On Ehrenfest's Paradox

(...)"That Ehrenfest took the Lorentzian standpoint in his argumentation, I conclude from the questions directed by him to v. Ignatowsky[1], and mainly from that, that he thinks to find this contradiction at the tracing images and as well. It seems to me that those tracing images must be identical; they will have the same radius and the same periphery.
To justify this, it shall be allowed for me to take recourse to the uniform translation of a rigid body, at which that contraction is ordinarily demonstrated as a concomitant of that translation. A mirror shall be fixed at the front end , and a light source at the back end . The doubled length of the rod is measured by the time required by a light signal,(...)".