, in the three-dimensional representation, are given by (41). In fact, it follows from (50) that for
,
(equal to the negative energy per unit volume), as it should, according to the theorem of the equivalence of mass and energy, and according to the physical interpretation of the energy tensor given above. If an external force (four-dimensional vector,
) acts upon the matter, by the principles of momentum and energy the equation
must hold. We shall now show that this equation leads to the same law of motion of a material particle as that already obtained. Let us imagine the matter to be of infinitely small extent in space, that is, a four-dimensional thread; then by integration over the whole thread with respect to the space co-ordinates