VELOCITY,— I. 767 
ersed. Because gravity varies inversely as the squares of distances, a limit is 
reached where increase of distance fails to have effect in accelerating terminal 
velocity. That limit as may be seen is a distance equal to about 1,000,000 solar 
radii, for an increase of 9,000,000 radii adds only one foot per second to terminal 
motion. If a mass be let fall at a distance of 20,000,000, it will reach the sun 
with the same velocity within a fraction of a foot per second as though dropped 
at a distance of 10,000,000 radii of the sun. 
This is clear — for if 2,022,008 be multiplied by .99999999 the product is 
equal to itself; no change being produced in the product if we increase the 
number of .9s to infinity. This is equivalent to the assertion that i is the limit- 
ing velocity of fall on the sun i. e. 382.95607 becomes i ; from the principle that 
any constant can be made unity. We make the solar constant equal to one, 
when column III gives less velocities in regular progression. 
In the table— 2i4r, is the earth's distance, hence, a mass falling on the sun 
from a distance equal to that of our world will strike it with a velocity only 361 
feet less than if it had fallen from an infinite distance. 
The distance 644or, is that of Neptune, whence, a mass will dash on the sun 
with but 87 feet less velocity than if it had been falling forever; while 20,000,- 
ooor, or in round numbers 10 trillion miles, represents half the distance to 
Alpha Centauri the nearest star. A stone let fall at a distance from the sun of 
10 trillion miles will plunge into its fiery wastes with the same velocity it would 
have acquired had it been falling since the universe was made. Gravity at any 
distance from the surface of a sphere is equal to gravity on its surface divided 
by the square of the given distance. Since we expressed solar gravity in terms 
of velocity i. e. 893.75 feet or 10,725 inches per second, we can find the velocity 
of a falling body at any distance at the end of the first second of its fall. If we 
square 20,000,000 and divide 10,725 inches by the square, the quotient will be 
.0000000000268 of an inch per second velocity that a falling body will acquire 
at the close of one second at a distance of 10 trillion miles, a velocity such that 
a mass moving at that rate will require 1,182 years to fall i inch. In these 
researches we find velocity infinitely slow and rapid. If we make the limit of 
distance one-half that to the nearest sun, then initial and terminal motion will lie 
within the limits of .0000000000268 inch and 382.95607 miles per second. And 
it is by such calculations as these that we hope to learn something of the sidereal 
structure. We have considered the most simple variety of motion — that on a 
straight line ; but before we can comprehend all is in the great subject of velocity 
we must make computation of other modes of motion, such as that displayed on 
ellipses, parabolas and hyperbolas. 
New Windsor, III., March 13, 1884. 
