Chase. ] 304 (Jan. 18, 
system, as well as in the group of densest planets, the number 3, which 
represents the uneven harmonics of an organ-pipe, as well as the oscilla- 
tory divisions of a linear pendulum, holdsa prominent place. For we find, 
at the outset, the following approximations to important nebular centres : 
3° — 9? —— 6061 6518 = Neptune’s secular aphelion. 
3° 2187 2222  Saturn’s secular aphelion. 
Soa os 729 735 Cybele. 
3° 243 229  Earth’s secular aphelion. 
Sato: 81 83 Mercury. 
3° 27 
3H 9 
3l 3 4 
ay ty il 1  Sun’s semi-diameter. 
This accordance is the more significant, because Saturn’s secular aphelion 
is at the centre of the ring of secondary condensation, which extends from 
Sun’s surface to Uranus’s secular aphelion. 
““Bode’s Law,’’ was based on successive differences of 2° x 3, 2! x 3, 
2? x 38, ete. If we substract 1 from each of the theoretical Bode numbers, 
and divide the remainders by 3, the quotients are 1, 2, 3, 5, 9, 17, ete., 
each of the quotients, except those for Venus and Neptune, being of the 
form dn +1= 2 dn —1 ; the dense-belt series being of the form dn +1 = 3 
dn — 1. 
In the infinite series, } + 3—% +3—¢+14.,..38—-1-+4 394 3143? 
+ ..., successive sums, in the neighborhood of unity, give the following 
accordances : 
Harmonic 
Sums. Divisors. Quotients. Observed. 
4 = 4 27.38 27.00 = 8°. 
+-—o—eo 
=, 
ab 5 : ‘ : 
+3—4 45 26.40 26.20 Extreme major-axis. 
+3—8 3 24.64 24.39 Mean major-axis. 
+3—2 3 20.538 20.68 Extreme secondary radius. 
+3-1 1 13.69 13.69 Nebular radius. 
+ 3° 2 6.85 6.85 Deimus. 
+ 3! 5 2.74. 2.73 Phobus. 
+ 3? 14 .98 1.00 Semi-diameter of Mars. 
+ 33 41 89 .38 Oscillatory centre. 
+ 3+ 122 120.56 Moon’s major-axis. 
+ 3° 365 365.26 Terrestrial acceleration. 
+ 3° 1094 1096.20 Jupiter’s semi-major-axis. 
The ‘‘ Extreme major-axis’’ is the major-axis of an ellipse, connecting 
the inner planets of the two outer two-planet belts at the secular aphelia of 
Uranus and Jupiter ; the ‘‘ Mean major-axis’’ is the sum of the mean dis- 
