and Results of Harmonic Motion. 195 
3 erst 
go+n(=-) = V7 9opo = Yo = radial velocity acquired by 
falling from p, to the centre of a homogeneous nebular 
sphere = self-sustained velocity at surface of the sphere 
(= 269-42 miles per sec. at Sun’s surface) =269°42 x 
11011227 miles in ¢,. 
ete (Om: \ P : d 
es 5(s-) =v,= simple harmonic radial component 
of stellar equatorial velocity of rotation (=*7826 mile 
per sec. for our Sun) =2p)+7 in &. 
The cumulative influence of mean luminous undulation and 
solar action is shown by the proportions 
° 48 ee ripall 
Up e Vo ee Vo e 2VdAy 
CO ae 
In the second of these proportions v, is parabolic velocity, 
or velocity acquired by infinite fall, at Sun’s surface. 
In studying planetary harmonies, regard should be paid to 
the following cyclical tendencies:— 
_ t, oc (d)? in simple oscillation under a constant force. 
t, a d in cyclical motions which are immediately determined 
by luminous undulation, or by other constant velocities. 
t; oc d? in different orbits, under different original forces of 
projection but with the same central force. 
t, « d” in arotating and uniformly expanding or contracting 
nucleus. 
If d in each instance is equivalent to the Kantian limit (p,), 
and if the mean density of the rotating mass is represented by 64, 
Ii, 1\3 
eth | Seb), 
1\3 1\3 
to «(5) 3 ty (5) ° 
If the mean density of Harth’s Kantian rotation is taken as 
the unit, the corresponding reciprocals of density for Sun and 
for the several planets, except Neptune, are nearly as follows:— 
SIH cede cesacees 649°800 Mars tescceaee 1:053 
Mercury ..... ele 20 Jupiter ...... “L271 
IPOH US: Sceicces ce 1:031 SPhaligal | eeBeee 182 
