452 Prof. P. E. Chase on the Nebular Hypothesis. 



At the time of the late total solar eclipse, Watson and Swift, 

 each observed two small planets between the orbit of Mercury 

 and the sun. By comparing the published position of the 

 planet which was first announced by Watson, with some of the 

 most trustworthy of the recorded observations which were 

 thought by Leverrier to indicate intra-Mercurial Transits, 

 Gaillot and Mouchez found an orbital period of 24*25 days*, 

 which represents the third interior term of my series and the 

 second strict verification of my prediction. 



If a nebula condenses until all the particles in the equato- 

 rial plane have an orbital velocity, the mean radial vis viva at 

 the orbital centre of linear oscillation (^r) is equivalent to the 

 orbital vis viva at dr. This equality may, perhaps, help to 

 account for the following approximate division of the planetary 

 system, the unit being Sun's radius : — 



9V= 81r. Mercury's mean radius vector 83*17 r. 



9 3 r= 729?-. Asteroid 76 732*42r. 



9 4 r = 6561r. Neptune's extreme radius vector... 6546*677-. 



The relatively rapid motion of Phobos (the inner satellite of 

 Mars), as well as the newly found meteoroidal character of the 

 corona, may reasonably lead us to look for an indefinite number 

 of further verifications among the results of future discovery. 

 Many of them, like many of the Neptunian harmonies which 

 are modified by the overshadowing mass of Jupiter, will pro- 

 bably elude all attempts at discovery; but the apparent import- 

 ance of 9 as a cosmical factor gives interest to the second series 

 in the following Table. The denominators in the first series are 

 of the general form (4?2 — 3) ; those in the second series are of 

 the form (4v— 3 = 144n — 111), v being equivalent to 9(4n — 3). 



According to the nebular hypothesis, when Sun was ex- 

 panded to the present orbit of Jupiter, the collisions of subsi- 

 ding particles would tend to form a ring at two thirds the dis- 

 tance, or at 3*469 times Earth's mean radius vector. If we 

 take this as a harmonic unit, }, we find that Venus's mean 

 perihelion is well represented by £, Mercury's mean distance 

 by -g, and Kirkwood's estimated semi- major axis of "Vulcan" 

 by jj. Here are, therefore, four terms of the first harmonic 

 series, w T ith a denominator-difference of 4. 

 First Series. 



No. 



Har 



monic prediction. 



Confirmation. 





1. ... 



JL 



= 3*469 



Node of subsidence 



3*469 



2. ... 



1 



•694 



Venus, mean perih. 



•698 



3. ... 



... i 



•385 



Mercury, mean d. 



•387 



4 



... A 



•267 



De la Hue, Stewart, 

 and Loewy 



•267 



o. ... 



.1 



= *204 



Kirkwood 



•209 



6. ... 



] 7 



= -165 



Watson 



•164 



Comptes JRendus, August o, 1878. 



