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authors who (until recently) have commented on the relative-rigidity question, and this was independent of the position taken by the authors at other occasions regarding the rigidity problem. For clarities sake, the relevant comments shall be shortly summarized in chronological order:

M. Born^[1] admits the previous result, and consequently decides himself to the following assumptions: 1. The electrons actually satisfy the rigidity requirement, yet they don't rotate. The theory of electrons nowhere unconditionally requires the assumption of rotating electrons. 2. The macroscopic "rigid" bodies are molecular aggregates, thus they are elastically deformable, so they don't satisfy the rigidity requirement and are able to rotate.

M. Planck^[2]: 1. The macroscopic "rigid" bodies are to be seen as elastic, and the theory of their motion must be founded by stating the kinetic potentials of elastic deformations. "The attempt, to make the abstraction of the rigid body (which is so important for ordinary mechanics) also useful for the theory of relativity, doesn't appear to me as promising any real success." 2. The maintenance of the rigidity requirement for the single electron, would deprive itself from any real verification as to "whether it brings us physically further than the general principles of relativity theory".

M. Abraham^[3]: "The attempt undertaken .... by Born, to generalize ... Einstein's definition of length, must be considered as failed, after Ehrenfest, Herglotz, Noether und Levi-Civita have demonstrated, that the employed concept of rigidity is not applicable to rotational motions."

M. Born^[4], in a later paper, sticks to the idea (in opposition to Planck) that the extension of the rigidity concept to relativity theory is necessary, and he develops – by reseting his original rigidity definition as too narrow – a new rigidity definition. There he accepts, that any rigid body must be imagined as having – with respect to the rigidity definition – a preferred point once and for all.^[5] Yet also in this way, by far not all difficulties of the rotation problem can be totally resolved: As demonstrated by Born, a stationary (!) rotation about a fixed axis takes place here, so that the resting observer sees the multi-axial layers rotating with larger angular velocity as the peripheral layers, thus the "rigid" body (starting from the axis) increasingly stirs itself.^[6]

§ 2. Now – in a paper recently published^[7] – also v. Ignatowsky comments on the problem of rotation of relative-rigid bodies. His standpoint is mainly characterized by the following statement (§ 5, end):

"Let us again consider the cylinder of § 3, namely the passage from rest to uniform rotation. It will be set in motion under the influence of external forces, yet always under maintenance of condition (20) § 2. The effect of these forces will propagated with a certain velocity, so that the angular velocity for a certain moment $t$, is not the same for all angles. At the same time it will apparently be compressed, until its motion passes into a uniform motion after some time."

Does v. Ignatowsky – to arrive at this claim – probably uses a rigidity definition deviating from the (original) one of Born?

No! His initial equation

$\left(dw_{0}\right)^{2}=\left(dw'_{1}\right)^{2}$

(6)

is identical to the (original) requirement of Born, and his equation

${\frac {d}{dt}}\left(dw'_{1}\right)^{2}=0$

(7)

emerges out of it by total differentiation. Eq. (13) derived from it by conversion, is the temporal derivative of that form of Born's rigidity equation, with which I and Herglotz have operated, and finally the previously mentioned eq. (20) is the additional conversion of eq. (7) and (13) from the Lagrangian into the Eulerian from, according to the procedure of Noether.

Also the following statement regarding the stationary rotating cylinder, made by v. Ignatowsky at the end of § 3, is in best agreement with that:

"Let us consider now a spherical cylinder, rotating with constant angular velocity about a resting axis. It is easy to demonstrate, that eq. (20) is satisfied identically in this case."

Indeed: that Born's rigidity definition allows stationary rotation, is

1. M. Born, this journal 11, 233, 1910.
2. M. Planck, this journal 11, 294, 1910.
3. M. Abraham, this journal 11, 527, 1910.
4. Gött. Nachr. 1910, 28. May.
5. l. c, § 3, M. Born calls this point "center".
6. l. c., § 5, M. Born thus remarks: "By that, the globe were hardly a "rigid" body in this sense."
7. Ann. d. Phys. 33, 607, 1910.