44 STATEMENT AND EXPOSITION OF 



of the disturbing planet was very nearly a multiple of the periodic time of an 

 " abandoned" ring; very similar eft'ects would follow, which have, in part, at least, 

 been indicated by Prof. Daniel Kirkwood in his paper On the Nebular Hypothesis 

 and the Approximate Commensurabiliti/ of Planetary Periods, in the Monthly 

 Notices of the Royal Astronomical Society, vol. xxix. In that paper, at p. 99 of 

 the volume quoted, he sums up, in part, what he had discussed, as follows : — 



" A planetary particle at the distance 2.5 — in the interval between Thetis and 

 Eestia — would make precisely three revolutions while Jupiter completes one; 

 coming always into conjunction with that planet in the same parts of its path.^ 

 Consequently its orbit woixld become more and more eccentric until the particle 

 would unite with others, either interior or exterior, thus forming the nucleus of an 

 asteroid. Even should the disturbed body not come in contact with other matter, 

 the action of Jupiter would ultimately change its mean distance, and thus destroy 

 the commensurability of the periodic times. In either case the primitive orbit of 

 the particle would be left destitute of matter.^ The same reasoning is, of course, 

 applicable to other intervals;" and Prof. Kirkwood produces evidence to show that 

 the " intervals in the asteroid zone" — however small at best — are yet appreciably 

 greater in the instances of " nearly commensurable periods." With respect to the 

 interval between the two Rings (or system of rings) of Saturn, Prof. Kirkwood, 

 after a discussion of the distances and periodic times in question, concludes, " It 

 is thus seen that the interval occupies precisely the space in which the periods of 

 satellites would be commensurable with those of the four members of the system 

 immediately exterior. As, therefore, the powerful attraction of Jupiter produces 

 the observed gaps in the asteroid zone, so the, distnrhing influence of Saturn's in- 

 terior satellites is the physical cause of the permanent interval between the two bright 

 rings." 



Prof. Kirkwood concludes his paper with the declaration that the Nebular 



Hypothesis "assigns an obvious cause for the establishment of nuclei in 



such positions that their periods will be nearly commensurable with that of the 

 disturbing body. As these nuclei would receive accretions of matter from portions 

 of space both interior and exterior to their respective orbits, their distances from 

 the central body, during their planetary growth, would not be liable to great 

 variation." 



(65) Now, with our half-planetary arrangement of the Asteroid-mass, (60), the 

 periodic times of Jupiter, the exterior half-planet mass, the interior half-planet 

 mass, and Mars, will, respectively, be related as follows; the coincidences, though 

 not absolute, being yet very close — 



P. Time (T) of Jupiter = 2 (T) of exterior asteroid-mass, 



= 3 (T) oi interior asteroid mass; and 

 (T) of interior asteroid-mass = 2 (T) of Mars. 



Thus with the action of Jupiter on the one side, and Mars on the other, there 

 would be abundant occasion for the effects vmder discussion. 



' All hnt the very distance of the interior asteroid-mass, as exhibited in (60). 

 ^ See, again, Consistency 9, in (44) ; referred in Note 2, on p. 30, to this place. 



