We now proceed to the second argument, to which, moreover, we shall return later.  If the principle of relativity (in the restricted sense) does not hold, then the Galileian co-ordinate systems K, K1, K2, etc., which are moving uniformly relative to each other, will not be equivalent for the description of natural phenomena.  In this case we should be constrained to believe that natural laws are capable of being formulated in a particularly simple manner, and of course only on condition that, from amongst all possible Galileian co-ordinate systems, we should have chosen one (K[0]) of a particular state of motion as our body of reference.  We should then be justified (because of its merits for the description of natural phenomena) in calling this system " absolutely at rest,” and all other Galileian systems K " in motion.”  If, for instance, our embankment were the system K[0] then our railway carriage would be a system K, relative to which less simple laws would hold than with respect to K[0].  This diminished simplicity would be due to the fact that the carriage K would be in motion (i.e."really")with respect to K[0].  In the general laws of nature which have been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part.  We should expect, for instance, that the note emitted by an organpipe placed with its axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular to this direction.

Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second.  If the principle of relativity were not valid we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation in space with respect to the earth.  For owing to the alteration in direction of the velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical system K[0] throughout the whole year.  However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, i.e. a physical non-equivalence of different directions.  This is very powerful argument in favour of the principle of relativity.

The theorem of the
addition of velocities
employed in classical mechanics