The previous developments are valid however rapidly the masses which generate the field may move relatively to our chosen system of quasi-Galilean co-ordinates. But in astronomy [Pg 93] we have to do with masses whose velocities, relatively to the co-ordinate system employed, are always small compared to the velocity of light, that is, small compared to 1, with our choice of the unit of time. We therefore get an approximation which is sufficient for nearly all practical purposes if in (101) we replace the retarded potential by the ordinary (non-retarded) potential, and if, for the masses which generate the field, we put Then we get for and the values {\qquad}r}>{\quad}r} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -\sigma \end{array} \right\}. \qquad \text{(104)} "> For we get the value , and, finally, for the values, {\qquad}c}>{\quad}r} \dfrac{\sigma}{2} & 0 & 0 & 0 \\ 0 & \dfrac{\sigma}{2} & 0 & 0 \\ 0 & 0 & \dfrac{\sigma}{2} & 0 \\ 0 & 0 & 0 & -\dfrac{\sigma}{2} \end{array} \right\}. \qquad \text{(104a)} "> We thus get, from (101), [Pg 94] while all the other , vanish. The least of these equations, in connexion with equation (90a), contains Newton's theory of gravitation. If we replace by we get We see that the Newtonian gravitation constant , is connected with the constant that enters into our field equations by the relation From the known numerical value of , it therefore follows that From (101) we see that even in the first approximation the structure of the gravitational field differs fundamentally from that which is consistent with the Newtonian theory; this difference lies in the fact that the gravitational potential has the character of a tensor and not a scalar. This was not recognized in the past because only the component , to a first approximation, enters the equations of motion of material particles. In order now to be able to judge the behaviour of measuring rods and clocks from our results, we must observe the following. According to the principle of equivalence, the metrical relations of the Euclidean geometry are valid relatively to a Cartesian system of reference of infinitely small dimensions, and in a suitable state of motion (freely falling, and without rotation). We can make the same statement for local systems of co-ordinates [Pg 95] which, relatively to these, have small accelerations, and therefore for such systems of co-ordinates as are at rest relatively to the one we have selected. For such a local system, we have, for two neighbouring point events, where is measured directly by a measuring rod and by a clock at rest relatively to the system; these are the naturally measured lengths and times. Since , on the other hand, is known in terms of the co-ordinates employed in finite regions, in the form