Prof. J. Perry on Choking Coils. 435 



and hence, if V or I is given as a periodic function of the time, 

 the other can be found and A and therefore c or 0. 



If Y is a simple sine function of the time, I is so also, with 

 very great, but not perfect accuracy. Assuming that I is 

 a simple sine function, the neglected terms in Y can now be 

 calculated. The only problem, however, of importance is 

 the calculation of C assuming that Y follows the law Y = 

 Y sin Jet. 



We may take <? = N 2 /R. Hence 



-I=(Y /m) cos let 



very nearly, and if e = n 2 crk/r, being called the eddy-current 

 effect, / being the hysteresis term, 



C = V [~(l + 2e sin/+ e 2 )> sin f fa-90° + tan"Vtan/+ -tS\ 1 - 



bcos3kt — mcos5kt]-r-Wak (2) 



We see that the effect of eddy currents without hysteresis 

 is to increase the amplitude of the important term in 0, and 

 to produce a lead of 90°— cot - e, whereas the effect of hys- 

 teresis without eddy currents is to keep the amplitude 

 unaltered and to produce a lead /. If/ is put equal to 0, 

 that is if we assume no hysteresis, we obtain results which 

 seem to be in accordance with such experimental observations 

 as have yet been made. 



The effective current C (if V is the effective voltage), with 

 constant permeability, is C = V /WaJc. With hysteresis (or 

 with no hysteresis but some saturation of the iron), but no 

 eddy currents, = 1*02 Y/NV&, taking h as '2. 



With eddy currents and hysteresis, 



C = Y y 1-04 + 2e sin/ + e 2 fN 2 crL 



The average power given to, the choking coil or average- 

 value of Y C is 



YO(e + sin/)/(l + e 2 +2esin/), 



neglecting the small terms due to b and m, and this may be 

 done in all cases where there is not much saturation. 



Probably there are always traces of the terms in SJct and 

 the higher harmonics in both V and I, but they must certainly 

 exist in either Y or I even when there is not much saturation. 



It almost seems that in a choking coil we have found 

 what has long been looked for, a method of increasing 

 frequency by mere magnetic means. A condenser shunting 

 a non-inductive part of the circuit would receive currents 



