Evening star., 1896-11-27
At THE EARTH'S CENTER
What Would Become Of Hundred Pound
Ball.
Star Correspondent Argue the Point
The Question of Momentum
and Weight.

A number Of communications have been
received in continuation of the discussion
as to the action of an iron ball at the GEN.
ter of the earth. E. L. F. writes:
'The most amusing conclusion is that of
Mr.. Lightbourn, who states that it would
remain suspended at the center in a state
of rest, until crowded out Of position by
some heavier mass! 1t might be interesting
II Mr.. Lghtbourn would tell US which
would be a heavier mass at the center Of
the earth, an iron ball ball of yarn?'
Another writes: I'VE must eliminate from
the question everything that may appear
as incidental. This, of course, would rule
out Mr.. Lightbourn's idea in reference to
the hole filling up with the atmosphere,
and Its sequence. Because if we once COM
mence on incidentals, the next thing we
would be treated to would be cave In,
here and there, and the hole would be filled
up before the ball would be fairly in mo-
ton. But would the ball rest when it
reached the earth's center? Assuredly not
The center Of the ball would become, for
the part OF space 1t would occupy, the CEN
ter OF the earth's axis, and instead of being
In state of inertia. would really be turn.
ing around from west to east, slowly; once
In twenty-four hours. In perfect harmony
with the diurnal motion Of the earth upon
its axis.
WOuIu DBy IuEtQer tndt IL IS Impossible,
In view OF the law of physics, which this
question Is supposed to illustrate, to agree
with the solution as given by X. Y. H., be-
cause 1t Is more or less contradictory. His
deductions are certainly not reasonable,
and have not harmonious relation the
one to the other. Ii the greatest weight of
the ball was when 1t arrived at the center
or plane of the horizon which divides the
earth longitudinally into two equal hemis-
pheres, then its velocity would also be at
Its maximum, and 1t would be- as s. S. h.
says, a-going all the time, theory not In
accordance with the law of gravita ton or
attraction, no matter how specious the ar
grments may be on those lines"
Another correspondent states:
"All the previous explanations seem to
have flaws. 1t Is true that for bodies above
the surface OF the earth the attrac ton de-
creases as the square Of the distance from
the center. But this law does not apply to
bodies below the surface. In this case the
attraction diminishes approximately. as the
distance from the center. That is. a body
1000 miles from the center would weigh
approximately one-half as much as it did
at the surface. and consequently at the
center would have no weight and no on
force Of attraction tends to always in
crease the velocity, the same would in
crease continually until the body reached
the center. But increase of velocity should
not be confused with increase of accelera-
tfon or the rate Of increasing velocity. This
rate Is constantly diminishing all the way
from the surface to the center, or. in other
words. the velocity is increasing more
slowly. When the body passes the center
1t has its greatest velocity. but no increase
In velocity or acceleration. and from that
point on the acceleration is negative. and
the velocity decreasing, until 1t reaches the
opposite surface. where 1t Is zero. If al
lowed to start back again. the same laws
would apply. until 1t reached the point
from which 1t first started. and would con-
tinue to SO vibrate.
THE above Is thought of as taking place
In vacuum. If air was present the body
would ultimately come to rest at the CEN
ter. the vibration becoming shorter and
shorter. This Is due to the fact that the
initial. or potential energy, has gradually
become converted through kenitic energy.
or energy of motion. into heat, by friction
with the atmosphere. Therefore, the body
comes to rest Just as pendulum stops
swinging
D. 8. contributes the following: Refer
ring to the communications which appeared
In last Tuesdays Star. questioning the cor
rectness OF the result given by 8. s. X as
to the motion of a 1O0-pound ball If drop
ped into hole through the center of the
earth, 1t appears to me that a very i'm
portant factor has not been considered by
those who do not agree with his deductions
1t Is assumed in what follows that the ball
Is 100 pounds at the surface and that at
the center 1t is without weight: that the
Dal. IS iree TO vfbrate in the hole from
surface to surface. and that the hole is a
perfect vacuum; then the only force to
operate on the ball in passing through the
earth Is gravity,
:. Placing Placing the ball into the hole, velocity
Is impaired to it by its weight, and, by the
laws OF falling bodies, this velocity is neces-
sarliy increased at every instant until il
reaches the center. where its velocity is
the greatest.
TO make this plain, suppose that the
distance between the surface and tn. CEN
ter Is divided into large number of eoua1
parts; then at the end of the first part it
i1ss,.;a.. mas attained certain velocity Now. II
gravity ceased at this point, the ball would
continue to move on in the same direction
ana with the same velocity it then had
because there is nothing to prevent it from
tha uoli,s o.nerwise. But though at this point
the weight OF the ball is slightly dimintsha1
through loss of gravitation, the force ~
that weight increases the velocity If al
Isaoy nad, ana so on until it has reached
tn'. me ,ast h part. where 1t has almost ceased,
1ut mere, 1t Is important to observe thai If
yet mas definite weight, giving it a1di.
tlonal velocity, and, therefore. has tho
greatest velocity at the center.
In examining this subject, the question
naturally arises, Can the bali, In its nsss-
age through the center of the earth ha~e
momentum where, If deprived of its ve.
iocity. 1t would evidently be without
weight! II 1t has momentum then it must
De because OF its velocity and mass
Taking another view Of tho rnat+o :.
may be supposed that from a certain MINT
IN the descent of the ball to the center its
veioclty IS gradually diminished. and that
when 1t has reached the center n conas -
rest, but. since this view is contrarv to +ho
l Jaw OF falling bodies. it does not appear to
The result arrived at above amounts to
s onis' .nat tne ball has its greatest velocity
ana momentum at the center. and that
with gradually decreasing velocity from
the center. it must continue to ascend IN.
til 1t reaches the opposite surface. where II
comes 10 rest; then returns on its course.
kQanQ VII hrof
that gravity does not destroy or otherwise
interfere with the momentum of matter
In motion. where. if at rest, it would he
1T would be very satisfactory r. Tho r,,.. nc.
wa was decided by some person competent to
BEATING THE BANK.