Chase.] 474 [Oct. 3. 



Peikce's Phyllotactic Planetary Series. 



Chauncey "Wright, in the Mathematical Monthly, vol.1, p. 244, referred 

 the phyllotactic law to nodes of extreme and mean ratio, which he called 

 "the distributive ratio." The same law which distributes leaves most 

 evenly around the stem, would distribute planetary perturbations most 

 evenly around the Sun. 



Kirkwood (Proc. Anier. Phil. Soc, v. 12, p. 163) gave a harmonic 

 series which differed from Peirce's phyllotactic series by the omission of 

 the asteroidal term, and by the substitution of £ %, T V 2/, and | 0, for 

 T \ Ast., \ <5\ and r 8 g ®, in the expressions for the periodic times of Mars, 

 Earth, and Venus, respectively. His approximations were closer than 

 Peirce's for Mars and Earth, but not so close for Venus. The omission 

 of any terms which depend directly upon the asteroidal belt and upon 

 Mars, renders his series less symmetrical than Peirce's. 



In the following table, the errors of the closest planetary approxima- 

 tions in each series are given for the purpose of comparison : 



Errors of Theoretical Planetary Positions. 



Peirce. 



+ .0144 

 .0000 



— .0071 

 + .0180 

 — .0045 

 + .0152 

 — .0136 



.0000 



— .0018 

 All of these approximations are so close as to preclude the idea of 



merely accidental coincidence, and to encourage an attempt to find some 

 causal nexus through which they may all be referred to the law of gravi- 

 tation. 



Peirce's series has the special merit of being the first for which any 

 reason was given. It represents the mean planetary distances more 

 nearly than either of the other series, and if we accept the nebular 



