Page:The Foundations of Science (1913).djvu/534

516 electrostatic and electrodynamic phenomena in supposing that electrons (whose name was not jet invented) exercise, one upon another, attractions and repulsions directed along the straight joining them, and depending not only upon their distances, but upon the first and second derivatives of these distances, consequently upon their velocities and their accelerations. This law of Weber, different enough from those which to-day tend to prevail, none the less presents a certain analogy with them.

Tisserand found that, if the Newtonian attraction conformed to Weber’s law there resulted, for Mercury’s perihelion, secular variation of 14”, of the same sense as that which has been observed and could not be explained, but smaller, since this is 38”.

Let us recur to the hypotheses A, B and C, and study first the motion of a planet attracted by a fixed center. The hypotheses B and C are no longer distinguished, since, if the attracting point is fixed, the field it produces is a purely electrostatic field, where the attraction varies inversely as the square of the distance, in conformity with Coulomb’s electrostatic law, identical with that of Newton.

The vis viva equation holds good, taking for vis viva the new definition; in the same way, the equation of areas is replaced by another equivalent to it; the moment of the quantity of motion is a constant, but the quantity of motion must be defined as in the new dynamics.

The only sensible effect will be a secular motion of the perihelion. With the theory of Lorentz, we shall find, for this motion, half of what Weber’s law would give; with the theory of Abraham, two fifths.

If now we suppose two moving bodies gravitating around their common center of gravity, the effects are very little different, though the calculations may be a little more complicated. The motion of Mercury’s perihelion would therefore be 7” in the theory of Lorentz and 5”.6 in that of Abraham.

The effect moreover is proportional to n²a², where n is the star’s mean motion and a the radius of its orbit. For the planets, in virtue of Kepler’s law, the effect varies then inversely as $$\sqrt{a^{5}}$$; it is therefore insensible, save for Mercury.