Chase.] 606 [April 18, 
The linkage of Earth and Uranus, Note 442, gives the following loga- 
rithms : 
865.2565 2.5625979 67 
338.2183 2.5291971 68 
(67 — 68) 1.07994 0384008 69 
459, Moon's Mass and Harth’s Hecentricity. 
The harmonies of lunar mass and Karth’s orbital eccentricity (Notes 
431-3) introduce the following logarithms : 
n 4971499 10 
7989 8.902492 val 
20000000 7.8010300 12 
(70 97 — 99) 0012549 B.0986128 713 
~~ (78) 2.9013877 "4 
(74) — 2 (70) 80.74 1.9070879 15 
43082.04 = ty 4.6842963 716 
(44) + 2 (76) — 2 (70) 6.6579983 11 
(55 — 77) 80.957 1.9082566 78 
81.957 1.9135861 719 
(44 +. 76) 2.4180018 80 
2 (80) + (78) — 2 (56) — (79) T.9686987 81 
460. Series of Harmonie Hquations. 
The harmonic analogy between the Neptune-Uranus and the Mars- 
Mercury belts may be still further extended by the following equations, 
which enable us to deduce all the masses of the primary planets from the 
harmonic value of the mass at the chief centre of condensation : 
0, m 
j= tr a 
Be Soh hia res i B 
ta + = eh - Ms ne 
— /) NY 
7 (1 + €3) (Mg -+ M,) = Mz n) 
7? (1m, ++ mm) = my, + Mz € 
ps! > pr = ohio - m5 § 
My M, My, = m,* ut) 
A pm) + mo ¢ 
Pa Ps = m,? + m,? 
461. Haplanation. 
In the foregoing note g = gravitating acceleration of any mass m, at 
any distance 7, provided m and 7 are expressed in units of Sun’s mass and 
semi-diameter ; 0, == velocity of light ; ¢ = time of solar half-rotation ; n= 
solar gravitating acceleration at Harth’s mean radius vector (p3)3 tg = 
time of theoretical satellite rotation at Barth’s equatorial surface 
ion 
