Chase.] 434: [Oct. 



By taking the rotating locus of the linear centre of oscillation, for La- 

 place's terrestrial limit, I, we find that the velocity of rotation at | Us vir- 

 tually identical with Moon's mean velocity of revolution. Let^^?;?"^; 



then t^ = 2W7''- = 8G164.1 seconds ; n = 6.60704 ; ^ I = 2.20235r, ; 



velocity of rotation at | Zr= 4.40469 ^r^ per sidereal day, or 4.41675 -i\ 

 per mean solar day. If this is Moon's mean orbital velocity, the circum- 

 ference of her orbit is (27.321661 X 4.41675 = 120.673) ^?v Moon's or- 

 bital eccentricity being .0549081, her orbit is .999246 X 2 "a and « = 60. 382 

 ?■.<,. Proctor's estimate is 60.263 7-3 ; Littrow's, 60.278 i\ ; Newcomb's 

 60.639 7-3. See, also, Note 296. 



295. Spectrum of Comet Wells. 

 Huggins {Nature, June 22, 1882, p. 179) gives a band spectrum, with 

 measured wave-lengths for the brightest portions. Its harmonies are 

 shown in the following comparisons : 



Hugsius. Divisors. Harmonic. 



,/. 4769 1 4769 



,i 4634 1 + a 4634.2 



;' 4507 1 + 2 « 4507.2 



,J ^ 4412 1 + 2i 4412.1 



e ~ 4253 1 + 3 ^* 4252.9 



i^-r ■■ r-^ : : 1 : 2 

 y_. : ,5_s : : 2 : 3 

 In other words, y is the centre of linear oscillation between £ and ;?. 

 Other phyllolactic approximations are indicated by the jiroportions : 

 8s : y-e : : 5 : 8 nearly, 

 ^-e :«-.:: 1 : 2 " 

 These several relations show a primitive phyllotactic tendency, which 

 is controlled and modified by y and the harmonic divisors. The follow- 

 ing values Avould exactly satisfy all the phyllotactic harmonies : 4760.71, 

 •4633.86, 4507, 4411.86, 4253.29. 



296. Harmonic Nebular Time-Integrals. 

 The second "photodynamic problem of three bodies," which is specially 

 implied in my three primitive time integrals (Notes 281-3), may be as- 

 sociated with the first through a harmonic relation which involves Moon's 

 orbital time (^5), Earth's rotation {to), Earth's superficial gravitating 

 acceleration {(j^)' and Sun's gravitating acceleration at the perihelion 

 centre of gravhy of Sun and Jupiter {rj^^). The relation is expressed by 

 the proportion. 



^ .3 ■ ta ■■ -.ffo- Oi 



Tlie resulting equation, //j^j = i/o<^, indicates two important harmonic 

 time-integrals, which seem much more likely to be permanent, than to be 



