581 



336. Mean Harmonic EHtimate of Saturn's Mass. 



[Chase. 



"We have seen in Note 326, that in some harmonic approximations the most 

 satisfactory results are reached, as in the foregoing note, by adding satellite 

 or subordinate masses to their primaries, -while in other cases it seems best 

 to consider the primary mass alone. The choice of methods, in any in- 

 stance, may be governed by considerations of static or kinetic equilibrium, 

 instantaneous or progressive action, primitive or subsequent conditions, or 

 other relations which may be unfolded by a more minute study of har- 

 monic astronomy, If we substitute the rotary estimate of Note 313, (m^ 

 H- mg — 330463) in Note 335, we get w„ -r- «?„ = 3500.62. Combining 

 this value with the two whic^ are given in Note 314, we find an exact 

 mean accordance with Bessel's estimate, as follows : 



From central primitive nucleation, 3500.62 



final " 3522.33 



" nucleation, condensation, nebulosity and inertia, 3481.86 



Arithmetical Mean, 3501.60 



337. Inner Limit of Saturn's Preponderating Influence. 



The two foregoing notes regard all the intra-asteroidal planets as in 

 some sense satellites of Jupiter, which have been made planetary by the 

 superior attraction of the Sun, somewhat as our Moon is both a solar planet 

 and a terrestrial satellite. It may be asked whether Saturn's attraction 

 when in opposition to Jupiter, is not sufficient to invalidate this hy- 

 pothesis. Jupiter's mass being 3.3415 times as great as Saturn's, the ex- 

 tent of its equal gravitating disturbance is |/3.3415 = 1.828 times as great. 

 Saturn's relative disturbance of intra-Jovian matter is greatest when Saturn 

 is at secular perihelion (8.734451^3) and Jupiter is in opposition, at secular 

 aphelion (5.519271^.,). The limit of equal attraction is then at |f|| of 

 14.253722/,, = 9.2134/>3 from Jupiter, or 3.6941/,., from Sun, on the side 

 towards Saturn, so that it includes all the orbits of the dense planets, and 

 nearly all of the asteroidal belt. This fact gives new meaning to Notes 

 330 and 334. 



338. More About Comet Wells. 



Notes 295 and 302 illustrate the probable formation of spectral bands by 

 the combination of different harmonic tendencies, as well as the precision 

 of delicate measurements by a skillful observer and accuracy of judgment 

 in estimating the centres of ma.ximum brilliancy. It is, therefore, not un- 

 likely that careful study may discover successive evidences of phyllotactic 

 and other harmonic influences, as was the case in investigating atomic 

 phyllotaxy. If we take the difference between lines a and e in the Wells' 

 spectrum (Note 295 ; 4769 — 4253 = 516), the phyllotactic numbers 2, 3, 5, 

 13, 34, serve in the following sub-multiples ; f of ^g of 516 = 31.754 ; 3 X 

 31.754 = 95.262 ; 4 X 31.754 =127.015 ; 5 X 31.754 = 158.769 ; * X i X 

 II of 516 = 134.954. These numbers give the following accordance : 



