Review Article The Cubit: A History and Measurement Commentary - Hindawi

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Hindawi Publishing Corporation
Journal of Anthropology
Volume 2014, Article ID 489757, 11 pages
http://dx.doi.org/10.1155/2014/489757
Review Article
The Cubit: A History and Measurement Commentary
MarkH.Stone
AuroraUniversity,Aurora,Illinois,USA
CorrespondenceshouldbeaddressedtoMarkH.Stone;[email protected]
Received20August2013;Accepted7November2013;Published30January2014
AcademicEditor:KaushikBose
Copyright©2014MarkH.Stone.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,which
permitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Historicaldimensionsforthecubitareprovidedbyscriptureandpyramiddocumentation.AdditionaldimensionsfromtheMiddle
Eastarefoundinotherearlydocuments.Twomajordimensionsemergefromahistoryofthecubit.Thefirstistheanthropological
orshortcubit,andthesecondisthearchitectualorlongcubit.Thewidegeographicalareaandlongchronologicalperiodsuggestthat
cubitdimensionsvariedovertimeandgeographicarea.GreekandRomanconquestsledtostandardization.Morerecentdimensions
areprovidedfromastudybyFrancisGaltonbaseduponhisinvestigationsintoanthropometry.ThesubjectsforGalton’sstudyand
thoseofseveralotherinvestigatorslackedadequatesampledescriptionsforproducingasatisfactorycubit/forearmdimension.
Thisfindingisnotsurprisinggiventhedemiseofthecubitintoday’sworld.Contemporarydimensionsfrommilitaryandcivilian
anthropometryfortheforearmandhandallowcomparisontotheancientunit.Althoughthereappearsnopressingneedfora
forearm-hand/cubitdimension,thehalf-yardorhalf-meterunitseemsausefulonethatcouldseemoreapplication.
1.Introduction adistancelocatedbetweentheoutstretchedthumbandlittle
finger, or from the elbow to the tip of the middle finger.
If we know anything of the cubit today, it probably comes Thesealternatedescriptionsfurthercomplicatethematterof
fromacquaintancewithHebrewScriptureand/ortheOldand determining a specific unit measure of the cubit. Hereafter,
NewTestaments.Peoplehaveheardorreadaboutthedimen- the latter description, elbow to the tip of the middle finger,
sionsofNoah’sArkorSolomon’sTemple.Acquaintancewith willsignifythecommonunit.
Egyptian history might have brought some awareness from Thehumanfigure(typicallymale)hasbeenthebasisfor
the dimensions given for pyramids and temples. The cubit manydimensions.Thefootisimmediatelyrecognizedasan
was a common unit in the early East. It continues today in example [1]. Less commonly heard is onyx (nail), but onyx
some locations, but with less prominence having been remainsamedicalterm.TheOldEnglishynche,ynch,unce,
replacedbymoderndayunits.Earlyemploymentofthecubit or inch was a thumb-joint breadth. The anthropomorphic
throughouttheNearEastshowedvarieddimensionsforthis basisformanystandardssupportsthestatement“manisthe
unit. Some variants can be examined easier with reference measureofallthings”attributedtoProtagorasaccordingto
tobiblicalpassages.Additionalvariantscanalsobefoundin Plato in the Theaetetus [2]. Small wonder the cubit was
numerousseculardocuments,butthesearelessknownand initially employed for measurement given its omnipresent
lessaccessiblethanscripture. availabilityforuse.Wealwayspossesstheunit.Humanfigure
The word cubit (󸀠kyu¨-bJt) in English appears derived units are arbitrary but universal are especially effective by
fromtheLatincubitumforelbow.Itwas𝜋𝜂𝜒́ 𝜐𝜍(pay󸀠-kus)in their bodily reference producing a crude standard that is
Greek.Thecubitisbaseduponahumancharacteristic—the immediatelyaccessable.
lengthoftheforearmfromthetipofthemiddlefingertoend Thecubitprovidesaconvenientmiddleunitbetweenthe
oftheelbow.Manydefinitionsseemtoagreeonthisaspect foot and the yard. The English yard could be considered a
oftheunit,yetitdoesnotproduceauniversalstandardfor double cubit said to measure 12 palms, about 90cm, or 36
therearemanywaystodetermineacubit.Itcanbemeasured inches measured fromthecenter ofa man’sbody to thetip
from the elbow to the base of the hand, from the elbow to ofthefingersofanoutstretchedarm[3].Thisisausefulway
2 JournalofAnthropology
Table1:Therelativelengthsoffourcommondimensions.
Meter
Yard
Cubit
Foot
ĎĹĂ
ofmeasuringclothheldcenterbodytoanoutstretchedhand whose height was six cubits and a span. (1 Samuel
(twocubits),oracrossthebodytobothoutstretchedhands 17:2–4RSV)
(fourcubitsasspecifiedinExodus26:1-2,7-8).TheEnglish
(5)Inthefourhundredandeightiethyearafterthepeople
ellisalargervariantofthecubitconsistingof15palms,114cm,
ofIsraelcameoutofthelandofEgypt,inthefourth
or 45 inches. It is about equal to the cloth measure ell of
year of Solomon’s reign over Israel, in the month of
earlyScotland.Aman’sstride,definedassteppingleft-right,
Ziv,whichisthesecondmonth,hebegantobuildthe
producesadoublecubit,orapproximatelyayard[1].
house of The Lord. The house which King Solomon
ThedimensionsinTable1givethe(approximate)relative
builtforTheLordwassixtycubitslong,twentycubits
lengthsformeter,yard,cubit,andfoot.
wide,andthirtycubitshigh.(1Kings6:1-2RSV)
ThecubitwasabasicunitinearlyIsraelandthesurround-
Thecubitdeterminedameasureformanyaspectsoflife
ingNearEastcountries.Itis inHebrew(pronounced
󸀠 inBiblicalhistory.ASabbathday’sjourneymeasured2,000
am-mah ), which can be interpreted “the mother of the
cubits(Exodus16:29).Thisstatueproscribedalimittotravel
arm”ortheorigin,thatis,theforearm/cubit.Selectedbiblical
ontheSabbath.ThedistancebetweentheArkoftheCovenant
references [4] for the cubit include these five rather well-
andthecampoftheIsraelitesduringtheexodusisestimated
knownselections.
atabout914meters,1,000yards,or2,000cubits[5].
