two-fold application of the transformation-equations, we obtain
,
, etc.
Since the relations between (x', y', z', t'), and (x, y, z, t) do not contain time explicitly, therefore K and k' are relatively at rest.
It appears that the systems K and k' are identical.
,
Let us now turn our attention to the part of the y-axis between (), and (). Let this piece of the y-axis be covered with a rod moving with the velocity v relative to the system K and perpendicular to its axis ;—the ends of the rod having therefore the co-ordinates
Therefore the length of the rod measured in the system K is . For the system moving with velocity (-v), we have on grounds of symmetry,