On Magnetic Induction in Iron and other Metals. 457 



The amplitudes of the octave and the third harmonic are 

 inappreciable, ns indeed the shape of the curve itself would 

 suggest. 



The presence of the epochs in the harmonic constituents is 

 of course the indication of hysteresis and of residual magnetism 

 in the material. 



Equation (11) Part I. may be written in the form 



where D r , x, and 6 r are constants whose values are to be 

 determined. 



For the curve in question it appears that r assumes odd 

 values only. 



This last condition suggests a modification of fig. 5, Part L, 

 as a possible form of the graph for Ia. =0 which would apply 

 to such an. experimental curve as we have under examination. 



A somewhat prolonged arithmetical study of the matter 

 leads me to a general form of graph for J x=0 like that shown 

 here in fig. 6. 



Fi<?. 6. 



To find the equation to this graph, let 

 l x=0 =c from H = to H=X ; 

 I a . =0 =c— «(H— X) from H = X to H= ^- ; 



I x =o=— c from H= 2 to H= ^^l 



I x=0= _ c + rt (H- ? -X) from H= 5 +X to H = R. 



By the application of Fourier's methods, we find as the 