(1)And God said to Noah, I have determined to make Biblicalcitationsandhistoricalarcheologysuggestmore
anendofallflesh;fortheearthisfilledwithviolence than one standard length for the cubit existed in Israel. In
through them; behold, I will destroy them with the II Chronicles 3:3 the citation may imply cubits of the old
earth. Make yourself an ark of gopher wood; make standard.Ezekiel40:5;43:13maybeindicatingthecubitplus
rooms in the ark, and cover it inside and out with ahand.ArcheologicalevidencefromIsrael[6]suggeststhat
pitch.Thisishowyouaretomakeit:thelengthofthe 52.5cm = 20.67and 45cm = 17.71 constitute the long and
arkthreehundredcubits,itsbreadthfiftycubits,and shortcubitsofthistimeandlocation.Tosomescholars,the
itsheightthirtycubits.(Genesis6:13–15RSV) Egyptian cubit was the standard measure of length in the
Biblicalperiod.TheBiblicalsojourn/exodus,war,andtrade
(2)Theyshallmakeanarkofacaciawood;twocubitsand are probable reasons for this length to have been employed
ahalfshallbeitslength,acubitandahalfitsbreadth, elsewhere.
andacubitandahalfitsheight.Andyoushalloverlay TheTabernacle,theTempleofSolomon,andmanyother
itwithpuregold,withinandwithoutshallyouoverlay structuresaredescribedintheBiblebycubitmeasures.These
it,andyoushallmakeuponitamoldingofgoldround alsooccurwithtwodifferentcubitsdimensions,thelongor
about.(Exodus25:10-11RSV) royal (architectural) cubit and the short (anthropological)
cubit. Scholars have used various means to determine the
(3)Andhemadethecourt;forthesouthsidethehang-
length of these cubits with some success. The long cubit is
ingsofthecourtwereoffinetwinedlinen,ahundred
givenasapproximately52.5centimetersandtheshortcubit
cubits; their pillars were twenty and their bases
asabout45centimeters[4,5].
twenty,ofbronze,butthehooksofthepillarsandtheir
TheIsraelitelongcubitcorrespondstotheEgyptiancubit
filletswereofsilver.Andforthenorthsideahundred
of7handswith6handsforshorterone.Eerdman’sDictionary
cubits, their pillars twenty, their bases twenty, of
oftheBible[7,page1373]states“...archeologyandliterature
bronze, but the hooks of the pillars and their fillets
suggestsanaveragelengthforthecommoncubitof44.5cm
wereofsilver.Andforthewestsidewerehangingsof
(17.5in.).” This citation also gives a range of 42–48cm (17–
fiftycubits,theirpillarsten,andtheirsocketsten;the
19in)forthecubit.Rangeisanimportantparameterbecause
hooksofthepillarsandtheirfilletswereofsilver.And
itindicatesthevariationoperatingonthismeasure.Variation
forthefronttotheeast,fiftycubits.(Exodus38:9–13
indicatesmultipleinfluences.
RSV)
The English use of cubit is difficult to determine. The
(4)And Saul and the men of Israel were gathered, and exactlengthofthismeasurevariesdependinguponwhether
encampedinthevalleyofElah,anddrewupinline itincludedtheentirelengthfromtheelbowtothetipofthe
of battle against the Philistines. And the Philistines longest finger or by one of the alternates described earlier.
stood on the mountain on the one side, and Israel Some scholars suggest that the longer dimension was the
stoodonthemountainontheotherside,withavalley originalcubitmakingit20.24inchesfortheordinarycubit,
betweenthem.Andtherecameoutfromthecampof and21.88inchesforthesacredone,orastandardcubitfrom
󸀠󸀠
the Philistines a champion named Goliath, of Gath, theelbowtoendofmiddlefinger(20 )andalowerforearm
JournalofAnthropology 3
Table2:Hebrewlinearmeasures. Table3
Commonscale Ezekiel’sscale GreatPyramidatGizeh,Khufu 20.620±−005
Measure
Millimeters Inches Millimeters Inches SecondKhafra 20.64±−03
Cubit 444.25 17.49 518.29 20.405 Granitetemple 20.68±−02
Span 222.12 8.745 259.14 10.202 ThirdPyramidMenkaura 20.71±.02
Handbreadth 74.04 2.91 74.04 2.91 Periboluswalls 20.69±−02
Finger 18.51 0.72 18.51 0.72 GreatPyramidofDahshur(?) 20.58±−02
PyramidatSakkaraPepi 20.51±−02
ČŐĆ
Fourthtosixthdynasty,meanofall 20.63±−02
󸀠󸀠
cubitfromtheelbowtobaseofthehand(12 ).Thesearethe
same dimensions for Egyptian measurements according to Table4
Easton’sIllustratedBibleDictionary[9].TheInterpreter’sBible
Egyptiancommoncubit 18.24inches
[10,page154]givestheCommonScalelengthas444.25mm
Egyptianroyalcubit 20.64inches
or 17.49 inches and Ezekial’s Scale as 518.29mm or 20.405
GreatAssyriancubit 25.26inches
inches for the two cubit lengths. Inasmuch as the Romans
Bela´dicubit 21.88inches
colonized England the shorter cubit previously mentioned
Blackcubit 20.28inches
mayhavebeenthestandard.
A rod or staff is called (gomedh) in Judges 3:16,
which means a cut, or something cut off. The LXX (Septu-
result from strong disagreement over the dimension of the
agint)andVulgaterenderit“span”whichinHebrewScripture
cubit. Kaufman [11] argues against the “central location
ortheOldTestamentisdefinedasameasureofdistance(the
theory”defendingacubitmeasuring0.437meters(1.43feet).
forearm cubit), roughly 18 inches (almost 0.5 of a meter).
David[12]arguesforaTemplecubitof0.56meters(1.84feet).
