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Dodecagon

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 1-to-1 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 so-called "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 "dozenal-metric" metrology, similar to the Tim-Grafut-Maz (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 = 10d, Ɛ = 11d, 10z = 12d, 100z = 144d, etc.

The English language is fairly well-equipped with a nomenclature for dozenal arithmetic, having well-established 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 co-opting "galore", an English word of Irish origin, meaning "in abundance". This word is unusual in being a post-positive 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 pre-positively, without necessarily interfering with its customary meaning when post-positioned. 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 single-character abbreviations. The dozenal additions maintain this uniqueness.

SDN also accommodates existing combination forms of these numeric roots, keeping intact their pre-existing 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
(10Nz)
Negative Powers
(10Nz)
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 san-serif 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 place-value arithmetic principle that Hindu-Arabic 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
(10Nz)
Negative Powers
(10Nz)
Prefix Abbr Prefix Abbr Prefix Abbr Prefix Abbr
10z unnil unnili- un•
un*
unnilinfra- un\
un\
unnilqua- un↑
un@
unnilcia- un↓
un#
11z unun ununi- uu•
uu*
ununinfra- uu\
uu\
ununqua- uu↑
uu@
ununcia- uu↓
uu#
12z 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 265z, bihexa-pentqua- (bh•p↑) represents 26×105z, bina-hexpentqua- (b•hp↑) represents 2×1065z, and bihexpentqua- (bhp↑) represents 10265z.

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, bihexa-pentqua- (bh•p↑), representing 26×105z, can also be expressed as bidothexa-hexqua- (b.h•h↑), representing 2.6×106z. 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 0.6z, 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 penta-septinfra-. (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 septinfra-penta- (s\p•). This will not be confused with 7/5, because that would be expressed as septa-pentinfra- (s•p\), or pentinfra-septa- (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 great-gross". 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 ′morsel-length. 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 ′thumb-length. Because the unqua′lengthel approximates the customary "hand" measure, Primel proposes to nickname this the ′hand-length. Because the trina-unqua′lengthel approximates the customary foot, Primel proposes to nickname this the ′foot-length. 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 ′hand-length 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 ′hand-length, is nicknamed a ′hand-area. The triqua′volumel, a volume of one cubic ′hand-length, is nicknamed the ′hand-volume. The triqua′massel, a mass of one ′hand-volume of water, is nicknamed the ′hand-mass. The triqua′forcel or triqua′weightel, the force or weight of one ′hand-mass in Earth's gravity, is nicknamed a ′hand-force or ′hand-weight. The quadqua′energiel or quadqua′workel, the energy or work needed to lift a ′hand-mass by one ′hand-length against Earth's gravity, is nicknamed a ′hand-energy or ′hand-work. The unqua′timel, the time to traverse one ′hand-length at one ′velocitel, is nicknamed the ′hand-time. The triqua′powerel, a rate of power which applies one ′hand-energy per each ′hand-time, is nicknamed a ′hand-power. The unqua′pressurel, a pressure which applies one ′hand-weight per each ′hand-area, is nicknamed a ′hand-pressure. 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.

1-to-1 Coherence

Primel endeavors, where feasible, to relate its coherent units for different physical quantites using simple 1-to-1 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 (10-6z day), as the coherent unit of time (the ′timel), equivalent to 50/1728d (0.042z) seconds (nickname: ′jiff). (This differs from TGM, which starts with a pure dozenal fraction of the hour instead.) Because of 1-to-1 coherence, this choice affects the sizes of all other coherent units in the metrology. It turns out that this yields many conveniently-sized 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 9.79651584d m/s2, or exactly 32.1408d ft/s2. 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 1-to-1 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 19thd-Century estimate of gravity at median latitude, i.e. 45°d or 16z 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 1.0204704d km/h), or 1 foot per second (it is exactly 0.93d fps).

