[footnote omitted]

This expression has nothing to do with "unitary" field theory due to Einstein, Weyl, Eddington, and others where the problem consists of uniting the theories of gravitational and electro-magnetic fields into a kind of non-Riemannian geometry. Specially some of Eddington's formulae, developed in § 101 of his book

have a remarkable formal analogy to those of this paper, in spite of the entirely different physical interpretation.

Also

The attempt to avoid this difficulty by a new definition of electric force acting on a particle in a given field, made by

is very ingenious, but rather artificial and leads to new difficulties.

See

See

[footnote omitted]

See

The proof is simple: by a transformation with the Jacobian $I = \frac{\partial (\bar{x}^1\ldots \bar{x}^4)}{\partial (x^1\ldots x^4)} d\tau$ is changed into $d\bar{\tau} = I d\tau$ and $\vert a_{kl}\vert$ into $\vert \bar{a}_{kl}\vert I^{-2}$; for the $dx^k$ are contravariant, $a_{kl}$ covariant.

This assumption has already been considered by