Page:The principle of relativity (1920).djvu/101

 §9.

Let us now see how far the fundamental equations assumed by Lorentz correspond to the Relativity postulate, as defined in §8. In the article on Electron-theory (Ency, Math., Wiss., Bd. V. 2, Art 14) Lorentz has given the fundamental equations for any possible, even magnetised bodies (see there page 209, Eq^n XXX´, formula (14) on page 78 of the same (part).

(IIIa´´) Curl (H - [uE]) = J + dD/dt + u div D - curl [uD].

(I´´) div D = ρ

(IV´´) curl E = - dB/dt, Div B = O (V´)

Then for moving non-magnetised bodies, Lorentz puts (page 223, 3) μ = 1, B = H, and in addition to that takes account of the occurrence of the di-electric constant ε, and conductivity σ according to equations

(εqXXXIV´´, p. 327) D - E = (ε - 1) {E + [uB]}

(εqXXXIII´, p. 223) J = σ(E + [uB])

Lorentz's E, D, H are here denoted by E, M, e, m while J denotes the conduction current.

The three last equations which have been just cited here coincide with eq^n (II), (III), (IV), the first equation would be, if J is identified with C, = uρ (the current being zero for σ = 0,

(29) Curl [H - (u, E)] = C + dD/dt - curl [uD],