1877.] 99 | Chase. 
nation will be the more interesting and suggestive, because like ten- 
dencies must exist in all central forces which vary inversely as the square of 
the distance. 
Ennis* has called attention to the fact, that the difference between the 
velocity of infinite radial fall G 2 gr) and circular-orbital velocity (V gr)s 
must be accounted for in some way, and he thinks that it may be 
sufficient to explain all the phenomena of planetary rotation and revolution. 
G : 4 tes 
In nebular condensation from 7 to ay the increase of radial velocity is 
——— qe — 
(/n — 1) Y 2 gr; the circular-orbital velocity at ial ‘ ngr; therefore the 
increase of radial velocity would be sufficient to produce orbital velocity 
in the periphery of a stationary nebula, when j/n = 7/2 (7/n —1), and 
2 
i) = $273 = 11.656854. If r be made torepresent, successively, all 
points between secular aphelion and secular perihelion, in the hypotheti- 
cal nebulous belts which were condensed into Neptune, Uranus, Saturn 
and Jupiter, this fall of condensation from Neptune would give orbital 
velocities in the asteroidal belt ; from Uranus, in the Mars belt ; from Saturn, 
in the Venus belt ; and from Jupiter, in the Mercury belt. Earth, as I 
have already shown, is at the centre of the primitive inter-asteroidal belt, 
which appears to have been then broken up by the action of Uranus, 
Saturn and Jupiter. 
Neptune, = i, SS Bay Astrea, ae EY 
Uranus) s:p¢= » = Lod’ Mars, S= 1150! 
Saturn, Ss. ps '- ge = W749 Venus, a., == i749 
Jupiter, s.a., = n = .A473 Mercury, $22.5 =) ANd 
This would leave the orbital velocities of the four outer planets to be 
accounted for by like condensation from an earlier nebulous condition, of 
which we have no visible evidence, but if the main hypothesis is correct, 
we may reasonably look for confirmation of a different kind, within the 
present limits of the solar system. If we consider the v/s viva of orbital 
and radial velocity for unit of mass, the v. v. added by radial fall from 7 to 
r ‘ : P 
ai is (m —1) gr, while the v. v. added by equivalent orbital contraction 
is only $ (m — 1) g7, or one-half of the radial addition. A simple nebular 
, 
2 
condensation from 7 to would, therefore, add gr to the v. v., which is 
Y 
7 
equivalent to the ». ». of circular-orbital revolution at >. There is, there- 
~ 
tg! cop r 
fore, a tendency to repeated nebular ruptures at O £2? B °f°* on 
Starting from the present outer limit of our system, Neptune’s secular 
** Origin ofthe Stars.” 
ta., aphelion; p., perihelion ; s., secular, 
