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The first term of this series represents Jupiter's linear centre of oscil- 

 lation, at which the planetary masses would balance the Sun, with a 

 centre of gravity at the Sun's surface, which is the source of its radiant 

 undulation ; the second, the mean distance of Venus ; the third, Mer- 

 cury's mean distance ; the fourth, a possible unknown planet, planetoid 

 group, or other seat of solar and planetary perturbation, with a period of 

 53.54 ± days ; the fifth, a planet with a period of 34.25 days, Kirkwood's 

 estimated period being 34.92 days. 



It is especially noticeable that in these thi-ee harmonic series, em- 

 bracing sixteen terms in all, only one appears to be destitute of an obvi- 

 ous planetary representative. The lack of actual known planets at some 

 of the principal centres of linear oscillation, may, perhaps, be accounted 

 for by the action of masses, which, though not sufficient to introduce new 

 series, may have concurred in breaking up the tendency to nodal aggre- 

 gation. It is possible that future observations may show a somewhat 

 analogous action between Mercury and Vulcan. I am, however, inclined 

 to believe that improvements in astronomical instruments will, at some 

 day, enable careful observers to detect some form of actual material con- 

 centration, at I %', }j 21, I 11, and £ 5 ®. 



These harmonic pointings to intra-Mercurial planets are corroborated 

 by the z series of planetary pairs, which was given in my communication 

 of the 4th ultimo. The division of Mercury's perihelion distance by x 

 brings us to a point considerably within the limits of the solar retarda- 

 tion, which, if the aether is material, would interfere with any permanent 

 orbital revolution, bringing any planetary masses more or less rapidly to 

 the Sun. There is, however, a certain portion of the region in which 

 planetary stability would be possible, and analogy would lead us to look 

 for a pair of mutually balancing planets, wherever the conditions are 

 favorable for one. The closeness of the harmonic accordance in the posi- 

 tion which Kirkwood has assigned to Vulcan, seems to me a strong con- 

 firmation of his views, and an equally strong indication ol the importance 

 of making special observations in the portion of the Zodiacal belt which 

 is embraced between the orbits of Vulcan and Mercury. If Wolf's sup- 

 posed Sun-spot period of twenty-seven days* is a sidereal period, it might 

 be readily explained by the perturbations and transits of a planetoid or 

 meteoric group, at a distance which would complete the terrestrial har- 

 monic series. If the proper balancing of orbital undulations requires 

 any extra Neptunian planets, we may, perhaps, have reason to look for 

 some analogy between them and the intra-Mercurial pair, which may 

 complete the symmetry between the outer and inner planetary limits to 

 which I have invited attention in my modification of Bode's Law. 



* Cited by Kirkwood , ante, xi. 97. 



