Magnetic Hysteresis with Frequency. .121 



sending back per cycle to the magnetizing circuit energy to 

 the amount — D 3 , and similarly it* D- &c. arc negative. 

 We have (see § 7) 



5=1= H ^- { sin 6\ + M z b s sin 3 (0 3 - </> 3 ) + 5A 5 6 5 sin 5(0 5 - <£ 5 ) + Ac.} 



=I 1 4-I 3 +fH-&c. (say), 



where v i> the volume of iron in the ring : 



hence D } = 1& = v \-^ sin 6 ] 



4 



D 3 = l,v = r SS x U B b d sin 3 (0 3 - <£ 3 ) 



D 5 = I 5 j;=«5^3 x5/i 5 &5 sin 5(^5-^5). 



For example, in calculating I by means of the above 

 formula for experiment 14 (Table I.) in which 



H = 9-42{sino>£--1635 sin 3(arf-8"72) 



-MI565 sin 5(a>f-29'78) + '0159 sin 7(^-15*86)} 

 B = 158b4>{sin (^-34*94) + -1865 sin 3(^ — 39-71) 



+ -U434 sin 5(^-44-12) + -0117 sin 7(a)^-47-9)} 

 we find that 



I = 37350{'5727--0914--0116-'0OO9} 

 = 21390-3414-434-34 

 = 17508, 

 or I 1 = 2i390, L 3 =-3414, 



1,= _434, I 7 =-34, 



which shows that per cm. :J of iron per cycle 21390 ergs 

 entered the ring by means of the first harmonics, and of this 

 there was sent back or reflected to the primary circuit 3414 

 ergs by means of the third, 434 ergs by means of the fifth, 

 and 34 ergs by means of the seventh harmonic, while the 

 remainder, =1=17508 ergs, was dissipated as heat in the 

 iron of the ring. 



These reflected current harmonies will obviously, if of 

 sufficient magnitude, greatly modify the wave-form of C, 

 and they will also by their reaction reduce the amplitude- 

 and change the phases of the corresponding harmonics of F 



