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_?
image014
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.
It is clear that we have the problem of Section VI again before us. The
tube plays the part of the railway embankment or of the co-ordinate
system _K_, the liquid plays the part of the carriage or of the
co-ordinate system _K _, and finally, the light plays the part of the
man walking along the carriage, or of the moving point in the present
section. If we denote the velocity of the light relative to the tube by
_W_, then this is given by the equation (A) or (B), according as the
Galilei transformation or the Lorentz transformation corresponds to the
facts. Experiment[10] decides in favour of equation (B) derived from
the theory of relativity, and the agreement is, indeed, very exact.
According to recent and most excellent measurements by Zeeman, the
influence of the velocity of flow _v_ on the propagation of light is
represented by formula (B) to within one per cent.
[10] Fizeau found
image015
where
image016
30