The ′lengthel is the distance traversed by an object moving at a constant 1 ′velocitel for 1 ′timel. It is exactly 31/96d (0.322916d) inches, or exactly 8.202083d mm. Primel nicknames this the ′morsel-length. This results in a trina′lengthel (nickname: ′thumb-length) of exactly 0.96875d inch, or exactly 24.60625d mm, which closely approximates the USC inch; an unqua′lengthel (nickname: ′hand-length) of exactly 3.875d inch, or exactly 98.425d mm, which closely approximates both the 4-inch USC hand measure as well as the SI decimeter; a trinan-unqua′lengthel (nickname: ′foot-length) of exactly 11.625d inches or 0.295275d m, which approximates the USC foot; and a biqua′lengthel (nickname ′ell-length) of exactly 46.5d inch or 1.1811d m, which approximates the traditional 45d-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 0.5518d ml. The triqua′volumel (nickname, ′hand-volume) comes remarkably close to a customary quart or a metric liter. (It is about 1.00754d quarts or 0.95349d 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 0.55d grams (nickname: ′morsel-mass); with the triqua′massel (nickname: ′hand-mass) 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 ′morsel-masses or ′hand-masses, and its weight in ′morsel-weights or ′hand-weights, using (approximately) the same magnitudes. (Contrast this with the situation in SI, with kilograms of mass versus newtons of weight, with the factor of 9.80665d m/s2 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 ′massic-heatcapacitel). 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 0.4d 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 0.7143d°F), or exactly 25/63d (21/53z) of a Celsius degree (about 0.3968d°C), such that the range from water's melting point to its boiling point is exactly 190z (252d) quadqua′temperaturels, a round multiple of twelve. The ′massic-heatcapacitel has been set to about 4198.76d J/K/kg, specifically to yield this result; it is slightly above the theoretical average specific heat capacity of water over its liquid phase (4190d J/K/kg), but slightly less than the so-called "dietary kilocalorie" (4200d 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 ′stadial-length (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 40z ′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)
′jiff

hexciaday

*28.93518d milliseconds
*42z triciaseconds
2 unciaTim

Acceleration
′accelerel

 (′Acℓ)
′gravity

Earth's gravity
at sea-level
at latitude
34°01′34.56″d

(11.73ӾƐ567%⊙z)
′Lgℓ ′Tmℓ−2

*9.79651584d m/s2
*32.1408d ft/s2
~ 1 Gee

Velocity
= Speed
′velocitel

 (′Veℓ)
= ′speedel (′Spdℓ)

′accelerel × ′timel

′Lgℓ ′Tmℓ−1

*28.3464d cm/s
*1.0204704d km/h
*0.93d ft/s
*0.63409d* mph
~ 2 unciaVlos

′lightspeed

 (c0)

speed of light
in a vacuum

256,232,Ɛ32z ′velocitels
299,792,458d m/s
186,282.397d mi/s
~4Ӿ,Ɛ49,923.08z Vlos

Length

= Width
= Height
= Depth
= etc.

′lengthel

 (′Lgℓ)
= ′widthel (′Wdℓ)
= ′heightel (′Htℓ)
= ′depthel (′Dpℓ)
= etc.
′morsel-length

′velocitel × ′timel

*8.202083d mm
*0.322916d inch
~ 4 biciaGrafut

unqua′lengthel (u↑′Lgℓ)
′hand-length
′manipular-length

10z ′lengthel

*0.98425d dm
*3.875d inch
~ 4 unciaGrafut

Area
= Square
Measure

′areanel (′Arℓ)
′morsel-area

′lengthel2

′Lgℓ2

*67.27417100694d mm2
*0.10427517361d in2
~ 14z quadciaSurf

biqua′areanel (b↑′Arℓ)
′hand-area
′manipular-area

102z ′areanel

*0.9687480625d dm2
*15.015625d in2
~ 14z biciaSurf

Volume
= Cubic
Measure

′volumel (′Voℓ)
′morsel-volume

′lengthel3

′Lgℓ3

*0.551788356779875d ml (cc)
0.033672191478588d in3
0.111949104137d tsp
~ 54z hexciaVolm

triqua′volumel (t↑′Voℓ)
′hand-volume
′manipular-volume

103z ′volumel

*0.953490280515625d L
*58.185546875d in3
1.00075419372d quart
~ 54z triciaVolm

Density ′densitel

 (′Dsℓ)

Maximal
density
of water
(at 4°C)

