94 PROCEEDIXGS OP SECTION A. 



Tims wheu the induction — 

 B = B, sin {od - ^,) + B, sin 3 {i»t — 0^) + B, sin 5 (oj/ ~B.) -\- &c., 

 is produced by — 



H =: Hj sin Mt. 



Bj, Bj, &c., cannot in any direct way be due to H, but must be due to 

 Bj, arisine^ f roui the latter by means of some property of the oscillating 

 system within the ultimate magnetic particle. We may, therefore, 

 assume that with a fundamental harmonic B^ of the induction there 

 are necessarily associated magneto-motive forces «?, , ««., &c., of 

 periods T/8, T/5, &c., which would produce inductions B^, B. , &c., 

 provided no reactions due to induced currents in the circuits round the 

 iron ring tend to modify these inductions. But as there must be at 

 least one circuit there will always be modifying reactions. Thus, 

 considering only the third harmonic, if aB, be the resultant flux of 

 this order (a being the sectioiial area of the ring) variation of this will 

 induce a current C, in the magnetizing circuit, and from C, we have 

 the magneto-motive force (M.M.F.) 4iirn Cj acting round the ring. 

 The resultant magneto-motive force is, therefore, the vector sum of m^ 

 and -^-n-n C,, and B, is the induction produced by this resultant M.M.F. 



In the simple case in which the copper circuit is non-inductive, 

 aud, when magnetic lag is neglected, the relations between m^, C,, and 

 a Bj, can easily be expressed by a vector diagram, as follows: — 



Draw a line OF (Fig. I-)) to represent in amplitude and phase 

 the resultant flux F ^ aB^ multiplied by the reluctance of the ring. 



Ym. I. 



Variation of F generates an e.on.f. whose amplitude is 3w??F and whose 

 phase position is 90° behind OF. 



[27r/w=T=period of fundamental, and n = number of magnetizing 

 turns on ring.] 



