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)
But we can carry out this consideration just as well on the basis of the theory of
relativity. In the equation
x1 = wt1 B)
we must then express x1and t1 in terms of x and t, making use of the first and
fourth equations of the Lorentz transformation. Instead of the equation (A) we
then obtain the equation
eq. 09: file eq09.gif
which corresponds to the theorem of addition for velocities in one direction
according to the theory of relativity. The question now arises as to which of these
two theorems is the better in accord with experience. On this point we axe
enlightened by a most important experiment which the brilliant physicist Fizeau
performed more than half a century ago, and which has been repeated since then
by some of the best experimental physicists, so that there can be no doubt about
its result. The experiment is concerned with the following question. Light travels
in a motionless liquid with a particular velocity w. How quickly does it travel in
the direction of the arrow in the tube T (see the accompanying diagram, Fig. 3)
when the liquid above mentioned is flowing through the tube with a velocity v ?
In accordance with the principle of relativity we shall certainly have to take for
granted that the propagation of light always takes place with the same velocity w
with respect to the liquid, whether the latter is in motion with reference to other
bodies or not. The velocity of light relative to the liquid and the velocity of the
latter relative to the tube are thus known, and we require the velocity of light
relative to the tube.