act in the direction thus determined, its magnitude being unaltered by the planet's motion. This amounts to supposing that gravity is subject to an aberrational effect similar to that observed in the case of light. It is easily seen that the modification thus introduced into Newton's law may be represented by an additional perturbing force, directed along the tangent to the orbit in the opposite sense to the motion, and proportional to the planet's velocity and to the inverse square of the distance from the sun. By considering the influence of this force on the secular equation of the moon's motion, Laplace found that the velocity of the gravific fluid must be at least a hundred million times greater than that of light.
The assumptions made by Laplace are evidently in the highest degree questionable; but the generation immediately succeeding, overawed by his fame, seems to have found no way of improving on them. Under the influence of Weber's ideas, however, astronomers began to think of modifying Newton's law by adding a term involving the velocities of the bodies. Tisserand[1] in 1872 discussed the motion of the planets round the sun on the supposition that the law of gravitation is the same as Weber's law of electrodynamic action, so that the force is
,
where f denotes the constant of gravitation, m the mass of the planet, μ the mass of the sun, r the distance of the planet from the sun, and h the velocity of propagation of gravitation. The equations of motion may be rigorously integrated by the aid of elliptic functions[2]; but the simplest procedure is
,
