SI

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Introduction

Antique Apothecary Weights
The SI, or Système International is a standardised system of weights and measures defined and managed by CICEP. Most countries in IB use this system as their official and common system of weights and measures; the few countries that don't subscribe to the SI must comply in commercial exportation for expediency sake. (Likewise, countries exporting from SI to non-SI countries have to label their products accordingly or else face import fines & penalties.) SI units of measure were established at the Libra Convention in Paris in 1875, and are based on the traditional Roman system of measures already in use throughout much of Europe. The Convention standardised all the units and authorised the creation of physical standards - the famous platinum pes and libra which serve as standards against which all other measuring devices may be compared for accuracy. These physical standards are on deposit in the French Royal Academy of Sciences; and many countries have produced exact replicas for their own domestic use. All of the units find their derivation from the PES or foot - 600 stadiae are one degree of Latitude, passing through Paris.

Each measure has a scientific name, which is either of Latin or Greek origin; and often a local form, which varies as to local language. Thus, the libra (Latin) has variants in French (livre), English (pound), Brithenig (llifr), etc. Only the Grecco-Latin names are official, however; in general, governmental and academic research departments and publishers of text books and other standard reference works have adopted the policy of using only the official names in their documents (sometimes with local variants in parentheses).

Linear measures:

1 LUCIS ANNUAE (la) = 6.3923 x 1012 mi 9.4607 x 1012 km <-- This unit is a proposal, not QSS
1 PARCSECA (pa) = 2.0849 x 1016 mi 3.0856 x 1016 km <-- This unit is a proposal, not QSS
1 TERRUM (tm) = 101.079.729,73 MILLES [149.598.000 KM] (A.U. *here*) <-- This unit is a proposal, not QSS
1 MILLE (mi) = 5000 PEDES [1.48km, .925 mi]
1 STADIUM (st) = 125 ps / 625 p [185m, 607']
1 PERTICA (pc) = 10 PEDES [2.96m, 9'9"]
1 PASSUS (ps) = 5 PEDES [1.48m, 4'11"]
1 PES (p) = 12 UNCIAE [29.6cm, 11.7"]
1 UNCIA (uc) = 16sc or 12 dc [2.467cm, .971"]
1 DOCICULA (dc) = 16 LILIPUTICAE [2.06mm, .0809"]
1 SESTICULA (sc) = 12 LILIPUTICAE [1.54mm, .0607"]
1 LILIPUTICA (lc) = 100 UNCICULAE [128µm, .00506"] <-- This unit is a proposal, not QSS
1 UNCICULA (uuc) = [1.28µm, .0000506"]

(The MILLE is short for MILLE PASSUS)

Area:

1 CARUCATA (cc) = 120jg [74.88 ac]
1 JUGERUM (jg) = 120x240 PEDES [.252 hectare, .624 ac]
1 ACNUA (acn) = 120x120 PEDES [.312 ac]
1 UNCIAGRIA (ucjg) = 1/12 JUGERUM [210 sq. m, 251 sq. yd]
1 SCRIPULUM (scp) = 1/288 JUGERUM 10x10 PEDES

Weight:

1 TONNEAU (ton) = 50 TALENS [975.45kg, 2280 lbs] (proposal)
1 TALENS (tl) = 60 LIBRAE [19.509kg, 45.6lb]
1 LIBRA (lb) = 12 UNCIAE [325g, .76lb]
1 UNCIA (uc) = 8 DRACHMAE [27.1g]
1 DRACHMA (dr) = 60 GRANA [3.39g]
1 GRANUM (gr) [56mg]

1 C of water at 1 atm at 2.33º (max. density of water) weighs 10 LIBRAE. Each successive twelfth of a libra or pes is named thus: sextans (2); quadrans (3); triens (4); quincunx (5); semis (6); septunx (7); bessis (8); dodrans (9); dexcunx (10); deunx (11).

