JANUABT 20, 1911] 



SCIENCE 



87 



2:1. Similar results can be obtained con- 

 cerning the distribution round the other 

 ratios, but these I must dismiss in a few 

 words, mainly because the details have not 

 yet been worked out. It can be stated, 

 however, that the inclination can not in 

 general be neglected when the difference 

 between the two terms of the ratio exceeds 

 unity. Nevertheless, the general result 



an eccentricity greater than one fifth. 

 This is nowhere more strikingly illustrated 

 than at the values 7 : 3 and 9 : 4. There is 

 a large maximum of small eccentricities be- 

 tween these ratios, and only three asteroids 

 wdth eccentricities so great as twenty-five 

 in the same space. A similar phenomenon 

 is observable between the ratios 7 : 2 and 

 4:1. 



holds that larger eccentricities are more 

 likely to be absent very close to the gaps 

 than smaller ones. 



Referring again to the chart of the gen- 

 eral distribution of the eccentricities (Fig. 

 3), we notice that no one of the ratios, even 

 when the difference of the two terms is 5 

 (corresponding to a libration with a co- 

 efficient depending on the fifth power of 

 the eccentricity), has a close asteroid with 



The application of the theory to the 

 satellites and rings of Saturn, though not 

 within the title of my address, can not well 

 be passed over. It is now known that the 

 mean periods of the revolutions of Titan 

 and Hyperion round Saturn are exactly in 

 the ratio of 4 : 3 and that the actual periods 

 librate about this ratio. The case is quite 

 similar to that of a ratio 2:1. But here 

 tlie relative disturbing force is much 