Amongtheseveralcubitsmentionedisthecubitofamanor
Differencesinthelengthofthecubitarisefromvarious
commoncubitinDeut.3:11andthelegalcubitorcubitofthe
historical times and geographical locations in the biblical
sanctuarydescribedinEzra40.5[6].
period.Theseverylongtimeperiodsandvariedgeographical
Barrios[5]givesasummaryoflinearHebrewmeasures
locations frustrate determining a more exact length to the
(seeTable2).
cubit. Israel’s location between Egypt and Mesopotamia
Barrois[5]indicatesthedimensionofthecubitcanonly
suggest that many influences came into play over the space
be determined by deduction and not directly because of
ofhundredsandhundredsofyearsinthiswell-traveledarea.
conflictinginformation.HereportstheaqueductofHezekiah
Theseinfluencesprobablycontributedtothevarieddimen-
was 1,200 cubits according to the inscription of Siloam.
sionsencounteredoverthislongtimeframe.Stories,myths,
Its length is given as 5333.1 meters or 1,749 feet. Absolute
anddramaaddtheirshare.
certaintyforthelengthofacubitcannotbedetermined,and
The earliest written mention of the cubit occurs in the
there are great differences of opinion about this length fos-
Epic of Gilgamesh. The incomplete text is extant in twelve
teringstrongobjectionsanddebates.Somewritersmakethe
tabletswritteninAkkadianfoundatNinevehinthelibrary
cubiteighteeninchesandotherstwenty,twenty-oneinches,
of Ashurbanipal, king of Assyria (669–630? BCE). Other
orgreater.Thisappearscriticallyimportantforthoseseeking
fragments dated from 1800BCE contain parts of the text,
to determine the exact modern equivalent of dimensions
and still more fragments mentioning this epic have been
takenfromscripture.Taking21inchesforthecubit,theark
found dating from the 2nd millennium BCE. The cubit is
Noah built would be 525 feet in length, 87 feet 6 inches in
specifically mentioned in the text when describing a flood
breadth, and 52 feet 6 inches in height. Using the standard
󸀠󸀠 󸀠󸀠 asremarkablysimilarandpredatingthefloodmentionedin
20 cubitand9 span,Goliath’sheightwouldbe6cubitsplus
󸀠󸀠 Genesis.Obviously,thecubitwasanearlyandimportantunit
a span for about 10 feet and 9 inches. With a cubit of 18
oftheMiddleEastfundamentaltoconveyinglinearmeasures
hisheightis9feet9inches.TheSeptuagint,LXX,suggests4
asshowninTables2,3,and4.
cubitsplusaspan,oramoremodest6feetand9inches.There
aremanyimplicationsdependinguponwhichdimensionis
selected [7]. The story requires young David to slay a giant 2.Egypt
and not simply an above average sized man! Likewise for
manyotherdimensionsanddescriptionfoundinearlywrit- The Egyptian hieroglyph for the cubit shows the symbol of
ings, the larger the dimensions, the better the story. Sacred a forearm. However, the Egyptian cubit was longer than a
dimensionsrequiresolemn,aweinspiringones,butthisfrus- typicalforearm.Itseemstohavebeencomposedof7palms
tratesanexactdetermination. of4digitseachtotaling28partsandwasabout52.3-52.4cm
RabbiDavidbenZimra(1461–1571)claimedtheFounda- inlengthaccordingtoArnold[13].
tionStoneandHolyofHolieswerelocatedwithintheDomeof The earliest attested standard measure is from the Old
theRockontheTempleMount.Thisviewiswidelyaccepted, KingdompyramidsofEgypt.Itwastheroyalcubit(mahe).
butwithdifferencesofopinionovertheexactlocationknown Theroyalcubitwas523to525mm(20.6to20.64inches)in
as the “central location theory,” some of these differences length:andwassubdividedinto7palmsof4digitseach,for
4 JournalofAnthropology
a 28-part measure in total. The royal cubit is known from Nichholson[20]inMenandMeasuresdevotedachapter
OldKingdomarchitecturedatingfromatleastasearlyasthe to The story of the cubit. His summary (page 30) provided
constructionoftheStepPyramidofDjoseraround2,700BCE comparativelengthstofivecubitsasshowninTable4.
[13–15]. Nichholsonproposesalonghistoryofthecubitbeginning
Petrie[15]beginsChapterXXthefollowing.Valuesofthe before the time of the Great Pyramid of Kufu c. 2600BCE.
CubitandDigitwriting. Heclaimsameasureof500commoncubitsforthebaseside
indicatingonlyasix-inchdifferencefromthebasemeasure
Themeasurementswhichhavebeendetailedinthe
madebyFlindersPetrie.Hefixesthedateoftheroyalcubit
foregoing pages supply materials for an accurate
atabout4000BCE.ThegreatAssyriancubitisdatedc.700
determinationoftheEgyptiancubit.Fromsucha
BCE.TheBela´diccubitisdatedc.300BCE.Nichholsonfixes
massofexactmeasures,notonlymaytheearliest
theBlackcubitasfullyrealizedataroundtheninthcentury
value of the cubit be ascertained, but also the
ofthiserawhichsuggestsaparalleltothegrowthandspread
extent of its variations as employed by different
of Islam. While his measures for these variants of the cubit
architects.
appeartodovetailwithsomeoftheotherestimatesgivenin
thispaper,thereareseriousquestionsaboutthechronological
Petrie’smethodsandfindingsaresoclearlyandprecisely
sequenceassociatedwiththesevariants.Nichholsonoffersno
describedtheycanbestbequotedasfollows.
evidence or support for this sequence. His estimates of the
Forthevalueoftheusualcubit,undoubtedlythe commonandroyalcubitsconformtootherestimates,butthe
most importantsourceistheKing-sChamberin othervaluesarelessconforming.
the Great Pyramid; that is the most accurately
wrought,thebestpreserved,andthemostexactly
4.Greek/RomanPeriods
measured,ofallthedatathatareknown.
The Greek 𝜋𝜂̃𝜒𝜐𝜍 (pay󸀠-kus) was a 24-digit cubit. The
Arranging the examples chronologically, the cubit used
Cyrenaica cubit measured about 463.1mm with the middle
wasasshowninTable3.
cubitabout474.2mmmakingthemroughly25/24and16/15
Petriewritesthefollowing.
Roman cubits. Other Greek cubits based on different digit
measures from other Greek city-states were also used. The
ForthecubitIhaddeduced([16,page50])from
Greek 40-digit-measure appears to correspond to the Latin
a quantity of material, good, bad, and indiffer-
ent, 20–64±.02 as the best result that I could gradus,thestep,orhalf-a-pace[21].
get; about a dozen of the actual cubit rods ItshowsthattheGreeksandRomansinheritedthefoot
that are known yield 20–65±−01; and now fromtheEgyptians.TheRomanfootwasdivided intoboth
fromtheearliestmonumentswefindthatthecubit 12 unciae (inches) and 16 digits. The uncia was a twelfth
first used is 20–62, and the mean value from part of the Roman foot or pes of 11.6 inches. An uncia was
the seven buildings named is 20–63 = 𝑏 .02-. 2.46cm or 0.97 of our inch. The cubitas was equal to 24
...Onthewholewemaytake20–62±−01asthe digitior17.4inches.TheRomansalsointroducedtheirmile
originalvalueandreckonthatitslightlyincreased of 1000 paces or double steps, with the pace being equal to
on an average by repeated copyings in course of fiveRomanfeet.TheRomanmileof5000feetwasintroduced
time.(pages178-179). into England during the occupation.Queen Elizabeth, who
reignedfrom1558to1603,changedthestatutemileto5280
feetor8furlongs,withafurlongbeing40rodsof5.5yards
3.GreekandRomanComparisons
each.Thefurlongcontinuestodayasaunitcommoninhorse
In the writings of Eratosthenes, the Greek 𝜎𝜒oˆı]o𝜍 racing.
