Idaho semi-weekly world. [volume] (Idaho City, Idaho Territory) 1875-1908, 1888-07-06

preceding enigma Oh the i"'i""y'
,roblem NAV safely be left to the ex-
animation Of the ingenious
(Which. of any given moment, Is
moving forward fastest, the top OF
coach-wheel or the bottomP 10 tins
apparently very simple question nine
persons out of ten, asked at random.
will give an incorrect reply. For at
first sight it appears evident hat both
The top and bottom Of The wheel must
of necessity be moving forward at The
same rate, namely, The speed at which
The carriage is travelling. b It little
thought will show that this is far fr IN
being the case. A point on the bot
tom of the wheel is, in fact, by the di-
rcction OF its motion round the axis.
moving backward. In an opposite d.
rection 10 that in which the carriage
is progressing. and is consequently
stationary in space; while a point on
the top Of the wheel is moving for
warI, with the double velocity of it
own motion round the axis and tn
speed at which the carriage moves.
Tho following paradox which has
given rise to much discussion, issome-
what akin to the preceding: How can
ship sail faster than the windP'
Every yachtsman knows that ship
can sail faster than the wind; that is
TO say. if the wind is blowing ten
knots an hour. a ship may be making
twelve or fifteen knots an hour. Now.
it is obvious that if the ship Is sailing
straight before the wind it can not. at
The utmost, travel faster than the
wind itself is blowing-as matter OF
fact, it will travel much more slowly.
II, on the other hand, the ship i, sail
ing at an angle with the wind, seems
At first sight that the wind must act
with less effect than before. and the
ship in consequence sail moro slowly
still. But, as matter of fact, the ship
not only sails more quickly than be-
fore, but more quickly than the wind
itself is blowing. This is paradox
which few. even of those who are well
acquainted by experience with the
fact, have found themselves able TO
explain.
Lot us consider the difficulty in the
light of the following experiments:
ri ce a ball at one side of billiard
table and with the long cue held
lengthwise from end to end of the
table. push the ball across the cloth.
The cue here represents the wind, and
the ball the ship sailing directly before
II; only as there is here no waste OF
energy, which in the case of the wind
and ship is very great. the ball, OF
cuc-cvidcntly it can not possibly
travel faster. NV. suppose groove
to be cut diagonally across the table
from one corner pocket to the other,
in which the ball may roll. II the
bal be now placed at one end of the
groove. and the cue held hor zontally
and moved forward as before. the bal
will 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 n
an angie with the direction of tn,
wind. The groove is considerable,
longer than the width of the table
more than double as long. in fact
The ball, therefore. travels much fast
or han the cue which impels IL, sine
it covers moro than double the dis
lance in the same time. 1t is in precise
| ly The same manner that tackins
ship is enabled to sail faster than tn,
wind.
The foregoing mysteries of motion
bring to mind the famous paradox o
Lsno, by which he sought TO prove tina
all motion is i'm possible. "A body. >
thus argues the ingenious philoso
pher. must move eithor in the plac
whore it is, or in the place where it i
no. Now, body in the place whcr,
1t is is stationary, and can not be il
lsoion; nor. obviously. can it be il
motion in the place where it is not
Therefore, it can not move at all. 2"
was of this paradox it was said. solvitu
ambulando-'.It is solved by walk
ing" A more practical solution coulC
hardly b required.
Another paradox familiar to tn
Greeks-tha of Achilles and the tor
toise--is well known. Achilles 9th
swift-foo,eO allows the tortoise
hundred yards start and runs te
wards while the tortoise runs one
Now. when Achilles has run hun
,lred yards the tortoise has run te
yards. and is, therefore. still that dis
lance aiead. When Achilles has I'll
these tea yards, the tortoise has ru
one yard. When Achilles has run tn
"ne yard; The tortoise has run one
tenth Of yard. And when Achillc
has run the one-tenth of yard IL
tortoise has run one-hundredth Il
only necessary to continue the san
process of reasoning to prove TIL;
Achilles can never overtake the to
tose.
A mach better paradox, thouo
somewhat OF the same kind. runs
follows: "A man. who owes shi
ling proceeds TO pay it at the rate
sixpence tho first day, threepence Il
uext day. three-halfpence the mex
three farlhings tho next and so on
paving each day half the amount
paid che day before Surprising hi
to be furnished with counters of sms
value. SO us to be able readily to p,
fractions of a penny, how long won
il take hin to pay the shillingp" ii
answer is, that lie would never pay
1t is true that he will pay clever
pence-farthiug in four lays. But Il
emaining three farthings no CT
meyer nav