1873. 1 4: f d [Chase. 



The assumed "failure"' of Bocle's series, in the case of Neptune, dis- 

 appears if we make the series symmetrical, as I have already suggested, 

 by introducing two equal differences at the outer, as well as at the inner 

 limit of the planetary belt. In the following table, Earth's mean dis- 

 tance is taken as the unit. 



Bode's Series, Modified. 



The following table exhibits Peirce's phyllotactic series of sidereal 

 periodsf hi the form iu which the original investigation was made by 

 Dr. Thomas Hill, in 1849, at Professor Peirce's request. For conveni- 

 ence of comparison with other series, I give not only the error («) of 

 time, but also the corresponding errors ( / j) of mean distance, (v) of mean 

 or perihelion distance. 



*m, mean; a, mean aphelion ; p. mean perihelion, 

 t Proc. Anier. As«soc. , v,2. Cambridge meeting-. 