Volume:

1 AMPHORA (aa) = 8 C. or 1 cu. PES [26.01 l]
1 CONGIUS (C) = 8 O. or 216 UNCIAE [3.25 l]
1 SEXTARIUS (S) = 36 UNCIAE [542 ml]
1 OCTARIUS (O) = 27 UNCIAE [406 ml]
1 UNCIA (fl.uc) = 8 DRACHMAE [15 ml]
1 DRACHMA (fl.dr) = 60 GUTTAE [1.882 ml]
1 GUTTA (gtt) = [31 ul]

Household:

1 CALICULA (cx) = 6 fl.uc. (a lg. cup)
1 POCLUM (P) = 4 fl.uc. (a sm. cup)
1 fl UNCIA (fl.uc) = 2 CONCHA
1 CONCHA (CC) = 4 COCHLEA (tablespoon)
1 COCHLEA (cc) = 1 fl DRACHMA (teaspoon)


Time:

1 ANNUM (an) = 365.242190 DIES [1 tropical year]
1 DIES (ds) = 24 HORAE [1 day]
1 HORA (hr) = 60 MINUTAE [1 hr]
1 MINUTA (min) = 60 SECUNDA [1 min]
1 SECUNDA (sec) = 60 TRISAE [60 trices]
1 TRISA (ts) = 60 QUADRISAE [1/60 sec]
1 QUADRISA (qs) = [1/60 trice]

(The MINUTA and SECUNDA are short for PARS MINUTA and PARS MINUTA SECUNDA respectively. The ANNUM is used mostly in astronomical observations.)

Temperature:

The official SI scale for temperature is called the Sextigrade scale, and was arrived at by comparing and synthesising the 60 degree scales devised by Celsius and Roemer. While its degrees are officially called GRADUS SEXTIGRADIS, the scale is best known as the "Celsius scale". Some handy figures:

= freezing point of water at 1atm of pressure
13° = pleasant room temperature
16° = a rather warm day
20° = a hot day
22.2° = normal human body temperature (oral)
24° = summer day in Casablanca
60° = boiling point of water at 1atm of pressure

If you're into candy making, mark these in your cookbooks!

Thread Stage 66-67.2°
Soft-Ball Stage 67.2-69°
Firm-Ball Stage 70.8-72°
Hard-Ball Stage 72.6-78°
Soft-Crack Stage 79.2-85.8°
Hard-Crack Stage 89.4-92.4°

Lord Kelvin developped an absolute temperature scale using the same basic degree scale but based upon absolute zero - the point at which molecular energy is at a minimum. Absolute zero, or 0° K, is equal to -163.89° C.

Many other temperature scales are or have been in use by various countries around the world, notably Farenheit, Roemer and Reaumur.

Computer Memory:

bit
word 4bits
byte 8bits
tryte 64bytes
quadryte 4096bytes
quintyte 216.000bytes
hexyte 12.960.000bytes

Metal Purity:

There are two, sometimes debated, methods for reckoning metal purity. The Scandinavian countries prefer the reckoning of purity by mass of metal; the Commonwealth countries prefer the reckoning of purity as an absolute percentage, regardless of mass of metals involved or of volume occupied.

The Commonwealth's usage divorces purity from mass, volume and indeed any physical aspect except real number of atoms of metal, relative to each other in the alloy by measuring purity in terms of a pure number. This number represents a pergross of the total amounts of metal in the alloy, regardless of any actual weight, mass or process used to create the alloy.

16 LOTHIA, lode (ld) = 1.000 silver (16/16ths)
24 CARRATUS, carat (ct) = 1.000 gold (24/24ths)

The Scandinavians disagree with that reckoning method, in stead prefering their own tradition of measuring purity in terms mass of metal. Currency values, in the SR, are afterall still defined by weight, and so divorcing mass from purity is seen as unnecessarily complicating the definition of coinage standards.

