http://hem.bredband.net/b153434/Works/Einstein.htm
Divine Albert: "In a space which is free of gravitational fields we
introduce a Galilean system of reference K (x, y, z, t), and also a
system of co-ordinates K' (x', y', z', t') in uniform rotation
relatively to K. Let the origins of both systems, as well as their
axes of Z, permanently coincide. We shall show that for a space-time
measurement in the system K' the above definition of the physical
meaning of lengths and times cannot be maintained. For reasons of
symmetry it is clear that a circle around the origin in the X, Y plane
of K may at the same time be regarded as a circle in the X', Y' plane
of K'. We suppose that the circumference and diameter of this circle
have been measured with a unit measure infinitely small compared with
the radius, and that we have the quotient of the two results. If this
experiment were performed with a measuring-rod at rest relatively to
the Galilean system K, the quotient would be [pi]. With a measuring-
rod at rest relatively to K', the quotient would be greater than [pi].
This is readily understood if we envisage the whole process of
measuring from the "stationary" system K, and take into consideration
that the measuring-rod applied to the periphery undergoes a Lorentzian
contraction, while the one applied along the radius does not. Hence ...
