MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 43 



factor, i.e., the ratio of the volume occupied by metal to the total 

 volume of the core. 



The flux density in the spheres is larger than the apparent flux 

 density by the factor r~^/'. The eddy current resistance for such a 

 structure then becomes 



Re = -^ 1 UmLmP, (17) 



5pr 



where Hm is the permeability of the core, as calculated from the in- 

 ductance Lm.^ With p in microhm-cm., this equation becomes 



0.0124/2 



Ke = ^~ fJLmLmJ-. (18) 



In cases where merely comparative tests are to be made, or where 

 p and / are not known, it is convenient to lump the coefficient of the 

 eddy current resistance in the form 



Re = en^L„,f. (19) 



Simple Analysis of Hysteresis Resistance 

 In addition to the power loss due to eddy currents, there is a loss 

 caused by magnetic hysteresis. The energy in ergs dissipated per 

 cubic centimeter of core during one hysteresis cycle is 



W ^~fHdB=-^\ (20) 



where ai is the area of the hysteresis loop in gauss-oersteds. The power 

 consumption on this account in an annular core of volume irAd, 

 carried through / cycles per second, is 



Ph = WirdAf = laidAf X 10^7 watt. (21) 



In the same manner as above, this power is observed by an a-c. 

 bridge balanced for the frequency / as a resistance 



Rh = -i-Y f^mLmf = =^ M„,L„J ohm. (22) 



By this relation, the hysteresis resistance can be used to compute the 

 energy loss per cycle W, or the hysteresis loop area a\, which would be 

 obtained by ballistic galvanometer measurements of sufficient sensi- 

 tivity. 



5 Cf. R. Cans, Phys. Zeit. 24, 232 (1923). 



