Chase.J -^"o [jan. 7, 



at '^ 

 the fundamental equation li -= ^, of Sun's, homogeneous sethereal, or 



light-propagating atmosphere. The values of L and M are found as follows : 



The mean time of light-propagation from Sun to Earth being 497.837 



seconds, the velocity of light /« \ is 214.547-0 --- 497.837 = .43095?'o ; % = 



^g^ ro = — "-^ - -^---J^^-^A- 3= .00062565ro ; go = < ^ ''n = .00000039144ro; 

 ^ ^" " 365.356 X 86400 o , yo o o o 



t 



ir = ^ -^ ffo 



1100965 sec; L = 314..547'n ^ / Jialf-year y ^ 



Vll00965sec./ 



ay 



'V . 



36.86rn ; M = I ^ 1 ?-n ="• 474460?-, 



% 

 VIII. By introducing tiie ratio of dissociative subsidence, (^^j with the 



general equation x^^ = fT;"^"-, we find a series of paraboloidal abscissas 

 which complete the photodynamic demonstration of a harmonic nodal ac- 

 tion, uniting the solar, planetarj^ and stellar systems. Take for the 

 middle abscissa, fL, and for the limiting abscissas of centripetal action, |^?'o 

 and LM h- ?•(,. The relative vis viva, or the locus of projection against 

 uniform resistance, of the linear centre of oscillation of L, is fL; ^Tq is the 

 paraboloidal vertex ; LM -~- Tq bears the same ratio to M as L to Tq. If we 

 take 18 successive abscissas on each side of the middle abscissa, the loga- 

 rithms of Y/ and f can be readily found by the equation ; 

 Log. S = log. i = —.778151. 



Log. 1^ -f 19 log. ry + 361 log. f = log. |L =: 1.308453. 

 Log. ? + 38 log. :,; + 1444 log. ^ = log. LM = 7.236836. 



Of these 39 abscissas, 9 are between the vertex and ^Vq, the locus of solar 

 dissociative subsidence (f ); 9 are between ^ Tq and L ; 9 are between Land 

 the locus of reciprocal action, which will be presently explained ; 9 are be- 

 tween the reciprocal locus and LM -=- r^- 



The 40th abscissa is 46353000?-o, (log. 46353000 =: 7.666079). This is in 

 the region of the fixed stars, and at the probable locus of a Centauri, the 

 four most recent estimates of its distance ranging between 45340000ro 

 and 48479500ro. Both in the centripetal and centrifugal branches of para- 

 boloidal action, 13 of the abscissas are between Sun's centre and surface ; 

 9 are between Sun's surface and the planetary region ; 9 are in the plane- 

 tary region ; 9 are between the planetary region and a. Centauri. 



Dividing the planetary abscissas by 214.54, in order to reduce them to 

 terms of Earth's semi-axis major, we find the following accordances : 



Centrip- Centrif- 



II. etal ab- Planetary loci. n. ugal ab- Planetary loci. 



scissas. scissas. 



31 .3095 I Mercury .1985—31 .2494 Mercury s. p. .2974 



22 .3632 i Venus .3617 —22 .4362 Mercury m. a. .4555 



33 .6459 I Earth m. p. .6441 —23 .7820 Venus s. a. .7744 



24 1.1788 fMars 1.1424—24 1.4392 Mars m. p. 1.4033 



35 2.2080 4 Asteroid 55 2.3080—35 3.7179 Asteroid 45 3.7300 



26 4.3433 | Jupiter 4.3357 —36 5.2666 Jupiter 5.2028 



37 8.3673 f Saturn 8.1763—27 10.4720 Saturn s. a. 10.3433 



38 16.9309 f Uranus 16.7857—38 31.3663 Uranus s. a. 30.6793 

 29 35.1533 | Neptune 35.0395—29 44.7323 # Neptune m. p. 44.5985 



