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The Primel Metrology
Primel is a proposed system of measurement units (a "metrology") comparable to the metric system, but grounded in dozenal (base twelve) arithmetic, rather than decimal. Primel units are derived from certain physical phenomena experienced by humans in their environment, primarily the mean solar day, the acceleration due to Earth's gravity, the maximal density of water, and other properties. These are comparable to the metric system's basis in physical phenomena, but the chief distinction is that Primel uses Earth's gravity, rather than its circumference, as a basis for deriving its units.
Primel is a "coherent" system of measure, in that, for each type of physical quantity, it defines a specific, primary unit of measure, known as its "coherent" unit for that quantity; the coherent units for all types of physical quantity bear direct 1to1 relationships to each other, without any arbitrary extraneous factors. Primel makes use of a set of generic names for such units, each formed transparently from the name of the physical quantity itself, plus the suffix "el", short for "element of" (by analogy with "pixel" being an "element of" a picture). Such generic names are termed "quantitels", and are meant to be usable across potentially many systems of measure. The name "Primel" derives from the fact that it happens to be the first (or "prime") system of measurement to make use of quantitels. All Primel unit names bear the "prime" character ( ′ ) as a common prefix, to distinguish them from the units of any other system.
Beyond the "coherent" units, Primel defines many auxiliary units for each type of physical quantity. First, it scales its quantitels to any power of dozen, and sometimes to convenient factors of dozen, using a system of dozenal scaling prefixes called Systematic Dozenal Nomenclature (SDN). These are comparable to the decimal scaling prefixes defined for the metric system, but take advantage of the high factorability of base twelve. Second, Primel also introduces many socalled "colloquial" names for its units, as alternatives for the formal names derived from quantitels and SDN prefixes. Each colloquial name attempts to provide an intuitive sense of scale by relating the given Primel unit to a customary unit that it might approximate, or to some physical object known to human experience, that might be comparable in size. Such colloquial names themselves become amenable to scaling using SDN prefixes.
See the Table of Primel Coherent Units at the bottom of this page for details about the units defined by the Primel system. It contains links to further pages in this wiki for each category of physical quantity.
Dozenal (base twelve) arithmetic
Primel is a measurement system grounded in duodecimal or "dozenal" base arithmetic. Given the high factorability of the number twelve compared to ten, dozenal is arguably a more convenient base for human use than decimal. It is for that reason that so many historical systems of measure naturally incorporated factors of twelve. However, when they did so, it was only piecemeal. Primel can be characterized as a "dozenalmetric" metrology, similar to the TimGrafutMaz (TGM) metrology devised by Tom Pendlebury. Like TGM, Primel systematizes its units around powers of twelve to the same degree that the metric system (now known as the International System of Units, or SI) systematizes its units around powers of ten.
Pages within this wiki compare dozenal quantities of Primel units with many decimal quantities of conventional SI and United States Customary (USC) units. To avoid confusion, this wiki explicitly annotates the base of every number longer than a single digit. It uses the standard mathematical convention, placing the base annotation into a right subscript. However, instead of expressing the base itself as a number in decimal, a subscript "d" indicates decimal, and a subscript "z" indicates dozenal: For instance, Ӿ = 10_{d}, Ɛ = 11_{d}, 10_{z} = 12_{d}, 100_{z} = 144_{d}, etc.
The English language is fairly wellequipped with a nomenclature for dozenal arithmetic, having wellestablished terms for the first and second powers of twelve: one dozen and one gross. The situation is not so good at the third power, traditionally referred to by the rather awkward phrase "a great gross". With each higher power simply prefixing another "great", the result quickly gets unwieldy. Instead of this, this wiki adopts the expedient of coopting "galore", an English word of Irish origin, meaning "in abundance". This word is unusual in being a postpositive adverb; in other words, unlike other English modifiers, it always follows the word it modifies, and never precedes it. This means that we have an opportunity to ascribe another meaning to it if we position it prepositively, without necessarily interfering with its customary meaning when postpositioned. Therefore, Primel proposes to use one galore for the third power of twelve, one dozen galore for the fourth power, and one gross galore for the fifth. For higher powers still, Primel concatenates "galore" with a numeric prefix derived from Classical Latin or Greek, indicating a certain power of one galore. Thus, rather than coining an analog for "million", Primel proposes calling the sixth power of twelve one bigalore, the seventh power of twelve one dozen bigalore, the eighth one gross bigalore, the ninth one trigalore, and so forth.
Systematic Dozenal Nomenclature
Systematic Dozenal Nomenclature (SDN) provides a set of dozenal power prefixes (usable with any metrology) that are analogous to SI's decimal scaling prefixes. However, SDN does not require an international committee to generate higher and higher order prefixes. Instead, it derives its prefixes systematically from a set of twelve familiar Greek and Latin numeric roots, each directly expressing the exponent in a power of twelve. These roots are identical to those used by the International Union of Pure and Applied Chemistry (IUPAC) to construct Systematic Element Names, extended to support dozenal base with the addition of two roots, dec and lev, to represent ten and eleven as single dozenal digits (Ӿ and Ɛ). IUPAC chose its roots carefully so that they all begin with unique letters, making them amenable to singlecharacter abbreviations. The dozenal additions maintain this uniqueness.
SDN also accommodates existing combination forms of these numeric roots, keeping intact their preexisting meanings as simple multipliers. To avoid clashing with these forms, the power prefixes are derived by appending distinct syllables onto the roots: qua for positive powers, cia for negative powers. The following table lists the roots, the existing multiplier prefixes, and the corresponding power prefixes:
Digit (N)  Root Form  Multipliers (N ×)  Reciprocals (N^{−1})  Positive Powers (10^{N}_{z})  Negative Powers (10^{−N}_{z})  