(schoe󸀠nus)was12,000royalcubitsassuminga0.525meter. Theintroductionoftheyardasaunitoflengthcamelater,
The stade was 300 royal cubits or 157.5 meters or 516.73 butitsoriginisnotdefinitelyknown.Somebelievetheorigin
feet. Eratosthenes gave 250,000 stadia for circumference of wasthedoublecubit.Whateveritsorigin,theearlyyardwas
the earth. Strabo and Pliny indicated 252,000 stadia for the dividedbythebinarymethodinto2,4,8,and16partscalled
circumference and 700 stadia for a degree [13, 17]. Reports the half-yard, span, finger, and nail. The yard is sometimes
ofEgyptianconstructionindicateonlya0.04inchdifference associatedwiththe“gird”orcircumferenceofaperson’swaist,
between cubit of Snefru and Khufu pyramids according to or with the distance from the tip of the nose to the end of
Arnold[13]andGillings[17]. the thumb on the body of Henry I. Units were frequently
Lelgemann [18, 19] reported the investigation of nearly “standardized”byreferencetoaroyalfigure.
870metrologicalyardstickswhoselengthsrepresent30dif- The distance between thumb and outstretched finger to
ferentunits.Hearguesfortheearliestunit,theNippurcubit, theelbowisacubitsometimesreferredtoasa“naturalcubit”
to be 518.5mm. Lelgemann gives the ancient stadion = 600 of about 1.5 feet. This standard seems to have been used in
feetandreportsthestadionatOlympiaat192.27meterswhich theRomansystemofmeasuresaswellasindifferentGreek
hebelievesisbasedontheRemenoroldEgyptiantradecubit systems.TheRomanulna,afour-footcubit(about120cm),
derived from the Egyptian royal cubit (523.75mm) and old wascommonintheempire.Thislengthisthemeasurefroma
tradecubit=448.9mm. man’shiptothefingersoftheoutstretchedoppositearm.The
JournalofAnthropology 5
Table5:MiddleEastnamesanddimensionsforthecubitandrelatedmeasures.
Egypt
󸀠󸀠
Digit,zebo 1/28royalcubit 0.737 18.7mm
󸀠󸀠
Palm,shep 1/7 2.947 75mm
󸀠󸀠
Royalfoot 2/3 13.95 254mm
Royalcubit unit 20.62 524
Ater,skhoine 12,000royalcubits 3.9miles 6.3km
Hebrew
󸀠󸀠
Finger,ezba 1/24cubit 0.74 19mm
󸀠󸀠
Palm,tefah 4fingers,1/6cubit 2.9 75mm
󸀠󸀠
Span,zeret 3palms,1/2cubit 8.8 225mm
Royalcubit 7/6standardcubit 20.7 525mm
󸀠󸀠
Pace 2cubits 35.4 900mm
󸀠󸀠
Stadion 360cubits 528 162meters
Greek
󸀠󸀠
Palm 4fingers 3.0 77mm
󸀠󸀠
Span 12fingers 9.1 231
󸀠󸀠
Cubit 24fingers 18.2 463mm
Stade 604feet 185meter
Romancubitusisasix-palmcubitofabout444.5mmabout 0.68inch).TheArabicHashimicubitofabout650.2mm(25.6
17.49inches[17]. inches)isconsideredtomeasuretwoFrenchfeet.Sincethe
establishedratiobetweentheFrenchandEnglishfootisabout
5.OtherNearEastDimensions 16to15,itproducesthefollowingratios:5Hashimicubits≈
10 French feet ≈ 128 English inches. Also, the length of 256
Over time and the geographic areas of the Middle East Romancubitsandthelengthof175Hashimicubitsarenearly
variouscubitsandvariationsonthecubithavebeenrecorded: equivalent[16].
6 palms = 24 digits, that is, ∼45.0cm or 18 inches (1.50ft); Theguardcubit(Arabic)measuredabout555.6mm;5/4
7 palms = 28 digits, that is, ∼52.5cm or 21 inches (1.75ft); oftheRomancubitproducing96guardcubits≈120Roman
8 palms = 32 digits, that is, ∼60.0cm or 24 inches (2.00ft); cubits≈175Englishfeet.TheArabicnilcubit(orblackcubit)
and9palms=36digits,thatis,∼67.5cmor27inches(2.25ft) measuredabout540.2mm.Therefore28Greekdigitsofthe
[1].Oates[22,page186]writingofmesopotamianarcheology Cyrenaicacubit≈25/24ofaRomanfootor308.7mm,and
states“measuresoflengthwerebasedonthecubitor“elbow” 175 Roman cubits ≈ 144 black cubits. The mesopotamian
(veryapproximately0.5m).” cubitmeasuredabout533.4mm,6/5Romancubitmaking20
The Histories of Herodotus [23, page 21] described the Mesopotamian cubits≈ 24 Roman cubits ≈ 35 English feet.
walls surrounding the city of Babylon as “fifty royal cubits The Babylonian cubit (or cubit of Lagash) measured about
wide and two hundred high (the royal cubit is three inches 496.1mm.ABabyloniantradecubitexistedwhichwasnine-
longer than the ordinary cubit).” An accompanying note to tenthsofthenormalcubit,thatis,446.5mm.TheBabylonian
thetext providestheinformationgiveninparentheses,and cubitis15/16oftheroyalcubitmaking160Babyloniantrade
theendnotereportsthesevaluesas“exceedinglyhigh”raising cubits ≈ 144 Babylonian cubits ≈ 135 Egyptian royal cubits.
questions about the height of these walls which would be ThePergamoncubit520.9mmwas75/64oftheRomancubit.
well over three-hundred feet high if the royal cubit of 20 TheSalamiscubit484.0mmwas98/90oftheRomancubit.
inchesisimplied,or100metersiftheroyalcubitis50cm.For The Persia cubit of about 500.1mm was 9/8 of the Roman
comparison,thegreatpyramidofKhufuislistedasoriginally cubitand9/10oftheguardcubit.Extendingthegeographic
146.59 meters [24, page 895]. The credibility of Herodotus area still further produces more names and values for the
has often been questioned, and these dimensions might be cubit[16,18,19,25,26].
suspect also or subject to the same exaggerations found From the Encyclopedia Britannica [24] section on
elsewhereinhisreportings. WeightsandMeasuresgiveninVolume23,theunitspecifi-
In 1916, during the last years of Ottoman Empire and cationsfortheMiddleEastcubitareshowninTable5.
during WWI, the German Assyriologist Eckhard Unger FromatableinA.E.Berriman’sHistoricalMetrology[8]
foundacopper-alloybarduringexcavationatNippurfromc. wefindhissummaryofcubitstandardsinTable6.
