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LXXII. On the Treatment of Electrodynamics. 

 To the Editors of the philosophical Magazine. 

 Gentlemen, — 



IN the February number of your Magazine Dr. Lehfeldt, 

 in an article on Electrodynamics, speaks o£ the highly 

 artificial nature o£ the ordinary method o£ calculating the 

 induction inside a magnetic material. I have always felt 

 this, and for some years ha^e abandoned the " crevasse " 

 method in favour of the follow' 111 g- 



Consider an area of one square centimetre drawn in the 

 interspace between the molecular magnets and at right 

 angles to the direction of magnetization, then from the 

 definition of intensity of magnetization (I) it follows in the 

 usual way that the resultant amount of N pole on one side 

 of this area and of S pole tfpon the other side is I. Each 

 unit of N pole gives rise to 4<7r lines which cross the area 

 to the S side, and hence the induction within the material 

 due to the arrangement of *k elementary magnets is 4ttL 

 Adding this to the field H du° to other sources we obtain 



B = fI + 47rL 



The following proof of the work done in taking a specimen 

 through a hysteresis cycle may be of interest, as it depends 

 upon first principles. 



If m is the magnetic mom™* of a molecular magnet and 

 6 the angle its axis makes witP the direction of magnetization, 

 I = 2mcos0 for 1 c.c, and £m sin 0=0. On causing m to 

 rotate through an additional angle d6 the work done with 

 or against, the existing field H is equal to Hm sin OdO and 

 for 1 c.c. the total work is 20™ smtf^ = HS»isin^^, 



but since I = %m P os 6, 



dl = i£mcos0 



= _2 msul Odd. 

 .-. Work done = Hdl- 

 The integration for a cycle u pon the H-I diagram follows 

 in the ordinary way. 



The above proofs are independent of any assumption as to 

 the nature of the ultimate magnetic particle. 



S. G-. Starling. 



Municipal Technical Institute, 

 West Ham, E. 

 Feb. 5, 1909. 



