Page:Eddington A. Space Time and Gravitation. 1920.djvu/110

94 Finally is the force of gravitation propagated instantaneously, or with the velocity of light, or some other velocity? Until comparatively recently it was thought that conclusive proof had been given that the speed of gravitation must be far higher than that of light. The argument was something like this. If the Sun attracts Jupiter towards its present position $$S$$, and Jupiter attracts the Sun towards its present position $$J$$, the two forces are in the same line and balance. But if the Sun attracts Jupiter towards its previous position $$S^\prime$$, and Jupiter attracts the Sun towards its previous position $$J^\prime$$, when the force of attraction started out to cross the gulf, then the two forces give a couple. This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observation if the speed is at all comparable with that of light. The argument is fallacious, because the effect of propagation will not necessarily be that $$S$$ is attracted in the direction towards $$J^\prime$$. Indeed it is found that if $$S$$ and $$J$$ are two electric charges, $$S$$ will be attracted very approximately towards $$J$$ (not $$J^\prime$$) in spite of the electric influence being propagated with the velocity of light. In the theory given in this book, gravitation is propagated with the speed of light, and there is no discordance with observation.

It is often urged that Newton's law of gravitation is much