2650BCE.Heclaimedittobeameasurementstandard.This If one assumes the values from Berriman’s table to be
bar, irregular in shape and irregularly marked, was claimed reasonableestimates,thenthedescriptivestatisticsfromthe
tobeaSumeriancubitofabout518.5mmor20.4inches.A datainTable7offerasummaryofthesevarieddimensions.
30-digitcubithasbeenidentifiedfromthe2ndmillennium The estimates in Berriman’s table for Greek and Roman
BCEwithadigitlengthofabout17.28mm(slightlymorethan cubits align reasonably well with the Egyptian short cubit
6 JournalofAnthropology
Table6:CubitdimensionsfromBerriman[8]. Table8:Humandimensionsrelativetothesix-footmale.
Cubit Inches Meter Unit Inches
Roman 17.48 0.444 Finger 0.75
Egyptian(short) 17.72 0.450 Palm 3
Greek 18.23 0.463 Foot 12
Assyrian 19.45 0.494 Cubit 18
Sumerian 19.76 0.502 Height 72
Egyptian(royal) 20.62 0.524 Pace 72
Talmudist 21.85 0.555
Palestinian 25.24 0.641
Table7:DescriptivestatisticsforA.E.Berriman’stable.
Inches Meter Flemish ell Yard
Mean 20.04 0.51 Cubit English ell
Span French ell
Median 19.61 0.50
Fathom
Standarddeviation 2.57 0.07
Range 7.76 0.20
Minimum 17.48 0.44 18 handbreadths
Maximum 25.24 0.64
6 feet
suggestinganaverageofapproximately18inches.Thisdimen-
sion is about two inches shorter than the overall mean in
Table7.Thefullrangeofvaluesisabouteightinchesfrom17.5
to 25. The varied originsfor these data and previousvalues
Figure1:VitruvianMan.
suggest considering a family of cubits accumulated from
manygeographicareasovermanydifferenttimesratherthan
view these differences as suspects of one exact dimension.
Figure1 gives the famous picture associated with these
Such variants may not be simple differences, or differences
dimensions.Theunitgivenshowsonemoreexampleofthe
aroundanexactunit,butratheracompositeofdimensions
dimensionofthecubit[1].
accumulated over a large chronological period from many
geographical locations that cannot be disentangled. These The figure of the Vitruvian Man by Leonardo da Vinci
multiple dimensions suggest local applications rather than depicts nine historical units of measurement: the yard, the
simply differences about a single standard which frustrates span, the cubit, the Flemish ell, the English ell, the French
greateraccuracy. ell, the fathom, the hand, and the foot. The units depicted
A rounded value of 18󸀠󸀠 seems common for this period. are displayed with their historical ratios. In this figure the
󸀠
TheHellenisticcubitappearsinlinewithwhathasbeeniden- cubitis25%ofthe6 individualandabout18inches.Weare
tified as the short cubit. Standardization of the cubit began remindedoncemoreoftheimportanceofthehumanfigure
during Hellenism coinciding with Alexander’s conquests in forestablishingunitsofmeasure.
theMiddleEast.Itsstandardizationwasprobablyincreased AnotherexamplefromthisperiodcomesfromtheAuto-
greatlyundertheRomanEmpirefromtheinfluencesofwar, biography[27]ofBenvenutoCellini(1500–1571).Indescrib-
travel, and trade. These influences contributed to bringing ing his casting of Medusa, Cellini’s narration uses cubit to
the cubit into a more standard operational unit. Roman illustratelengthascasuallyaswemightusefootoryard.At
engineersinviaduct,bridge,androadconstructionbrought leastinthiscontext,ifnotothers,thecubitappearsofcom-
standardizationthroughouttheempire. mon usage. How more generalized a cubit dimension pre-
Cubits were employed through Antiquity to the Middle vailedthroughthistimeperiodisnotknownexactly.Bythe
Ages and continue even today in some parts of the East. timeoftheFrenchRevolutiontheCommitteeofWeightsand
Continuedusageprevailedformeasuringtextilesbythespan Measureshadabandonedthecubitamongotherdimensions
of arms with subdivisions of the hand and cubit in less infavorofthemetricsystem.
industrializedcountries.
Moving forward to Da Vinci (1452–1519) we have his 6.TheHumanCubit
specificationsandcommentaryonVitruviusPollio(1stcen-
turyBCE)forthehumanfigureanditsdimensions[1].They The history of metrology provides interesting data on the
canbesummarizedasfractionsofa6-footmanasgivenin varied dimensions of the cubit. Metrology first utilized the
Table8. human figure in establishing dimensions. History to this
JournalofAnthropology 7
Table9:Frequencyofleftcubitmeasurebyinches.
Staturebyinches Under16.5 Under17 Under17.5 Under18 Under18.5 Under19 Under19.5 Above19.5
71+ 0 0 0 1 3 4 15 7 30
70 0 0 0 1 5 13 11 0 30
69 0 1 1 2 25 15 6 0 50
68 0 1 3 7 14 7 4 2 38
67 0 1 7 15 28 8 2 0 61
66 0 1 7 18 15 6 0 0 47
65 0 4 10 12 8 2 0 0 36
64 0 5 11 2 3 0 0 0 21
−64 9 12 10 3 1 0 0 0 35
Total 9 25 49 61 102 55 38 9 348
Inches 16.5 17 17.5 18 18.5 19 19.5 19.5
Frequency 9 25 49 61 102 55 38 9
󸀠󸀠
pointsuggeststhatavalueofabout17-18 seemsaverageand 120
mostcommon.
SirFrancisGalton(1822–1911)offersdatagatheredfrom 100
theinvestigationsheconducted.Galtondeservesrecognition
80
as one of the first investigative anthropometrists. He was
a scientist producing some of the first weather maps for
60
recordingchangesinbarometricpressure[28]andstrategies
for categorizing fingerprints [29]. Galton stands out for 40
his investigations involving thousands of subjects. Some
investigations were conducted at the International Health 20
Exhibition in London held 1884-85 and at other field loca-
0
tions.Galtonhadearliermadeananalysisoffamousfamilies
16.5 17 17.5 18 18.5 19 19.5 20
fromwhichhecompiledHereditaryGenius[30]andlaterin
Cubit frequency by inches
NaturalInheritance[31].Hemaintainedalife-longinterestin
determiningthephysicalandmentalcharacteristicsofgroups Frequency
ofindividuals.