Prefix  Abbr  Prefix  Abbr  Prefix  Abbr  Prefix  Abbr  
0  nil  nili  n•n*
 nilinfra  n\n\
 nilqua  n↑n@
 nilcia  n↓n#

1  un  uni  u•u*
 uninfra  u\u\
 unqua  u↑u@
 uncia  u↓u#

2  bi  bina  b•b*
 bininfra  b\b\
 biqua  b↑b@
 bicia  b↓b#

3  tri  trina  t•t*
 trininfra  t\t\
 triqua  t↑t@
 tricia  t↓t#

4  quad  quadra  q•q*
 quadinfra  q\q\
 quadqua  q↑q@
 quadcia  q↓q#

5  pent  penta  p•p*
 pentinfra  p\p\
 pentqua  p↑p@
 pentcia  p↓p#

6  hex  hexa  h•h*
 hexinfra  h\h\
 hexqua  h↑h@
 hexcia  h↓h#

7  sept  septa  s•s*
 septinfra  s\s\
 septqua  s↑s@
 septcia  s↓s#

8  oct  octa  o•o*
 octinfra  o\o\
 octqua  o↑o@
 octcia  o↓o#

9  enn  ennea  e•e*
 enninfra  e\e\
 ennqua  e↑e@
 enncia  e↓e#

Ӿ  dec  deca  d•d*
 decinfra  d\d\
 decqua  d↑d@
 deccia  d↓d#

Ɛ  lev  leva  ℓ•L*
 levinfra  ℓ\L\
 levqua  ℓ↑L@
 levcia  ℓ↓L#

Two styles of abbreviations are shown for each prefix. Both combine the initial of a digit root with a special symbol representing the glue syllable for the particular prefix. The first abbreviation, set in sanserif font, represents the glue syllable using a special symbols available in Unicode; this should be the preferred choice for typesetting. The second abbreviation, set in monospaced font, represent the glue syllable using a pure ASCII alternative; this can be used as a substitute in disadvantaged environments that do not support Unicode.
When a multiplier contains multiple digits, or when the exponent of a power contains multiple digits, SDN expresses these by concatenating digit roots. This relies on exactly the same placevalue arithmetic principle that HinduArabic numerals employ. The final digit is then terminated as either a multiplier or power form; this determines the form for the whole string. So for example, the following table shows the multiplier and power prefixes corresponding to the next 3 dozenal values beyond eleven:
Digit (N)  Root Form  Multipliers (N ×)  Reciprocals (N^{−1})  Positive Powers (10^{N}_{z})  Negative Powers (10^{−N}_{z})  

Prefix  Abbr  Prefix  Abbr  Prefix  Abbr  Prefix  Abbr  
10_{z}  unnil  unnili  un•un*
 unnilinfra  un\un\
 unnilqua  un↑un@
 unnilcia  un↓un#

