MAGNETIC LOSSES AT LOW FLUX DENSITIES 213 



ceived most study is the "residual" or "viscosity" loss.^ It appears 

 related to hysteresis loss because it is nominally independent of fre- 

 quency, but it differs in being proportional to Bm^ instead of Bm^ which 

 would be required by Rayleigh's law for hysteresis loops. Any satis- 

 factory investigation of this anomalous loss demands precise determina- 

 tion of its value, and of its variation with frequency. For this purpose, 

 ballistic galvanometer measurements of the hysteresis loop have been 

 made and compared with bridge measurements of a well annealed 35 

 permalloy laminated core. 



In a previous paper, the magnetic properties of a ring of compressed 

 powdered iron were studied at low flux densities using a sensitive 

 vacuum galvanometer ^ and a multiple swing ballistic method.^ 

 Hysteresis loops were measured at flux densities Bm ranging from 1.8 

 to 115 gauss, which showed energy losses proportional to Bm^ in ac- 

 cordance with Rayleigh's law. Alternating-current measurements 

 agreed with the ballistic measurements as to the magnitude of the 

 energy loss and the proportionality to B^^, but in addition showed a 

 residual loss proportional to Bm"^ which was of the same order of magni- 

 tude as the Rayleigh hysteresis at these low flux densities. 



The analysis of measurements made on the compressed dust core was 

 complicated by the inhomogeneous structure, by the variety of particle 

 shapes and thickness of insulation, and by the mechanical stresses inci- 

 dent to forming the core. To eliminate these objections, the present 

 study was undertaken using a core consisting of well annealed sheet 

 material, for which eddy current losses can be calculated by classical 

 formulae. 



Selection of Material 



Considerable a.-c. data were at hand from which to select material 

 for this experiment. The properties of a few representative materials 

 are given in Table I. The constants are defined by the equation 



= aBm -\- ef -\- c = ^-T- , (1) 



where R/ is the difference between the resistances measured with a.-c. 

 and with d.-c. on a toroidal coil with inductance of L/ due to core ma- 

 terial of permeability Hm, when the maximum flux density is ± Bm 

 and the frequency is / cycles per second. Here the hysteresis coefficient 



* H. Jordan, E. N. T., 1, 7 (1924); H. Wittke, Ann. d. Phys. (5) 23, 442 (1935); 

 F. Preisach, Zeit.f. Phys., 94, 277 (1935); R. Goldschmidt, Zeit.f. tech. Phys., 13, 534 

 (1932). 



