Mineral Point tribune. (Mineral Point, Wis.) 1869-1938, 1888-04-05

itself is blowlng-as matter OF fact,
ii will travel much more slowly. If,
on the other hand, the ship is sailing
AT an angle with the wind. it seems at
tirst sight the wind must act with less
effect than before, and tie ship in
consequence, sail more slowly still.
But as Il matter Of fact, the ship not
only sails more quickly than before,
but more quickly than tho wind itself
Is blowing This is "a paradox which
few. even Of those Tho are W II ac-
1uaintcd by experience With the fact
nave found themselves able TO ex-
plain.
Let us consider the difficulties in the
light Of the following experiment.:
Place a bali at one side of billiard
table, and with the long cue held
lengthwise, from end TO end of the Ia
BILE, push the bali across the cloth.
The cue mere represents the wind and
the ball the ship sailing directly before
it; only as there is here no waste of
energy, which in the case Of the wind
and ship is very great, the ball Of
course travels at the same rate as the
cue-evidently it can not travel faster
Now, suppose a groove be cut diagon-
ally across the table from one corner
pocket to the other, in which the ball
may roll. If the ball be now placed
at one end Of the groove, and the cue
held horizontally and moved forward
as before, Che ball VIII travel along
the groove (and along the cue) in the
same time as the cue takes TO move
across the table. This is the case of
the ship sailing at an angle with the
direction of the wind. The groove is
considerably longer than the width of
the table, more than double as long,iu
fact. The bali therefore travels mucJ
faster than the cue which impels 10,
since IL covers more than double the
distance in the same time. II is in
precisely the same manner that
lacking ship is enabled to sail faster
than the wind.
The foregoing mysteries of motion
bring to mind the famous paradox Of
Reno, by which he sought to prove
that ali motion is impossible. "a
body" thus argued the ingenious
philosopher, "mu5t move either in the
place where ID rs, or Id the place where
tits not Now, a body in q place
whore ii is stationary, can not be i'm
motion; nor, obviously, can it be in
motion i'm the place where it is not.
Therefore, il can not move at all, 1t
was Of this paradox it was said.
sotgitHr aulJutaHdo-''lt is solved by
walking A more practical solution
could hardly be required.
Another paradox familiar TO the
Greeks-tuat Of Achilles and the tor
toise-is we'll known. Achilles (tne
swift footed allows the tortoise a
hundred yards start, aud runs ten
wards while the tortoise runs one.
Now, when Achilles has run a hum
bred yards the tortoise has run ten
! Yards, and is therefore still that dis
/ lance ahead. When Achilles has run
/ these ten yards, the tortoise has run
one yard. When Achilles has run
one ward, the tortoise has run one
tenth of yard And when Achilles
1 has run the one-tenth of yard the
| tortoise has run one-hundredth. 1t is
only necessary to continue the same
/ process of reasoning TO prove that
Achilles can never oyertake the tor
toise
A much better paradox, though
of the same kind. runs as follows:
! "A man who owes shilling, proceeds
| to pay it at the rate of siXpenee the
| first day, thrcepence the next, three
halfpcncc the next, three farthings the
next, and so ou-payiug each day half
the amount he paid the day before.
/ Surprising him to be furnished with
counters of small value, SO as to be
! able readily topaz fractions of a penny,
/ how long would it take him to pay tine
! shilliugp' The answer is that he
viii never pay it. 1t is true that he
! will pay elcyen-pence-farthing in four
days, but the remaining three farth-
ings he can never pay.
This paradox varies from the pre-
oeding in one important particular,
and deserves to be called better par
dox for this reason, that we know
| Achilles, in spite of all reasoning, will
certainly oycrtake the tortoise. But
/ it is mathematically demonstrable that
! the debtor, under such circum-
stances, can never pay his shilling,
even though he should be cudQed, like
/ Iithonus, with the Gift of immortality.
The following is a really excellent
paradox "A train starts daily from
SAN Francisco to New York, and one
/ daily from New York To San Francisco,
. The Journey lasting seven days. How
many trains will a traveller meet i'm
iourueyjug from san Francisco TO
New York;
1t appears obvious at the first glance