-: A :-
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- A *
A symbol used in this gloss to represent augmented. The designation
of a scale as A3 means that the units are 1 1/3 times larger than they ought
be. For example, the Austrian pound and its divisions are A5 of the normal
It is typically applied to segments.
See also D.
- abacus *
A stone-board, formerly used for calculating numbers. In practice, it has
two-ish rails, and many columns. Several numbers might be stored on the
same row of columns: an abacus with 18 digits might be used for adding say
two eight-digit numbers, or holding several small numbers.
The European forms are typically open tables, with freely movable stones.
Eventually, these stones would become beads mounted on rails, which would
be moved up and down as the calculation proceeded.
One understands much about the history of notations from the abacus. The
operations from column to column were identical, which leads to a general
radix or base. The vertical arangements were generally different,
which generally leads to an alternating base, eg 10, 20, 40, 60, 80, 120.
top rail | | D | L | V | U I
unit rail | M | C | X | I | N X bit
One reads columns to completeness, but can start from any position.
The most common form is in order, eg UNIX vs IXUN. However, one can read
the columns top or bottom first, eg NUXI or XINU. Of the four, we have
eg (common) UNIX, vs IXUN (arabic), along with a few samples of NUXI (eg
Mayan, and 'one hundred, four and twenty'.
The denominational form gives a special symbol for each cell, and
repeats this symbol for each stone in the cell. It is not unlike using
coins. One only needs a zero to indicate an empty collection, ie 0 specific
The measured forms gives each column a name, and one has forms for
a given column. It resembles a measure, like 5 ft, 2 in. Empty
columns are ignored, eg 1C 8I and 1C 0X 8I are the same.
The alphabetic form is where one has a symbol for each combination
of number and column, eg 7X. The system is used with the Demotic
system in Egypt, and also with the Hebrew and Greek alphabets. One still
sees it in stamps for making up money, eg 70c + 2c stamps.
The rail-digit has symbols for each combination in a rail, eg 2V or
3I. One typically represents top-rail numbers with letters, eg A=10, B=20,
and the unit-rail with numbers, eg 1, 2, .... The sumerian wrote numbers
in terms of rail-digits, in UNIX fashion, viz 1.33.24 = 1C3B5. Spacing
provided for absent medial and semi-medial zeros, and sometimes a full-stop
was used, eg 0:00,00,32,14 = '...C2A4', but 40.01 = D 1, not D1 (41).
The column-digit system is used where a digit stands for a whole
column. This is how modern western numbers are implemented, eg 16777216.
Of zero, one notes it is more than just 'the empty column',
and the failure to replicate current usage does not imply that zero was
- single zero = nothing only, eg Egyptian
- significant = to move a number from named column, eg 1 from 1,000
- nonsignificant = adding zeros makes no change, eg 1. vs 1.0000
- medial = 1C 8I = 108 vs 1 8
- semimedial = where top and unit rails have different digits, 4L 1I
= 4 1 vs 41 4V1I. [Sumerians could use this!]
- Ace, As *
A Roman Unit, divided into a standard fraction system, and reckoned
A system of Roman fractions derives from using weights of a pound
as weights here. cf Carat, which would be 1/2304,
For weights, the wey-stones were 1,2,4,8 oz, the pound migrated upwards
to 15, and later 16 ounces.
|as|| 1 || foot, pound, hour &c.
|uncia|| 1/12 || so inch, ounce
|digit|| 1/16 || so nail, clove [1/16 of foot]
|solidus|| 1/72 || so dennier, zoltnic
|drachm|| 1/96 || drachm [handful of obolus, as a gold coin]
|scruple|| 1/288 || Greek = little stone
|obolus|| 1/576 || Greek measure = spear [reduced from copper -> gold]
|siliqua|| 1/2304 || carat [as 1/24 dennier = drachm]
|calcus|| 1/6912 || rock-let, grain, corn
- acre *
A English land unit, being 160 perches. For a given perch, one can make
the proportional cadastral units: perch, furlong, mile, rood, acre and chain
mile \ 8 furlongs \ 40 rod \ 6 fells, later mile \ 80 chain \ 100 link
sq mile \ 640 acre \ 4 rood \ 40 perch
One can reconstruct the system as a comma system, based on a fathom.
mile \ 800 fathom ; acre \ 1000 sq fathom
The french use an arpent = 100 sq perches, of 18 or 22 feet.
Units tend to be smaller in the cities than in the open country: the idea is
that one is supposed to live off an acre or so of land, the acre varies as the
|System|| perch || mile || acre || Notes
|Metric|| 5 m || 1600 m || 4 000 sq m || fantasy, on rood = 5 m
|Imperial|| 16.5 ft || 5280 ft || 43560 sq ft || Statute
|Woodlands|| 18 ft || 5760 ft || 51840 sq ft || -
|Scottish|| 18 ft || 5760 ft || 51840 sq ft || Scottish ft = 12.064864 inches
|Nautical|| 19 ft || 6080 ft || 57760 sq ft || fantasy, on Nautical mile
|Plantation|| 21 ft || 6720 ft || 70560 sq ft || -
|Normandy|| 22 ft || 7040 ft || 77440 sq ft || French ft = 12.789 inches
|Cheshire|| 24 ft || 7680 ft || 92160 sq ft || -
In india, the perch \ 6 gaz or gudge , and the beegah an arpent.
- Added Fractions *
A fraction representation by allowing the numerator to be
a mixed fraction, this continues onwards.
Such fractions derive naturally from measurements, where one might read
a ruler as 3 and 1 1/2 eightths, or 3 & 1/8 & 1/2.
