352 



KNOWLEDGE. 



September, 1910. 



one is that of Jove, and lines are drawn joining 

 the simultaneous positions of these bodies. (In 

 order not to complicate the iigure only a few 

 of these are drawn.") The body here makes a single 

 revolution round Jo\e. and is then drawn off to the 

 Sun. but it ma\- happen that se\'eral revolutions 

 round the former would be made until conjunction 

 takes place at "' apojove " (greatest distance of planet 

 and Jove.) and then it will revert to the Sun again. 

 " It seems likely that a body of this kind Mould in 

 course of time find itself in every part of the space in 

 M'hich its motion is confined" (Darwini. Thus it 

 would at last collide either with the Sun or ]nw. 

 and it has been suggested by the same writer that in 

 this way stray bodies are gradually swept up b\" Sun 

 and planets. Some non-periodic orbits passing from 

 Jove to the Sun are drawn in Figure 4, and it will 

 be seen that one of these paths has a sharj) cusp 

 (Iving on the curve of zero velocitx 

 looped, and so on. 



Regions within which stable 



except inside the " horse-shoe " shaped space. 

 Here the distinction between planetary and satellite 

 motion does not exist, and the bod\- may change 

 from an\- one of these modes into an\- other. When 

 C lies between 34'91 and 55, the onh- regions where 

 motion is not possible are within the leaf-like folds 

 on each side of the line S J. and these diminish to 

 the pair of points marked with crosses (Figure 1), for 

 the value C = 33. Lastly when C is less than 33 the 

 body ma\' move an\-where. As a general result it is 

 concluded that unstable orbits are such as to lead to 

 the ultimate absorption of bodies moving in them 



into one or other of the larger bodies, 



and though 



)rl)its 



and others for which 

 thev cannot exist, are 

 found, and in this con- 

 nection we ma}" later 

 find an explanation of 

 Bode's Law as to the 

 distances of the planet "Fo^ 

 and satellites from 

 their primaries. In his 

 later work, Sir George 

 Darwin has considered 

 possible retrograde 

 orbits, all his former 

 researches having been 



anotlier is 

 ire possible. 



FiGl'Rl-: 4. Non-periodic orbits passing from Jove to the Sun 

 (after Darwin). 



Outer thick line curve of velocity C=^9*o. 



on orbits where the motion is direct, i.e.. the same 

 direction as that of all the planets and most of the 

 satellites, and has traced the forms of jiaths of 

 bodies ejected fnmi Sun towards [ove and vice 

 versa. Modes of transition between direct and 

 retrograde orbits are also considered, passage through 

 the apices of the equilateral triangle on S J as base 

 already mentioned being suggested as one method. 

 From a consideration of the figures given we niav 

 gain much information as to the kind of orbits 

 possible, and the limit of distance between planets 

 and satellites. For values of C greater than 40" 18 

 the third body must be either a superior planet 

 moving outside the larger curve, or an inferior planet 



the problem in our planetary s\'Stem is much more 

 complicated from the large number of planetary 

 bodies, yet. as we have seen, several interesting 

 features have indicated explanations. We have now 

 to briefi\' notice the bearing of these results upon 

 cosmogonic theor\-, and some modifications suggested 

 by Professor See. By supposing the existence of a 

 resisting medium universalh" diffused throughout our 



SN'Stem, of whose pre- 

 sence we have some 

 evidence, we get the 

 well-known result that 

 when a body revolves 

 about the Sun or a 

 planet, the resisting 

 medium at every point 

 decreases the velocity, 

 and thus gives the 

 central attraction more 

 effect, the revolving 

 body being gradually 

 drawn nearer to the 

 centre of force. For Encke's comet this change 

 seems more rapid than for an\' other known member 

 of our system. For orbits differing from circles, the 

 result of the action is also to diminish the eccentricity, 

 or make them more nearly circular. This was well 

 known to Laplace, and the proof is given in works 

 on anabtical d\"namics. Thus a particle moving 

 within one of the inner closed surfaces, of which 

 we ina\' regard the cur\es (shown in Figure 1) 

 to be the traces on the jilane of paper, will gradually 

 draw nearer its centre, and. its speed increasing, 

 its periodic time will be diminished ; for a 



bod\ 



ithin the " hour glass " shaped 



moving inside the larger internal 



or a satellite 



inside the smaller oval, and it can never change 

 from one of these forms to either of the others, " so 

 that this limiting value gives superior limits to the 

 radii vectores of inferior planets and of satellites 

 which cannot sever their connection with their 

 primaries." When C is less than 4()-l.s. and 

 greater than 38'S8, the third body ma\- be a superior 

 planet, or an inferior planet, or satellite, or a bodv 

 moving in an orbit partaking of the two latter charac- 

 teristics, but it cannot exchange from the first role into 

 either of the others. When C is less than 38'88, 

 and more than 34'91, the bodv mav move anvwhere 



space or the pear shaped region surrounding both 

 bodies (Figure 1) will drop nearer and nearer to one or 

 other of the masses, and ma\' finally pass within the 

 closed surface and acquire a constant of relative 

 energ\- such that it can never escai)e again from that 

 region. The Moon is now within such a closed 

 surface about the Earth, and cannot escape tlierefrom, 

 and it has been accordingly supposed that it has not 

 at any time been outside ; but if we admit the action 

 of the resisting medium there is a p<)ssil>ility of our 

 Moi Ill's having been an independent planet which 

 approached too nearly to the earth and became 

 captured. .Kt present most astronomers give in 

 their adhesion to Sir George Darwin's theory of 



