in which the are so small compared to 1 that we can neglect the higher powers of the and their derivatives. If we do this, we learn nothing about the structure of the gravitational held, or of metrical space of cosmical dimensions, but we do learn about the influence of neighbouring masses upon physical phenomena. Before carrying through this approximation we shall transform (96). We multiply (96) by , summed over the and observing the relation which follows from the definition of the , we obtain the equation If we put this value of in (96) we obtain When the approximation which has been mentioned is carried out, we obtain for the left-hand side, [Pg 91] or in which has been put We must now note that equation (96) is valid for any system of co-ordinates. We have already specialized the system of co-ordinates in that we have chosen it so that within the region considered the differ infinitely little from the constant values . But this condition remains satisfied in any infinitesimal change of co-ordinates, so that there are still four conditions to which the may be subjected, provided these conditions do not conflict with the conditions for the order of magnitude of the . We shall now assume that the system of co-ordinates is so chosen that the four relations— are satisfied. Then (96a) takes the form These equations may be solved by the method, familiar in electrodynamics, of retarded potentials; we get, in an easily understood notation, [Pg 92] In order to see in what sense this theory contains the Newtonian theory, we must consider in greater detail the energy tensor of matter. Considered phenomenologically, this energy tensor is composed of that of the electromagnetic field and of matter in the narrower sense. If we consider the different parts of this energy tensor with respect to their order of magnitude, it follows from the results of the special theory of relativity that the contribution of the electromagnetic field practically vanishes in comparison to that of ponderable matter. In our system of units, the energy of one gram of matter is equal to 1, compared to which the energy of the electric fields may be ignored, and also the energy of deformation of matter, and even the chemical energy. We get an approximation that is fully sufficient for our purpose if we put In this, is the density at rest, that is, the density of the ponderable matter, in the ordinary sense, measured with the aid of a unit measuring rod, and referred to a Galilean system of co-ordinates moving with the matter. We observe, further, that in the co-ordinates we have chosen, we shall make only a relatively small error if we replace the by , so that we put