352 The Followers of Maxwell. 



mechanical momentum, which could be yielded up to the 

 conductor. It is readily seen that such momentum must be 

 directed at right angles to the tube and to the magnetic 

 induction a result which suggests that the momentum stored 

 in unit volume of the aether may be proportional to the vector- 

 product of the electric and magnetic vectors. 



For this conjecture reasons of a more definite kind may be 

 given.* We have already seenf that the ponderomotive forces 

 on material bodies in the electromagnetic field may be accounted 

 for by Maxwell's supposition that across any plane in the aether 

 whose unit normal is N, there is a stress represented by 



P N = (D . N) E - J (D .E)N + (l/47r) (B . H)H - (I/Sir) (B. H) N. 



So long as the field is steady (i.e. electrostatic or magnetostatic) 

 the resultant of the stresses acting on any element of volume of 

 the aether is zero, so that the element is in equilibrium. But 

 when the field is variable, this is no longer the case. The 

 resultant stress on the aether contained within a surface S is 



JJ PN . dS 



integrated over the surface : transforming this into a volume- 

 integral, the term (D . N) E gives a term div D . E + (D . V) E, 

 where V denotes the vector operator (9/9a?, d/dy, d/dz) ; and the 

 first of these terms vanishes, since D is a circuital vector; 

 the term - J (D . E) N gives in the volume-integral a term 

 J grad (D . E) ; and the magnetic terms give similar results. 

 So the resultant force on unit- volume of the aether is 



(D . V) E + J grad (D . E) + (l/4ir) (B . V) E + (I /Sir) grad (B . H), 

 which may be written 



[curl E . D] + (l/47r) [curl H . B] ; 



* The hypothesis that the aether is a storehouse of mechanical momentum, 

 which was first advanced by ,T. J. Thomson (Recent Researches in Elect, and Mag. 

 (1893), p. 13), was afterwards developed by H. Poincare, Archives Neerl. (2) v 

 (1900), p. 252, and by M. Abraham, Gott, Nach., 1902, p. 20. 



tCf. p. 302. 



