48 Mr. 0. Heaviside on Maxwell's Electromagnetic 



(except in the very artificial form of balanced exchanges). 

 When there is propagation, and H is involved, we have 



Now this is, not an electromagnetic law specially, but strictly 

 a truism, or mathematical identity. It becomes electromag- 

 netic by the definition of A, 



curl A=/aH, 



leaving A indeterminate as regards a diverging part, which, 

 however, we may merge in — V^- Supposing, then, A and 

 ^ to become fixed in this or some other way, the next ques- 

 tion in connexion with propagation is, Can we, instead of the 

 propagation of E and H, substitute that of ^ and A, and 

 obtain the same knowledge, irrespective of the artificiality 

 of ■^ and A ? The answer is perfectly plain — we cannot do 

 so. We could only do it if ^, A, given everywhere, found E 

 and H, But they cannot. A finds H, irrespective of ■^, but 

 both together will not find E. We require to know a third 



vector, A. Thus we have '^, A, and A required, involving 

 sei^en scalar specifications to find the six in E and H. Of these 

 three quantities, the utility of A is simply to find H, so that 

 we are brought to a highly complex way of representing the 



propagation of E in terms of ^ and A, giving no information 

 about H, which is, it seems to me, as complex and artificial 

 as it is useless and indefinite. 



Again, merely to emphasize the preceding, the variables 

 chosen shou]d be capable of representing the energy stored. 

 Now the magnetic energy may be expressed in terms of A, 

 though with entirely erroneous localization ; but the electric 

 energy cannot be expressed in terms of ^. Maxwell (chap, 

 xi. vol. ii.) did it, but the application is strictly limited to 

 electrostatics ; in fact, Maxwell did not consider electric 

 energy comprehensively. The full representation in terms of 

 potentials requires ^ and Z, the vector-potential of the mag- 

 netic current, [This is developed in my work " On Electro- 

 magnetic Induction and its Propagation," Electrician, 1885.] 

 This inadequacy alone is sufficient to murder ^ and A, con- 

 sidered as subjects of propagation. 



Now take a concrete example, leaving the abstract mathe- 

 matical reasoning. Let there be first no E or H anywhere. 

 To produce any, impressed force is absolutely needed. Let it 

 be impressed e, and of the simplest type, viz. an infinitely 

 extended plane sheet of e of uniform intensity, acting nor- 

 mally to the plane. What happens? Nothing at all. Yet 



