The question of the form of the momentum-energy tensor of the electromagnetic field (in a medium) remains debatable to this day. The dilemma of whether the photon momentum in a medium is equal to $nhv/c$ (Minkowski) or $hv/nc$ (Abraham) therefore remains unresolved (n is the refractive index). Simple considerations based on the law governing the motion of the center of gravity of the ``field + medium'' system lead, however, to a unique choice of Abraham's tensor. The Jones--Richards experiments do not contradict this, although they do not lead to a solution of the problem. In principle, measurements of the Jones--Richards type (of the pressure of light in media) in the pulsed regime would yield the solution of the problem. Considerable space is allotted to an analysis of the question of the ``rejection'' of Abraham's tensor, a question advanced by Laue and supported by many authors. It is shown that the use of the Laue criterion is based on an error in the very formulation of the question. The arguments advanced in this connection are illustrated by using as an example analogous relations in the case of the motion of a simple static system, namely a charged capacitor. The conservations laws applied to a static electromagnetic field having angular momentum also lead to Abraham's expression for the field momentum density.