Ohase.] ->'3v [April i, 



changes from meteoric influences, in proportion to its mass, so as to main- 

 tain a permanency of relative mass among the principal members of our 

 system. 



I have already pointed out various harmonic mass relations (Law 3), in- 

 cluding the following equation involving figurate [lowers of the supra- 

 asteroidalk masses, as well as of their distances.* 



Saturn 10 = Neptune 1 X Uranus 3 X Jupiter 6 (6) 



I have also called attention to the fact that these four planets, together 

 with Earth and Sun, represent important centres of nebular or $w. si- nebu- 

 lar influence, viz : 



Neptune, centre of primitive annular condensation. 



Earth, centre of belt of greatest density. 



Sun, centre of nucleal condensation. 



Uranus, centre of primitive "subsidence" collision (Law 2). 



Jupiter, centre of Neptuno-Urauian nebula. 



Saturn, nebular centre of mean planetary inertia. Saturn is also the 

 centre of paraboloidal subsidence when Neptune was focal and Sun was at 

 the vertex. 



Tin' report of Professor Pierce's lecture led me to look for some ecpiation 

 to connect the masses at the two remaining centres (Earth and Sun) with 

 those of the two chief planets, and I soon found that 



Jupiter 3 = Sun X Earth X Saturn (7) 



This equation gives 



Sun's mass = 328,600. ~\ 



' ' parallax = 8. "832 ' (7 2 ) 



" distance = 92,549,000 miles. ) 



Combining (6) and (7), we find 

 Saturn 9 = Jupiter 3 X Uranus 3 X Sun X Earth X Neptune (8) 



The masses of Neptune and Uranus seem to be so related as to give them 

 equal ratios between their present orbital momentum and the orbital mo- 

 mentum at their respective abscissas in the solar-stellar paraboloid (f- Nep- 

 tune and | Uranus). 



7 X Neptune = 8 X Uranus } 



.-. v '£ X Neptune = j/f X Uranus j ( -> 



Equation (8) may be stated under the form 



/ Sat. Sat. Sat. \ / Sat. Sat. \ 3 



VSuu. X Ear. X Nep. / \ Jup. : Ura. / — 1 (10) 



Here the equation of planetary stability groups the centres in two sets, 

 as in equation (7), the first introducing the first powers, the other the cubes, 

 of the relative masses. The same exponential grouping also occurs in (3), 

 but with linear factors instead of mass factors. If we consider that, in a 

 rotating nebula, the time of rotation varies inversely as the square of the 



* A nte, xiv, 652. 



