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Excursus from the main page's chapter : " The digital foot already exists
".
The Viennese yard is exactly 1728 / 1000 Nippur cubit.
The third part of this Viennese yard equals the length of the modern digital foot.
The deduction of the Viennese yard by ancient measures (number of digits) :


Three raw Nippur cubits : 3 × 518.40  mm

90
 ×
 17.2800
 mm
 =
 1555.24
 mm


Six Nippur pygmes : 6 × 311.04  mm

108
 ×
 17.2800
 mm
 =
 1866.24
 mm


Six atticolympic feet : 6 × 311.04  mm

96
 ×
 19.4400
 mm
 =
 1866.24
 mm

96 atticolympic digits are 100 Viennese digits

96
 ×

19.4400
 mm
 =
 1866.24
 mm


100
 ×

18.6624
 mm
 =
 1866.24
 mm










Six Viennese feet equal two Viennese yard,* i.e. the Viennese klafter.










Thus these idealistic Viennese measures :

Foot :
 16
 × 18.6624 mm
 =
 298.5984 mm

Yard :
 48
 × 18.6624 mm
 =
 895.7952 mm

Klafter :
 96
 × 18.6624 mm
 =
 1791.5904 mm


* The Viennese yard is the Stephansdom linenell, Leinenelle. The Viennese ell or draperyell, Tuchelle, is deduced by that yard. (See below.)
In a early fit of decimalisation the attested atticolympic orguia – a klafter measuring 96 digits – was shared into 100 parts.
From this attempt results the Viennese digit of about 18.66 mm. Naturally, the real Viennese klafter equals only 96 new digits.
Caution : Don't confound the Viennese measuring system and the Austrian system.

The Austrian Klafter – legal between 1756 and 1871 – was defined, in 1760, by Joseph Liesganig as 1.02764 toise de Peru exacly one.
Since 1799 the French toise is 27 000 / 13 853 metres exactly one. So, the historical Austrian Klafter is :
2^{ 6} × 3^{ 3} × 5^{ 8} × 7^{ 1} × 23^{ 1} × 1117^{ 1} × 1979^{ 1} = 1.896 6139 m.
Face of these three doubtfull prime factors : 23, like 1117 and 1979 :
BISMH prefer the 7smooth : 2^{ 4} × 3^{ 3} × 5^{ 7} × 7^{ 3} = 1.896 6528 m.
This gives a Klafter 38.898 µm shorter, i.e. minus 0.002 051 %.
Whenever the Austrian klafter is mentionned on this domain, that defined, idealistic value is meant. It is identical to the ancient Greek pous metrios.


The Viennese Klafter equals two Viennese Stephansdom's yards.
Both Viennese ells are attested since 1685, but should be mediaeval. The Viennese yard – see above – equals 1728 / 1000 Nippur cubit.
The value of the Viennese Yard :
Since the raw Nippur Cubit equals 2^{ 2} × 3^{ 4} × 5^{ 4} = 0.5184 metre,
the idealistic Viennese Klafter is 2^{ 6} × 3^{ 7} × 5^{ 7} = 1.7915904 m.
Thus, the idealistic Viennese yard equals 895.7952 millimetres.
The Austrian engineer Franz Twaroch measured 896 millimetres.
This gives a yard exactly 0.2048 mm shorter, i.e. minus 0.022 857 %.
So, the Stephansdom foot and the idealistic digital foot are identical. * 

one Austrian foot 
1 × 2^{ 6} × 3^{ 2} × 5^{4} × 7^{ 3}
 =
 316.1088 mm

 ≠

 the Viennese foot
 1 × 2^{ 8} × 3^{ 6} × 5^{4}
 =
 298.5984 mm


 one Austrian klafter
 6 × 2^{ 6} × 3^{ 2} × 5^{4} × 7^{ 3}
 =
 1896.6528 mm

 ≠

 one Viennese klafter
 6 × 2^{ 8} × 3^{ 6} × 5^{4}
 =
 1791.5904 mm
 
* In ancient times, according to the statistical ressearches of R.C.A. Rottländer, the metrological incertitude factor was generally about ± 0.17 %.
Of course, it diminished since Renaissance times. However, during the European MiddleAges, a precission of ± 0.02 % was certainly excellent.
Therefore, a difference of 0.02 % is not significant. Thus, the Viennese yard and the length of three digital feet can be considered to be identical.

Strictly, that justified reproach could be expressed :
Both values are not comparable, because the first one is a
measured
value with a millimetre  precision, the other one is a
defined value, 3 × (2 ^{8} × 3 ^{6} × 5 ^{4})
= 895. 5984 millimetres, four
rightsided decimal positions. However in reality, a measure of
896 mm must be inside the interval : 895. 5 and 896. 4999 mm.
In all cases, the measured Viennese yard is inside ± 0. 17 %.


Measured yard
896 mm


Idealistic yard
895. 5984 mm


Scientific yard
895. 7464 mm


maximum:
 896.5000 mm


+
 0.079 %




+
 0.084 %



supposed:
 896.0000 mm


+
 0.023 %




+
 0.028 %



minimum:
 895.5000 mm


–
 0.033 %




–
 0.028 %





When in 1990, M. Florencetime defined the digital foot by using the major radius of Earth, he ignored the existence of this Viennese yard.
If the ratio of the Viennese yard to the Nippur ell is surely not a coincidence, but issue of the wellknown exchange of measures in history;
in contrary, the concurrence of the Viennese foot and the modern digital foot must be considered to be a "happy coincidence".
Now the terms : hexadecimal foot, digital foot, univeral foot, Viennese foot, Stephansdom's foot and even Steven's foot are all synonym.
A hypothetical speculation that the Viennese foot itself is deduced by measures of Earth would be unfounded, pseudoscientific.