11_{z}  unun  ununi  uu•uu*
 ununinfra  uu\uu\
 ununqua  uu↑uu@
 ununcia  uu↓uu#

12_{z}  unbi  unbina  ub•ub*
 unbininfra  ub\ub\
 unbiqua  ub↑ub@
 unbicia  ub↓ub#

Because the power prefixes are distinct from the multiplier forms, both can be freely combined without ambiguity, to create an analog of scientific notation. So for instance, bihexpenta (bhp•) represents 265_{z}, bihexapentqua (bh•p↑) represents 26×10^{5}_{z}, binahexpentqua (b•hp↑) represents 2×10^{65}_{z}, and bihexpentqua (bhp↑) represents 10^{265}_{z}.
To completely represent scientific notation, we need one additional lexical element, to represent a fraction point. SDN uses the syllable dot for this purpose (abbreviated with the usual period). Hence, bihexapentqua (bh•p↑), representing 26×10^{5}_{z}, can also be expressed as bidothexahexqua (b.h•h↑), representing 2.6×10^{6}_{z}. A multiplier digit is only required to the right of dot. If there is no digit to the left, it is assumed to be nil (0). So for example, dothexa (.h•) represents 0.6_{z}, i.e., a half.
SDN also provides a set of prefixes representing the reciprocals of whole numbers, using the marking suffix infra (abbreviated with a backslash \ ). This derives directly from the Latin word infra, which means "below" or "under". The sense is that the preceding digits are being placed under the horizontal line of a fraction. So, for example, a fifth can be expressed as pentinfra (p\); a seventh as septinfra (s\); and so forth. These can be freely combined with the ordinary multipliers to express any rational number. Thus, 5/7 could be expressed as pentaseptinfra. (p•s\). Interestingly, these reciprocal prefixes act as distinct multiplicative factors, so there is no order dependency like there would be with an actual division operator. Hence 5/7 could be expressed equivalently as septinfrapenta (s\p•). This will not be confused with 7/5, because that would be expressed as septapentinfra (s•p\), or pentinfrasepta (p\s•).
The syllable per can be combined with powers of dozen to provide dozenal analogs of decimal percent (%) and permille (‰). Dozenalists have often expressed these as "pergross" and "per greatgross". However, in SDN, these can be pronounced perbiqua and pertriqua. To some extent these are redundant with bicia and tricia, but it is often helpful to think of a fraction as a number of parts from a group. So for example, a ratio of 1/3 could be expressed as 40%_{z} ("four dozen perbiqua") or even 400‰_{z} ("four gross pertriqua"). This could be extended to any power of dozen, so for instance analogs for "parts per million", "parts per billion", "parts per trillion", etc., could be expressed as perhexqua, perennqua, perunnilqua, etc.
Quantitels
Quantitelsare systematic names for coherent units of measure derived directly from the names of the physical quantities they measure, plus the ending el, which signifies "element", as in the familiar word "pixel" = "picture element". For example, lengthel is the quantitel for a coherent unit of length. When a quantity has multiple synonyms (e.g. "work" and "energy"), it can have multiple synonymous quantitels (e.g. workel and energel); such synonyms can be used interchangeably.
Quantitels are generic and can be used across potentially many metrologies. This particular metrology is named "Primel" because it is the first (i.e., prime) system to use such unit names. "Primel" can be used as a disambiguating adjective to distinguish Primel quantitels from those of other metrologies (e.g. Primel lengthel), but this is optional and may be omitted when the discussion is exclusively about Primel units. The prime character ( ′ ) serves as an abbreviation for this prefix, marking every Primel unit as such (e.g. ′lengthel). It may be left silent, or pronounced "prime" or "Primel" as needed.
Colloquial Names
In addition to systematic quantitel names, Primel proposes "colloquial" names, or "nicknames", for some of the coherent units, as well as for some useful multiples and dozenal powers of the coherent units. Some of these proposed nicknames will be purely fanciful. For instance, because the ′timel is rather short and fleeting, Primel proposes the colloquial name ′jiff for this. Because the unqua′timel is about the time to blink an eye, Primel proposes nicknaming this the ′twinkling. Because the ′lengthel is about the size of a bit of food pinched between thumb and forefinger, Primel proposes nicknaming it the ′morsellength. And so forth.
But in many cases a nickname will be proposed because a unit closely approximates a customary or SI unit. For instance, because the trina′lengthel approximates the customary inch (which in other languages is called a "thumb", e.g. Latin pollex), Primel proposes to nickname this the ′thumblength. Because the unqua′lengthel approximates the customary "hand" measure, Primel proposes to nickname this the ′handlength. Because the trinaunqua′lengthel approximates the customary foot, Primel proposes to nickname this the ′footlength. And so forth.
