Sumerian Numeration and Metrology. Dissertation, University of Minnesota, 1971

315 Pages·07.257 MB·English

by  Marvin A. Powell, jr.

72-lU,‘m5
POWELL, Jr., Marvin Adell, 1939-
SUMERIAN NUMERATION AND METROLOGY.
University of Minnesota, Ph.D., 1971
History, ancient
University Microfilms, A XEROX Company, Ann Arbor, Michigan
©
1973
MAIVIK ilOILL VanUs, Jr.
ALL RIGHTS RESERVED
TOIS DISSERTATION HAS BEEN MICROFLIMEO EXACTLY AS RECEIVED
StMEUAR mJMERATlOi AMD KETKOLOGY
A TRESIS
8UBKITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF TBS UNIVERSITY OF MINNESOTA
By
I
Hurvln Adall Powtll, Junior
IH PASTIAL FULFILLKEKT OF THE REQUUEKENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPRY
D«c«Bb«r, 1971
PLEASE NOTE:
SofM pssu hsM imfistinct
print FUnwd M rtoewwL
Univtnity Mkrofilrm, A Xarox Education Compviy
PUFACX
TIm ifork vbieh 1 pr«s«at her* under th* title **8uB«rlan
■uMrAtloQ and Metrology^ r«quir«t « f«w words of «cplsnatloo.
It *• a study of Old Suasrlan Mtrolofy, as tha rasult
of a suggastioD aada to m In 1967 by Frofassor D. 0. Ediard.
Aftar about two yaars of praliainary vork, it bacaaa claar to
■a tbat any atudy of Suaarlan Mtrolofjr would bava to daal vltb
tha problsBis of Kasopotaaian aatrology at a vhola if it «as to
daal vltb tba probls« of absolute standards. Tba work as it
MW stands, although resting upon a auch larger foundation,
focasas oo two central problsM of Saaarlaa aetrologyt tba
mmAmv systsa and the weight systsa. Tbs woth is laid out in
as rational a aanner as tiae and tba subject has paxaitted.
Tha Table of Contents is intended to be analytical and is
sopplsaantad by the Index. In general, words and subjects
listed in tha Table of Contents are not entered in the Index.
X should like now to express ay thanks to those who have
cootributad to ay education. Tha pressnt work owes aore than
is superficially apparent to two of ay undergraduate teacherst
Villiaa C. Kobinsoo, Jr., who adrisad aa in 1956, when Z waa
considering a ainisterial career, to study histoty and Gaxaan,
and Hsrcus V. Orr, who guided ae toward aa acadaiic career. To
11
both of thas« Iniplrlag tMchara, X axpraaa wj haartfalt thaaka.
To tba Voodrow Vllaoo FoundAtloa 1 aa grataful for tba opportu-
alty to puraua ay grttduata caraar at tba acbool of ay cbolea.
To Irla Lalcbty 1 aa grataful, for bla Inaplratlon, for all
tbat ba taagbt aa aboat Aaayrlology, and for bla cootlnolng
balp ainea 1963. To tba Falbrlght-Kcaalaalon in dar Bundaa-
rapabllk Dautacbland X aa aapaclally gratafal for aaklng It
poaalbla for aa to apand two frultful yaara ln tha MBnchanar
Aaajrlologlaehaa Saalnar. To Profaaaor Mats Otto Iduird I owa
aoat of «bat I knov aboot Saaarology, and I aa alncaraly grataful
for tha t«o yaara tbat X «aa abla to laaxn froa hla. To mf
tanehar, Frofaaaor Toa B. Jooaa, «ho baa guldad aa for ovar
Bin« yaara «Ith patianea and «ladoa, X cannot raadlly axpraaa
tha gntltnda X faal. X ahould alao ba aoat tagrataful If X dld
aot raeall tha fundaaantal dabt X owa to ay paranta, «ho aada
it poaalbla for aa to paraua an acadaale caraar ln tba flrat
plaea« And flnally, for tha tncaaalng aneoaragaaant X bava
raealrad, for tha ballaf that to work la hoaan and good, and
for apandlng two aootha typlng tha final oopy, X thank «y daar
«ifa, Victoria.
