When sources are added at their right-hand sides, and g (ik) is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g (ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g (ik) , however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély's physically correct metric is adopted.

The issue of the form that the energy tensor of the electromagnetic field should be given in matter is reconsidered, and the neat derivation of Abraham's tensor once provided by W. Gordon is recollected. In order to extend to the high frequency domain the experimental evidence gathered up to now in favour of Abraham's tensor, a method for detecting the Abraham's force supposedly exerted by light on a transparent, homogeneous medium is outlined. It avails of the Fresnel-Fizeau effect associated with the motion of matter that should be caused by the above mentioned force.

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