0. For this value of _t_ we then obtain from the first of the equations
(5)
_x _ = _ax_
Two points of the _x _-axis which are separated by the distance _x _ =
1 when measured in the _K _ system are thus separated in our
instantaneous photograph by the distance
image043
But if the snapshot be taken from _K _(_t _ = 0), and if we eliminate
_t_ from the equations (5), taking into account the expression (6), we
obtain
image044
From this we conclude that two points on the _x_-axis separated by the
distance 1 (relative to _K_) will be represented on our snapshot by the
distance
image045
But from what has been said, the two snapshots must be identical; hence
_x_ in (7) must be equal to _x _ in (7_a_), so that we obtain
image046
The equations (6) and (7_b_) determine the constants _a_ and _b_. By
inserting the values of these constants in (5), we obtain the first and
the fourth of the equations given in Section XI.
image047
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