1S83.I Oii [Chase. 



Tliis represents a comparative acceleration of the velocitj' of rotation 

 ■which may be very closely represented by the quotient of (Jupiter's year 

 X Earth's year) by (the sum of Jupiter's and Earth's years X Earth's 

 day), or by 4333.5848212 x 365.2563582 -- (4332.5848212 + 365.2563582) 

 = 336.858. As this equation introduces considerations of the chief cen- 

 tres of nucleation, nebulosity and condensation which must still be effi- 

 cient, it furnishes another reason for caution in dogmatizing about tidal 

 friction and thermodynamic laws. 



313. Joint Relations of Sun, Jupiter, Earth and Venus. 



A succession of important harmonic motions is shown in the relations 

 of solar mass and density, which make S'o'o^^^a! the relation of Sun's 

 mass to Jupiter's mass which makes Sun's surface the projectile locus, or 

 secular perihelion centre of gravity, of Sun and Jupiter; the relations of 

 terrestrial mass and density which make g.J..^ = circular orbital velocity 

 at the mean centre of gravity of Sun and Jupiter; and the relation of 

 Venus to Earth which makes the incipient orbital vis viva of Venus (at 

 secular aphelion) equal to Earth's mean orbital vis viva. If we adopt the 

 British Nautical Almanac estimate of Sun's apparent semi-diameter 

 (961. "83), the accordance of harmonic and computed values will be as 



follows: 



Harmonic. Computed. Authority. 



Sun --Venus 427-326 427240 Hill. 



" " Earth 330463 331776 (Oscillatory) 



" " Japiter 1047.879 1047.879 Bessel. 

 Earth's semi-axis major, 92,661,600. 



314. Joint Relations of Sun, Jupiter, Earth and Saturn. 



Alexander's harmony (m-^d^ == m^d^) is rendered more significant by 

 SatLirn's orbital situation at the nebular centre of planetary inertia, 

 {I md? -^ S m^h == p^. The slight deviation from exact accordance is 

 very nearly, if not precisely compensated by the equation, Sun X Earth 

 X Saturn == Jupiter^. Alexander's approximation gives, to„ = 3522. 

 33 Jrtg; the other approximation gives, according to the foregoing note, 

 Wg r=r 3481.86; the arithmetical mean being wig = 3502.1, which 

 differs by less than ^^ of one per cent, from Bessel's estimate. If 

 f>b< Pg represent Stockwell's estimates of the mean perihelia of Jupiter 

 and Saturn, Bessel's estimates of their respective masses, and the equation 

 (Sun ~- Jupiter) x (Earth -f- Jupiter) = (p^ -=- ^g)^ give m^ -i- m^ = 

 330240. The harmonic accordances which were given in Note 310 cor- 

 roborate these evidences of joint relations, and encourage a search for 

 modifications by combined harmonies in other cases. 



315. Photodynamic Relations of Uranus and Neptune. 



The increasing number of harmonic influences with increasing distance 

 from Sun, was illustrated in my Relations of Mass, [Proc. A. P. S., xviii, 



PKOC. AMER. PHILOS. SOC. XX. 113. 3t. PRIKTED MARCH 12, 1883. 



