and Results of Harmonic Motion. 193 
preponderating that its oscillatory tendencies are not mate- 
rially modified by the perturbations of attendant planets or 
companion stars. 
Within our solar nucleus all the tendencies to orbital revo- 
lution have been converted into constrained rotation, which 
shows a retardation by collision, subsidence-oscillations, &c., 
such that the velocity of every particle is only about =}, as 
great as that of free and self-sustained revolution. The con- 
tinual violent agitation of Sun’s mass indicates the probability 
of synchronous radial and tangential oscillations, which are 
dependent upon simple harmonic motions. The measure of 
gravitating acceleration for the oscillatory unit of time being 
— ua f , (& being the distance from the point of suspension 
to the centre of oscillation in a linear pendulum /), we have 
Sun’s semidiameter ( 
and the quotient of circular 
aim 
2 
orbital velocity by equatorial velocity of rotation 
2\ 2 
ee = (+) = 219-17. 
The principle of conservation of areas requires that the 
angular velocity should vary inversely as the square of radius, 
without the nucleus as well as within it, provided we look 
merely at the orbit of any given mass or particle, It is only 
when we compare different extra-nucleal orbits in the same 
system, each of which has its own original force of projection, 
that we find angular velocities varying inversely as the 3 
power of the mean distance. If the nucleus is expanding or 
Eemeuciing. the Kantian radius, p,, should, accordingly, vary 
as the 4 power of the nucleal radius, so that 
3 
pe= (FF a ) Po= 36°39 po. 
The free undulatory velocity at po, both radially and tan- 
gentially, is »/go79 The mean harmonic radial velocity of 
1 BOP): 
rotary exiation at the same point is — a of 33 "= as 
2 
great, or Ga 6885 fT as great as the fundamental velocity, or 
the gravitating acceleration in the fundamental Vet ak 
unit of time. 
As the idea of “ fundamental velocity ” will be new to many 
readers it may be well to explain it. In whatever way g may 
