[ 162 ] 



XIII. On the Mechanical Relations of Dielectric and 

 Magnetic Polarization. By G. H. Livens *. 



1. fT^HERE still appears to be some uncertainty as to 

 X the exact expression for the mechanical forcive of 

 electric or magnetic origin acting on the elements of a 

 polarizable medium in an exciting field of force, and as to 

 the consequent reduction of this forcive to its representation 

 by means of an applied stress system. 



The original procedure of Maxwell f, based, for the case of 

 magnetic media, on the most elementary physical ideas 

 respecting the nature of the polarization involved, leads to a 

 definite expression for the forcive on any medium which is 

 independent of the law, or even of the existence of a law, for 

 the induction of the polarization by the exciting field, and 

 which should therefore hold in the case of all substances in 

 which the polarization is of the nature of that described, even 

 if this polarization involves hysteretic qualities. This, the 

 original, procedure has been elaborated and extended in the- 

 more recent developments of the theory of electrons, and 

 the general validity of the result obtained is thereby fully 

 confirmed and substantiated both for dielectric and magnetic 

 media. 



A more general mode of discussion based on the method o£ 

 energy, but avoiding molecular theory, has been originated by 

 Korfceweg |, formulated in general terms by von Helmholtz§ 

 and further developed by Lorberg, Kirchhoff||, Hertz ^[, 

 Cohn **, and others. The expression for the forcive on the 

 polarized medium obtained by this method is, however, in- 

 consistent with that obtained by Maxwell on his simpler 

 form of the theory. The discrepancy is regarded by some 

 authors as due to incompleteness in Maxwell's formulation, 

 but Larmorff has shown that, at least in the simplest case of 

 isotropic media, it is due mainly to fundamental errors both 

 in the physical assumptions on which the energy method is 

 based and also in the analytical processes by which that 

 method is developed. This criticism appears, however, to 

 have been entirely overlooked and the energy method is still. 



* Communicated bv the Author. 

 f Treatise, vol. ii. '§§ 641, 642. 

 I Wied. Ann. ix. (1880). 



§ "Wied. Ann, xiii. (1882) ; Abhandlungen, i. p. 798. 

 || Wied. Ann. xxiv., xxv. (1885) ; Abhandlungen, ' Nachtrag/ p. 91. 

 % Wied. Ann. xli. (1890) ; ' Electric Waves ' (English Edition), 

 pp. 259-268. 



** ' Das electromagnetische Feld,' Ch. viii. 

 ft Phil. Trans. A. cxc. p. 280 (1897). 