Primel colloquial names often follow a pattern that concatenates the thematic "prime" prefix, plus a "colloquial" adjective (often of Classical origin ending in al or ar), plus the plain English word for the physical quantity being measured. For instance, the colloquial adjective hand, plus the physical quantity length, yields the nickname ′handlength for the unqua′lengthel. Primel leverages this pattern to name related units for derivative physical quantities, by reusing these colloquial adjectives with different physical quantity names. For instance, the biqua′areanel, an area of one square ′handlength, is nicknamed a ′handarea. The triqua′volumel, a volume of one cubic ′handlength, is nicknamed the ′handvolume. The triqua′massel, a mass of one ′handvolume of water, is nicknamed the ′handmass. The triqua′forcel or triqua′weightel, the force or weight of one ′handmass in Earth's gravity, is nicknamed a ′handforce or ′handweight. The quadqua′energiel or quadqua′workel, the energy or work needed to lift a ′handmass by one ′handlength against Earth's gravity, is nicknamed a ′handenergy or ′handwork. The unqua′timel, the time to traverse one ′handlength at one ′velocitel, is nicknamed the ′handtime. The triqua′powerel, a rate of power which applies one ′handenergy per each ′handtime, is nicknamed a ′handpower. The unqua′pressurel, a pressure which applies one ′handweight per each ′handarea, is nicknamed a ′handpressure. And so forth.
Primel's length units have a robust set of colloquial names running up and down the magnitude scale, from the microscopic to the macroscopic, associating these lengths with certain objects that exist at those scales. Because of this, and because of the above naming pattern, Primel can construct colloquial names for many derivative units at all these scales.
1to1 Coherence
Primel endeavors, where feasible, to relate its coherent units for different physical quantites using simple 1to1 ratios, without arbitrary extraneous factors. (TGM also mostly adheres to this principle.) Primel starts deriving its units by considering time first.
The Day
Primel uses a pure dozenal fraction of the mean solar day, namely the hexciaday (10^{6}_{z} day), as the coherent unit of time (the ′timel), equivalent to 50/1728_{d} (0.042_{z}) seconds (nickname: ′jiff). (This differs from TGM, which starts with a pure dozenal fraction of the hour instead.) Because of 1to1 coherence, this choice affects the sizes of all other coherent units in the metrology. It turns out that this yields many convenientlysized units, either in the coherent units themselves, or when scaled using simple whole number multiples and/or pure dozenal powers (in the form of SDN prefixes).
Earth's Gravity
For its unit of acceleration, the ′accelerel, Primel uses a value for net gravitational acceleration experienced on Earth's surface. The advantage of using gravity as the accelerel is that it means that the ′forcel (the coherent unit of force) will also be the weight of the ′massel (the coherent unit of mass) in Earth's gravity.
Earth's gravity varies over an appreciable range, based on a number of factors, but chiefly latitude, due to the effect of centrifugal force produced by Earth's rotation about its axis. Any value within this range is a candidate for a "standard" gravity. Primel chooses as its standard a value of exactly 9.79651584_{d} m/s^{2}, or exactly 32.1408_{d} ft/s^{2}. This choice allows for exact conversions between Primel units and both SI and USC units, not only for acceleration, but also for velocity and length, which Primel derives from the ′accelerel via the principle of 1to1 coherence.
The ′accelerel is somewhat lower than the SI standard for Earth's gravity, which is often described (erroneously) as an "average" of Earth's gravity. In actuality, the SI standard appears to be a 19th_{d}Century estimate of gravity at median latitude, i.e. 45°_{d} or 16_{z} bicia′turns (an eighth of a turn, or 1 octant, of latitude). Latitudes cover progressively more surface area toward the equator, so the actual average gravity when integrated over Earth's surface area is somewhat lower. The Primel standard approximates this much more closely than the SI standard.
The ′velocitel is the velocity a body achieves after falling for 1 ′timel under 1 ′accelerel of acceleration. This turns out to be remarkably close to 1 kilometer per hour (it is exactly 1.0204704_{d} km/h), or 1 foot per second (it is exactly 0.93_{d} fps).
