1S82.] 413 [Chase, 



length of a theoretical pendulum, at the stellar equatorial surface, which 



would swing synchronously with the rotary oscillations ; </ = — =^ ~^. 



The value of g determines the mean orbital velocity, i/gr^, for any semi- 

 axis major, r^^. 



2. The actions and reactions, between the stellar centre and the primary 

 centre of planetary condensation (Note 23), involve tendencies towards 

 the linear centre of gravity Q), the centre of linear oscillation (|), the cen- 

 tre of conical oscillation, (i), and centripetal accelerations which vary as 

 the fourth power of the velocity of circular orbital revolution. These ten- 

 dencies may all be satisfied by a stellar mass which is (2 x 3 x 4)* = 331- 

 776 times the mass of primary condensation. 



3. The orbital control of the stellar centre is exercised on the planet and 

 satellite alike, at the mean distance p.^. If the planet transfers to the satel- 

 lite a projectile vis mm, II), corresponding to its superficial energy of rota- 

 tion (Note 246), the relative masses of the planet and satellite, which satisfy 

 their joint oscillatory relations and Sun's projectile energy, may be repre- 

 sented by the proportion ; 



o, :l::m.,: n. 



There are other harmonic tendencies which seem likely to have been less 

 permanent and more open to modification. The following instances of 

 primitive tendency may be given as interesting : 



4. The radii of static equlibrium are inversely as the masses ; rupturing 

 vis viva is acquired by subsidence through -^ radius ; if the rupturing locus 

 of simple subsidence becomes a centre of linear oscillation for satellite 

 semi-axis major, ^, we have 



p^:r^::i m^ : 2 ,j, 



5. The relations of scthereal density are found by the method of Note 

 240. 



Notes 162, 23, and 246 give the following mass values which precisely 

 satisfy the first three of these requirements, viz : m^ ■== 331,776 m^ ; m^ =^ 

 81.186 /jf. The fourth requirement points to the valile, m^ = 80.872 ,j.. 

 This slight discrepancy may, perhaps, be partly owing to the fact that 

 Earth's oscillation is mainly rotational while Moon's is nearly that of s 

 circular pendulum. 



256. Other Approximations to Moo/i's Mass. 



a. The formula, mf oc p^, gives the following approximations to the 

 value oi p.: (1 year h- 1 lunar mo.)^ = 178.724 ; {p,^ h- p^f = 58,609,000 ; 

 (TO„ + m^) = 827,980 (m^ + ;j.) = 831,777 m^;m^ = 86.241 ;/. 



b. A close harmonic approximation is given by the proportion : 



m., : p : ■.Qt.-.t : : 2191.54 dy : 27.32166 dy : : 80.214 : 1. 



