. . (3).
is fulfilled in general, where l 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') = µ(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 l and µ,
where
eq. 29: file eq29.gif
and
eq. 30: file eq30.gif
we obtain the equations
eq. 31: file eq31.gif
We should thus have the solution of our problem, if the constants a
and b were known. These result from the following discussion.
For the origin of K1 we have permanently x' = 0, and hence according
to the first of the equations (5)
eq. 32: file eq32.gif
If we call v the velocity with which the origin of K1 is moving
relative to K, we then have
eq. 33: file eq33.gif
The same value v can be obtained from equations (5), if we calculate
the velocity of another point of K1 relative to K, or the velocity
(directed towards the negative x-axis) of a point of K with respect to
K'.
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