When a detached region[19] of matter is at rest at any moment, therefore
the vector _u_ is zero, for a system (_x_, _y_, _z_, _t_)—the
neighbourhood may be supposed to be in motion in any possible manner,
then for the space-time point _x_, _y_, _z_, _t_, the same relations (A)
(B) (V) which hold in the case when all matter is at rest, shall also
hold between ρ, the vectors C, _e_, _m_, _M_, _E_ and their
differentials with respect to _x_, _y_, _z_, _t_. The second axiom shall
be:—
Every velocity of matter is < 1, smaller than the velocity of
propagation of light.[20]
The fundamental equations are of such a kind that when (_x_, _y_, _z_,
_it_) are subjected to a Lorentz transformation and thereby (_m_ - _ie_)
and (_M_ - _iE_) are transformed into space-time vectors of the second
kind, (C, _i_ρ) as a space-time vector of the 1st kind, the equations
are transformed into essentially identical forms involving the
transformed magnitudes.