Those space-time points (events) which satisfy (1) must also satisfy (2). Obviously this will be the case when the relation
(x′ – ct′) = λ(x – ct) . . . (3).
is fulfilled in general, where λ 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 λ and μ where
and
we obtain the equations