The ′lengthel is the distance traversed by an object moving at a constant 1 ′velocitel for 1 ′timel. It is exactly 31/96_{d} (0.322916_{d}) inches, or exactly 8.202083_{d} mm. Primel nicknames this the ′morsellength. This results in a trina′lengthel (nickname: ′thumblength) of exactly 0.96875_{d} inch, or exactly 24.60625_{d} mm, which closely approximates the USC inch; an unqua′lengthel (nickname: ′handlength) of exactly 3.875_{d} inch, or exactly 98.425_{d} mm, which closely approximates both the 4inch USC hand measure as well as the SI decimeter; a trinanunqua′lengthel (nickname: ′footlength) of exactly 11.625_{d} inches or 0.295275_{d} m, which approximates the USC foot; and a biqua′lengthel (nickname ′elllength) of exactly 46.5_{d} inch or 1.1811_{d} m, which approximates the traditional 45_{d}inch English ell.
From the ′lengthel in turn, Primel derives units of area and volume, the ′areanel (1 square ′lengthel) and the ′volumel (1 cubic ′lengthel). The ′volumel is approximately 0.5518_{d} ml. The triqua′volumel (nickname, ′handvolume) comes remarkably close to a customary quart or a metric liter. (It is about 1.00754_{d} quarts or 0.95349_{d} liters.)
Density of Water
Primel uses the maximal density of water as its coherent unit of density, the ′densitel. This leads to a unit of mass, the ′massel, of about 0.55_{d} grams (nickname: ′morselmass); with the triqua′massel (nickname: ′handmass) being just under 1 kilogram and just over 2 pounds. Because Earth's gravity is the unit of acceleration (1 ′accelerel = 1 ′gravity), whatever the mass of anything is in ′massels, the force of its weight in ′forcels (or ′weightels) will be numerically the same (approximately, on Earth). So we could easily speak of the mass of something in ′morselmasses or ′handmasses, and its weight in ′morselweights or ′handweights, using (approximately) the same magnitudes. (Contrast this with the situation in SI, with kilograms of mass versus newtons of weight, with the factor of 9.80665_{d} m/s^{2} in between.) Units for energy (the ′energiel or ′workel), power (the ′powerel), pressure (the ′pressurel), and the rest of Newtonian mechanics, are derived in straightforward fashion.
Massic Heat Capacity of Water
To relate the phenomenon of heat and thermodynamics to the foundations of mechanics, Primel starts with a coherent unit for massic heat capacity (the ′massicheatcapacitel). This is set to a representative value for the massic heat capacity of water, within its natural range. This leads to a unit for temperature (the ′temperaturel) defined as the increase in temperature induced in a 1 ′massel sample of water by applying 1 ′workel of heat energy. Since this turns out to be a very tiny amount of temperature, a dozenal power of this, the quadqua′temperaturel, comes out to about 0.4_{d} kelvins, and thus is convenient for everyday use.
To be precise, the quadqua′temperaturel is defined as exactly 5/7 of a Fahrenheit degree (about 0.7143_{d}°F), or exactly 25/63_{d} (21/53_{z}) of a Celsius degree (about 0.3968_{d}°C), such that the range from water's melting point to its boiling point is exactly 190_{z} (252_{d}) quadqua′temperaturels, a round multiple of twelve. The ′massicheatcapacitel has been set to about 4198.76_{d} J/K/kg, specifically to yield this result; it is slightly above the theoretical average specific heat capacity of water over its liquid phase (4190_{d} J/K/kg), but slightly less than the socalled "dietary kilocalorie" (4200_{d} J/K/kg).
The quadqua′temperaturel is nicknamed the ′stadigrade, because of the equivalence of heat energy to mechanical work: The heat required to raise the temperature of a body of water by one ′stadigrade is the same amount of energy as the mechanical work necessary to lift the same body of water one ′stadiallength (1 quadqua′lengthel) upward against Earth's gravity.
Primel provides three temperature scales based on the ′stadigrade, but with different choices for a zero point: an Absolute scale zeroed at absolute zero, analogous to the kelvin and rankine scales; a Crystallic scale zeroed on the freezing point of water, somewhat resembling the Celsius scale; and a Familiar scale zeroed 40_{z} ′stadigrades below freezing, bearing remarkable similarities to the Fahrenheit scale.
Impedance of Free Space
For the moment, the table below shows what Primel electrical units would look like if the impedance of free space were used as the coherent unit of resistance/reactance/impedance, with all other electrical units derived from that. However, the author has not yet decided whether to settle on this scheme. While it has a certain elegance and symmetry from a theoretical basis, this would not make the electrical system as "friendly" to interconversion with SI and USC as the mechanical or thermodynamic systems. The author is still investigating whether to go with an approach similar to SI's, based on Ampere's Force Law.
Table of Primel Coherent Units
The following table provides an executive summary of the Primel coherent units for each type of physical quantity. The names in the first column (will) serve as links to the wiki pages covering each type of physical quantity in more detail.
MECHANICS  

