throughout the system does not represent the distribution of effective resistance. 
In fact the energy required to produce the losses in any wire is supplied by the currents 
flowing in the other wires, and therefore the other wires behave as if certain resistances 
were added to them. 
In order to determine these equivalent resistances, consider two coils (I) and (II) 
carrying currents I 15 I 2 which produce fields acting on a cylinder carrying no current. 
Ultimately these currents will be assumed equal, so that for simplicity they will be 
considered in phase. Let the fields in the neighbourhood of the cylinder due to these 
currents have intensities 
Hj = al l5 Ho = /3I 2 
(54) 
and let them be inclined at an angle <p. 
