Chase.] O^^ [Sept. 17, 



THE BEGINNINGS OF DEVELOPMENT. 

 By Flint Earle Chase, 

 Frofessor op Mathematics in Haverford College. 

 {Bead before the American PMlosopMcal Society^ 8e])temher 17, 1875.) 

 Ill speculations upon the nebular hypothesis exclusive regard has 

 jjsually been paid to action at the limit of possible atmosphere, or the 

 f)oint at which the velocity of rotation becomes equal to the velocity of 

 :revolution. Hence many popular text books state that, if the Sun vrere 

 expanded untjLit reached the orbit of each of the planets in succession, 

 Its times of rotation jvould correspond with their respective times of revo- 

 lution. This stateruent is generally understood as referring to the expan- 

 sion of the nucleus^ and with such reference it is false. 



The times of rotation vary as the squares of the nucleal radius, while 

 *he times of revolution yary as the f power of the radius vector. The 

 rotation-radius, or the radius of a nucleus which would have a rotation 

 synchronous with orbital revolution, therefore varies as the | power of 

 the radius vector.. In my eommunication on " Flanetary lUustratioos of 

 the Creative Fiat," I represented the rotation radii by approximate cir- 

 cular pendulums, the pendulum.-unit being | of Sun's radius, because the 



centrifugal force, as Alexander has stated,* varies as — ; and the distance 



at which the velocity av^quired by infinite fall would equal orbital velocity 



1 -- 



at d, being 3d, — ^ |. The unit of orbital distance is | r, or {^Y of the 



fP're^-jeiit height of possible solar atmosphere, 



I;m fclie following table, the actual values of the rotation radii for the 



• several planetary mean distances are given, for comparison with the theo- 

 retical p.endulums and for further study. An inspection of the numbeis 

 of penduium-units shows three simple nodal groupings, with a br* ak be- 

 tween Bar tii and Mercury, and Venus serving as a link. If we extend 

 the nodal .divisions, we find that Earth appears to have established a 



. secondary -system of its own, drawing the larger portion of the nodal 



material from iS to Venus, and uniting with Sun, Venus, and Venus- 



Mereury iii.cajrrpjjg the rest to Mercury. 



Theoretical. 



Prime Multiple 504 



112 

 Neptune,! 392 



112 

 •Uranus, 280 



112 



• Saturn, 168 



63 

 Jupiter, 105 



63 

 Mars, 42 



* " statement and Exposition of Certain Harmonies in the Solar System, by Stephen 

 Alexander, LL.D.,' (Smithsonian Contributions, 280,) p. 17. 



t The names of the Planets will be used to denote their rotation-radii throughout 

 rthe present ,pa,per, unless otherwise expressly stated. The unit of rotation-radius is % 