It has been proposed that both methods can be combined such that the same units are used, and that (when necessary) one can specify whether one means mass or fluid (fl) measures or a pure pergross. Of course, the chemically pure metal ace is the same for both measures, the ace being 144p/g (i.e., 100% pure). The Commonwealth, and many other countries beside, has not agreed to the compromise because the end result is the same: a reckoning of metal purity as an absolutely pure pergross of metal content in alloy. In other words, it makes little difference that the Scandinavians say a piece of metal has silver and copper in an alloy of 24 semunciae each -- the result is that the alloy is 72p/g silver (i.e., 50%) and 72p/g copper (i.e., 50%).

Masswise:
AS, ace (as) = 24 SEMUNCIAE, semiounces (suc) = 288 SCRUPULI, scruples (scr)
Volumewise:
AS, ace (as) = 24 SEMUNCIAE, semiounces (fl.suc) = 288 SCRUPULI, scruples (fl.scr)
Pergrosswise:
AS = 144p/g (i.e., 100%)

The ten most popular fractions of metal purity in silver and gold coins are:

SILVER GOLD
16/16 = 1.000 24/24 = 1.000
15/16 = 0.938 22/24 = 0.917
14/16 = 0.875 21/24 = 0.875
13/16 = 0.813 18/24 = 0.750
12/16 = 0.750 15/24 = 0.625
10/16 = 0.625 14/24 = 0.583
08/16 = 0.500 12/24 = 0.500
06/16 = 0.375 10/24 = 0.417
04/16 = 0.250 09/24 = 0.375
02/16 = 0.125 06/24 = 0.250

NB: In the NAL-SLC, any article that contains less than 12/24 can not be advertised as or sold as "gold".

However, as countries use these fractions differently, they do not express whether purity is measured as a fraction of mass or volume or a pure number, as all sides have agreed on the fractional representation of their respective reckoning methods. For instance, the Federated Kingdoms measures metal purity as a pure pergross, where its current coins are 15 ld ("traditional") and 13 ld for silver, and 22 ct ("traditional") and 15 ct for gold. The Scandinavian Realm measures purity by mass, where main coins are traditionally 21 suc for both silver and gold coins.

Precious metals are weighed in SI ounces (there being no distinction between avoirdupoid and troy weights as there is *here*). Other local or traditional units exist as well, though have largely been brought in line with the SI units.

1 mark (an old unit of metals weight) = 2/3lb = 218.0g.
1 farthing (another old metal weight) = 1/6lb or 1/4 mark = 54.5g

Thus, a bullion piece of gold might be sold as a "2 uc 22 ct farthing", which means that the piece of metal in question weighs 2 ounces and that 22/24th of the volume is gold. However, to calculate its actual gold content, one must know what alloy is used and its specific weight. If the alloy used is silver, then it contains 1 uc 7 dr 15.8 gr of gold; if the alloy used is copper, then it contains 1 uc 7 dr 21.4 gr of gold; if the alloy used is aluminium, then it contains 1 uc 7 dr 48.4 gr of gold. Had the bullion piece been sold as a "2 uc 22 suc farthing", which means that the piece of metal in question weighs 2 ounces and that 22/24th of its mass is gold, then it would be much easier to determine that the actual gold content regardless of what alloy is used: 22/24th of 2 uc is 1 uc 6 dr 40 gr. This illustrates why most are trending away from measuring purity in terms of volume towards continuing to describe metal purity in terms of mass. Purity by mass is simply easier to deal with than purity by volume or pergross, claim the Scandinavians. The Commonwealth remains unconvinced, given the mathematical gymnastics required in order for them to derive the purity of their metals. In the Commonwealth's view, you look at the inscription on a raw bullion ingot, say, "Silver, 4/16 pure", you know immediately that four parts out of sixteen total -- 36p/g (i.e., 25%) of the total metal content -- is pure silver, the remaining twelve parts being alloy.

