space, _i.e._ a physical non-equivalence of different directions. This
is very powerful argument in favour of the principle of relativity.
VI.
THE THEOREM OF THE ADDITION OF VELOCITIES EMPLOYED IN CLASSICAL
MECHANICS
Let us suppose our old friend the railway carriage to be travelling
along the rails with a constant velocity _v_, and that a man traverses
the length of the carriage in the direction of travel with a velocity
_w_. How quickly or, in other words, with what velocity _W_ does the
man advance relative to the embankment during the process? The only
possible answer seems to result from the following consideration: If
the man were to stand still for a second, he would advance relative to
the embankment through a distance _v_ equal numerically to the velocity
of the carriage. As a consequence of his walking, however, he traverses
an additional distance w relative to the carriage, and hence also
relative to the embankment, in this second, the distance w being
numerically equal to the velocity with which he is walking. Thus in
total he covers the distance _W = v + w_ relative to the embankment in
the second considered. We shall see later that this result, which
expresses the theorem of the addition of velocities employed in
classical mechanics, cannot be maintained; in other words, the law that
we have just written down does not hold in reality. For the time being,
however, we shall assume its correctness.
VII.
THE APPARENT INCOMPATIBILITY OF THE LAW OF PROPAGATION OF LIGHT WITH
THE PRINCIPLE OF RELATIVITY
There is hardly a simpler law in physics than that according to which
light is propagated in empty space. Every child at school knows, or
believes he knows, that this propagation takes place in straight lines
with a velocity _c_ = 300,000 km./sec. At all events we know with great
exactness that this velocity is the same for all colours, because if
this were not the case, the minimum of emission would not be observed
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