Januaby 20, 1911] 



SCIENCE 



83 



comb invoked the same idea to combat the 

 opinion that instability was the cause of 

 the gaps in the distribution of the asteroids. 

 In a word, the oscillations become libra- 

 tional and have finite limits, or in physical 

 terms, the motion is stable. Thus instead 



throw upon the screen a chart (Fig. 1) 

 in which the abscissse represent the mean 

 periods in days and the ordinates the num- 

 ber of planets with those periods. Each 

 vertical division represents ten days and 

 the number of planets whose periods fall 



of causing an absence of asteroids at the 

 positions of commensurability, with this 

 idea the action of Jupiter should rather 

 tend to increase the number, since a defi- 

 nite proportion of those very near would 

 be compelled to librate about the exact 

 ratio. It is not clear to what extent the 

 published elements are dependent on the 

 terms of very long periods, but the main 

 issue is not affected; none of the known 

 asteroids in the principal lacunte appear 

 to librate. 



In order that you may see the extent of 

 the inequalities in the distribution I shall 



within any division is shown by the height 

 of the curve at that place. There are about 

 630 asteroids represented. The curve falls 

 to zero at 2,160, 1,850, 1,730 and 1,440 days 

 and there are less well marked minima in 

 other places. Now these four minima in- 

 clude the places where the periods are in 

 the respective ratios of 2:1, 7:3, 5:2, 3:1 

 to the period of Jupiter. There are also 

 indications of minima at the places where 

 the ratios are 8 :3, 7 :2, 9 :4. These are aU 

 the whole number ratios within the range 

 with a denominator less than 5. 



I am going to speak more particularly 