Figure2:Cubitfrequencybyinchesfor348subjects.
Not only did Galton collect data from his laboratory
onhumansubjects,heinvestigatedstatisticaltechniquesfor
analyzing tables, graphs, and plots of data. In doing so he
createdtheoriginsforwhatisnowrecognizedascorrelation Figure2 indicates the modal category of forearm/cubit
and regression analysis. Correlation became more formally measuresforGalton’ssamplewas18.5inches.Thefrequency
developedbyPearson[32]astheproductmomentcorrelation distributionofforearmmeasurementsissomewhatbalanced.
coefficient.Ithasbecomethemostknownandusedstatistical Thismightbeexpectedgiventhatthesemeasureswouldbe
procedure of our time. Other statisticians, especially Sir determined by chance through heredity. This was Galton’s
Ronald Fisher [33–35] and Tukey [36], have criticized the viewpointandemphasis.Consequently,hisattentionderived
correlation coefficient for its abuse arising from simplistic fromthisdataandotherdatamovedhisinteresttoeugenics.
applications and dubious interpretations. Nevertheless, the Many other English scientists and statisticians shared this
correlationcoefficientremainsapopularanalytictechnique. interest; Fisher, Pearson, Haldane, Cattell, and others [40].
Pearson[37]alsoproducedthreevolumesonthelife,letters, Galton (and the others) received considerable criticism for
andworksofGalton. takingthisposition.However,itwasasascientistandcom-
Galton’sdataforthecubitofhisdayisgiveninTable9.It piler of human data that led Galton to draw his inferences.
wastakenfromStigler[38,page319]TheHistoryofStatistics. Hispronouncements[30,31,41]concerningeugenicsdonot
Its original source is Galton [39] whose investigation gives smack of a political or personal agenda. One may disagree,
data gathered from about 130 years ago on the forearm or but it is important to understand that Galton’s work was
cubit. Stigler [38, page 319] indicated three of Galton’s row focusedupondataandmethodologyasthebasisforforming
totalsweresummedincorrectly.Thesesumswerecorrected hisconclusions.
inTable9. ThemeanfortheGaltonsampleof348personsinTable9
Figure2 summarizes the relative frequency of fore- wasalmost18inchesbringingestimatesofacenterlocation
arm/cubit lengths from Galton’s data on 348 subjects given (i.e.,mode,median,andmean)insyncwithanapproximate
inTable9. normaldistributionasshowninTable10.
8 JournalofAnthropology
Table10:Millimetersandinchesoftheleftcubit. Left cubit to stature
Millimeters Inches 20 y=0.2546x+0.7623
R2=0.5715
Mean 67.06609 17.83621 es 19
h
c
Standarderror 0.126798 0.042699 n
n i 18
Median 67 18 bit i 17
Mode 67 18 u
c
Standarddeviation 2.365384 0.796541 eft 16
L
Samplevariance 5.595043 0.634478
15
Kurtosis −0.9142 −0.42833 62 64 66 68 70 72
Skewness −0.09243 −0.16653 Stature in inches
Range 8 3.5
Figure4:Plotofleftcubittostature.
Minimum 63 16
Maximum 71 19.5
Sum 23339 6207 analytic methods. These matters are not directly connected
Count 348 348 totheissuesofcubitlengthandthereforenotdiscussedhere.
However,therelationshipofcubittostatureisusefulandit
canbecomparedtoDaVinci’sestimate.
Galton’s data on cubit length by inches
Stigler [38, page 319] indicated “Galton’s ad hoc semi-
graphicalapproachgavethecorrelationvalue𝑟 = 0.8.”This
30 wasGalton’sapproachpriortothePearsonproductmoment
correlationwhichwhencalculatedforhisdatagave𝑟=0.75.
25
Figure4isaplotofdatafromTable9withalinearregres-
20 sionlineandshowingthevariationinforearm/cubitateach
y
c levelofstature.Itisveryimportanttonotethewidevariation
n
ue 15 ofleftcubitmeasures(vertical)foreachindicationofstature
q
e
Fr 10 (horizontal).Individualdifferencesinthecubit/forearmare
clearly evident at each point of stature thwarting anything
5 more specific than a generalized indication for the fore-
19.5hes arm/cubit from Galton’s data. The shared variance between
0 [phone]St66a99ture66 88by i66n77ch66es66 65 64 −64 1166.5511C8ubit by inc satraeturSerelevaetaerndadlbcquuutbenistotiitoscnaosbmoeupmtlea5tn7eal%yte.sfurgogmestGinagltothne’ssedatwtaorvegarairadbilnegs
forearmlengthorthecubit.
Figure3:Athree-dimensionalviewofGalton’sdata.
(1)Howrepresentativeisthissampleofthegeneralpop-
ulation?
From Galton’s data summarized in Figure2 and Tables (2)Howmuchchange,ifany,inhumandimensionshas
9 and 10 about 2% had forearms at 16.5󸀠󸀠 or less and 2% occurred from ancient times and over the one hun-
had forearms greater than 19.5󸀠󸀠. Approximately 63% or 218 dred plus years from Galton’s sample to the present
personsandclosetotwo-thirdsofthe348personsampleare day?
withinone-halfinch+or−themeanof18.3inchesoralmost (3)Is there any gender difference or other sources of
󸀠󸀠
18.5 ifroundedoff.About95%varylessthananinchabove influenceandbias?
andbelowthemeanestimate.Roundingfromthesefrequen-
cies makes these values approximate, but they still provide FromwhatweknowofGalton’smethodsthereappearsno
agenerallyusefulsummaryfromhissample.Skewnessand indicationofoutrightbias.Stigler[38]inchapters8,9,and10
kurtosis appear as minimal influences on the distribution ofhisbookraisednoquestionswhendescribingGalton’sdata
furtherconfirmingabalanceddistribution. andmethodsforanalysingdata.Galton’ssampleswerelarge
Figure3 provides a three-dimensional view of Galton’s andofteninthethousands.Thiscubitsampleismoderatein
data. It usefully shows the clustering of values along the scope. Galton was aware of gender differences and utilized
center diagonal from the upper left to lower right. Galton’s 1.08asacorrectionfactorformale/femaledifferences[38].
figureswerenotshownasthree-dimensional,butherecorded However, there is little information regarding sample
the frequencies at each intersection of his two-way table representation.ItappearsthatGaltonwasgenerallyfastidious
which were used to produce this three-dimensional figure. in his investigations. He utilized gatherings of the general
PonderinghisdatagaverisetoGalton’sworkonassociation/ populationfromwhichtoprocurehissamplesandmakehis
correlation for which the word regression has now evolved measurements. Given that right handedness predominates,
beingderivedfromhiseffortstointerpretwhatthisandother Galton measured the left hand to avoid what might result
data express. See Stigler [38] for more details on Galton’s from possible environmental influences upon the mostly
JournalofAnthropology 9
Table11:ForearmpercentilesforanunidentifiedBritishpopulation. Table12:Elbow-fingertiplengthpercentiledistributioninmillime-
ters.
