Oxford Democrat. [volume] (Paris, Me.) 1833-1933, 1888-01-24

wi,h the lcng cue held lsng,hsi,e. from
cad 10 std q the table push the ball
acro.. the cloth. The cue here rtpie.
sent, the ~iad ard the ball the ship 'ail.
ing directly b-ioic i; only n there i'
here no vase 4 snsrsy which in the case
of the -itd and .hip !, very great. the
ball - cour.c travels AZ the same rate o.
the eas--svii,nlly u can GO, p1'iibly
travel f..isr. Now, suppose groove 10
BE- ca, disgon.lly across the table ffom
one eorner pocket TO The other. IN ~hieh
ihs ball may roll II the ball be 20"
placed =, one end of the groove. AL The
cue held hoIiE3a,ally aud moved forward
As b,fof. the ball will travel Alorg the
grooys and Aloag the cue In the same
time a. the cue take, 20 move aero. the
table. To, /. The case Of the shiP sail.
ins a. an ansls With the direction of the
~ihd The groove Is considerably long.
e. than tie width Of the table, mote than
double a, loag. IN fact. ID, ball there.
tore travel, much faster than the cue
Which impsl. 10. ,inee It covers more
than double the dis,atee Ia the same time.
l, j, Ia precisely the same manner ,ha, =
aeking ,hip !, eaab!sd TO ,Ail faster than
the vind.
The foregoing mysteries oi motion
b,ing q miad the f.noa, paradox u
ZsEo. BY which be ,ougk, 10 prove iha,
Ill motion 10 impossible. "a body"
thu, argued The iagshiou, philosopher.
"mg,, move either IN the place ~hcie !,
10. OF Ia ,h. place wasre O. !, no.. Now,
a body in The place vhste ii i' l' station.
ay. and can no, be ia motion ncr
Obviously. can !, te in motion Ia the
place where ii !, not, Therefore /, eau
no, move a. all IL va, Of ,h!, paradox
Il W.. ,aid. iolriiur an.buiiHio-"i, i
solved by wAlsins" A more practical
solution could hardly be required.
Ano,hsr pAradoI familiar 10 the UUek'
-ihl, Of Aehills. and the ,Or,oi's--s
well Known. Aekills, The ,~ii,.foo,sdl
allow, The tortoise a bundled yard. start,
ard rup, tea yard, while the tortoise
tun, oae. Now. when Achilles Ia, run =
hundred yard, the toI,oi.e has run ten
yard,. And !, therefore .,,il tbs, distance
ahead When Aehllls, hA, ian these ten
yard, the tortoise has iun one yard.
When Aehills. has ign one yard, the TOT.
,oi,e hA, run one.ieh,h Of a yA;d. And
when Achilles has iun the one.,en,h of a
yard the tortoise hs, run ose.hundiedIh.
|, !, only Necessary TO eon,Inus tbs sans
piece" Of rsAsonlns TO Prove that Achilles
can never o,sfiAke the tortoise.
A much letter paradox. though some.
what II the same sind.run. =, follows !:
"a mAa. ~ho owes shilling proceeds to
pay /, =, the rate of,iIPenee the fret day,
,hreepenee the nsS, day. three halfpenee
the ns1i. three fsrihins, the nsSi. Aad 90
on--plyIog each DAY half The amour, he
pail The day before. SapFo,ios him 10
BE- furnished with counters of,mall value.
90 I. 10 be able readily TO pay fraction,
Of psany. how long would l. take bin
10 pay the shilling I" The answer !,
that be would never pay IL. l, j, true
that be will pay eleven. Peres i.r,hing in
four days, ba, the rsmAitias three far
things be eAn never pay.
Thi. paradox wares from the pf,esd.
ius in ohs important pariieulIr. AID de.
serves ~ be called batter paradox iof
,hi, reason. that ~e know thu, Aehillea,
ia spite Of al reasoning. will esrtAinly
ov,f,sks the tortoise. Bi, /, !, m,lhs-
ma,kisAlly dsmons,r.ble ,h,, the debtor,
under such eiicum,,Ateu can never pay
hi, shilling svsn ,hoash be should be en-.
dusI. Ike Ti,aoau,. with the ~, Of in.
mortality.
The following /, really eIeslleh, par.
doI: "a train starts daily from San
FfaLsi,eo TO New York. And one daily
from New York 10 San Francisco. the
journey lasting seven days How m,ny
train, will traveller NEE, 10 journsyins
from San Francisco 20 New York
1, appears osviou, a, the frs, glance
ih., the traveller mus, NEE, seven tlin',
snd this /. the answer which will be given
by nine people oui " ten TO whom the
question Is new. The fac, !, overlooked
ihl, every day darirs the jiurnsy a r. -
train /. starting from the other end, while
there ATE seven on the ~sy 10 begin Niih.
The traveller will therefore NEE, not seven
trains, bot fourteen.
The following proposition !, both ca.
rious in itself. and amii. Of some inter.
,s,irg variations in the application Of the
prineiple on which !, depends; III there
are more people in the world than my
one person has hairs upon bis head, then
there mus, exist a, leAs, two person, who
posses, idsn,ieally the same number OF
hairs, TO . hsir."
II the reader fail, to perceive A. once
the necessity Of this conclusion le, him
frs, consider as a simpler case. instead Of
the hair. on . mans head. the number o'
teeth 10 bis Jaw. Let him suppose thirty
four persons to be assembled in oGs
room then. the full number Of teeth In .
mans Jaw being ihir:y.t~o, !, !, easily
seen ,ha,-even supposing one member
Of the party 80 unfortunate as 10 have 20
teeth ~ all-,here must be AZ least two
persons present possessed Of iden,ieally
the same number OF teeth. The aPplies'
ton Of this example to the proposition In
question Is quite evident i, i'. In fact,
merely q matter Of larger numbef.
Now, TO apply this principle to other
cases. II has been asserted. for example
ths, ia a field Of grass there can no, b
found two blades In ell respects identical
IL will be seen, however. th,, II ih'
blades Of grass are more numerous thar
the differences between them pefesp,ibl'
TO the eye. then there mus, be =. lsss
two blades exactly alike, or, at least. NO
to be distinguished from each other b,
in'psc,ioa. oa.-Templs Bar.
----------------
.,T,s. -, 4, ,,,ch ,ka f.sy ~ heinu