where is the velocity of the charge in the direction of , the velocity of light, and the square bracket signifies antedated values. To the first order of , the denominator is equal to the present distance , so the expression reduces to in spite of the time of propagation. The foregoing formula for the potential was found by Liénard and Wiechert.
Note 7 (p. 97).
It is found that the following scheme of potentials rigorously satisfies the equations , according to the values of in Note 5, where and is any constant (see Report, § 28). Hence these potentials describe a kind of space-time which can occur in nature referred to a possible mesh-system. If , the potentials reduce to those for flat space-time referred to polar coordinates; and, since in the applications required will always be extremely small, our coordinates can scarcely be distinguished from polar coordinates. We can therefore use the familiar symbols , , , , instead of , , , . It must, however, be remembered that the identification with polar coordinates is only approximate; and, for example, an equally good approximation is obtained if we write , a substitution often used instead of since it has the advantage of making the coordinate-velocity of light more symmetrical.
We next work out analytically all the mechanical and optical properties of this kind of space-time, and find that they agree observationally with those existing round a particle at rest at the origin with gravitational mass . The conclusion is that the gravitational field here described is produced by a particle of mass —or, if preferred, a particle of matter at rest is produced by the kind of space-time here described.
Note 8 (p. 98).
Setting the gravitational constant equal to unity, we have for a circular orbit , so that .
