376 



H. XAUAOKA AND K. HONDA-. 



§ 5. Calculation of KirchhofTs coefficients k and k .Comparison 

 between theory and experiment. 



According to KirchhofTs theory of magnetostriction, ]) the coef- 

 ficients k, ¥, k" are defined by the equations 



ax- 



il. 





Iz 



where /,, Y,„ L are the components of the intensity of magnetization 7, 

 H x , H y , H z the components of the magnetizing force H, u, r, w the 

 component displacements of the medium at point x y z. The coefficient 

 fcis nearly equal to susceptibility as the strains due to magnetization is 

 negligibly small. The determination of the coefficients // and /," 

 involves considerable difficulty, because the strains produced by 

 magnetization or the effect of stress on magnetization generally depend 

 on both of these coefficients. 



In a joint paper with Mi*. E. T. Jones, one of us remarked that 

 the easiest method of testing Kirchhofes theory would be to measure 

 the change of volume of a ferromagnetic ring. The volume change 



would be theoretically equal to ^3—^—= .„., , ..^. (I—k'H). Un- 



fortunately there is great experimental difficulty, if the test be made 

 by means of a dilatometer, except in the manner introduced by 

 Bidwell 2) of measuring the change in the section of the ring. 



Cantone 3; found that the change of length and of volume of an 

 elongated ovoid are given by the formulae 



1). Kirchhof 1 :, he. cet ■ see also Puckels, Archiv f. Mathem. u. Physik (2) 12, L893. 

 2). Bidwell, Proc. Hoi/. Soc. 56, 94, is M. 

 3). Cantone, lor. cit. 



