and
are letters for which the four numbers representing the four dimensions of space-time must be substituted in pairs. There exist, therefore, a number of gravitational equations—sixteen in all. When we discard those which are mere repetitions of the others, hence which yield us no new information, we find that this number reduces to ten.
Now we have already a general idea of the significance of these equations. The left-hand side gives us the curvatures of space-time from point to point as measured in our mesh-system, and the right-hand side gives us the various aspects of matter, energy and momentum situated at the same points where the curvature is being calculated. If we agree to select the nearest possible approach to a Galilean mesh-system, and for reasons of simplicity agree to treat it as a Galilean system, we are able to write out the components of the energy-tensor of matter in this mesh-system, and as a result we obtain:
This gives us all the equations, since the six we have omitted to write out, namely,
are mere repetitions of
We have thus written out the ten equations. In them,