Postscript in 2007, on March 20th: 
With the historical measures of length, BISMH recognizes five metrological kommata :
• three 7smooth kommata and
• two metrological correction factors. Latter ones implie respectively the primary factors 127 and 19, 109 257.
Remark : The term « metrolocical komma » means that – intrinsically – it is the matter of the same measure. since by ancient measures
the
coefficient
of
variation
is
generally ±
0.17
%.
Similary,
the
Viennese
foot
is
a
digital
foot
without
its
modern
precision,
silicet :
19. 109
257
m
/
64. 
Three 7smooth kommata
 Ratio
 7smooth factors
 Value





(commun) komma  2400 / 2401
 (2^{ 5} × 3^{ 1} × 5^{ 1}) : (7^{ 4})

=
 1.000 416


poppy(seed komma)
 4375 / 4374
 (5^{ 4} × 7^{ 1}) : (2^{ 1} × 3^{ 7})

=
 1.000 229


metric (komma)
 250 047 / 250 000
 (3^{ 6} × 7^{ 3}) : (2^{ 4} × 5^{ 6})

=
 1.000 188






Two other kommata
 Ratio
 Metrological correction factors
 Value





English komma  15 876 / 15 875
 (2^{ 2} × 3^{ 4} × 7^{ 2}) : (5^{ 3} × 127)

=
 1.000 063


digital komma
 19. 110 2976 / 19. 109 257
 (2^{ 18} × 3^{ 6}) : (19 109 257 × 10)

=
 1.000 054





Intrinsically, both measures are the same, however the terms idealistic Viennese yard and idealistic digital yard are – rigorously – notsynonym :

Ratio : Viennese Yard
 The conventional Viennese Yard measures well 896 mm.
 7smooth factors
 Value

250 047 / 250 000
 The idealistic Viennese yard is 1728 / 1000 idealistic NC.
 2^{ 3} × 3^{ 6} × 5^{6} × 7^{ 4}


1 / 1
 The metric decreased iVY equals the komma increased iDY.
 2^{ 7} × 3^{ 0} × 5^{0} × 7^{ 1}


2400 / 2401

But the idealistic digital yard equals 1728 / 1000 raw NC.
 2^{ 8} × 3^{ 6} × 5^{4} × 7^{ 0}


298. 722 816 000 mm :
 The idealistic Viennese foot
 =
 the metric increased cVF
 =
 the komma increased iDF.

298. 666 666 667 mm :
 The metric decreased iVF
 =
 the conventional Viennese foot
 =
 the poppy increased iDF.

298. 598 400 000 mm :
 The komma decreased iVF
 =
 the poppy decreased cVF
 =
 the idealistic digital foot.

298. 582 140 625 mm = one milliametre : The scientific digital foot equals one idealistic digital foot, decreased by the digital komma.

Since the decimal metre value is doubtless also a 5smooth number : 2^{ 3} × 5^{ 3} mm, one can say that the decimal metre is a metric decreased Drusian yard, i.e. three Roman pygmes.
 The metric decreased idealistic Roman digit would be 18.518 mm and the metric decreased idealistic Nippur cubit is 518.518 mm. These possible, recurring values didn't be retained. 



The deduction of the Viennese ell, also said : drapery ell, by the Viennese yard, also said : linen ell,
according to the works of Dipl.Ing. Franz Twaroch, Vienne : "Die Maßstäbe am Wiener Stephansdom" in Wiener Geschichtsblätter 57/2002.
Whilst the Viennese foot and yard was unused after MiddleAges, the drapery ell kept its legal status in Austria till 1871, next to the Austrian foot. (See above.)
From the two measures – materialised as standards outside of the cathedral at the left of its main door – only one posseeds subdivisions. This is the drapery ell.
According to the ressearches of Franz Twaroch, its total length is 77.6 cm, subdivision marks are reported at 1/8, 1/4, 1/3, 1/2, 2/3, 3/4 and at 7/8 of ell's length.
In his publication : "Die Maßstäbe am Wiener Stephansdom", Wiener Geschichtsblätter 57/2002, he demonstrated the connection of the two reported measures.
Therfor see this image below, click on to enlarge it. Parts of his works are avaibable in a third work as .pptdocument – on a slow server ! – at Viennese Univerity.

Here a copy of Twaroch's original draw, which is an extract of the quoted
"
Normen und Regelungen, St. Stephandom im Mittelalter
", Vienne 2003,
I. Pastner and S. Haiden, including the lengths measured by F. Twaroch.
If Franz Twaroch noted "Roman feet", it is however proofed, by different works *,
that the Roman foot approached to the value 296.35 mm, not about 298.65 mm,
but, Twaroch contribued a precious work for the understanding of the measures.
* Other references :
Vormetrische Längeneinheiten by Rolf C. A. Rottländer, Rottenburg / Köln
Recovery of the Ancient System Foot/Cubit/Stadion — Length Units by Dieter Lelgemann, TU Berlin.
On the Ancient Determination of Meridian Arc Length by Eratosthenes of Kyrene Dieter Lelgemann,
WS – History of Surveying and Measurement, Athens, Greece, May 2227, 2004.
Knobloch, Eberhard, Dieter Lelgemann und Andreas Fuls:
"Zur hellenistischen Methode der Bestimmung des Erdumfangs und zur Asienkarte des Klaudios Ptolemaios."
zfv (Zeitschrift für Geodäsie, Geoinformation und Landmanagment) 128. Jahrgang, Heft 3/2003, S. 211217.



This page is online since 2006, October 14 ;



