Note 1 — PART II The General Theory of Relativity

But if rods of every kind (i.e. of every material) were to behave in the same way as regards the influence of temperature when they are on the variably heated marble slab, and if we had no other means of detecting the effect of temperature than the geometrical behaviour of our rods in experiments analogous to the one described above, then our best plan would be to assign the distance one to two points on the slab, provided that the ends of one of our rods could be made to coincide with these two points; for how else should we define the distance without our proceeding being in the highest measure grossly arbitrary? The method of Cartesian coordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies.1 The reader will notice that the situation depicted here corresponds to the one brought about by the general postulate of relativity (Section XXIII).