Chase.) 598 {April 18, 
ference between his perihelion radius vector and the corresponding har- 
monic radius is less than 7, of one per cent. 
434, Correction for Secular Hecentricity. 
In Note 428, Sun’s distance was estimated upon the hypothesis that 
Earth’s orbit was circular. The mean distance, however, may be con- 
sidered as having been established at the time of original rupturing pro- 
jection, or, in other words, at secular perihelion. The circumference of an 
uh 1a Nit all, 
ellipse is 2 z a (1 — 7? — orp et — 5242. G ef, ete.) 
Substituting the theoretical value e = .06954, this becomes 2 z a X 
.99879. The corresponding value of Harth’s mean radius vector is 
92430800 -+- .99879 = 92542790, which differs by less than ?y of one per 
cent, from the value which was deduced in Note 426, from the incipient 
subsidence of Jupiter. The corresponding value of m, + mg is 829196. 
435. Twin Planets. 
Action and reaction, in a system which is fundamentally dependent 
upon two largely preponderating bodies, may naturally lead to a grouping 
in pairs. Laplace’s modification of the nebular hypothesis, which supposes 
that the first ruptures are in the form of rings or belts, and Herschel’s hy- 
pothesis of subsidence until the acquired velocity becomes rupturing, also 
favor the simultaneous formation of companion perihelion and aphelion 
planets. Accordingly, we find two supra-asteroidal groups, Neptune- 
Uranus, Jupiter-Saturn, and two infra-asteroidal, Mars-Mercury, Earth- 
Venus. The grouping in the belt of greatest condensation indicates a 
double tendency ; Earth-Venus representing influences which appear to 
have orignated in the Sun, while Mars-Mercury seem to be more specially 
referable to activities at the centre of condensation, than to those at the 
centre of nucleation. 
436. Mass Relation of Jupiter and Saturn. 
The discovery, by Prof. Stephen Alexander, that the masses of Jupiter 
and Saturn are nearly in the inverse ratio of the squares of their mean 
vector-radii, was the first step towards a demonstration of the fundamental 
principles of harmonic astronomy. This ratio represents the moments of 
sethereal or nebular rotary inertia for the two planets, respectively. The 
closeness of the approximation is shown by the proportion 
5.202798? : 9.53852? ; : 104.879 : 3522.3. 
Hall’s estimate of Sun -- by Saturn is 3482; Bessel’s 3501.6; Lever- 
rier’s 3512. The greatest difference between either of these estimates and 
Alexander’s approximation, is only about 1} per cent, the least difference 
is less than + of one per cent. I know of no other mass-approximations 
which rest upon purely rhythmical laws, except my own. 
