-: A :-

Glossary: Home Tables A B C D E F G H I J K L M N O P Q R S T Th U V W X Y Z

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 series.
      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.

column byte +------+-------+------+------+ top rail | | D | L | V | U I +------+-------+------+------+ unit rail | M | C | X | I | N X bit   +------+-------+------+------+ ABACUS COMPUTER

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.
      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 absent.

• 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 decimally.
      A system of Roman fractions derives from using weights of a pound as weights here. cf Carat, which would be 1/2304,

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

For weights, the wey-stones were 1,2,4,8 oz, the pound migrated upwards to 15, and later 16 ounces.

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.

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	-

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 terrain.
      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.

Look-up form Look-down form 3 l. s. d. 10 3 10 ---- (20) (12) 1 --- --- 1 12 1 10 3 20 12 ----------- 20 1 & 10/20 & 3/12 1 \20&10 \12&3

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.
      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 are identical.

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 circles, so
      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.

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

division: pound \ 12 ounce \ 8 drachm \ 3 scruple \ 2 obol \ 10 grain

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 value.
      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.