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