Page:The principle of relativity (1920).djvu/239



Note 1. The fundamental electro-magnetic equations of Maxwell for stationary media are:—

curl H = 1/c ([part]D/[part]t + ρν) (1)

curl E = -1/c [part]B/?]t (2)

div D = ρ B = μH

div B = ο D = k?]E

According to Hertz and Heaviside, these require modification in the case of moving bodies.

Now it is known that due to motion alone there is a change in a vector R given by

([part]R/[part]t) due to motion = u''. div R + curl [Ru]''

where u is the vector velocity of the moving body and [Ru] the vector product of R and u.

Hence equations (1) and (2) become

c  curl H = [part]D/[part]t + u div D + curl Vect. [Du] + ρν (1·1)

and

-c curl E = [part]B/[part]t + u div B + curl Vect. [Bu] (2·1)

which gives finally, for ρ = ο and div B = O,

[part]D/[part]t + u div D = c curl (H - 1/c Vect. [Du]) (1·2)

[part]B/[part]t = -c curl (E - 1/c Vect. [uB]) (2·2)