Januaet 20, 1911] 



SCIENCE 



89 



colliding masses suiBciently to cause them 

 to pass away from the region of libration. 

 Such collisions may affect the motion in 

 two ways. They may increase the extent 

 of the libration so that the body passes 

 outside of the limits within which libra- 

 tions are possible, or they may at the time 

 diminish the extent of the librations so 

 far that the lower limit of the eccentricity 

 at which librations can be maintained is 

 reached. In either case the body escapes 

 from the region of libration and describes 

 an orbit at an altered mean distance and 

 with a period whose difference from the 

 exact ratio never becomes zero. Thus 

 while the apparent divisions of the ring 

 are not directly caused by the instability 

 of the librations, they are partly caused by 

 perturbations of large amplitude and 

 perhaps also by the results of collisions 

 arising from those large perturbations. 



I have hitherto spoken of the effect of 

 Jupiter's attraction on certain groups of 

 the asteroids. A little space must be de- 

 voted to the phenomena which are caused 

 in the distribution of the perihelia and 

 nodes of the approximate ellipses in which 

 the asteroids move. 



When the orbits of but fifty of the aster- 

 oids were known it was noticed that the 

 positions of their perihelia tended to group 

 themselves round the perihelion of Jupiter. 

 A similar phenomenon appeared, though 

 not in so marked a degree, with their nodes 

 and the node of Jupiter. Neweomb proved 

 that the groupings were consequences of 

 the attraction of Jupiter. His explanation, 

 briefly stated, amounts to this. Jupiter 

 causes the perihelia of the asteroids to re- 

 volve very slowly round the sun; some of 

 them will librate about the perihelion of 

 Jupiter. In the former ease the rates of 

 motion of the lines which join them to the 

 sun are least when these lines are crossing 



the perihelion of Jupiter, and most rapid 

 when crossing the aphelion of Jupiter. 

 Hence at any given time we are likely to 

 observe more asteroids whose perihelia are 

 near that of Jupiter than asteroids whose 

 perihelia are in other positions. Asteroids 

 whose perihelia librate must be compara- 

 tively few in number. The variations of 

 the eccentricity follow the same law. "With 

 the nodes and inclinations the effect is less 

 marked. In the latest published investiga- 

 tion by von Brunn, who followed New- 

 comb's methods with 400 bodies, the ex- 

 planation is confirmed. The chart (Fig. 

 5) which is before you on the screen shows 

 the extent of the variations. It is formed 

 with 630 asteroids. The points joined by a 

 continuous curve represent the numbers of 

 asteroids whose perihelia lie in the twelve 

 divisions into which the whole circumfer- 

 ence has been divided. The points joined 

 by a dotted line represent the average 

 eccentricity of those asteroids whose peri- 

 helia lie in the corresponding divisions. 

 Below are placed the letters /, M, E, 8, 

 representing the positions of the perihelia, 

 and the letters J', M', E', 8', representing 

 the positions of the aphelia of the planets 

 Jupiter, Mars, the earth and Saturn. The 

 two upper charts show the results for the 

 first 300 and the last 330 discoveries, and 

 the lower chart the whole 630. The effect 

 of Jupiter is quite clear. The traces of the 

 other planets are doubtful. It is true that 

 there is a distinct minimum of the perihelia 

 at the group 10 which contains the aphelia of 

 Saturn and the earth and that it is present 

 in all three charts. But there is no cor- 

 responding rise at the perihelia, or at any 

 rate the rise is doubtful. 



The features of the distribution which 

 are the same in the earlier and later dis- 

 covered planets can, without much danger 

 of error, be laid aside as consequences of 

 the attractions of the sun and planets. 



