from an Electric Source, 165 



for a non-magnetic insulator, 



5 = KeE + mM, 



and the developed form of (h') becomes 



K(E-e)E + (M-m)M=-divF'. 



This, the equation of energy, could be satisfied in a variety 

 of ways, according to the manner in which Maxwell's equa- 

 tions (a) are modified within the " sources/' i. e. within the 

 seats of e, m. Heaviside's modification consists in replacing 

 0)by 



KBE/d* = c. curl (M-m), dNT/d£ = c. curl (e-E). (b) 



The soleuoidal conditions remain unchanged. The equation 

 of energy is obviously satisfied by (h), with 



F' = cV(E-e)(M-m) 



as the energy flux. The boundary conditions are : con- 

 tinuity of the normal components of M and (in absence of 

 charges) of KE, precisely as in the case of no impressed 

 forces, and continuity of the tangential components of E — e 

 and M — m. This is all we shall require in the sequel. 



A peculiar feature of Heaviside's, as compared with Max- 

 well's, equations is that the former contain explicit functions 

 of the time, the impressed forces, so that the physical com- 

 pleteness of the system * is given up. The introduction of 

 such functions, far from being a methodological disadvantage, 

 is but the manifest, and very desirable, expression of our 

 ignorance of the intrinsic mechanism of the sources of 

 electromagnetic energy f. And when it is first found out 

 which are the appropriate " impressed forces " it will always 

 be possible to attempt to replace them by mechanisms and 

 thus to amplify the system until it has become complete. 



Mean Energy of the Source. 



Let the source be a sphere of radius a. Impressed electric 

 force, £ = £ sin/t£, homogeneous throughout the source. No 

 magnetic impressed force ; also, magnetic permeability of 



* That is, the property of its past and future being determined by its 

 present state alone. 



t It seems also worth noticing that equations (b), at least for K=l, 

 satisfy rigorously the principle of relativity. But this property, with 

 some of its consequences, is better reserved for a later publication. 



