36G THE ASTEROIDS BETWEEN MARS AND JUPITER. 



etary nucleus formed in this manner would be at some distance from 

 the primitive orbit of the particle disturbed. A gap or chasm would 

 thus be produced at the distance 3.27, or wherever the period of an 

 asteroid would have to that of Jupiter a simple relation of commensiu- 

 ability. It may be objected that the mutual attractions of those primi- 

 tive masses were too inconsiderable to result in the formation of plane- 

 tary nuclei. But eveu granting the force of this objection, the fact still 

 remains that the orbits of asteroids at the specified distances would in- 

 crease in eccentricity till the masses in perihelio would reunite with the 

 central nebula. In either case, therefore, chasms would be left in the 

 primitive annulus. Let us now inquire whether the facts presented in 

 Table II sustain the conclusions derived from physical considerations. 



S. The mean distance of Hilda =3.9505 



That of Flora =2.2014 



Breadth of zone =1.7491 



As small bodies in the remoter parts of the ring are more difficult of 

 detection, the zone will be considered under three divisions of equal 

 breadth. The innermost section, A, extending from 2.2014 to 2.7844, 

 contains 115 of the 1G9 asteroids whose elements are known ; the mean 

 interval between the consecutive orbits being 0.00511. Now the inter- 

 val at the distance 2.50 — between Thetis and Hestia — where an asteroid's 

 period would be one-third of Jupiter's, is 0.0643, the widest in the section 

 and about twelve times the mean interval. The middle section, B, extend- 

 ing from 2.7844 to 3.3G75, contains 47 minor planets, the average interval 

 between their consecutive orbits beiugO.01268. The widest of these gaps, 

 which is 0.1, or eight times the mean, is found at the distance 3.27, 

 where an asteroid's period would be half that of Jupiter. Finally, 

 the most remote section, G, extends from 3.3675 to 3.9505, includ- 

 ing seven known asteroids. The mean interval in this section is 0.0972. 

 The widest hiatus (between the orbits of Camilla and Hilda) contains 

 the distances 3.58, 3.70, 3.80, and 3.85. The second in extent (between 

 Sylvia and Camilla) contains the distance 3.51, where nine asteroid 

 periods would be equal to five of Jupiter. 



The nine di^tauces * at which the periods of minor planets would have 

 simple relations of commensurability to the period of Jupiter are thus 

 found in the widest chasms of the zone. The result may be somewhat 

 modified by future discoveries and by the more exact determination of 

 orbits. The general features of the ring, however, depend on too wide 

 an induction of facts to be regarded as merely accidental. The marked 

 'irregularity of distribution throughout the cluster is presented at one 

 view in the following table : 



Interior to the distance 2.25 2 asteroids. 



From 2.25 to 2.35 7 asteroids. 



From 2.35 to 2.45 32 asteroids. 



* See table in 6. 