111
TAM.» or oarrafTs
........................................................................................................................... ^
LIST or TABLES.........................................................................................
LIST or ABBtKVXATlONS............................................................................ 1*
BAIT X. mMSATXON: VHaK NOKBOIS
Chapter
X. xmooocnoM to ntmexals................................................... 2
XX. TBB SaSUAM NIMEIULS ONE TO TEN.................................. 13
Cam............................................................................................. 13
d i i ..................................................................................... 18
t ............................................................................................. 21
TWO............................................................................................. 23
Tfara«......................................................................................... 26
Four ......................................................................................... 33
F lv o ......................................................................................... 35
S ix............................................................................................. 36
S«v«i......................................................................................... 39
lig h t........................................................................ Al
Rino ........................................................................................ 42
T m ............................................................................................. A3
XXX. TEI SOMEIIAH NUKSXALS ABO^ TEN...................................... A5
Introductioo to Tablas ...................... . . . . . . . 45
T iran^................................................................... 48
T h lr^ ................................................... 48
Forty.................................................................... 49
F ifty......................................................................................... 50
Sixty . .................................................................................... 50
Th* ftaclprocal Tablas 1st. S 485 and ST 399 . . . 54
Xat. S 485 55
Mot«« on tha Taxt of 1st. S 485 .......................... 56
ST 399 58
Errors of laandatloo or Kastoratlon................. 60
Irrora of Copying ...................................... 62
Iv
commrrs! coutimued
Chapter *»8«
AooMilies of Uncertain Origin.............................. 62
The Organisational Principle Underlying the
ST 399 Typo of Reclpi-ocal Table . . . . . . 66
Tentative ftecoostructlon of a Reciprocal
Table of the ST 399 Type.................................. 69
120.............................................................................................. 71
180.........................................................................« . • . . 71
240............................................................................................. 71
300 .............................................................................................. 71
360 .............................................................................................. 71
420 .............................................................................................. 71
480 .............................................................................................. 71
540 .............................................................................................. 72
600 .............................................................................................. 72
1200 ......................................................................................... 73
1800 ................................... 73
2400 .......................................................................................... 73
3000 .......................................................................................... 73
Tba aeaning of f a r , i a r g a l , and
i a r g a l - I T t t n u t a s a .......................... 78
IV. SOfflAKT OP RIMBIALS................................................................ 79
fAXr n . RDMEimOllt hactional kukbzxs
V. sxm , 0MB.snni, axd tbb simsuah mcnoNS . . . S4
VI. TBB SBK4SICL061CAL BACXGtOUND (F SUMERIAK
TtACnOHAL TEXHUfOLOCT...................................................117
VII. NOTATION OF FtACTIONS AND ITS LINCUISTIC lESOLUTION 130
Tha Words for TWo-Thirds and One^Half . . . . . . 137
The LAL Nuabers « .......................... 139
Tha Coapound« and the Keading of
1<AL * J&JlftjLSL 143
Tba Coapound Signs IÌL Sa& and UÙ. ♦ NIGIN, 143
Tha Syntactic Fosition of Measured Conodltles . 150
VIII. FIACnOMS IN TBB LEXKML TEXTS.......................................155
Fractions Vrittan vltb Ma3 ...........................................155
Fractions Vrittan with bartenii . . . . . . . . . 161
COKTKNTSt COKTlKUn)
Chapter
PAKT 111. VSIGBT KBASUUS
XX. TBB MCTHODOLOCY CP WBIGHT KETiaOGY........................... 167
