of Magnetic Stress in Magnetostriction. 455 



the terms depending on changes of density are neglected, the 

 expressions reduce to those given by Maxwell in Art. 105. 



In 1884, Kirchhoff* gave a still more general theory, in- 

 cluding in his equations terms depending on elongations in 

 the direction of the electric or magnetic force, as well as 

 terms depending on the change of density. The fundamental 

 relations between intensity of magnetization I (A, B, C) and 

 resultant magnetizing force H («, ft, 7) are thus : — 



C. \d^ oy oz J dxj 



(. Xdx d# ^z / dyJ 



(. \ox oy dz ) qz J " 



where u, v, w are the component displacements of a particle 

 of the medium at (x, y, z) in the directions of the axes of co- 

 ordinates, and K, K 7 , K" are coefficients depending on the 

 nature of the medium. It is to be noticed that the quantities 

 in the brackets are nearly equal to the susceptibility, because 

 the elongations and change of volume are considered to be 

 very small. From these and the principle of Conservation of 

 Energy, Kirchhoff deduces his general expressions (in Max- 

 wellian notation) for the stresses in a substance magnetized 

 by induction : — 



P " = -(^ +K+ T) a2 + *(^ + K - K ') (a2+/32+72) ' 

 p " = ~(s +K+ T ) ^ + *(s + K - K ')(« 2 +/3 2 +r 2 ), 



/ 1 W\ 



P ye = P^=-(i+K+^j/S 7 , 



/ 1 K"\ 



/ 1 K" \ 



P^=P sx = -(i+K+^-)^. 



These expressions reduce to those of v. Helmholtz if it be 

 assumed that K" = 0, and to those of Maxwell for electric 

 stress (Art. 106) if we put K'=K"=0 ; and 14-4ttK = specific 

 inductive capacity of the medium. 



It will be seen from these expressions that KirchhofF's 



* Wied. Ann. xxiv. p. 52 (1885) j Ges. Abh., NacMrag, p. 91 (1891). 



