APPENDIX 111 



no effect on the reactance of the circuit. The effect of 

 the part of the component inside the strand may be esti- 

 mated by stating that it would increase the term 103 

 in the formula for 7 wires, by about i per cent, assuming 

 that half of the wires are 2 per cent longer than the axis 

 of the strand. Now, changing 103 to 104 in the formula 

 would make a change in the final result of less than 

 % of i per cent, even for overhead lines of very narrow 

 spacing. The above change would be negligible in the 

 usual tables with three significant figures. 



Suppose that the current in each small wire has unit 

 value. Then the flux density due to that current, at a 



2 



distance x from the centre of the wire, is . 



x 



If / is the distance between any two wires of the 

 cable, the required voltage induced in the second by 

 the first, per centimetre, is 



dx=2irfX2 log, 



= 2 nfM 



where / is the frequency, and M is the inductance for 

 the pair of wires. 



The inductance of a wire due to its own current is 

 given by the usual formula, 



5 i 



T 2 



in which r is the radius of the wire, and in which > 

 expresses the effect of the flux inside the wire. 



The inductance per centimetre of cable of a single- 

 phase circuit composed of 7-wire cables (Fig. 12) is 

 porportional to 



