WAVE PROPAGATION OVER CONTINUOUSLY LOADED WIRES 195 



such a depth as to give an internal inductance of about .025 henry 

 per wire mile. The magnetic material in the sheath has been assumed 

 to have a permeability of 3,000 and a conductivity of .77 x 10~^ in 

 e.m.u. (resistivity 13 microhm-centimeters, in practical units). The 

 data shown by the solid lines are exact while the points give the 

 results obtained by means of the approximate formula (5). A com- 

 parison of results is tabulated below for the largest wire (16 B. & S. 

 gauge), where the errors of the approximate formula are greatest. 



The errors are roughly proportional to the quantity, WajM2X2. 

 For a loading material having, say, one-quarter the permeability and 

 the same conductivity, the errors would be about twice as large, 

 therefore, if the inductance and the wire size remain the same. 



Hysteresis Loss 

 The real part of the internal impedance given by (2) or (5) is the 

 effective internal resistance of the bi-metallic wire, taking into account 

 the heat losses that arise from the electric current, namely, d.-c. 

 resistance, eddy current loss and "skin effect loss." The formulas 

 do not take into account hysteresis loss, which is a magnetic phe- 

 nomenon as distinguished from these electric phenomena. The de- 

 termination of hysteresis loss rests upon experimental data. If the 

 energy loss due to hysteresis in the magnetic material per unit volume 

 per cj'cle is Ji (ergs), then the resistance increment due to hysteresis is 



R, 





hrdr. 



(6) 



For the low values of magnetic force that obtain in telephony, it is 

 found that // = ■qB'^, where r? is the hysteresis coefficient and B the 

 induction density. Therefore 



Rk 



1' X 



IPrdr. 



(7) 



