1881.] '^^'^ [Chase. 



orbits are ever exactly circular, and therefore the only ones that indicate 

 nebular activities which extend to the very surface of a rotating nucleus. 



29. The Moons of Jupiter. 

 "We may reasonably look for a greater variety of satellite harmonies in 

 connection with the giant planet which represents the primitive nebular 

 centre of our system, than in connection with any of its subordinate com- 

 panions. Some of those harmonies have been already indicated in Note 

 14. It may be well to restate two of them in a different form, together 

 with some others which seem especially significant. 



I. If we take axial rotation at the centre of density as the unit of com- 

 parison, the synchronous rotation and revolution of the nebular hypothesis 

 has been accelerated 366.2565 fold, by Earth's condensation and other causes. 

 Earth's accelerated rotation, is to the acceleration by fall to a centre of 

 linear oscillation, as Jupiter's synchronous radius is to Callisto's synchro- 

 nous radius : 



366.2565 : 9 : : 4332.58483 : 16.68913 

 The significance of this rhythmical accordance between the nebular 

 centre and the centre of density is increased by the fact that the nascent 

 velocity at each of those centres is directly traceable to the maximum of 

 planetary velocity (y'gr at Sun's surface). 



II. The significance is further increased by the fact that Callisto repre- 

 sents the mean centre of gravity of Earth and Jupiter, at Jupiter's ruptur- 

 ing locus. Jupiter's mean perihelion being 4.9782, Its distance from Earth's 



1 

 semi-axis major is 3.9782. Jupiter's mass being -.».- qq , this relation gives 



00197= for Earth's mass, as will be seen in the following proportion, 



.012585 being Callisto's semi-axis major : 



1 1 



3.9782 : .01258o : : ^q^- §8 ' 331245 



This estimate of Earth's mass gives 92,786,000 miles for Earth's semi- 

 axis major, and 1,167,100 miles for Callisto's semi-axis major. 



III. The harmony of planetary and satellite influences, at the centres of 

 density and of nebulosity, is shown by the proportion, 



Jupiter's secular perihelion : Earth's semi-axis major : : Callisto's semi- 

 axis major : Moon's semi-axis major. 



4.8863 : 1 : : 1,167,100 miles : 238,850 miles. 

 Herschel's estimate is 237,000 miles. 



Lockyer's " 238.793 " 



Chamber's " 238,830 " 



Von Littrow's " 238.870 " 



Newcomb's " 240,300 " 



TV. An elliptic orbital influence, between Jupiter and the dense belt, with 

 a major-axis of 6.131, is indicated by the proportion : 

 6.131 : .012585 : : 186282 : 382.38. 



PROC. AMEK. PHILOS. SOC. XIX. 108. 2t. PRtSTED MAY 3, ISSl. 