Physical Quantity  Primel Unit (Abbrev) Colloquialism (Abbrev)  Derivation or Decomposition  SI, USC, & TGM Equivalents (* = exact) (~ = approximate)  
Time 
′timel (′Tmℓ)  hexciaday 
*28.93518_{d} milliseconds  
Acceleration  ′accelerel
(′Acℓ)  Earth's gravity at sealevel at latitude 34°01′34.56″_{d} (11.73ӾƐ567^{%⊙}_{z}) 
*9.79651584_{d} m/s^{2}  
Velocity = Speed  ′velocitel
(′Veℓ)  ′accelerel × ′timel ′Lgℓ ′Tmℓ^{−1} 
*28.3464_{d} cm/s  
′lightspeed
(c_{0})  speed of light in a vacuum 
256,232,Ɛ32_{z} ′velocitels  
Length = Width  ′lengthel
(′Lgℓ)  ′velocitel × ′timel 
*8.202083_{d} mm  
unqua′lengthel (u↑′Lgℓ)  10_{z} ′lengthel 
*0.98425_{d} dm  
Area = Square Measure 
′areanel (′Arℓ)  ′lengthel^{2} ′Lgℓ^{2} 
*67.27417100694_{d} mm^{2}  
biqua′areanel (b↑′Arℓ)  10^{2}_{z} ′areanel 
*0.9687480625_{d} dm^{2}  
Volume = Cubic Measure 
′volumel (′Voℓ)  ′lengthel^{3} ′Lgℓ^{3} 
*0.551788356779875_{d} ml (cc)  
triqua′volumel (t↑′Voℓ)  10^{3}_{z} ′volumel 
*0.953490280515625_{d} L  
Density  ′densitel
(′Dsℓ)  Maximal density of water (at 4°C) ′Msℓ ′Lgℓ^{−3} 
999.972_{d} kg/m^{3}  
Mass 
′massel (′Msℓ)  ′densitel × ′volumel 
0.551772906706_{d} g  
triqua′massel (t↑′Msℓ)  10^{3}_{z} ′massel 
0.953463582788_{d} kg  
Momentum 
′momentumel (′Mmℓ)  ′massel × ′velocitel ′Msℓ ′Lgℓ ′Tmℓ^{−1}  15.7027077475639_{d} gcm/s ~ Ӿ8_{z} septciaMav  
Action 
′actionel (′Actℓ)  ′momentumel × ′lengthel ′Msℓ ′Lgℓ^{2} ′Tmℓ^{−1}  12.8286944234717_{d} gcm^{2}/s ~ 368_{z} ennciaMavGrafut  _ 
quadqua′actionel (q↑′Actℓ)  10^{4}_{z} ′actionel  12.8286944234717_{d} gcm^{2}/s ~ Ӿ8_{z} septciaMav 
Force = Weight 
′forcel (′Fcℓ)  ′massel × ′accelerel ′Msℓ ′Lgℓ ′Tmℓ^{−2} 
5.40545202052705_{d} mN  
triqua′forcel (t↑′Fcℓ)  10^{3}_{z} ′forcel 
9.34062109164354_{d} N  
Work = Energy 
′workel (′Wkℓ)  ′forcel × ′lengthel ′Msℓ ′Lgℓ^{2} ′Tmℓ^{−2} 
44.3359679275_{d} μJ  
quadqua′workel (q↑′Wkℓ)  10^{4}_{z} ′workel 
0.919350630945_{d} J  
Power  ′powerel
