122 Prof. T. R. Lyle on the Variations of 



from which thev arise, thus modifying the wave-form of F 

 (the flux). 



Now I find that when the upper harmonics of the flux are 

 damped as above, /a or Bj/Hx becomes greater, and the iron 

 loss I for the same value of 2}, or even of B 1? becomes 

 greater. To make up for this greater iron loss as well as to 

 supply the energy that is reflected, more energy must enter 

 the iron by means of the first harmonic of C, and this is 

 effected by a considerable increase in 6 V the angle of lag of 

 F 1 behind G r 



If the applied E.M.F. (supposed sinusoidal) and the circuit 

 be so controlled that while F L or cxB l is kept constant the 

 impedance is regularly diminished, the reflected energy due to 

 any of the upper harmonics (C 3 , F 3 , say) will not go on 

 increasing as the impedance diminishes, bat will at first 

 increase to a maximum and then diminish, in the limit 

 vanishing when the impedance becomes zero. This would 

 follow if we assumed that on account of some property of the 

 iron there is always associated with a given primary sinu- 

 soidal flux oscillation F x or ocB 1 of frequency n a series of 

 magneto-motive forces M 3 , M 5 , &c, of frequencies 3n, 5n, &c, 

 given in amplitude and fixed in phase relative to F x . 



F 3 would then, for a given impedance, be the flux pro- 

 duced by the vector resultant of M 3 and 47r/* 1 C ;J , where C g is 

 the reflected current produced in the circuit by variation 



ofF »- 



In the simple case in which the circuit outside the ring is 

 non-inductive, and when magnetic lag is neglected, the re- 

 lations between M 3 , G 3 , F 3 , and the reflected energy can be 

 shown by means of a vector right-angled triangle of which 

 the hypotenuse is proportional to M 3 and is fixed. One of 

 its sides is proportional to C 3 and the other to F 3 , while the 

 area of the triangle is proportional to the reflected energy. 

 The locus of the right-angled vertex is thus a semicircle, and 

 as ; . increases from zero until the triangle becomes isosceles, 

 the reflected energy increases from zero to a maximum, after 

 which any further increase of C 3 causes a diminution in the 

 reflected energy, which finally vanishes with F 3 . 



If we took account of magnetic lag and of the inductance 

 of the circuit the vector diagram would be more complicated, 

 but the general result would be similar. 



The following results of three experiments with King I. 

 will illustrate the preceding. 



The ring was rewound with two layers of 207 .turns each, 

 one or both of which could be used, thus enabling me to 