Percentile 5 50 95 (a)
Male 440 475 516 1st 2.5th 5th 10th 25th 50th 75th 90th 95th 97.5th 99th
Female 400 430 460 435 442 448 455 468 483 499 515 523 532 542
(b)
Mean 484.04 (19.05inches)
dominant right hand. Volunteering could be a potential Standarderror 0.55
source of bias, but volunteering probably allowed a larger Median 483 (19.01inches)
sampleofindividuals.Hepaidindividualsamodestamount Mode 472 (18.58inches)
toparticipatenotunlikewhatissometimesdonetoday.
Standarddeviation 23.32
Johnson et al. [42] reviewed and reanalyzed Galton’s
Samplevariance 544.09
original data. They report on mean scores, correlations of
Kurtosis 0.43
themeasureswithage,correlationsamongmeasures,occu-
Skewness 0.22
pationaldifferencesinscores,andsiblingcorrelations.Acor-
relation of cubit/forearm to stature indicated the former Range 192
wasabout25–27%ofstature.Nothingfurtherisaddedtoa Minimum 386
knowledgeofforearm/cubitdinemsionbytheirwork. Maximum 578
Relevance of the forearm/cubit length in more recent Count 1774
times comes from anthropometric dimensions utilized in
industrialpsychologyandapplicationstotheclothingindus-
try. Data from Mech [43] gives more recent data of human
dimensionsincludingtheforearm.Forearmlengthsreported 7.Discussion
forpercentiles5,50,and95aregiveninTable11.
The varied dimensions for the historical cubit of ancient
ThesepercentilesarefromanunidentifiedBritishsample
timesandplacesspeaktoavariationinthedimensionitself.
ages 19 to 65. Lacking more information one can only
Two major units predominate; one estimate centers around
compareandcontrastthesedimensionstoprevioussamples
18 inches and the other around 20 inches. There are other
discussed earlier. These males had a median cubit measure
of 475mm or ∼18.7 inches. Females measured a slightly variations,somesmallerandsomemuchgreater.Thereistoo
shorter median measure of 430mm or ∼16.9 inches. Mech wideageographicalareaandtoogreatachronologicaltime
period to consider any of these latter variations normative.
[43]indicateda medianvalueclose to thatgiveninTable9
forGalton’sdataor∼18.7to∼18.3. Each variant was more likely to be locally relevant rather
than widely prominent. Only in the Greek and Roman
The Lean Manufacturing Strategy reports a forearm
󸀠 󸀠 󸀠 empiresthroughwar,trade,andconstructiondidthesevalues
mean=18.9 ,standarddeviation=0.81 ,minimum=15.4 ,
󸀠 coalescetosomewhatofastandard.
andmaximum=22.1 basedondatafromMcCormick[45].
Howhasthehumanphysiquechangedovertime?Roche
Nothingfurtherisgivenregardingthissampleanditschar-
[48] reported that rates of growth during childhood have
acteristics.
increased considerably during the past 50–100 years. He
There are numerous sites and organizations providing
indicatedincreasesinratesofgrowthandmaturationforall
carefullydetermineddimensionsforthehumanbody.How-
developednations,butnotevidentinmanyothercountries.
ever, these dimensions are developed to serve the clothing
TherewererecordedincreasesinlengthatbirthinItalyand
industryandfurnituredesignaddingnothingtoaknowledge
France,butlittlechangeintheUnitedStates.Anincreasein
ofthecontemporaryforearm/cubitdimension[46].
childhoodstaturewasgivenforabout1.5cm/decade for12-
TheanthropometrydatabaseANSUR[47]obtainedfrom year-oldchildren.Theincreaseinstatureforyouthwasabout
http://www.openlab.psu.edu/ gives a table of percentiles for 0.4cm/decadeinmostdevelopedcountries.Thechangesin
thehorizontalmeasuremade“fromthebackoftheelbowto bodyproportionsduringrecentdecadeswerereportedasless
thetipofthemiddlefingerwiththehandextended,”thatis, markedthanthoseinbodysize.Leglengthincreasedmore
cubit.Thesamplewascomprisedofunidentifiedmalearmy thanstatureinmenbutnotinwomen.Roachfurtherindi-
recruits. catedthatchangesinnutritionalonecouldnotaccountforthe
The ANSUR data sample [47] in Table12 provides trendswhichexceedtheoriginalsocioeconomicdifferentials.
descriptivestatisticsfortherightmaleforearmplusextended In the United States, Roach reported there have been per
hand in millimeters. The mean for this quite large contem- capitaincreasesintheintakeofproteinandfatfromanimal
porarysampleisaboutoneinchgreaterthantheshortcubit sources, decreases in carbohydrates and fat from vegetable
reportedmuchearlier.Soisthemedianalthoughthemodeis sources, and some changes in caloric intake. It is not clear
slightlyless.Thesampleappearsreasonablybalanced,butthe that these changes constitute better nutrition stimulating
variationindicatedbythestandarderror,standarddeviation, growth. The trends could reflect environmental improve-
andrangeshowthishumandimensiontovary.Variationhas ments, specifically changes in health practices and living
beenencounteredbeforeinthereportingofearliersamples. conditionsleading to improvementsfor mortalityrates and
10 JournalofAnthropology
lifeexpectancy[44].Nutritionvariesevenindevelopedcoun- [2] F. M. Cornford, Plato’s Theory of Knowledge: Theaetetus and
tries.Roche[48]reportedgeneticfactorsplayasmallrolein Sophist,LiberalArtsPress,NewYork,NY,USA,1957.
causing trends. However, the data speaks to considerable [3] E. Zupko, Revolution in Measurement; Western European
variation among contemporary samples as also noted in WeightsandMeasuresSincetheAgeofScience,TheAmerican
Galton’sdata. PhilosophicalSociety,Philadelphia,Pa,USA,1990.
