Ellsworth American. [volume] (Ellsworth, Me.) 1855-current, 1875-11-04
Vol. XXI. Whole No. l0S4. No. a.
nathematics for the Million.


by Cssnsiss.
Mathematical problems are In meas-
ure akin to puzzles. There 10 something
| exciting In the boldness with which our
understanding is challenged to prove its
strength. and 1t imparts q feeling of satls-
| faction to unrsvel mysteries which have
| for time baffied our efforts. Such men.
| tai exercises have In all ages been attrac-
| tive to both young and old, and for this
reason we think our readers will be anus
ed by some reflections concerning an alge.
braic quantity which has cleverly been
designated "Whew!" IL consists Of three
IS, the second as the exponent Of the first
and the thiyd az the exponent of the sec.
ond, which means that9 shall nrst be null
tiplied nine times by itself. viz 9x9x9x9x-
9x919x9x9. giving the number 3S7
The product thus found indicates how
many times a second time Is TO be multi
piled by itself; but what multiplied 3S7-
420, ,4s9 times by itself gives AS product 10
not so easily figured out as the former
multiplication. 1t would require 500 ,693,-
loo ctphers, and 10 count It, working ten
hours daily, would take Is years and 23O
days, not to mention the time passed In
computation.
Scientists tell us there arc infusoria SO
small that 40 900 900 coo of such are found
in one cubic inch of water. A ball the size
of the globe would contain 2.429. .O93 .OOO.-
900 OOO, 900, 900 900, 900 900, 900 900, or two
sextillions four hundred and twenty-uine
thousand and ninety-three qulntilions
such animals. But this number is far from
being 'whew.' A ball that should be able
to hold 'wbew' OF the iniusoria here men
toned, at the rate of 40 900, 900 600 to the
cubic inch OF water, would contain an ia.
conceivable number OF globes, for in the
distance betweea the surface OF such q ball
and its centre would require 654, 500 6l2
elphers for Its expression In miles Row
great length such a number OF milee
would have, can be seen from the follow
ing comparison:
Light travels 1872 900 miles a second,
thus using eight minutes and thirteen sec-
onds to traverse the distance from the sun
TO the earth. But to accomplish the dfsA
lance from the surface OF the aforesaid
ball TO its centre light would need num-
Der of years written with l23 ,23l Ola ~
ures.
Still another relation may serve to show
'whew's' crushing dimensions. Light ae-
composites in every second about five hun
dred billions OF oscillations, number 80
great that the loudest note ever measured,
which makes sc 900 vibrations ia second
must sound 40 years TO perform SO many
vibrations. But although in order TO tray
erse the radius of the above. mentioned
ball, light would require this vast number
OF years, yet II does not more tbHn infin-
itesmaIly approach the 'whew vibrations.
The story Of the inventor Of the game OF
chess Is well known. The King OF India
bade him name his own reward,upon which
he asard TO receive the number of grains
OF wheat that would be produced If ONE
of heat maid him 10
square on the chess board, two for the sec
oud, four for the third eight for the fourth
and so on doubled up for every square OF
the Sky four. When these amounts wsre
added the sum was iound TO be Is, ,t46 7l4-
O' 5.fO5,o3l l.blo OF grains or 10 other words
such quantity that Herewith all the con-
tInruI> OF the earth could be covered with
a layer "ne-thirI OF au inch IN thickness,
that II the same ground were sown With
wheat in the proper manner it would take
more than seventy years TO produce the
aoov" amount OF wheat, which is equal TO
thlrty-four bullion hnsheis'
One STANDS aehast before inns number.
ana SIN II Is next 10 nothIng as compared
win "hew' ,o' II we were IN the same
manner TO uouole up Inc amount until II
reasftd 'wne" number OF gralns the
chess board instead OF having d squares
must nave hau l'--o'o9a'o9t squares In
"hich case /" eaeh square hau one squarc
then vi surface 'hc space co'ereu "ouiu oe
III al al ca eq"ai W 40 acres
we once sa" some CALCULATIONS, IesS ln-
oeeu ~ proportion 'hah "he", YET OF
e"@' aCle' NV ieo9 a'touhu'hs' IN VINCE
numbers hatuIy 10 De conceived OF were
.naue III measure eolnptehehsioie oy De-
ny cou'pa'eu Win QUANTITIES OF more Ia
'Ar.a' ""ote
for instance QUO cent were SET OUT AZ
eo'hpouho lt'eIest III Tue year al iou' per
oeI'',' .'1' - VI 'a'ua'S' 80, "ou.o
20. ~ 900 iu'ntiiilo"' ii,i' quAuI
'Ioue' o'.,Voo T'Ilions o' uoIar': IL we
"eie - 'sAe 'i'.s Su'n as caPi'al ana
:, !" ou'u - 10 '"'e' cot \'o,i per centJ
'n.t' '"o '''oo.''o taA VIC ''.ouIu nay 10 ply
a. ''e "'e y! 5, one pc. I1''' "ou'u oe 4oo
tN"N' 'i,'T'' 80 - t'.'''"',> vi "''i'''
W Paiu ,"e az Coi.ectot , IN tIlis sum lh sl'Fti
nc ""u'u "eeu oO''of' W 'ooVooV
"" "" ''' u" p'i 'H'iou' o''ueu
'"e WHIT ca :" SUI '"No ootn iahu auu
Ma'e.' Msre peopaeu as nos closeiy as poslote'
Me ' s"ouiu iia'e out i-LoooVoo part VI the
urNels required, auu tne ilne Oh wagons
"Uulu N.,'. ha,e ieustn , oi lri''lcns tf-'op
vi ZOO 900 nc y. hs"t' a.
y. ', . 40 coo pe' 'eeou' anu
" m'u'u 'aAe 'f''ooo years 70 reaeh the
r = . =, -.
u he' - nave oe''er conlfol over me way
GUS Oh ooth sues e'at t'oneo h'msei IN Ihe
eehlle { oI .ie ,iho' Asa'p. roooefy cooiu
oI NM. y" t"e , 'I,iuiioSs W"sou
", ""IoI I5n. "ouiu no. 10 uiscoVeieu 'iI ,ns
-f'.9o'n senerh'ioh oi TAX coiIec'ors' H.
oh 'ne con inS'eau VI using .he lh-
=, .e' os' VI t''o Sap''a'.I"o JUN vi "hicn .oY
''e .! e''n Eoiu "ouiu ue edua 70 ~ eiooes
, "Is "Is t"pSa' "ei' u's'iiou'ed auaoheft
,ne no Peop'e no e VI the ta,'u' eaeh one oil its
i,Vo',oVo,ooV o! 'nhaoltahts would receive
ABOUT l-oo tr'iloh- OF aoilars 10 i've on
a. anu no ,ooIa nna e,eiy seupnu use 1,oVoooV Tor
oo'o'o,Voo Yeas without reaching Inc bot
'o'n oi us purse
nGai'' III auo'"et P.ace' 10 an article on
ahaS a'ne VI ''anSpoHt'ohs ot ieuers, san
mar eA'inpies are gwen as 10 the rapldlty
"lh "hic, numbers VIII increase. We
n"u men 'nst ."o ie'ters can oe changed
~ .inies, 'e.'e.s iALAo or tunes let
.e.s iAIAoA' OF ~ times letters lx2x3x-
fAo OF 1" times Which Is enough 10 Illus
tTAte tnc point ne trTnspoSltl0nS grow