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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′) = 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

image038

and

image039

we obtain the equations

image040

We should thus have the solution of our problem, if the constants

a and b were known. These result from the following discussion.