1878. | 545 [Chase, 
semi-axis major. The importance of my introduction of various apsides 
into the study of planetary harmonies, has been fully recognized by Alex- 
ander, the Nestor of harmonic astronomy ; but in order to avoid all possi- 
ble cavil, I assume the probability that each quotient of M by z%,/7 is of 
2r +1 
the form p + (r or less) = ; r being the maximum tabular error, 
and the unit of comparison being .001 of Earth’s semi-axis major. This 
gives a probability of more than 26(10)1° to 1 in favor of the assumed 
laws of planetary formation, a probability which is immeasurably increased 
by a consideration cf the various phyllotactic, teleologic, oscillatory, elastic, 
centrifugal, and centripetal influences, which have been pointed out. 
The three cardinal planetary centres, viz.: the centre of greatest annular 
condensation, (@); the centre of planetary inertia, (bh ); and the centre of 
incipient solar specialization, (WV); lend interest to the following table : 
Tr To Pp == Po p (0), E. 
( 2.667 = 3¢ 000 
2.637 = of O11 
= o eee 2.614 — ae aby 020 
| 2.780 — lpia == ae 043 
Bt 3! 13.5007, 13.490 — 2? h, 001 
43 4! 42.667, 42,474 = 27 W, 005 
914.86—r, 214.86° 4608347,  46164.7 — 214.86? 002 
2049.51 2049.515  932262r, 947511 = 2M 016 
6453.06 6453.063 4302218r, 4263801 — 9M—[x*]-~2 .009 
This table represents theoretical stages of nebular condensation, based 
upon forces which are now operating within the solar system. 7) = pre- 
sent solar nucleal radius ; 7 = past nucleal radius ; 7, — Earth’s semi-axis 
major ; ) — present nebular radius; » = past nebular radius ; O = ob- 
served positions ; E — ratio of error, found by dividing the difference be- 
tween O and p, by p; [>] = stellar distance, with parallax 0./’89, which 
is of the same order as the distance of g Centauri; the last three numbers 
in the left hand column represent, respectively, the semi-axes major of 
Earth, Saturn, and Neptune. 
It is further worthy of note, that Earth’s position is a mean proportional 
between the nebular radius when Sun’s nucleus reached the Earth, and 
Sun’s present surface ; that the nebular radius of the Jupiter-nucleal Sun 
was nearly M, (.89 M) ; that the nebular radius of the Uranus-nucleal Sun 
was nearly 5 M, (4.996 M) ; and that M, when Sun was expanded to the 
outer portions of the asteroidal belt, was coincident with [>], the origin 
of the incipient condensation of the nebular radius of the Neptune-nucleal 
Sun. 
PROC. AMER. PHILOS. soc. xviI. 101. 2Q. PRINTED APRIL 29, 1878. 
