Now in practice we can move clocks and measuring-rods only with
velocities that are small compared with the velocity of light; hence
we shall hardly be able to compare the results of the previous section
directly with the reality. But, on the other hand, these results must
strike you as being very singular, and for that reason I shall now
draw another conclusion from the theory, one which can easily be
derived from the foregoing considerations, and which has been most
elegantly confirmed by experiment.

In Section 6 we derived the theorem of the addition of velocities
in one direction in the form which also results from the hypotheses of
classical mechanics- This theorem can also be deduced readily horn the
Galilei transformation (Section 11). In place of the man walking
inside the carriage, we introduce a point moving relatively to the
co-ordinate system K1 in accordance with the equation

x1 = wt1

By means of the first and fourth equations of the Galilei
transformation we can express x1 and t1 in terms of x and t, and we
then obtain

x = (v + w)t

This equation expresses nothing else than the law of motion of the
point with reference to the system K (of the man with reference to the
embankment). We denote this velocity by the symbol W, and we then
obtain, as in Section 6,

W=v+w A)