432 



Dr. Silvanus Thompson on 



of the magnetizing current, is due to eddy-currents, and how 

 much to hysteresis. It is, indeed, already known * that the 

 effect of eddy-currents is to widen out the loop elliptically. 



§ 10. Effect of the Higher Sine- Constituents. 



The presence of the third harmonic has been noted in § 7 

 above. Indeed, it is usually present. A fine example is 

 afforded by the carve, fig. 21, which is taken from Fleming's 

 'Alternate Current Transformer,' vol. ii. p. 486 (edition of 

 1892), which affords the following analysis : — 



Fig. 22. 



A = 





11-23 



A 3 = 





1-71 



Ar,= 



— 



0-74: 



A 7 = 



+ 



O02 



A,= 



— 



0-29 



A n = 



+ 



0-03 



B l =-11-87 

 #,=- 0-72 

 B 5 = + 0-23 



J3 7 = + 0-07 

 B 9 = + 0-22 

 Ai=+ 0-57 



In the memoir of Angstrom already quoted, a curious 

 curve, fig. 22, nearly a pure third harmonic is given, having 

 been found by him as a differential hysteresis loop repre- 

 senting the difference between two steel rods, one having 

 0'2 per cent, the other 0*8 per cent, of carbon. 



It is obvious that the effect of superposing a third-term 

 sine-constituent upon the fundamental ellipse will be to 

 narrow it at the middle. It will widen it toward the ends, 

 the widening beginning at a distance of 0*134 of the semi- 

 major axis from the ends, as in fig. 23. 



If sine-constituents were present, of all orders, in the 

 following proportions, 



1 



A i — l J A z — 3 , A 5 



— l 



■A.= 



* See Angstrom, op. cited. 

 p. .500. 



and Heinke, Die Electrophysik (1904), 



