Motion in Stellar Systems. 203 



finally be found that they are all satisfied by adjustments of 

 orbital eccentricity. 



In seeking illustrations and estimating the relative import- 

 ance of the harmonic adjustments of cosmical masses, we may 

 be guided by the following considerations : — 



1. Sun (mo) is the chief centre of nucleation. 



2. Earth (ra 3 ) is the chief centre of condensation, since it 

 is the largest of the dense planets, and its orbit traverses the 

 secular centre of the belt of greatest condensation. 



3. Jupiter (m 5 ) is the chief centre of planetary nebulosity, 

 since it is the largest planet, and its orbit traverses the centre 

 of the planetary system when Neptune and Uranus are in 

 opposition. 



4. Saturn (m 6 ) is the centre of nebular planetary inertia, 

 since \/5)m? ,2 -f-2?n is in Saturn's orbit. 



The harmonic relation of solar gravitation to the velocity of 

 light appears to have exerted a secondary influence at the 

 chief centre of condensation, for we find 



9z '9o+9s'- Ov*-0o=*o) : (~r + ~ =1 year). 



The mass-ratio which satisfies this proportion is m = 327400m 3 . 



A combination of the harmonic influences of the chief 

 centres of nucleation, condensation, and nebulosity seems to 

 be shown by Earth's and Jupiter's modulus-velocities of rota- 

 tion ; since g^h= circular-orbital velocity at the mean centre 

 of gravity of and 1/ , while g 5 t 5 = circular orbital velocity 

 at Sun's surface. The equation which satisfies these har- 

 monics is m = 1054*6 m 5 . 



The total vis viva of gravitating subsidence in equal aethereal 

 spheres, which varies as m 3 , seems to have cooperated with 

 luminous undulation in determining the ratio of the two great 

 planetary masses, at the centres of nebulosity and of planetary 

 inertia. The proportion m\ : m\ : : p K : p gives 77i = 3491'8m 6 . 



The mass of the exterior belt seems to have been mainly 

 determined by simple oscillatory relations to the chief centre 

 of nebulosity, and the subdivisions of the belt by vis viva of 

 subsidence, as appears by the equations 



7r 2 (w 8 + m 7 )=m 5 , 



which give m = 22497 m 7 ; m = 19370 m 8 . 



The ratio of Venus to Earth appears to be such as to give 

 the two planets equal orbital momenta. This harmony would 

 be satisfied by the equation m = 384962 m 3 . 



