486 SCIENCE PROGRESS 



theories, the only values dealt with by Sir George Darwin are 

 those less than about 40'5, and in the main simply periodic and 

 direct orbits are considered {i.e. those which are re-entrant after 

 a single revolution, though some of them may contain loops). A 

 few non-periodic orbits are however dealt with in his later work, 

 and some real and apparent retrograde paths also. (Superior 

 planets whose motion is direct in space will of course appear 

 retrograde when referred to the rotating axes since these latter 

 revolve more quickly than outer planets.) For the case when 

 C = 39, Sir George Darwin gives a figure showing how a planet 

 at first moving round the sun in an elliptic orbit of moderate 

 excentricity, gradually experiences increasing disturbance from 

 the action of Jove, and the elliptic form will be altogether lost, 

 the body being either drawn off when near aphelion and in 

 conjunction with Jove, to circuit round the latter, or it may 

 revert once more to the sun, but its path will be of a totally 

 different kind. In general a body after being drawn off would 

 make several circuits round Jove until a concurrence of apojove 

 with conjunction produced a severance of this connection. This 

 may sometimes happen after one revolution only, but if the 

 " neck of the hour-glass " giving the curve of zero velocity be 

 narrow the body may move many times round one of the centres 

 before its removal to the other. " It seems likely that a body of 

 this kind would in course of time find itself in every part of 

 space where its motion is possible," Thus sooner or later it 

 would pass close to the Sun or to Jove, and colliding with one 

 or other, be absorbed. In this way stray bodies may be gradually 

 swept up by the sun and planets, a process which Dr. See 

 supposes to be the cause of the equatorial acceleration observed 

 in the rotation of the Sun, Jupiter, and Saturn, i.e. the fact that 

 regions nearer the equators of these bodies perform their rotation 

 in a shorter time than parts farther north or south. Some non- 

 periodic orbits round Jove and round the Sun, others passing 

 from Jove to the Sun, together with their conditions of stability 

 and instability, are determined by various criteria, and regions 

 within which stability is impossible are marked out. In some such 

 way as this it is hoped that an explanation of Bode's empirical 

 law as to the relative distances of the planets from the Sun may 

 be found. In his later paper {Monthly Notices R.A.S., December 

 1909), besides giving a fresh investigation of the stability of 

 periodic orbits founded on the suggestions of Hough, he dis- 



