1877.] oOo [Chase. 



nebulous mass, at the bsginning of interplanetary condensation (secular 

 aphelion) the mean vires vioce of the outer two-planet belts are equal. 

 For the internucleal v. v. OC md'^ ; log. md'^ {^ X S ) = 5.656948 ;* log. 

 md'' (I2 X :if )= 5.656817. See also (58) (64.) 



With Neptune at secular aphelion the mean vires vivcB of the outer and 

 inner Ihni.s of the outer two-planet belts are equal. For under uniform 

 sethereal resistance the v. v. is proportioned to the product of the mass by 

 the trajectory, and the mean orbital trajectory is proportioned to the 

 mean distance. Taking Uranus, Saturn and Jupiter at their mean dis- 

 tances, log md{'^ X h) — 3.334505 ; log wfZ (§ X 1? ) = 3.333751. .(65.) 



With Jupiter at Sun's nucleal surface, and the outer planets at tidal 

 crests (secular aphelion), the mean v. v. of the two outer = mean v. v. of 

 the two inner planets. For the v. v. of rotation in a shrinking nucleus 

 OCm ^ (?'■*; the orbital v. v. CCm^d; log. (2/ rot. X ^ orb.) v. v. = 

 2.480236; log. (§ x h) orb. v. v. =2.478969 (66.) 



In my equation of figurate powers, log. (i$'X§'x:Z/!^) = 8.069488 ; 

 log. I2 1» =: 8.091570 ; log. l^ theoretical mass == .806949 (67.) 



The internucleal v. v. (OC md'^) of Saturn is equivalent to the mean inter- 

 nucleal V. V. of the supra-asteroidal belt. For if we consider Neptune at 

 secular aphelion, Uranus and Saturn at mean distance, and Jupiter at 

 secular perihelion, log. md' for ^ = 3.029730; for § = 2.565859 ; for Ij 

 rr= 2.768149; for 11 = 2.712.548; (3.029720 + 2.565859 + 2.768149 + 

 2.712548) ^ 4 = 2.769069 (68.) 



The mean v. v. of sethereal rupturing projection (md) in the supra- 

 asteroidal belt is equivalent to that of the Sun (59). For log. [mass 

 (y^XSXh X '21) i~i- Q X secular perihelion t|; -h Q radius] = ^ 



(5.707091 -f 5.645107 + 4.454264 -f 5.979691) + 3.803423=1.999961; log. 



mass O -^ O radius — .000000 (69. ) 



Jupiter's mass is nearly equivalent to the mean mass of Sun, Earth and 

 Saturn. For log. i (0 X © X h ) = 1.338072 ; log. H = 1.334584... (70.) 



II. Chemical Atoms, Molecules arhd Volumes. 



In accordance with a suggestion of Professor Robert E. Rogers, I have en- 

 deavored to find what modes of central force will best represent some of 

 the most general forms of chemical activity, more especially those which 

 are the basis of the law of Avogadro and Ampere, of combination by 

 volume, and of approximate constancy in the product of atomic weight by 

 specific heat. 



The simplicity of the ratio, between the energy of H^ O and the solar 

 energy at Earth's mean distance, -f- furnishes good grounds for such an in- 

 vestigation, while the record of a parabolic orbit, connecting the Sun with 

 the nearest fixed stars,:}: indicates a proper course for conducting it. Al- 



* With Uranus as unit of mass, and Earth as unit of distance. 



t^n<exli, 394; xili, 142. 



XAnte, xii, 523, and subsequent papers. 



