(69) κ = 8πK/c² = 1.87 x 10⁻²⁷.
§22. Behaviour of measuring rods and clocks in a statical gravitation-field. Curvature of light-rays. Perihelion-motion of the paths of the Planets.
In order to obtain Newton’s theory as a first approximation we had to calculate only g₄₄, out of the 10 components gμν of the gravitation-potential, for that is the only component which comes in the first approximate equations of motion of a material point in a gravitational field.
We see however, that the other components of gμν should also differ from the values given in (4) as required by the condition g = -1.
For a heavy particle at the origin of co-ordinates and generating the gravitational field, we get as a first approximation the symmetrical solution of the equation:—
{ gρσ = -δρσ - α(xρ xσ)/r³ (ρ and σ 1, 2, 3)
{
(70) { gρ4 = g4ρ = 0 (ρ 1, 2, 3)
{
{ g₄₄ = 1 - α/r.