(′Pwℓ)  ′workel ÷ ′timel ′Msℓ ′Lgℓ^{2} ′Tmℓ^{−3} 
1.53225105158_{d} mW  
triqua′powerel
(t↑′Pwℓ)  10^{3}_{z} ′powerel 
2.64772871712_{d} W  
Pressure = Stress  ′pressurel
(′Psℓ)  ′forcel ÷ ′areael ′Msℓ ′Lgℓ^{−1} ′Tmℓ^{−2} 
80.3495894444_{d} Pa  
′atmosphere
(′Atm)  standard atmospheric pressure 
891.07576Ӿ190_{z} ′Psℓ  
Tension  ′tensionel
(′Tsℓ)  ′forcel ÷ ′lengthel ′Msℓ ′Tmℓ^{−2} 
0.659034028423_{d} N/m  
Frequency  ′frequencel
(′Fqℓ)  1 ÷ ′timel Tmℓ^{−1} 
34.56_{d} Hz  
tricia′frequencel (t↓′Fqℓ)  10^{3}_{z} ′frequencel 
0.02_{d} Hz  
ANGULAR (ROTATIONAL) MECHANICS  
Physical Quantity  Primel Unit (Abbrev) Colloquialism (Abbrev)  Derivation or Decomposition  SI, USC, & TGM Equivalents  
Rotation = Angular Measure  turn
(⊙)  1 full circle or "full angle" 
360°_{d}  
biciaturn (b↓⊙)  10^{−2}_{z} turn 
2°30′_{d}  
Radius  ′radiel
(′Rdℓ)  ′lengthel ÷ radian ′Lgℓ rad^{−1} 
*8.202083_{d} mm/rad  
unqua′radiel (u↑′Rdℓ)  10_{z} ′radiel 
*0.98425_{d} dm/rad  
Steradius = Square Radius 
′steradiel (′Srℓ)  ′radiel^{2} ′Lgℓ^{2} rad^{−2} 
*67.27417100694_{d} mm^{2}/sr  
biqua′steradiel (b↑′Srℓ)  10^{2}_{z} ′steradiel 
*0.9687480625_{d} dm^{2}/sr  
Radial Prefix Forms 
radua (R↑)  ′radiel^{1} × ′Lgℓ rad^{−1} × 
*8.202083_{d} mm/rad  
radia (R↓)  ′radiel^{−1} × ′Lgℓ^{−1} rad × 
*121.920243840488_{d} rad/m  
steradua (R2↑)  ′steradiel × ′Lgℓ^{2} rad^{−2} × 
*67.27417100694_{d} mm^{2}/sr  
steradia (R2↓)  ′steradiel^{−1} × ′Lgℓ^{−2} rad^{2} × 
*14864.545858124_{d} sr/m^{2}  
RECIPROCAL UNITS (see ISO 31)  
Physical Quantity  Primel Unit (Abbrev) Colloquialism (Abbrev)  Derivation or Decomposition  SI, USC, & TGM Equivalents  
Specific = Massic  ′massic ′massiquel (′Mqℓ)  1 ÷ ′massel ′Msℓ^{−1} 
1.81233980112_{d} per g  
Volumic Density = Volumic 
′volumic  1 ÷ ′volumel ′Lgℓ^{−3} 
*1.81228905560059_{d} per ml (cc)  
Surface Density = Areic 
′areic  1 ÷ ′areanel ′Lgℓ^{−2} 
*14864.545858124_{d} per m^{2}  
Linear Density = Lineic 
′lineic  1 ÷ ′lengthel

