Chase,] 582 ^ jan. 19, 



339. Phyllotaxy in the Joman System. 



The harmonies which are shown in Notes 330 and 334, supplement 

 and help to explain the first four harmonies of Note 29 and the five har- 

 monies of Note 14. Callisto's semi-axis major represents a phyllotactic 

 power of a phyllotactic multiple (3'), of Jupiter's semi-diameter. The 

 semi-axes major of the three inner satellites are approximately connected 

 with the nebular radius and with one another by the phyllotactic fractions 

 f and f, as follows : 



Observed. 

 Nebular radius 38.424 

 Ganymede 15.3503 



Europa 9.6235 



lo 6.0485 



The greatest difference between the phyllotactic and observed loci is f 

 of one per cent. 



The corresponding orbital times are connected by powers of the phyllo- 

 tactic number 2. 



2* r^ 16 Nebular radius 16.0135 



2^=: 4 Ganymede 4.0434 



21^ 2 Europa 2.0073 



2"= 1 lo 1.0000 



340. Phyllotaxy of Planetary Mass and Position. 



Peirce's phyllotaxy of orbital times (Note 135), my atomic phyllotaxy 

 (Note 289), and my phyllotaxy of virtual areas (Note 190), encourage a search 

 for phyllotactic relations of planetary mass and distance. Jupiter's mean 

 projectile locus (mean perihelion), is an approximate phyllotactic basis for 

 Saturn's mean locus of subsidence, the rupturing locus of tlie outer two- 

 planet belt and the mean centre of gravity of the belt : 



If Saturn's mean perihelion were in the same longitude as that of the 

 outer belt, the phyllotactic sum of their disturbing forces (2 -|- 5) would 

 become an important limit of oscillatory inertia. Simple phyllotactic com- 



