B = 2α/Δ = KM/2πΔ.
A ray of light just grazing the sun would suffer a bending of 1·7″,
whereas one coming by Jupiter would have a deviation of about ·02″.
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_ = 24π³_a²_/τ²_c²_(1 - _e²_) 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.