Overall, it seems unwise to be overly fastidious about [4] RevisedStandardVersionoftheBible:RSV,NationalCouncilof
any contemporary value for the cubit when such samples theChurchesofChristintheUnitedStatesofAmerica,New
York,NY,USA,1952.
arevaguelydescribed.Foranycomparisonofcontemporary
dimensions reported there are few characteristics given by [5] G.A.Barrois,ChronologyandMetrology.theInterpreter’sBible,
vol.1,AbingtonPress,NewYork,NY,USA,1952.
which to judge sample representation. The contemporary
estimatesappearsomewhatclosetogetherandsuggestatleast [6] G.Barkay,“MeasurementsintheBible:evidenceatSt.Etienne
for the length of the cubit and reed,” Biblical Archeological
forthesesamplesnogreatchangehasoccurredovertheyears,
Review,vol.12,no.2,article37,1986.
butwecannotbesurelackingvaliddata.Withoutmoresam-
[7] D.N.Freedman,Eerdman’sDictionaryoftheBible,Eerdmans,
ple definition, any fastidious analysis appears unwarranted.
GrandRapids,Mich,USA,2000.
TheGaltonvaluesarelikelytohavebeenlocalandrelevantto
[8] A.D.Berriman,HistoricalMetrology,Dent,London,UK,1953.
aBritishsample.Nowadayssamplesaremorelikelytoreflect
theroleofimmigrationwithwhateveradditionaleffectsthis [9] M. G. Easton, Illustrated Bible Dictionary, Thomas Nelson,
mightbringtobearondeterminingnationalhumandimen- Knoxville,Tenn,USA,3rdedition,1897.
sions.Ingeneral,EuropeansaretallerthanAsian/MiddleEast [10] G.A.Buttrick,TheInterpreter’sBible,vol.I,AbingtonPress,New
peoplesandAmericansaretallerthanEuropeans.Theseare York,NY,USA,1952.
generalizationsfromgrossestimates.KomlosandBaten[49] [11] A.S.Kaufman,TheTempleofJerusalem,HarYear’ahPress,Jer-
havemadeacomprehensiveanalysisofstatureovercenturies. usalem,Palestinian,2004.
The striking feature of their tables is the intravariation of [12] A. B. David, “Ha-midda ha-Yerushalmit,” Israel Exploration
values for each time period. Individual variation was also Journal,vol.19,pp.159–169,1969.
observedinGalton’sdata.However,systematicsamplingand [13] D.Arnold,BuildinginEgypt:PharaonicStoneMasonry,Oxford
sampledetailsmustaccompanyanydatabeforeestimatescan UniversityPress,Oxford,UK,1991.
bemorethangrossgeneralindications. [14] J.P.Lauer,“E´tudesurquelquesmonumentsdelaIIIedynastie
(pyramide a` degre´s de Saqqarah),” Annales du Service des
A variety of circumstances address the cubit, but most
AntiquitesdeL’Egypte,IFAO,vol.31,no.60,article59,1931.
of them offer little specific information beyond what has
[15] W.M.F.Petrie,ThePyramidsandTemplesofGizeh,Fieldand
already been presented. These biased sites typically serve
Tuer,London,UK,1883.
someagenda,oftenreligiousorpersonal.Overall,eventhese
[16] W. M. F. Petrie, Inductive Metrology, Saunders, London, UK,
sitestypicallyreportthetwomajordimensionsforthecubit
1877.
at18inchesor20inches.
[17] R. J. Gillings, Mathematics in the Time of the Pharaohs, MIT
The cubit as a dimension remains useful. We take the
Press,Cambridge,Mass,USA,1972.
cubit(handandfoot)whereverwetravel.Knowingpersonal
[18] D.Lelgemann,EratosthenesvonKyreneUnddieMesstechnikder
dimensions can sometimes prove useful for making quick
󸀠󸀠 AltenKulturen,Chmielorz,Wiesbaden,Germany,2001.
albeit gross estimates. The 18 ruler is a very handy device
[19] D.Lelgemann,RecoveryoftheAncientSystemofLengthUnits,
whenever measures just beyond a foot ruler are required,
InstituteforGeodesyandGeo-InformationTechnology,Berlin,
especially when it is necessary to draw straight lines for a
Germany,2004.
lengthjustbeyondtwelveinches.Tapemeasuresareaboon,
[20] E.Nichholson,MenandMeasures,Smith,Elder&Co,London,
butnotfordrawinglines.
UK,1912.
It appears that we might content ourselves with a cubit
[21] J.L.E.Dreyer,AHistoryofAstronomyfromThalestoKepler,
lengthof18inchesasasomewhatconsistentdimensionfor Dover,NewYork,NY,USA,1953.
thecubit.Evenasthefootevolvedfromaspecificalbeitarbi-
[22] J.Oates,Babylon,ThamesandHudson,London,UK,1986.
trarypersonage,anyassemblageofthemleadstoanabstract
[23] Herodotus, The Histories. (Trans. Aubrey De Se´lincourt; Notes
dimension,sothecubitcouldjustifymoreapplicationasa0.5
JohnMarincola),Penguinbooks,London,UK,1954.
yardand/ora0.5meter.Furtherprominenceofeitherorboth
[24] “Weightsandmeasures,”inEncyclopediaBritannica,vol.23,pp.
theseunitsmightprovemoreusefulthanfirstsurmised.
371–372,EncyclopediaBritannica,Chicago,Ill,USA,1971.
[25] M.A.Powell,“MetrologyandmathematicsinancientMesopo-
ConflictofInterests tamia,”inCivilizationsoftheAncientNearEastIII,Sasson,Ed.,
Scribners,NewYork,NY,USA,1995.
The author declares that there is no conflict of interests [26] D.Arnold,TheEncyclopaediaofAncientEgyptianArchitecture,
regardingthepublicationofthispaper. PrincetonUniversityPress,Princeton,NJ,USA,2003.
[27] B.Cellini,Autobiography:theLifeofBenvenutoCellini(Trans.J.
Symonds),P.F.Collier&Son,NewYork,NY,USA,1906.
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[28] F. Galton, Meteorgraphia: Methods of Mapping the Weather,
[1] H.A.Klein,TheScienceofMeasurement,Dover,NewYork,NY, Macmillan,London,UK,1863.
USA,1974. [29] F.Galton,Fingerprints,Macmillan,London,UK,1892.