Chase.] OOO [Oct. 15 and Dec. 3, 



Bode (T). Actual (O). (T-Oj -^ O. 



28 726.16 Asteroidal 



52 1070.06 2/i 1069.62 +.000 



100 2057.78 12 2 2049.51 +.004 



196 4033.25 §2 4121.76 —.022 



[292 6008.71] ^^ 6388.25 —.063 



388 

 It will be observed that I have interpolated the Neptunian term, but 

 this modification of the Bodeian law, as I have, in part, previously' stated, 

 increases its harmony, by giving three equal differences at each extremity 

 of the series, by placing Earth's pei-ihelion in a geometrical mean posi- 

 tion between the I2 nucleus and its limit of jjossible atmosi^here, and 

 by marking centres of linear oscillation of successive pendulums. 



After the hypothetical detachment of the several two-planet belts, and 

 their independent revolution preparatory to cosmical division, the har- 

 monic should replace the geometric ratios. In order to remove the in- 

 fluence of the theoretical planetary pendulum unit (|^3?') and the slight 

 uncertainty as to the precise period of solar rotation, let us examine the 

 ratios of the several planetary rotation- (or nucleal-) radii, and the con- 

 sequent harmonic differences, according to the above equation of varia- 



j. 

 bility, p oc t'^. 



t p 



^ .2408 .491 ^ ^ 9 z:= 5 -- 7, 



9 .6152 .784 0-^(5^ =^5 ^6.; 



© 1.0000 1.000 



<^ 1.8808 1.374 §— :^=r5.722 



% 11.8618 3.444 2/ — © = 2.444 



\ 29.4565 5.427 ©—©^1.000 



§ 84.0190 9.116 0—19= .392 



^ 164.7791 12.837 ^9 — i^ = .147 



By comparing the radii of aethereal nebulosity ; of synchronous central 

 and circular oscillation (2r : ?■) ; of incipient aggregation, or constant 



c nr -\ 

 pressure (1.4232/-) ; and of nebular rupture I ~~XT J 1 we find the fol- 

 lowing accordances : 



1. An aethereal atmosphere, rotating with planetary velocity at Sun's 

 present surface, would have the equatorial velocity of light at 088. 33r. 



3 X 688.33 2064.99 \^ 2049.51 



6 X " 4129.98 §2 4121.86 



9 X " 6194.97 Wi 6388.25 



2. If the radial oscillation and the radius of nebular rupture are spe- 



nr 2?" -^ •,. 



cially regarded, r = \ radius vector ; ?i = 2 ; — ~Tr'\ — "o" — ^ raaius 



vector. 



