194 Dr. P. EH. Chase on some Principles 
act, whether by constant, successive, or undulatory pressures, 
thrusts or pulls, all of its results may be accounted for on the 
hypothesis of successive instantaneous impulses. The entire 
accelerating force gt is always exerted, but a portion is usually 
counteracted by opposing resistances or momenta, Suppose, 
for example, three bodies in a vacuum—A falling freely for a 
second, B suspended from a string between cycloidal arcs so 
that its centre of oscillation is 3 of 32°08 feet from the point 
of suspension, C sliding on a frictionless plane in which 
h:l::1:a*. A will fall 16°04 feet, while B swings once 
and C slides 16:04 feet, falling through a height equivalent to 
one half the length of the pendulum. 
The choice of a second as the unit of time is altogether 
arbitrary. The desirability of a natural unit has often been 
felt and expressed. Maxwell suggested, as a suitable unit, 
the interval of some particular luminous wave-length. At 
the surface of a stellar nucleus, where gravity is a maximum, 
where the time of rotary oscillation can be linked with all 
possible times of revolution by simple formulas of harmonic 
vibration, and where a universal gravitating unit can be 
readily framed from the units of mass and density, the velo- 
city gt, which is indicated both by the gravitating and by 
the ethereal unit*, may properly be regarded as a fundamental 
velocity. 
It is at present impossible to test the oscillatcry velocities 
in remote stellar systems ; but as the considerations on which 
they are based are universal, there are good grounds for 
believing that their influence is equally universal, so that 
gt=, at every stellar surface. In the solar system we find 
t= 1101227 sec. = oscillatory unit of time = one half solar 
rotation. 
2 4 
0,1 pp (F) r0 = unit of gravitating acceleration in 
unit of time at px. 
2\ 4 
= n(=) po = unit of gravitating acceleration at pp in 
oscillatory unit of time = y, in oscillatory unit of time 
= solar modulus of light (=185505 miles per sec.) 
= 185505 x 1101227 miles = (688°54)"pp. 
* The time of virtual fall through one half homogeneous ethereal 
atmosphere. 
