1884,] 607 (Chase, 
Ue) 
2 aN Tite 
Ys’ 
tricity ; py’ = Neptune’s mean secular aphelion ; p; to ps == Mean vector 
a sidereal day ; ¢; = Neptune’s minimum secular eccen- 
radii and m2, to mg == masses of the eight primary planets, 
The equations represent various obvious radial and tangential actions 
and reactions. Equation (1), when applied at the Sun’s surface, which 
is the point of greatest gravitating acceleration in the solar system, gives 
gt=. This satisfies Ohm’s law, as applied to solar rotation in a mag- 
netic field, Fourier’s theorem, Laplace’s principle of periodicity, and the 
projectile velocity which balances ethereal resistance at Sun’s surface. 
The actions and reactions of centripetal gravitation and centrifugal radia- 
tion are thus codrdinated in such ways as to give simple forms of expression 
for all kinetic correlations. Equations (4) and (5) represent similar tan- 
gential tendencies to belt formation by the vis viva of primitive tangential 
motion, both at the outer limits of the solar system and at the outer limits 
of the belt of greatest condensation, Equation (2) represents a harmonic 
relation of tangential velocities, at the chief nucleal centre and at the 
chief centre of condensation, This equation satisfies Laplace’s demon- 
stration of the tendency to exactness in simple numerical relations. It 
also satisfies various tendencies of subsidence as well as of linear and of 
rotary inertia, Equation (9) gives harmonic tangential velocities to the 
two interior companion masses, in the belt of greatest condensation. 
EKquations (6), (7) and (8) represent radial and belt-rupturing tendencies 
of simple subsidence. In the mutual interactions of gravitating subsi- 
dence the sums of the gravitating accelerations, along mutually connect- 
my 
ing lines, vary as the respective masses ; therefore “9°, or the wis viva of 
subsidence, varies as m%. Equation (3) represents harmonic interactions 
between the centre of primitive subsidence (m,) and the chief centre of 
condensation (m,). The importance of these interactions is still further 
exemplified by the fact that (tg + tq)? = Harth’s oblateness according to 
Listing’s estimate (Note 440). This accordance seems calculated to throw 
great doubt upon Delaunay’s hypothesis of retardation by the ‘tidal 
brake.’’ 
462. Deduced Values. 
The following harmonic values satisfy the equations of Note 460. Some 
of the latest astronomic estimates are also given, in order to show the 
closeness of accordance : 
Harmonic. Astronomical, j 
My + ™ 4527977 4512885 Encke. 
Mo “- My 887066 896256 Hill. 
My -- Mg 829196 829161 Faye. 
My i My 2867780 2869157 Hall. 
My -- Ms 1049.4 1050 Leverrier. 
9 
PROC, AMER. PHILOS. $0c, xxi. 116, 8Y. PRINTED JULY 381, 1884. 
