A light-signal, which is proceeding along the positive axis of _x_, is
transmitted according to the equation
_x_ = _ct_
or
_x_ _ct_ = 0 . . . . . (1).
Since the same light-signal has to be transmitted relative to _K _ with
the velocity _c_, the propagation relative to the system _K _ will be
represented by the analogous formula
_x _ _ct _ = 0 . . . . . (2)
Those space-time points (events) which satisfy (1) must also satisfy
(2). Obviously this will be the case when the relation
(_x _ _ct _) = (_x_ _ct_) . . . (3).
is fulfilled in general, where indicates a constant; for, according
to (3), the disappearance of (_x_ _ct_) involves the disappearance of
(_x _ _ct _).
If we apply quite similar considerations to light rays which are being
transmitted along the negative _x_-axis, we obtain the condition
(_x _ + _ct _) = (_x + ct_) . . . (4).
By adding (or subtracting) equations (3) and (4), and introducing for
convenience the constants _a_ and _b_ in place of the constants and
where
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