Chase.] 4< () [Oct. 3. 



Jupiter's perihelion is therefore properly comparable with the aphelion 

 of Uranus. A like comparability with Saturn's aphelion is not immedi- 

 ately evident, but "the orbit of Saturn is affected only by the difference 

 of the perturbations by r Jupiter and Uranus ;" Saturn and Jupiter always 

 act on the inclination of the orbit of Uranus in opposite directions ; 

 "the eccentricity of the orbit of Saturn always increases, while that of 

 Jupiter diminishes, and vice versa ;" therefore while either apsis of one 

 of the planets is approaching the Sun, the corresponding apsis of the 

 other planet is receding and the opposite apsis approaching. Then, if 

 we look only to secular mean positions, Jupiter and Uranus are simul- 

 taneously in opposite apsides ; and opposite apsides of Jupiter and Saturn 

 are simultaneously approaching to, or receding from, the Sun. 



The fundamental centre of oscillation which forms the unit of the 

 - series, is determined by Jupiter's mean perihelion, with which, as we 

 have just seen, the mean aphelia of Saturn and Uranus are correlated, 

 and the same harmonic relations which subsist between these three im- 

 portant planets, fix, with close approximation, cardinal positions of the 

 other planets. 



If planetary positions and times have been determined by mutual 

 gravitating action, it seems probable that in planetary masses and in the 

 normal undulations of the aether itself, simple relations to the same ac- 

 tion maybe traceable. Stockwell says (p. xvii), " a comparison of the 

 values * * * has suggested the inquiry whether there may 

 not be some unknown physical relation between the masses and mean 

 distances of the different planets." I believe that Proctor, and probably 

 other astronomers, have also suggested such a relation, but I am not 

 aware that one was ever pointed out until I called the attention of the 

 Society (Proc. Amer. Phil. Soc, xiii, 141) to the equality between the 

 mean moments of inertia of the two principal planets (Jupiter, 5. 2028 2 X 

 9543 = 258318 ; Saturn, 9.53S9 2 X 2856 = 259851). 



Of the many correlations of light and gravity which I have hitherto 

 indicated, the two following seem especially interesting in this connec- 

 tion. 1. The synchronism between the passage of a luminous undula- 

 tion from the Sun to the centre of oscillation of the outermost planet, 

 and the rotation of the Sun on its axis ; 2. The equality of the limiting 

 velocity of rotation to the velocity of light. In my original announce- 

 ment of this equality, I introduced, as one of the elements of my calcu- 

 lation, the Sun's centre of spherical gyration. To this the very reason- 

 able objection has been urged, that we know nothing of the internal 

 density of the Sun. I therefore submit the following considerations, 

 which are entirely independent of solar density. 



In particles moving freely about an attracting centre, the mean (4/- -5- t) 

 velocity of oscillation through the centre of gravity, is to the velocity 

 (2 -r -s- t) of synchronous circular revolution about the centre of gravity, 

 as 2, is to -. The velocity acquired by falling, from an infinite distance, 

 to the extremity of any radius, is j/g „ r% If we suppose that the veloci- 

 ties of free oscillation and revolution are each retarded in the same pro- 



