VELOCITY.— I. 765 
why not inquire with what motion a mass would strike the sun that had fallen 
from an infinite, distance, or what is the same, had been falling forever ! This 
motion can be readily computed because the intensity of solar gravity is known, 
and it is also known what gravity is required to evolve any given rate of motion. 
Terminal velocity must have a limit even if the mass fell an infinite distance, 
since no force can exceed itself, an expression which may be given thus: — the 
attraction of the sun cannot cause greater velocity than it is able — if such state- 
ments fall within any rule of logic. The utmost motion that can be imparted 
by the sun to a body reaching its surface is equal to the square root of the pro- 
duct of twice the sun's gravity multiplied by its radius. Twice gravity= 
.i6927X2=.33854X433j 197=146,682 whose square root=382. 95607 miles= 
2,022,008 feet per second. It is with this appalling velocity that a cosmic mass 
will strike the sun on arrival from infinite distance ! 
This is one of the most important constants discovered by astronomers ; by 
its use, many problem wherein gravity, space and motion are factors can be 
solved without extended computation, and in this note it will be made equal 
toG. 
Having found final velocity from infinite distance, it is easy to determine 
terminal motion from finite distance. 
From finite, — the velocity is equal to G multiplied by the square root of the 
quotient obtained by dividing twice the distance less i, by twice the distance. 
This comes from the fact that the velocity of a body approaching the sun is at 
any instant equal to a constant velocity multiplied by the square root of the space 
fallen through, divided by the square root of the distance between the body and 
the centre of the sun. Let us find velocities of collision with the sun of masses 
that fall from several finite distances. We will call these distances r, and express 
them all in terms of the solar radius. 
Take r=i, that is — a distance=the sun's radius or 433,197 miles from its 
surface. From the formula we have — square root of twice i less i divided by 
twice i^square root of 1-^2=. 7071065X^=270. 79 miles=i,429, 776 feet per 
second. That is, a stone taken into space a distance equal to the radius of the 
sun and let fall will strike the sun with this velocity. But 382.956o7-=-27o. 78^ 
1. 4142 13 which is an important number because it is the square root of 2. We have 
arrived at the fact that, — velocity of fall from infinite space, is to velocity of fall 
from a distance equal to the radius of the sun, as the square root of 2 is to i ; 
i. e. as 1. 4142 13 is to i — only 40 per cent greater. This 270:79 miles velocity 
seems to possess peculiar properties ; and the thought arises, may it not be found 
by other processes? Making trial we find that 433, i97X- 16927=73330 whose 
square root=27o. 79 miles. 
But, here we multiplied the radius of the sun by the force of gravity and 
secured the same result by taking the square root of the product. From mechan- 
ics, we know that the radius of a revolving sphere multiplied by the intensity of 
gravity on its surface, equals the square of the velocity with which its equator 
must revolve in order that centrifugal tendency generated by such velocity of 
