Chase.J 366 [April 15, 



33. Neptune's Moon. 



Is Neptune the outer limit of our planetary system, or may we look for 

 still more distant members of our family of circling orbs? Astronomers 

 find indications of some further source of remote perturbation, and attempts 

 have already been made by Prof. George Forbes and D. P, Todd to furnish 

 a clue to its discovery. More than eight years ago, I communicated to the 

 American Philosophical Society* a planetary series which introduced the 

 ratio of the circumference of a circle to its diameter, which is also the 

 photodynamic ratio, at Sun's surface, between the reactions which repre- 

 sent the velocity of light and the reactions which represent the maximum 

 of planetary velocity at Laplace's limit. The two terms of the series 

 which immediately follow Neptune are 94.38 and 296.53 times Earth's 

 semi-axis major. Forbes, by investigating the perturbations which are 

 indicated by the aphelia of comets, has strikingly corroborated this forecast. 

 The abstract of his memoir read before the Royal Society of Edinburgh 

 saysf : "On tabulating the aphelion distances of all the known elliptic 

 orbits of comets, it was found that in no case was there any grouping of 

 aphelion comet distances which did not agree with the distances of planets, 

 except that beyond the distance of Neptune there were two groupings of 

 comet aphelion-distances, one at 100 Earth's radii, the other at 300 Earth's 

 radii, approximately." The perihelion or rupturing positions which are 

 indicated by his investigations are 96.7 and 385.2. 



Both of these investigations were entirely independent of my own, and 

 neither of the writers gives any indication of ever having read my paper. 

 There is, therefore, cumulative and conclusive evidence of harmonic influ- 

 ences, beyond the known limits of the planetary system as well as between 

 the interior limits of the system and the Sun. The similarity of those in- 

 fluences, their dependence upon photodynamic action, and their importance 

 as guides to investigation, are shown in the following note (33). 



Neptune's satellite-harmony is the only one which involves the consid- 

 eration of only two of the members of the system. Sun and itself. This 

 fact, as well as the slight secular eccentricity of Neptune's orbit, seems 

 to render it probable that the supra-Neptunian harmonies may indicate 

 asteroidal rather than planetary aggregation. If Neptune represents the 

 primitive belt of subsidence-collision, the corresponding nebular radius 

 was f X its secular aphelion radius- vector, or 45.704 X Earth's semi-axis 

 major. We find, accordingly, that 



I. Sun's mass : Neptune's mass : : Nebular radius : Neptune's lunar 

 radius-vector. 



19880 : 1 : : 45.704 : .00236. 



II. Sun's semi-diameter : Neptune's lunar radius : : Modulus of light : 

 virtual projection of light-velocity, very nearly; i. e., within 1.3 per cent. 



.00466 : .002S6 : : 1 : .5065. 



* Proceedings A. P. S., xiii, UO ; Feb. 7, 1873. 

 t The Observatory, No. 38, p. 441. 



