of the gravitational potential; the energy tensor of matter must appear on the right-hand side of this equation. On the left-hand side of the equation there must be a differential tensor in the
. We have to find this differential tensor. It is completely determined by the following three conditions:—
1. It may contain no differential coefficients of the
higher than the second.
2. It must be linear and homogeneous in these second differential coefficients.
3. Its divergence must vanish identically.
The first two of these conditions are naturally taken from Poisson's equation. Since it may be proved mathematically that all such differential tensors can be formed algebraically (i.e. without differentiation) from Riemann's tensor, our tensor must be of the form