192 Dr. P. H. Chase on some Principles 
stellar systems flow simply and naturally from the two fol- 
lowing important FACTS:— 
(1) The fundamental velocity in the solar system is the 
velocity of light. 
_ (2) This is not a merely accidental and temporary coinci- 
dence, but, according to the first proposition of Newton’s 
Principia, it must have existed, and must continue to exist, 
during all past and future stages of solar condensation. 
The first of these facts was discovered by investigating the 
tendencies to oscillatory nodal harmony in elastic media. It 
appears to be still regarded by some persons as merely curious 
‘ and without important significance. ‘This is, perhaps, because 
attention has been so often directed to the angular velocities 
in different orbits, which vary inversely as the 3 power of the 
mean distance, that the synchronous variability of angular 
velocity with the inverse square of the radius, in all the par- 
ticles of an expanding or contracting nebular nucleus, is 
forgotten or overlooked. 
We find in our stellar system three stages of material 
aggregation :—(1) A nucleus, probably consisting chiefly, if 
not entirely, of condensed gas, rotating in about 25°5 days. 
(2) An atmosphere of lighter gas, rotating synchronously 
with the nucleus, and therefore extending no further than 
Kant’s limit (p, = 36°35, py being Sun’s semidiameter). 
(3) A luminiferous ether which, if infinitely elastic, may be 
of infinite extent, but which would reach, if made homo- 
geneous, to 2210-74 times Earth’s mean distance from the Sun. 
If the Sun were homogeneous and unresisting, a particle 
would fall to its centre from its surface, or from any point 
within its surface, in 41°87 minutes, or in + of the time of 
free revolution at the surface (4 of ama | j = se / 7 The 
relation of radial oscillation to orbital revolution is therefore 
that of simple harmonic motion. ‘The velocity acquired by 
falling from the surface to the centre would be »/gr ; which 
is the same as would be acquired in falling from an infinite 
distance to 27, or from 2r to r, or in virtual fall through 47, 
or through one half the length of a cycloidal pendulum which 
would oscillate synchronously with circular orbital revolution 
at 7. It is also the velocity of wave-propagation in a homo- 
geneous elastic atmosphere of a depth equivalent to +. 
At all points within the nucleus the velocity acquired by 
fall to the centre would be preportional to the distance from 
the centre. Let us apply the principles which are here indi- 
cated to a stellar system like our own, with a nucleus so 
