Page:The principle of relativity (1920).djvu/128

 null point of the second system moving with constant velocity in a straight line, while the time parameter remains unchanged. We can, therefore, say that classical mechanics postulates a covariance of Physical laws for the group of homogeneous linear transformations of the expression

-x^2 - y^2 - z^2 + c^2    (1)

when c = [infinity].

Now it is rather confusing to find that in one branch of Physics, we shall find a covariance of the laws for the transformation of expression (1) with a finite value of c, in another part for c = [infinity].

It is evident that according to Newtonian Mechanics, this covariance holds for c = [infinity] and not for c = volocity of light.

May we not then regard those traditional covariances for c = [infinity] only as an approximation consistent with experience, the actual covariance of natural laws holding for a certain finite value of c.

I may here point out that by if instead of the Newtonian Relativity-Postulate with c = [infinity], we assume a relativity-postulate with a finite c, then the axiomatic construction of Mechanics appears to gain considerably in perfection.

The ratio of the time unit to the length unit is chosen in a manner so as to make the velocity of light equivalent to unity.

While now I want to introduce geometrical figures in the manifold of the variables (x, y, z, t), it may be convenient to leave (y, z) out of account, and to treat x and t as any possible pair of co-ordinates in a plane, refered to oblique axes.