Galilei transformation (Section XI). In place of the man walking inside
the carriage, we introduce a point moving relatively to the co-ordinate
system _K _ in accordance with the equation
_x _ = _wt _
By means of the first and fourth equations of the Galilei
transformation we can express _x _ and _t _ 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 VI,
_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
_x _ = _wt _
we must then express _x _ and _t _ 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
image013
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 are 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_.
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