392 ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



order to make these two statements, which we hold to be mutually 

 exclusive where there is intrinsic polarization, appear consistent, 

 Heaviside proceeds in the following, as it appears to us, artificial 

 manner. In our notation, Heaviside* considers the field F as made 

 up of a part h = 47r/ /yu,, defined as the intrinsic force, together with 

 a lamellar force which we shall denote by F h (F in Heaviside's 

 notation), 



In order to make the induction solenoidal, he then puts 



Ii = *F ht 

 instead of Ii = /cF. Then the induction is defined, not as 



but as $ = F h + 47T/. 



Inserting for / the sum of the intrinsic and induced polariza 

 tions, this becomes 



This gives, in conjunction with the equation supposed to be 

 fundamental, namely 



divg = 0, 

 the equation 



div (//J\) = div /j,h = div / , 



rTT 47T 



which we may compare with our equation (6). Accordingly 

 Heaviside's //J\ has the property of our Hertzian induction. The 

 difference in Heaviside's treatment may be summed up as : 1. A 

 different definition of the total field. 2. Induced polarization 

 produced by only a part of the field. 3. The Hertzian induction 

 considered solenoidal, even in case there is intrinsic polarization. 



We have stated the difficulties of Heaviside's treatment as they 

 appear to us, without wishing to dispute the dicta of so weighty 

 an authority. The theory as we have given it seems to be that of 

 Helmholtz and Hertz, both of whom explicitly state that real 

 magnetism exists in permanent magnets. Neither they, however, 

 nor any other author, so far as known to the present writer, have 



* Papers, Vol. i., pp. 4534. 



