Chase.] IS^ [April 21, 



15. Jupiter, the chief planet in the supra-asteroidal, and Earth, tlie chief 

 planet in the intra-asteroidal belt, are connected by the following propor- 

 tion. The number of light-oscillations (log. r= 20.09991G) which would 

 communicate the greatest gravitating velocity in our system \\/2gr at Sun^ 

 : the number (log. = 15.822542) in describing Sun's circumference (2 ~ r) 

 : : velocity of revolution at earth (l -i- |/214 86) : velocity of gravitating 

 fall at .Jupiter (1 h- 1051.298)^ the units of velocity being taken, respect 

 ively, at Sun's surface, and at the limit of equilibrium between© 2/ aggre- 

 gation or dissociation (1.4232 + 1049.875). 



16. The same chief planets are also connected by the proportion : — 



^/Modulus (688.3) : light -producing wave at the mean -perihelion centre of 

 gravity of Sun and Jupiter (" x 1.0198) : : Earth's mean radius vector: 

 Sun's radius. The value of Earth's radius-vector thus found, is 214.842; 

 the value which is derived from the observations which I have thought 

 the most accurate, being 214.86. 



17. Jupiter and Sun thus appear to be companion constituents of a binary 

 star, and the point of primitive rupture should be sought at the secular 

 perihelion centre of gravity. Bodies falling toward that point, or approach- 

 ing Sun, are subject to a force of about 1048 towards Sun, and 1049 towards 

 the slowly moving common centre of gravity. There are, therefore, two 



fl048 

 nodal points, with the least resistance to motion nearly midway .,^, 



betw-een them. If Sun is gaseous, as Hunt, Faye, and others have supposed, 

 there should hence arise linear oscillations of 2 X 2 r, synchronous with 

 the circular oscillations of 2 ~r. The corona may, perhaps, be due to such 

 radial oscillations. 



18. The loth accordance gives for the mass of Sun -=- Jupiter, 1049.875 — 

 2 = 1047.875; the 17th, 1049.874 — 2 = 1047.874; Bessel's estimate being 

 1047.879 zb .235. 



19. The discrepancy between the two astronomical estimates for the velocity 

 of light, seems to have arisen from ignorance of the interuodal oscillation. 

 Delambre, from his discussion of more than 1000 eclipses of Jupiter's first 



satellite,* estimated the time of light-passage from Sun to Earth at 493, ^198; 

 Struve, from the phenomena of aberration, at 497.' 827. If the time of 

 traversing 212.86 solar radii is 493.198, the time for 214.86 r should be 

 497.831, which differs from Struve's value by less than y^'^j of one per cent- 

 20. If Earth was at the nebular nucleal surface, when the Jovi-Saturnian 

 ring was nebularly atmospheric, the vis viva of interior nucleal rotation 



■ varied as r; and the velocity of resulting planetary revolution, as ;•-. We 

 thus obtain, for the theoretical time of present solar rotation, ]/214.86 : 1 : : 



365.^256 : 24. 912. The lowest estimate from observation is Sporer's 24.624; 

 the highest, that of Schwabe, 25.507. 

 *Stockwell, Proc. Amer. Asso. xx. 70-7. 