Scientific Units

These compound units are less well defined than *here*, however, CICEP have devised a standardised list of such measurements as are required for engineering, physics and the like. There is less of a tendency to use the names of famous scientists in naming measures.

Speed

For most scientific methods speed is measured in feet per second (p/s). However, in motor vehicles, miles per hour (mi/h) (0.925 mph here) is more commonly used.

1 PES PER SECONDA p/s = [0.296 m/s]
1 MILLE PASSUS PER HORA mi/h = 1.38 p/s [.925 mph]

Acceleration

The scientific acceleration unit is feet per second per second (p/s/s) or Gallileo (Gal). However, in motor vehicles again there is a difference - usually one talks about going "From 0 to 60 in x seconds".

1 GALLILEO Gal = [0.296 m/s/s]

Frequency

One Hertz (Hz) is once a second. There are 3600 Marconis in a Hz (once a trice).

1 HERTZ Hz = [1 Hz]
1 FESSEDEN Fn = 3600 Hz [3.6 KHz]
1 MARCONI Ma = 60 Fn [216 KHz]

1 Hertz = 3 600 Fesseden(Fn) = 216 000 Marconi(Ma)

Force

Is measured in the pondal (pdl) - (lb*gal) (or the force needed to increase the acceleration of one pound by one Galileo. Historically the pound-force (lb) was similarly defined but it was "undefined" in 1902 because it made calculations excessively complicated.

1 PONDAL pdl = [1.104 N]


Pressure

Is measured in poundals per square inch (pdl/uc^2) or Toricelli (Torr). The common person still thinks in terms of pounds per square inch (lb/uc^2) quite often though - especially in terms of tyre pressure. All tyres must be measured in poundals per square inch!

1 TORICELLI Torr = [1.814 kPa]

Energy

There are two measures of Energy - the calorie (cal) and the Joule (J). The Calorie is the amount of energy needed to raise one dram of water one degrees sextigrade and the Joule is amount of energy needed to exert the force of one poundal over the distance of one passus (pdl*ps). They are both considered "official" by CICEP but for most scientifical purposes the Joule is used. In fact, there have been various proposals to "undefine" the Calorie. Calories are mainly used on packaging for food, like here, and in weight considerations. The poncelhora (pon*h) is often used for the purpose of metering electricity for homes

1 PONCELHORA (ponh) = [5.8428 kJ]
1 JOULE J = [1.623 J]

Power

Is measured in Joules per second (J/s) or Watts (W). 60 Watts = 1 Ischus (i) (Joules per trisa) and 60 Ischi = 1 poncelet (pon) (Joules per quadrisa).

1 PONCELET pon = 60 i [5.8428 kW]
1 ISCUS i = 60 W [97.38 W]
1 WATT W = [1.623 W]

Charge

Is measured in Coulombs (C) - the amount of charge of 6.5e18 electrons. (Note: The concept of "conventional current" does not exist *there*. Also, it's worth noting that the Coulomb is a base unit but the Amp is not)

1 Coulomb C = [-1.0414 C]

Current

Is measured in Coulombs per second (C/s) or Amps. Because an amp is quite big, Coulombs per hour (Faradays) are also used.

1 AMPERE A = 3600 F [-1.0414 A]
1 FARADAY F = [-0.2897 mA]

Potential Difference

Measured in Joules per Coulomb (J/C). For bigger mains electricity Volts (poncelhora per Coulomb, ponh/C) is used. Volt is much bigger!

1 VOLT V = 3600 J/C [-5.6105 kV]
1 J/C J/C = [-1.558 V]

Momentum

Measured in Newtons (N) as (pdl*p/s). Note different unit "Newton"!

Sizes of Common Articles

IB's letter size is one foot tall and in the proportion 1:√2. In the trade, this is called "Quarto-post Royal".
An athletics track is 264 passus all the way around.
  • A veritable mathomhouse of interesting sizes and measures of common articles can be found here.
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