Closing Years of the Nineteenth Century. 423 



electrified corpuscle of charge e moving with velocity v in a field 

 defined by the electric force d and magnetic force h. 



In Lorentz' fundamental case, which has thus been examined, 

 account has been taken only of the ultimate constituents of 

 which the universe is supposed to be composed, namely, cor- 

 puscles and the aether. We must now see how to build up 

 from these the more complex systems which are directly 

 presented to our experience. 



The electromagnetic field in ponderable bodies, which to our 

 senses appears in general to vary continuously, would present a 

 different aspect if we were able to discern molecular structure ; 

 we should then perceive the individual electrons by which the 

 field is produced, and the rapid fluctuations of electric and 

 magnetic force between them. As it is, the values furnished 

 by our instruments represent averages taken over volumes 

 which, though they appear small to us, are large compared 

 with molecular dimensions.* We shall denote an average 

 value of this kind by a bar placed over the corresponding symbol. 



Lorentz supposed that the phenomena of electrostatic charge 

 and of conduction-currents are due to the presence or motion of 

 simple electrons such as have been considered above. The part 

 of p arising from these is the measurable density of electrostatic 

 charge ; this we shall denote by pi. If w denote the velocity 

 of the ponderable matter, and if the velocity v of the electrons 

 be written w + u, then the quantity pv, so far as it arises from 

 electrons of this type, may be written ^ w + pu. The former of 

 these terms represents the convection-current, and the latter 

 the conduction-current. 



Consider next the phenomena of dielectrics. Following 

 Faraday, Thomson, and Mossotti,f Lorentz supposed that each 

 dielectric molecule contains corpuscles charged vitreously and 

 also corpuscles charged resinously. These in the absence of an 



* These principles had been enunciated, and to some extent developed, by 

 J. Willard Gibbs in 1882-3 : Amer. Journ. Sci. xxiii, pp. 262, 460, xxv, p. 107 ; 

 Gibbs' Scientific Papei-s, ii, pp. 182, 195, 211. 



t Cf. pp. 210, 211. 



