VII

embankment, we see from the above that the tip of the ray will be transmitted with the velocity $c$ relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity $v$, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity $W$ of the man relative to the embankment is here replaced by the velocity of light relative to the embankment. $w$ is the required velocity of light with respect to the carriage, and we

have $w=c-v.$ The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than $c$.

But this result comes into conflict with the principle of relativity set forth in [chapter:V]Section V. For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference.

But, from our above consideration, this would appear to be impossible. If every ray of light is propagated relative to the embankment with the velocity $c$, then for this reason it would appear that another law of propagation