delations of Dielectric and Magnetic Polarization. 171 



of moving dielectric media, which necessitated in the first 

 instance the introduction of the electron theory in its main 

 aspects. 



5. Before concluding this discussion reference must 

 perhaps he made to a small discrepancy of a different kind, 

 which occurs in the form of the theory given by Pockels in 

 his article on " Magneto- and Elektro-striction " in the 

 Eneyklopadie der mathematischen Wissenschaften. It will 

 be observed that the stress system obtained on Maxwell's 

 theory is not in general self-conjugate, as must necessarily 

 be the case with all stresses in material media without polar 

 molecules, in order that the energy principle may be verified. 

 Now Pockels obtains by von Helmholtz's method a self- 

 conjugate stress in which the corresponding cross-terms are 

 each half the sum of the corresponding terms in Maxwell's 

 stress ; he secures this by including the effect of a general 

 virtual displacement possessing rotational as well as trans- 

 lational qualities. He attempts to assign the discrepancy 

 in Maxwell's determination to a neglect of the rotational 

 part of the displacement, and supports his contention by a 

 reference to Hertz's interpretation of the energy method of 

 von Helmholtz, as given in Lorentz's article on " Maxwell's 

 Theory" in the same work. It appears, however, that 

 Pockels criticism really redounds on himself, inasmuch as he 

 has neglected to include in the hypothetical expression of 

 the virtual work the effect of any possible applied couples 

 such as are necessitated by Maxwell's theory. His reference 

 to Hertz's work in no way helps the matter for, as is clearly 

 recognized by both Hertz and Lorentz, this method only 

 determines the sum of corresponding cross-terms of the stress 

 matrix and not each of them independently. Besides, the 

 difficulties encountered above and involved in the method of 

 application of the integration by parts also occurs in Pockels' 

 work, and in such a way as to obscure what in reality comes 

 to a mutual cancelling of the two additional parts of the 

 variation, one of which alone is included by Pockels, arising 

 on account of the rotational terms. 



The University, Sheffield, 

 April 15th, 1916. 



