_c_ curl H = ∂D/∂_t_ + _u_ div D + curl Vect. [D_u_] + ρν (1·1)
and
-_c_ curl E = ∂B/∂_t_ + _u_ div B + curl Vect. [B_u_] (2·1)
which gives finally, for ρ = 0 and div B = 0,
∂D/∂_t_ + _u_ div D = _c_ curl (H - 1/_c_ Vect. [D_u_]) (1·2)
∂B/∂_t_ = -_c_ curl (E - 1/_c_ Vect. [_u_B]) (2·2)
Let us consider a beam travelling along the _x_-axis, with apparent
velocity _v_ (_i.e._, velocity with respect to the fixed ether) in
medium moving with velocity _u__{_x_} = _u_ in the same direction.
Then if the electric and magnetic vectors are proportional to
_e_^{_i_A(_x_ - _vt_)}, we have
∂/∂_x_ = _i_A, ∂/∂_t_ = -_i_A_v_, ∂/∂_y_ = ∂/∂_z_ = 0, _u__{_y_} =
_u__{_z_} = 0