*121.920243840488_{d} per m  
HEAT AND THERMODYNAMICS  
Physical Quantity  Primel Unit (Abbrev) Colloquialism (Abbrev)  Derivation  SI, USC, & TGM Equivalents  
Specific Heat Capacity  ′massicheatcapacitel (′MqHcpℓ)  Specific heat capacity of water ("calorie") ′Lgℓ^{2} ′Tmℓ^{−2} ′Tpℓ^{−1} 
4198.762864_{d} J/K/kg  
Heat Capacity  ′heatcapacitel
(′Hcpℓ)  ′MqHcpℓ × ′Msℓ
′Msℓ ′Lgℓ^{2} ′Tmℓ^{−2} ′Tpℓ^{−1} 
2.316763589981_{d} J/K  
Temperature  ′temperaturel
(′Tpℓ)  ′Wkℓ ÷ ′Hcpℓ 
19.13702738879_{d} μK  
quadqua  10^{4}_{z} ′Tpℓ 
*25/63_{d} = 0.396825397_{d} K (or °C)  
′stadigrade 
absolute zero = 
−494.4_{z} ′Ϛ°c  
′stadigrade 
absolute zero = 
−454.4_{z} ′Ϛ°f  
′stadigrade 
absolute zero = 
0_{z} ′Ϛ°a  
ELECTROMAGNETISM  
Physical Quantity  Primel Unit (Abbrev) Colloquialism (Abbrev)  Derivation 
SI, USC, & TGM  
Electric Impedance Resistance Reactance 
′impedancel (′Imℓ) 
Z_{0} = μ_{0}c_{0} = vacuum impedance 
*29.9792458_{d}·2τ Ω (exact)  
Electric Admittance Conductance Susceptance 
′admittancel (′Adℓ)  Y_{0} = 1/Z_{0} = ε_{0}c_{0} = vacuum admittance 
2.65441872944_{d} mS  
Electric Current  ′currentel
(′Crℓ)  (′powerel ÷ ′impedancel)^{1/2} ′Chℓ ′Tmℓ^{−1} 
2.01673892448_{d} mA  
Electric Charge  ′chargel
(′Chℓ)  ′currentel × ′timel 
58.3547142499_{d} μC  
Electric Alternation  ′alternationel
(′Altℓ)  ′currentel ÷ ′timel 
69.6984972299_{d} mA/s  
Electric Potential  ′potentialel
(′Ptℓ)  ′powerel ÷ ′currentel ′Msℓ ′Lgℓ^{2} ′Tmℓ^{−2} ′Chℓ^{−1} 
0.759766687189_{d} V  
Electric Capacitance  ′capacitancel
(′Cpℓ)  ′chargel ÷ ′potentialel ′Msℓ^{−1} ′Lgℓ^{−2} ′Tmℓ^{2} ′Chℓ^{2} 
76.806097495315_{d} μF  
Electric Permittivity  ′permittivitel
(′Pmtℓ)  ′capacitel ÷ ′lengthel ′Msℓ^{−1} ′Lgℓ^{−3} ′Tmℓ^{2} ′Chℓ^{2} 
9.36421813507_{d} mF/m  
vacuum permittivity (ε_{0})  ′Pmtℓ ÷ (c_{0} / ′Veℓ) 
4.Ӿ665888366Ɛ e↓′Pmtℓ  
MagnetoMotive Force  ′magnetomotivel
(′Ctℓ)  ′currentel × turn ′Chℓ ′Tmℓ^{−1} ⊙ 
2.01673892448_{d} mAT  
Magnetic Flux  ′fluxel
(′Fxℓ)  ′potentialel × ′timel ′Msℓ ′Lgℓ^{2} ′Tmℓ^{−1} ′Chℓ^{−1} 
21.9839897913_{d} mWb  
Magnetic Flux Density  ′fluxdensitel
(′Fdℓ)  ′fluxel ÷ ′areael ′Msℓ ′Tmℓ^{−1} ′Chℓ^{−1} 
326.782024398_{d} T  
Magnetic Inductance  ′inductancel
(′Idℓ)  ′fluxel ÷ ′currentel ′Msℓ ′Lgℓ^{2} ′Chℓ^{−2} 
10.9007613849_{d} H  
Magnetic Reluctance  ′reluctancel
(′Reℓ)  ′currentel ÷ ′fluxel ′Msℓ^{−1} ′Lgℓ^{−2} ′Tmℓ^{2} ′Chℓ^{2} 
91.7367112894_{d} 1/H  
Magnetic Permeability  ′permeabilitel
(′Pmbℓ)  ′inductancel ÷ ′lengthel ′Msℓ ′Lgℓ ′Tmℓ^{−2} ′Chℓ^{−2} 
1329.02348609_{d} H/m  
vacuum permeability (μ_{0})  ′Pmbℓ ÷ (c_{0} / ′Veℓ) 
4.Ӿ665888366Ɛ e↓′Pmbℓ 
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