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



p = Sun's present nebular radius, or the distance at which 

 planetary revolution and solar rotation would be synchronous. 



The subscript figures denote apsidal positions : 1? secular 

 perihelion; 2 , mean perihelion; 3 , mean; 4 , mean aphelion; 

 5 , secular aphelion. 



The multiple 2 denotes the primitive nebular radius which 

 would give the vis viva of circular-orbital revolution, by con- 

 densation to the present planetary radius vector. 



It should be noted: — that critical positions of all the planets, 

 together with some asteroidal positions, are represented in the 

 Table ; that all the symmetrical combinations of it and n, which 

 ^are embraced in the Table, have planetary representations ; 

 that both of these rupturing-factors seem to have been simul- 

 taneously operative ; that, after the first conversion of linear 

 into circular motion, the exponential increments of ir form a 

 figurate series ; and that the relations have all been found, not 

 by happy guessing, but by following indications which are 

 mathematically deducible from the necessary action of central 

 forces. 



The character of the accordances is shown in the following 

 Table:— 



Divisor of 

 M. 



Quotient. 



Fact, 



Minimum 

 error. 



Maximum 

 error. 



7cn 



60210 

 19165 



5-165 



1-644 

 1-942 



1-392 



•730 

 •167 



2^3 



/ •» 

 l2h 3 



i 2 © 



2© 2 

 J c? 2 

 12$, 



{ ? 3 



12$ 3 



Geo 



60-068 



19-184 



19-078 



5-203 



5-168 



1-644 



1-932 



1-403 



1-396 



•723 



•774 



•167 



+ •142 

 -•019 



+ •087 

 -■038 



-•003 



•000 

 + •010 

 -•011 

 -•004 

 + •007 

 -•044 



•000 



+'142 

 -•019 



+ •087 

 -•038 



-•003 



+ •120 

 -•058 

 -132 

 -054 

 + •007 

 -044 

 •000 





7ra 2 



7T% 2 



irSi 



n? ... 



7T 7 ......... 



7T% 2 



The importance of my introduction of various apsides into 

 the study of planetary harmonies has been fully recognized 

 by Alexander, the Nestor of harmonic astronomy ; but in 

 order to avoid all possible cavil I give the maximum errors, or 

 deviations from the semiaxis major, as well as the minimum 

 errors, or deviations from the nearest apsis. 



The next Table gives the results of internal rupture which 

 are indicated by Grummere's criterion, starting from the theo- 

 retical origin of Neptune's present orbital vis viva. In each 

 instance the theoretical angular velocity of revolution, for the 



