278 Messrs. H. Nagaoka and K. Honda on Magnetostriction. 



the component elongations. The coefficient k is nearly equal 

 to susceptibility as the strain due to magnetization is negli- 

 gibly small. The determination of the coefficients k' and k" 

 involves considerable difficulty, because the strains produced 

 by magnetization or the effects of stress on magnetization 

 ganerally depend on both of these coefficients. In a joint 

 paper with Mr. E. T. Jones, one of us remarked that the easiest 

 method of testing Kirchhoff's theory would be to measure the 

 change of volume of a ferromagnetic ring. The volume 

 change is theoretically equal to 



~v =3 T = 4K(1 + 3@) (I ~* /H) ' 



following Kirchhoff's notation. Unfortunately there is great 

 experimental difficulty, if the test be made by means of 

 a dilatometer, except in the manner introduced by Bidwell 

 of measuring the change in the section of the ring. 



Canton e found that the change of length and of volume of 

 an elongated ovoid are given by the following formulae accord- 

 ing to Kirchhoff's theory : — 



11 H 2 f 4ttP ,. x • k-k f A" M „ x •) " 



8v H 2 / l2 , 3(*-A') k»\ ' 



^ = K(ITM) \ rf+ — i— - 4j' -..."<*) 



where E is Young's modulus, K the rigidity, and © a con- 

 stant denned by the relation 



E/ l + 2© \ 

 2U + 30/ 



In the above formulae terms involving the ratio 



/minor axis\ 2 , . , 



I : r I are neglected. 



\major axis/ " 



Corresponding expressions for a long prismatic body as 

 wires or rods placed in uniform magnetizing field can be 

 approximately calculated in the following manner : — 



Let the field-strength in the coil be denoted by H ; then 

 the potential of the magnetizing force would be 



where N is the demagn etizing factor, Jc the susceptibility, and 

 x the direction of magnetization. 



