214 RELATIVITY, THE GENERAL THEORYequivalence [principle] can hold only for infinitely small systems [and] that there-
fore Bonn's accelerated finite system cannot be considered as a static gravitational
field, that is, it cannot be generated by masses at rest. A rotating ring does not
generate a static field in this sense, although it is a field that does not change with
time. ... In the theory of electricity, my case corresponds to the electrostatic field;
on the other hand, the general static case would, in addition, include the analog
of a static magnetic field. I am not that far yet. The equations found by me must
refer only to the static case of masses at rest. Born's field of finite extension does
not fall in this category. It has not yet become clear to me why the equivalence
principle fails (or finite fields (Born)' [E23].* Einstein was not the greatest expert
in following the scientific literature, but he apparently did know Born's main
paper of 1909 on the relativistic treatment of rigid bodies [Bl]. At the Salzburg
conference in the fall of 1909, Born's presentation of his work on the rigid body
[B2] immediately preceded Einstein's own report on the constitution of radiation
[E25], and it is known that the two men used that occasion for private discussions
on scientific topics of so much common concern [B3]. In June 1912 Einstein was
brooding over Born's earlier work, as his letter to Ehrenfest shows. I find this
fascinating since Born's formalism of 1909 manifestly has Riemannian traits! It
seems sufficiently interesting to explain how this came about.
The two main points of Born's work are (1) to define rigidity as a limiting
property of a continuously deformable medium (ignoring all aspects of its atomic
constitution) and (2) to define rigidity only as a differential, not as a global, prop-
erty. Born considered first the case of nonrelativistic Newtonian mechanics. Let
£' (i = 1,2,3) denote the cartesian coordinates of some point in the medium at the
time t = 0. The distance ds between two points £' and £' + d£' at t = 0 is given
by
*In a short paper entitled 'Does There Exist a Gravitational Action Analogous to the Electrodyn-
amic Induction Effect?' [E24], published in the Quarterly for Forensic Medicine, Einstein briefly
pursued the electromagnetic analogy mentioned in his letter to Ehrenfest. This uncommon choice of
journal was made in order to contribute to a Festschrift for Zangger. It may also indicate that Ein-
stein felt less than secure about his results.
Let x'(l-',t) be the coordinates at time t of the point that was at £' at t = 0. Follow
the so-called Lagrangian method, in which the functions x' are used to describe
the history of every particle of the fluid [L2]. At t, the distance ds between two
infinitesimally close points is given by ds^2 = 'Z.(dx')^2. Since