202, 203] DIELECTRICS AND MAGNETIZABLE BODIES. 393 



worked the matter out in detail as has Heaviside, nor have any 

 problems been solved in which a difference becomes of importance. 

 In either treatment, the flux of induction issuing from a 

 magnet is the same, which is the quantity with which we are 

 concerned in practice, the ambiguity existing only in the substance 

 of the intrinsic magnet. The difference between intrinsic and 

 other magnets is that in the former two independent vectors are 

 necessary to characterize the state of the body, while in the latter 

 one suffices. These may be taken as 



% H and gj,, as g^, /, or as $ M , I. 



203. Variability of /A. Hysteresis. Throughout this chapter 

 it has been assumed that the value of //, at any point was constant 

 for that point. This assumption is not borne out by the facts, 

 but was necessary in order to make the subject amenable to 

 mathematical treatment. It is found that p is a function of the 

 strength of the field, and that for magnetic bodies, in which this 

 phenomenon has been most carefully investigated, as the force 

 increases, //, diminishes, finally tending towards the limit unity, so 

 that the ratio of the induction to the force approaches unity. At 

 the same time the difference between the induction and the force 

 tends towards a constant maximum value, which is equal to 4?r 

 times the greatest intensity of magnetization that the substance 

 can assume. This is known as the intensity of saturation. For 

 wrought-iron this intensity of saturation has been found to be about 

 1 700 c.G.s. units. The variability of p does not affect the validity 

 of Ohm's Law, which determines the distribution of the tubes 

 of induction, although it seriously complicates the mathematical 

 theory. In fact no cases of magnetization have been worked out 

 taking account of the dependence of /JL upon F. But this is not 

 the only defect of our theory. It has been found that for a given 

 value of F there is not a single determinate value of //,, but that 

 the value depends not only on the actual value of F, but upon the 

 values which have acted at the point in question at previous 

 times. If we plot a curve having as abscissas the values of F at 

 a given point at various times and as ordinates the values of g at 

 the corresponding times, we may express this phenomenon by say- 

 ing that the value of //, at any point of the diagram depends on 

 the path by which the substance has been brought to the point, 

 that is, on the whole history of the field at the point. This 