One can use look-up or look-down representations.
Note that one never reduces such fractions. While it is true that 10/20
is a half, the 3/4 refers to the gap between 10/20 and 11/20, not between
1/2 and 1.
Look-up form Look-down form 3
l. s. d. 10 3 10 ----
(20) (12) 1 --- --- 1 12
1 10 3 20 12 -----------
1 & 10/20 & 3/12 1 \20&10 \12&3
A lining presentation of lookup and look down fractions is given, where the
ampersand & precedes the numerator, and either / or \ the denominator, according as
the denominator is below-after (/) or above-before (\) the numerator. The fractions
- Admiralty System *
A geographic system, based on a nautical mile of 6080 BI feet,
rated as 6000 feet. The system is a proportional construction, and has not
been in common use.
- air *
Air can be treated as a di-atomic ideal gas, Ai_2. The molecular weight of
the air molecule is 28.96443.
The equation PM=dRT holds, where
P = pressure = 101325 Pa
M = molecular weight = 28.96443 for Air
d = density (found to be 1.2922567 kgms / cbc metre.)
R = universal gas constant = 8314.4126 N.m/kmol.K
T = thremmage, eg 273.15 K
- amphora *
A (wine) jug, with two handles = ambi- (both) + phoreus (carry), so english
amber, german Zuber, etc
See also eimer, zuber
- Angle Units *
The most common base unit is the circle, divided into a major fraction,
and then into lesser fractions. For example,
circle \ 6 sextant \ 60 degree \ 60 minutes \ 60 seconds
circle \ 4 quadrant \ 100 degree \ 100 minute \ 100 second [metric]
circle \ 120 degree \ 120 minute \ 120 second [twelfty]
radian \ decimals or other radix fraction [natural]
The sequence continues on to thirds, fourths, fifths, sixths, sevenths.
Isaac Newton gave an angle in sixths and sevenths, for example.
One can derive a nautical measure, based on one minute of arc on the
earth's surface, as
earth circle \ 360 degree \ 60 minutes = 1 n.mile of 6000 geo ft
earth circle \ 400 degree \ 100 minute = 1 kilometre of 3240 geo ft
earth circle \ 120 degree \ 120 minute = 1 mrinal of 9000 geo ft.
Exactly which circle is used can be to some extent set by the system,
the Telegraphic form uses the equator as its basis.
One can also use a time system as Right Assensiom, as in Astronomy.
circle \ 24 hours \ 60 minutes \ 60 seconds [time, as Right Assension]
- Angle, Solid
For solid angle, one might treat the circle as a line or as a fraction.
When treated as a line, one gets the solid angle as area, zB
steradian = radian square ; Sphere = 4pi
degree excess = radian * degree ; Sphere = 2C
square degree = degree * degree ; sphere = C²/pi
When treated as excess measure, one notes the sphere exceeds the plane by two
degree excess = Sphere / 2C
When treated as a fraction, one has the circle, sphere &c as equal to unity,
and the degree, minute &c are fractional places.
twelfty measure uses this division.
- Apothecaries Weight *
A system of weight formerly used in Medicine, the denominations were used
in medical books, the implememtations depended on the particular country.
division: pound \ 12 ounce \ 8 drachm \ 3 scruple \ 2 obol \ 10 grain
|lb / gram|| kg / oz || g / gr || Country
|350.037 50|| 34.282 041 || 16.455 379 780 || 5/6 Austrian
|350.783 25|| 34.209 15 || 16.419 928 262 || Prussia
|352.512|| 34.041 394 || 16.339 869 281 || SWS
|357.647 6|| 33.552 580 || 16.105 238 788 || Wuttenberg
|357.663 8|| 33.551 061 || 16.104 509 318 || Kurhessen
|357.853 8|| 33.533 322 || 16.095 958 741 || Nuremberg and much of Germany
|358.323 358|| 33.489 304 || 16.074 886 099 || Russia
|360.000 0|| 33.333 333 || 16.000 000 000 || Baden and Lubeck [Metric]
|373.241 954|| 32.150 726 ||15.432 348 743 || England and the US
|420.045 0|| 28.568 367 67 || 13.712 816 483 || Austria
- areas of *
These are used as area-units
Wales: 8016 sq miles
Texas: 2673439 sq miles
- assay ton *
A unit in mining, which represents a ton, where an assay ounce represents
a troy ounce. Typically, the assay unit is the milligram, but one can
use any likely-sized unit in its stead.
1 AT = 1 ton * 1 mg / 1 troy oz.
- atomic units *
A system of units, derived from the electron charge, dirac's constant,
and electronic mass, with the UES EU or EI rule applying. Conversion
factors were given in the 2002 Codata tables.
- Austral *
A unit for calculating easter. The unit represents an hour-like
measure, derived from subtracting the golden number from
nineteen times the date in the Lunae month. A Lunae day is 19 Australs.
An austral combines both the epact and the golden number in a single
The moon advances 360 Australs a year, with year zero as austral 304.
An epact shift equates to a Lunae, or 19 australs. At this time (1900-2100)
there are 9 such australs, making the base year zero 304+171 = 475 Australs.
The correction by golden jump advances the moon onto the
next slot where moons might fall, equating to 30 australs. For calendars
relying on golden jumps, to this time, five have occured, making the base
304+150 = 454 australs.
The australs run from 0 on 21 March to 569 on 18 April. The last two
days (17, 18 Apr) have 27 and 30 Australs respectively.
© 2003-2004 Wendy Krieger