Chase.] 



586 



[Jan. 19, 



347. Phyllotaxy of Orbital Periods. 



The closeness of the phyllotactic mass-harmonies (N"ote 340), may be 

 more strikingly shown by observing the discrepancies in Peirce's approxi- 

 mations to the orbital periods of the primary planets, which seem to have 

 been the first extensions of the phyllotactic theory beyond the vegetable 

 world : 



348. Photic Relations of Earth, Japiter, and Asteroid 130. 



In view of the many evidences of the important influence of Jupiter 

 upon planetary harmonies, tlie following proportion becomes suggestive : 



^a ■ ^^ • '■ P\ ■ Po 

 The second theoretical phyllotactic reduction of Jupiter's orbital period, 

 § Asteroid 139, is represented by t^ ; Earth's day, by t^ ; the'photic radius 

 (Note 345), by p^ ; Sun's semi-diameter, by p^. The value of p,,, as de- 

 duced from this proportion, is 214. 2^^, which is about ^j of one per cent, 

 less than the British Nautical Almanac estimate. This is only ^i? as great 

 as the mean accidental deviation (Note 288). 



349. Modifications of Harmonic Planetary Masses. 



The approximations of Note 342 are more closely connected than those 

 of Note 328, and indicate a simpler bond of harmony. Among the various 

 harmonic influences which may be presumed to have modified planetary 

 masses and to be represented in their liarmonic motions, are the following : 

 (1). Tlie fundamental velocity of Note 321, which was first indicated by 

 my barometric investigations {Proc. Am Phil. Soc, ix, 283-8). (2). Centres 

 of linear, spherical and explosive oscillation (lb., xii, 392-4, 411-7 ; etal.). 

 (3). The acquisition of nebula-rupturing velocities, by subsidence from 



nr to ~ I ~i {lb- xii, 518-22). (4). Tendency to rupture in the periphery 

 of a stationary nebula, at 2/- --- (3 — 1 «] {lb. xvii, 98-99). (5). Belt- 



' Instead of " minor axis of j/Sr " read " minor axis of v^ar." 



