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The measures of the Nippur cubit

The Nippur cubit is both

•  an attested measure, used in Near and Middle East since the end of 4th century B.C.

•  one graduated specimen of this measure in cupper-alloy, dating from about 2650 B.C.

 That specimen is nowadays exposed in the Archeological Museum of Istanbul (Turkey).

 The two draws below refer to the specimen.

 The third part contains our analysis with a modern definition.

Prof. Dr. Florian Huber, Ordo et Mensura III, page 188 ; St. Katharinen (Germany) 1995.

Prof. Dr. R. C. A. Rottländer, Ordo et Mensura V, page 113 ; St. Katharinen (Germany) 1998.

 

Our analysis of the specimen,

then, a modern smooth definition of the Nippur cubit measure.

The defined value of the « raw Nippur ell » equals 0.5184 m.

 
(0)   (1) (2)   (3)   (4) (5) (6)   (7)
  15 4 12 14 4 3 12 digits

  <---- 15 digits ----> <----- 16 digits ----> <------- 18 digits -------> <---- 15 digits ---->

 

 half-the-ell

  one foot

  one pygme

 half-the-ell

 
  <-----  1st Nippur Ell :  30 digits  ----->
 
  <-----  2nd Nippur Ell :  30 digits  ----->

Recollection of the measured values :

( 07 ) :

( 01 ) :

( 12 ) :

( 23 ) :

( 34 ) :

( 45 ) :

( 56 ) :

( 67 ) :

110.35 cm

25.6 cm

 6.7 cm

20.95 cm

24.15 cm

 6.75 cm

 5.3 cm

20.9 cm

*    *    *

Analysis of the specimen :

At the first regard, the graduation seems to be worked out without great precision.

  The smallest digit length ( 56 ) is 16.75 mm only one.

  Whereas the largest digit length ( 12 ) is 17.67 mm.

  In the head of the specimen ( 01 ) lacks about 3.2 mm.

  The tail of the specimen ( 67 ) is about 1.6 mm too long.

But actually, the very first preserved, more than 4500 years old, graduated rule

is  – really and certainly –  rather good, thousands of years before lazer steering.

  The over-all length of 1103.5 mm gives a mean digit of at least 17.24 millimetres.

  That first mean value is confirmed by the 14-digit measure, that gives 17.25 mm.

   If all the three small measures ( 12,  45  and  56 ) are too small  by about  1 to 2 mm,

in addition, palm ( 12 ) and 12-digit-span ( 23 ), the foot - digit measures 17.28 mm.

  The first  30-digit Nippur cubit measure ( 14 ) gives a mean digit of 17.27 mm.

  The second  30-digit Nippur cubit measure ( 25 ) gives one digit of 17.28 mm.

*    *    *

Thus,  also confirmed by the Rottländer statistical researches with 872 different ancient

graduated rule-sticks, about it eighteen other Nippur cubit rules –  one may certainly say:

Scientifically, the Nippur cubit  – as a general measure –  is  518.5 millimetres  ± 1 mm.

However, since the value  5185 tenths of millimetre contains the unpractical primary factor 1037

as 5 × 1037 = 5185,  the International Bureau for hexadecimal metrology ( BI-SMH ) defines the

so-called « raw Nippur cubit » of exact 518.4 mm, by a 3 - smooth number :  5184 = 2 6 × 3 4.

 

 

Measured:

Defined:   

 

 

1st half-ell :

( 01 )

256.0 mm

259.20 mm

98.8 %

 

Nippur foot :

( 13 )

276.5 mm

276.48 mm

100.0 %

 

Nippur pygme :

( 35 )

309.0 mm

311.40 mm

99.3 %

 

2nd half-ell :

( 57 )

262.0 mm

259.20 mm

98.9 %

 

 

 

 

 

 

 

1st Nippur Ell :

( 14 )

518.0 mm

518.40 mm

99.9 %

 

2nd Nippur Ell :

( 25 )

518.5 mm

518.40 mm

100.0 %

 

 

 

 

 

 

 

Sum of 124 digits :

 

2140.0 mm

2142.72 mm

 

 

Average* of digits :

 

17.258 mm

17.2800 mm

 

 

* The central measures enter

 more than once in this average.

 

99.87 %

100.00 %

 

 

It's generally admitted by the contemporary metrologists that the Roman foot is directly deduced from

the Nippur cubit measure, since the Egyptians, at the beginning of the 3rd millennium BC, shared the

old sumerian Nippur measure of 30 digits into 28 digits.  518 ÷ 28 = 18.5 mm.  18.5 × 16 = 296 mm.

That is the roman foot !  Neither the number 5185 nor 5184 is integrally divisible by 7. The number 518

is 7 × 740, but 740 contains the primary factor 37, never used in ancient measures. Therefore BI-SMH

decided to define  –  next to the « raw Nippur cubit »    an « idealistic Nippur cubit » of  518 616 µm.

The defined (2003)  « idealistic Nippur cubit » equals  518 616 (  2 3 × 3 3 × 5 0 × 7 4) micrometres.

By this defined 7-smooth conventional value   largely inside of the scientific coefficient of variation

determinated by Rottländer (e.g. Roman foot : 296.2 ± 0.5 mm)  the Roman foot is  296.352 mm.

« Raw Nippur cubit » and  « idealistic Nippur cubit » differ by a metrological komma, i.e. 2400 : 2401.

By the idealistic Nippur cubit, the ancient deduced measures obtain plain values.

Therefore the 7-smooth   over-all rounding   definition is adequated and consistent !

 

 

This page is online since 2007, March 15 .