1«^^0.J 19 [Chi.sc. 



The perihelion and aphelion values for f Ceres were found by taking 

 Nevvcomb's value for the eccentricity (.077) and mean distance (2.769/; 

 = 594.06?'(,). Tlie other values of P and A are comi)uted from Stoekwcll's 

 elements of planetary distance and secular variation, taking 214.o4/"o for 

 the value of Earth's semi-axis major [p^]. 



Dividing the values of T, in Table I, by the respective rupturing co- 

 efficients {h, |. f, • • • ). fiiicl reducing to units of Earth's semi-axis 

 major, we obtain the values in column C, Table II, for comparison with 

 Gaussin's values, which are given in column G. 



P. C. G. A. 



Mercury .297 .419 .363 ■ .477 



Venus .673 .726 .623 .774 



Earth .933 .969 1.073 1008 



Mars 1.311 1.572 1.848 1.736 



Asteroid 2.133 2.760 3.183 3.954 



Jupiter 4.886 5.093 5.483 5.519 



Saturn 8.734 9.761 9.445 10.343 



Uranus 17.681 19.348 16.269 20.679 



Neptune 29.598 30.120 28.025 30.470 



The perihelion and aphelion values of the asteroidal belt are represented 

 by the mean distances of (149) and (153). All the other values in columns 

 P and A are computed from Stockwell's eleniints. Gaussin's approxi- 

 mations to the distances of Venus, Earth, Mars, Uranus, and Neptune, are 

 all outside of the limits of secular excursion for those planets respectively. 

 My own values are all within those limits, and their approximations to 

 the mean values are closer than those of any other similar series that 

 has ever fallen under iwj notice. 



The data for the construction of the cosmothetic paraboloid were de- 

 rived from considerations of linear oscillation («), vis viva (^5 o), uucleal 

 rotation and synchi-onous orbital revolution {y), spherical oscillation (n\ 

 inter-stellar actions and re-actions of projection and attraction (;), lumi- 

 nous undulation (^) and universal nebular subsidence and rupture (r,). 



a- The focus of paraboloidal action is Sun's centre. The locus of the 

 directrix is also the locus of the linear centre of oscillation of Sun's di- 

 ameter, referred to Sun's surface {%d — r = ^ ?•)• 



/?, y. The fundamental abscissa r^) is f L ; | representing the relative 

 vis viva of the linear centre of oscillation (f), and L being Laplace's limit, 

 or the locus of synchronous rotation and revolution. 



d. The initial ratio {■q':"- — 1.66768) differs by less than ^i^ of one per 

 cent, from f ; | being the ratio of rupturing vis viva to residual vis viva of 

 rotation (1 — .4 = .6). 



e. The planetary field is geometrically intermediate between the fields 

 of solar nuclealion and of stellar projection. There are 9 abscissas be- 



