MAGNETIC LOSSES AT LOW FLUX DENSITIES 227 



pressed powder cores, where eddy-currents are confined to single particles 

 and cannot be increased by a modified direction of magnetic flux. 



The most notable feature of residual loss is its large value for unan- 

 nealed materials, and its extremely small values for well annealed al- 

 loys, particularly 78.5 permalloy and 45-25 Perminvar. (See Table I.) 

 The permeability is increased by annealing while both c and a are 

 decreased. On the other hand Br is slightly increased. The decreases 

 in hysteresis and residual loss are attributed to the decrease in work 

 done against internal strains, which also tend to limit initial per- 

 meability.^^ 



This suggests that residual loss may be due to elastic hysteresis or 

 even simple mechanical friction, with magneto-striction providing the 

 necessary coupling between the elastic or frictional variables and the 

 magnetizing field, as poi'nted out in our previous paper.^ Thus, in 

 addition to losses from eddy-currents and magnetic hysteresis, mechan- 

 ical work is done by the alternately expanding and contracting core — 

 work expended on itself and its supports and insulation. Since the 

 ballistic galvanometer measures only equilibrium values of B and H, 

 this work is not revealed in the area of the ballistic loop. However, in 

 the a.-c. loop the magnetostriction strains produce stresses too rapidly 

 to be relieved, so that B lags behind //with an absorption of energy into 

 the surroundings. This results in an additional effective resistance 

 beyond that due to magnetic hysteresis and eddy-currents. For a 

 sufficiently slow process in well annealed material supported with 

 minimum constraint, the stresses may relieve themselves by thermal 

 agitation and do very little work. But for sufficiently rapid traversals 

 of the loop, all the magnetostrictive stresses will do the same amount 

 of work on the core and its surroundings every cycle. Unannealed 

 materials, or materials rigidly constrained, should continue to show 

 residual loss at very low frequencies. The magnitude of c and its 

 variation with frequency thus should depend on the magnetostrictive 

 constant for the material, and on the types of dissipative constraints. 



" R. M. Bozorth, Elec. Eng., 54, 1251 (1935). 



