Hysteresis Loops and lAssajous' Figures. 429 



Example V. ^ 



The next example is taken from a memoir of K. Angstrom 

 in the ' Proceedings ' of the Royal Swedish Academy of 

 Sciences, 1899, p. 257, where the curves are given without 

 any scale-values. They relate to a rod of steel containing 

 0*2 per cent, of carbon. Fig. 18 was observed by a magneto- 

 static method, fig. 19 by using an alternating current of 20 

 periods per second, fig. 20 by using one of 60 periods per 

 second. 



The analyses, on an arbitrary scale, are : — 



B x =-7-29 

 J5 3 =4-0-59 

 B- } = -0-40 

 # 7 =-0-23 

 B 9 =-0 24 

 _£ n =-0-24 



B, =-8-45 

 B 3 = -0-42 

 ^ 5 =-0-04 



B 7 = 0-02 

 J5 9 =-0-07 

 B n =-0'07 



B x =-8-57 

 B z == 0*16 

 B 6 = 0-33 

 B 7 = 0-23 

 5 9 =-0'01 

 # 11 = _0 03 



The small scale of the original drawings of these three 

 loops makes the values of the higher harmonics quite un- 

 reliable. But the comparison is of interest as showing the 

 effect of eddy-currents in the substance of the rod in widening 

 the loops, and in increasing both A l and A z . 



§ 8. Work done in the cycle.— -It was early pointed out by 

 Warburg and by Ewing that the work spent in carrying the 

 iron through a cycle of magnetizing operations was repre- 

 sented by the area of the hysteresis loop. We now consider 

 this from another point of view. 



Whatever work is spent in magnetizing the iron is derived 

 from the electric energy which is imparted by the circuit, 

 and this, at any instant, is proportional to the product of the 



Ffg. 



18. 











A, = 



0-57 







A 3 = 



o-oi 







^5=" 



-0-02 







A 7 =- 



-0-005 







A 9 =- 



-0 01 







A a = 



0-07 



Fig. 



19. 











A Y = 



2-31 







A z = 



1-08 







A = 



044 







A 7 = 



0-16 







A 9 = 



0-05 







A n = 



0-04 



Fig. 



20. 











At = 



2-74 







A,= 



1-21 







A = 



o-io 







A.= 



-0-09 







A' 9 = 



-0-04 







A n = 



0-09 



I 



