Hysteresis Loops and Lissajous' Figures. 



433 



the form of the loop would become a pure rectangle, as 

 fie. 24. 



Fiff. 24. 



Fio-. 25. 



The half-width of any static hysteresis loop, which is 

 commonly taken (following Hopkinson) as a measure of the 

 coercive force, is independent of all the cosine terms, and is 

 in all cases equal to A 1 — A% + A§ — A 7 + A 9 — &c. 



For loops of equal height (that is equal maxima of flux 

 density) the coercive force is not proportional to the work 

 spent in the cycle ; for the work spent in the cycle is repre- 

 sented by the area of the loop, and as shown above, this is 

 invariably proportional to A i9 while the coercive force is 

 represented by the sum of the series named in the previous 

 sentence. Since in static hysteresis loops the fifth and higher 

 terms are practically absent, the coercive force is proportional 

 to A 1 — A z . 



§ 11. Effect of the Co sine- Constituents. 



As already seen, the fundamental cosine-constituent is an 

 oblique line. It is in reality a double line, traversed upwards 

 during half the cycle, and downwards during the other half. 

 The effect of superposing this constituent upon the funda- 

 mental ellipse is to shear it over. Cosine-components are 

 always negative, corresponding to lagging constituents of the 

 wave-curve. They shear the 1S-?I curve over toward the 

 right, on the ascending side. If a mass of iron undergoing 

 magnetization is traversed by an air-gap, or is constituted as 

 a non-closed magnetic circuit, the reaction of the air-gap 

 brings a lagging constituent into the magnetizing current, 

 imposing a negative cosine-constituent upon the loop, and 

 shearing it over. 



The presence of negative cosine-constituents in hysteresis 

 Phil. Mag. S. 6. Vol. 20. No. 117. Sept. 1910. 2 G 



