XXXII

theory of the development of species by selection in the struggle for existence, and in the theory of development which is based on the hypothesis of the hereditary transmission of acquired characters.

We have another instance of far-reaching agreement between the deductions from two theories in Newtonian mechanics on the one hand, and the general theory of relativity on the other. This agreement goes so far, that up to the present we have been able to find only a few deductions from the general theory of relativity which are capable of investigation, and to which the physics of pre-relativity days does not also lead, and this despite the profound difference in the fundamental assumptions of the two theories. In what follows, we shall again consider these important deductions, and we shall also discuss the empirical evidence appertaining to them which has hitherto been obtained.

Motion of the Perihelion of Mercury

According to Newtonian mechanics and Newton's

law of gravitation, a planet which is revolving round the

sun would describe an ellipse round the latter, or, more correctly, round the common centre of gravity of the sun and the planet. In such a system, the sun, or the common centre of gravity, lies in one of the foci of the orbital ellipse in such a manner that, in the course of a planet-year, the distance sun-planet grows from a minimum to a maximum, and then decreases again to a minimum. If instead of Newton's law we insert a

somewhat different law of attraction into the calculation, we find that, according to this new law, the motion would still take place in such a manner that the distance sun-planet exhibits periodic variations; but in this case the angle described by the line joining sun and planet during such a period (from perihelion–-closest proximity to the sun–-to perihelion) would differ from $360°$. The line of the orbit would not then be a closed one, but in the course of time it would fill up an annular part of the orbital plane, viz. between the circle of least and the circle of greatest distance of the planet from the sun.

According also to the general theory of relativity, which differs of course from the theory of Newton, a small variation from the Newton-Kepler motion of a

planet in its orbit should take place, and in such a way, that the angle described by the radius sun-planet between one perihelion and the next should exceed that corresponding to one complete revolution by an amount given by $+\frac{24{\pi }^3{a}^2}{T^2{c}^2(1-e^2)}.$

(N.B.–-One complete revolution corresponds to the angle $2\pi$ in the absolute angular measure customary in physics, and the above expression gives the amount by

which the radius sun-planet exceeds this angle during the interval between one perihelion and the next.) In this expression $a$ represents the major semi-axis of the ellipse, $e$ its eccentricity, $c$ the velocity of light, and $T$ the period of revolution of the planet. Our result may also be stated as follows: According to the general theory of relativity, the major axis of the ellipse rotates round the sun in the same sense as the orbital motion of the planet. Theory requires that this rotation should amount to $43$ seconds of arc per century for the planet Mercury, but for the other planets of our solar system its

magnitude should be so small that it would necessarily escape detection.Especially since the next planet Venus has an orbit that is