mON UNDER PERIODIC MAGNETIZING FORCES. 95 



This e.m.f. produces a current equal to 3ojh,!P over r, where r is 

 the resistance of the circuit, and hence the reacting M.M.F. is — 



127roj?i-r llTrwn-a 



= = B, = X say, 



and whose phase position is 90° behind B,. 



Hence, from F, draw FM perpendicular to OF and equal to X. 

 The vector MF completely represents X. Join OM. OM will 

 represent the M.M.F. w, arising from B, in the iron, for the resultant 

 of *w, and X is OF, which is the final M.M.F. producing the resultant 

 flux F or aB,. 



From the above we see that B, is always reduced in amplitude 

 and shifted in phase by this reflecting action of the iron, and more so 

 as the resistance (and, therefore, in general, the impedance) of the 

 magnetizing circuit is less. 



It is easy to show that the amount of reflected energy is propor- 

 tional to the area of the triangle OMF. 



3. In the above we saw that the M.M.F. due to reactions is — 



12 TTWW'a -T) 



T— ^' 



and dividing by Z, the length of the magnetic circuit, we get the mag- 

 netizing force due to reactions — 



127r<oW'a ^ 12770) n' , ^ 127rw^^„„ 

 = r— B3 = - la B, = WYB^ 



rl r I- r . ^ 



where N is the number of magnetising turns per unit length, and V is 

 the volume of the iron. 



Hence these disturbing reactions are, all other things being 

 equal, directly proportional to the volume of the iron used, and in- 

 versely as the impedance of the magnetizing or other circuits that may 

 embrace the ring. 



The fact that the effect is proportional to the volume of iron used 

 follows at once from general principles, if we admit that the effect is 

 due to some peculiar action in each ultimate magnetic particle. 



[The above discussion will, with slight modifications, apply to the 

 action of eddy currents in modifying the induction j)roduced in iron by 

 periodic magnetizing forces.] 



4. In order to keep tnis disturbing action small, the experiments 

 described in this paper were performed on a small single annular 