Z. THE BXISTENCB OP DirFEBBKT VEIGBT STANSMIDS . . . . 198
XX. TBB ORIGIN AND DBVBLOPHBMT OP THE MESOPOTAMIAN
VEIGBT SYSTEM................................................................. 208
The SoMrien Syttea...................................................... 208
Syetea One: Suaero•Akkadian................................... 212
Motet oo the Unite of Systea Okie....................... 214
V • .......................................................................... 214
1 I .......................................................................... 215
i I .......................................................................... 215
15 I ........................................................................ 215
SO I ........................................................................ 215
45 f ........................................................................ 216
60 i ........................................................................ 217
90 i ......................................................................... 217
120 I ...................................................................... 218
150 Se . . . . . . . . . . . . . . . . . . 220
Soaerian Kxprettiona for Shekel Fractions and
the Tera i g i . . . . . . . . . . . . . . 221
The Expression of Mina Fractions.................... 224
1 g i n ................................................................. 225
10 g i n ................................................................. 225
20 g i n ................................................................. 225
50 g i .................................................................... 225
40 g i n . . . . , .............................................. 226
50 g i n . ............................................................. 226
The Talent . . . . . . . . . . . . . . . . . 226
Systsa Two: The First Milleniua Systsa................ 226
Motes oo the Shekel Fractions in Systsa Two . . 228
228
uttetu . . . . . . . . . . . . .................... . 228
IttUaOL............................................................................. 22B
slrQ ......................................................................... 230
bitaa......................................................................... 231
IflM l......................................................................... 231
Ifwwwtfc . . . . . . . . . . . . . . . . . . . 231
rebutu/rebitu ......................................................... 231
ila lL .................................................... 232
tSiEL................................................................................. 233
ii££JL fiftSiSiU................................................................. 233
liiii UkiSU.......................................................... 233
▼1
coirrmst coktinuso
r«g«
APPEHBIX 1. BQUIPMKKT AND TERMINCLOCY BMPLOTKD IN
VEICHING.....................................................................................................237
Tha Balança............................................................................................237
Tha Parts of tha Balança...............................................................238
Tha Vslghts for Weighing...................................................................242
Tha Tanis for Wslghar, To Wslgh, and M ass..............................243
APFENDU II. TABLES OP NCTATION.......................................................2U
APPENDIX III. VEICSTS WITH MBSOPCfTAMIAN CONNECTIONS . . . . 246
BIBLIOCKAPHT.................................................................................................274
INSIX.............................................................................................................296
▼11
LIST OP TABLES
TabU *«g«
1. Tha MuaaraU 1 - 6 0 .................................................................... 47
2. Tha Riaarala 61 - 600 ................................................................ 70
9. Tha Ihaarala 600 - 3600 ............................................................ 72
4. Tha VuMrals froa 3600 - 12960000 ....................................... 73
5. Tha Foxaal Faetama of Suaarian Ruaaratica.................. SO
6. Tha Rotation of I o f a n a and i a n a b i in
SBS 9/1 and its Linguistic Resolution..........................135
7. Transiitaratad Excerpts froa a Text Illustrating
Rotation of Fractions in tha Ur 111 Period
Follovad bj a Theoretical Phonetic Transcription » 136
8» Mina Roms DariTabla froa Inscribed Weights • • • • • 205
9. The Utaits of Practical Weighing in Systea One • • • • 214
10. Tha Shekel Fractions in Systea IV o ...................................234
11. Tha InterrelatiMs of Shekel Fractions in Systsa Two 235
12* Standard Rotation • • • • • • • • • • • • • • • • • • 244
13. Pre-Ur III Rotation of Shekel Fractiona • • • • • • • 245
14« Ur III Rotation of Shekel Fractions • • • • • • • • • 246
15. Pre-Ur III Rotation of Mina Fractions...................... 247
16» Ur III Rotation of Hina Fractions . . . . • • • • • • 248
17. List of Wsight Speeimena .................. • • • • • • • • • 249
viil