Page:The principle of relativity (1920).djvu/237

 If we calculate the gravitation-field to a greater order of approximation and with it the corresponding path of a material particle of a relatively small (infinitesimal) mass we get a deviation of the following kind from the Kepler-Newtonian Laws of Planetary motion. The Ellipse of Planetary motion suffers a slow rotation in the direction of motion, of amount

(75) s = 24π^3a?]^2/Τ^2c^2(1 - e^2) per revolution.

In this Formula a signifies the semi-major axis, c, the velocity of light, measured in the usual way, e, the eccentricity, Τ, the time of revolution in seconds.

The calculation gives for the planet Mercury, a rotation of path of amount 43´´ per century, corresponding sufficiently to what has been found by astronomers (Leverrier). They found a residual perihelion motion of this planet of the given magnitude which can not be explained by the perturbation of the other planets.