Binary Star and its Attendants. 35 



1047-875— V(32) 4 = 23-875 solar radii. The corresponding 

 height of possible atmosphere, or the height of equality between 

 the velocities of rotation and revolution, is § of 23*875 = 35*813 r. 

 This would give, for the time of solar rotation, 



365-256-*-(214-86-*-35*813) l = 24*856days, 



differing less than ^ of 1 per cent, from the vis-viva esti- 

 mate (20). 



22. The ratio 1 : 32 2 is also simply connected with the mass 

 and distance of Jupiter's companion planet Saturn, and so 

 with the centre of planetary inertia. For 1024 + 1025 + *536 

 = 2049-54 (3, 17), Saturn's mean radius vector being 2049*51 

 solar radii; 1024 + (35*13-1- n/*4) = 1080*625 is the limit, of 

 which Jupiter represents a centre of explosive oscillation, and 

 the inertia! moment at the limit gives the mass of Sun -*- Saturn; 

 for 1080*625 x (f) 2 = 3501*2, Bessel's value being 3501*6. 



23. Among the many harmonies of planetary mass which 

 manifest a dependence on nebular influences, the following are 

 perhaps indicative of some of the earliest forms of activity : — 



a. The masses of Jupiter and Earth are nearly proportionate 

 to the square of their periodic times x the velocities due to 

 internucleal vis viva : 



5-2028 3 x 5*202-8^ = 321*2 ; 321-2 x 1047-875 = 336201. 



b. The influence of spherical gyration on Venus (11) seems 

 to be further shown by its ratio to Earth, which is the square 

 of the ratio of Uranus to Neptune ( */S :if) \ it 2 x 336201-7-8 

 = 415289. Hill's estimate of the mass of Sun -f- Venus is 

 408134. If the internucleal vis viva of Jupiter were taken at 

 secular perihelion, the resulting theoretical mass-denominators 

 would be Earth 326222, Venus 402460. 



24. The masses of the principal planets therefore seem to 

 have been primitively determined by the following influences: — - 

 Neptune, by the proportion between the time of direct fall to 

 the centre of planetary inertia, and the time of circular revo- 

 lution ; Uranus, by the time of describing the Sun's propor- 

 tional part of a circle in the circular orbit ; Saturn, by equality 

 of nebular vis viva with Jupiter when the two centres of con- 

 densation were in opposite parts of the nebular belt and on 

 opposite sides of the Sun ; Jupiter, by the ratio of variability 



'between incipient fall to a centre of linear atmospheric oscilla- 

 tion and circular revolution ; Earth, by the combined action 

 of vis viva and times of revolution ; Venus, by the action, in 

 a spherical mass, of the same forces as determined Uranus in 

 a circular disk. The mass-denominators are : — 



D2 