′Msℓ ′Lgℓ−3

999.972d kg/m3
1.0431463d lb/pt
1 Denz

Mass

′massel (′Msℓ)
′morsel-mass

′densitel × ′volumel

0.551772906706d g
0.0194681933693d oz
~ 54z hexciaMaz

triqua′massel (t↑′Msℓ)
′hand-mass
′manipular-mass

103z ′massel

0.953463582788d kg
2.10202488389d lb
~ 54z triciaMaz

Momentum

′momentumel (′Mmℓ)
′morsel-momentum

′massel × ′velocitel

′Msℓ ′Lgℓ ′Tmℓ−1

15.7027077475639d g-cm/s

~ Ӿ8z septciaMav

Action

′actionel (′Actℓ)
′morsel-action

′momentumel × ′lengthel

′Msℓ ′Lgℓ2 ′Tmℓ−1

12.8286944234717d g-cm2/s

~ 368z ennciaMavGrafut

_

quadqua′actionel (q↑′Actℓ)
′hand-action ′manipular-action

104z ′actionel 12.8286944234717d g-cm2/s

~ Ӿ8z septciaMav

Force
= Weight

′forcel (′Fcℓ)
= ′weightel ( ′Wtℓ)
′morsel-weight

′massel × ′accelerel

′Msℓ ′Lgℓ ′Tmℓ−2

5.40545202052705d mN
540.545202052705d dyne
~ 54z hexciaMag

triqua′forcel (t↑′Fcℓ)
= triqua′weightel (t↑′Wtℓ)
′hand-force
′manipular-weight

103z ′forcel

9.34062109164354d N
0.934062109164354d Mdyne
~ 54z hexciaMag

Work

= Energy

′workel (′Wkℓ)
= ′energel (′Ngℓ)
′morsel-work
′morsel-energy

′forcel × ′lengthel

′Msℓ ′Lgℓ2 ′Tmℓ−2

44.3359679275d μJ
443.359679275d erg
~ 194z quadciaWerg

quadqua′workel (q↑′Wkℓ)
= quadqua′energel (q↑′Ngℓ)
′hand-work
′manipular-work

104z ′workel

0.919350630945d J
9.19350630945d Merg
~ 194z octciaWerg

Power ′powerel

 (′Pwℓ)
′morsel-power

′workel ÷ ′timel

′Msℓ ′Lgℓ2 ′Tmℓ−3

1.53225105158d mW
15.3225105158d kiloerg/s
~ Ӿ8z septciaPov

triqua′powerel

 (t↑′Pwℓ)
′hand-power
′manipular-power

103z ′powerel

2.64772871712d W
26.4772871712d gigaerg/s
~ Ӿ8z septciaPov

Pressure

= Stress

′pressurel

 (′Psℓ)
= ′stressel (′Stsℓ)
′morsel-pressure

′forcel ÷ ′areael

′Msℓ ′Lgℓ−1 ′Tmℓ−2

80.3495894444d Pa
803.495894444d barye
0.602671482633d torr
0.0237262247d inHg
0.0116767723024215d psi
~ 4 biciaPrem

′atmosphere

 (′Atm)

standard
atmospheric
pressure

891.07576Ӿ190z ′Psℓ
101,325d Pa
1,013,250d barye
760d torr
29.92d inHg
14.6959488d psi
1 std. atm
~ 1 Atmoz

Tension ′tensionel

 (′Tsℓ)
′morsel-tension

′forcel ÷ ′lengthel

′Msℓ ′Tmℓ−2

0.659034028423d N/m
~ 14z quadciaTenz

Frequency ′frequencel

 (′Fqℓ)
′jiff-frequency

1 ÷ ′timel

Tmℓ−1

34.56d Hz
2073.6d BPM (or RPM)
6 Freq

tricia′frequencel (t↓′Fqℓ)
′trice-frequency

10-3z ′frequencel

0.02d Hz
1.2d BPM (or RPM)
6 triciaFreq

ANGULAR (ROTATIONAL) MECHANICS
Physical Quantity Primel Unit (Abbrev)
Colloquialism (Abbrev)
Derivation or Decomposition SI, USC, & TGM

Equivalents
(* = exact)
(~ = approximate)

Rotation
= Angular
Measure
turn

 (⊙)

1 full circle
or "full angle"

360°d
τ ("tau") radians (τ = 2π)
2 Pi

bicia-turn (b↓⊙)
turnlet (%⊙)

10−2z turn

2°30′d
τ biciaradians (τ = 2π)
2 biciaPi

Radius ′radiel

 (′Rdℓ)
′morsel-radius

′lengthel ÷ radian

′Lgℓ rad−1

*8.202083d mm/rad
*0.322916d inch/rad
~ 4 biciaGrafut/radian

unqua′radiel (u↑′Rdℓ)
′hand-radius
′manipular-radius

10z ′radiel

*0.98425d dm/rad
*3.875d inch/rad
~ 4 unciaGrafut/radian

Steradius
= Square
Radius

′steradiel (′Srℓ)
′morsel-steradius

′radiel2

′Lgℓ2 rad−2

*67.27417100694d mm2/sr
*0.10427517361d in2/sr
~ 14z quadciaSurf/steradian

biqua′steradiel (b↑′Srℓ)
′hand-steradius
′manipular-steradius

102z ′steradiel

*0.9687480625d dm2/sr
*15.015625d in2/sr
~ 14z biciaSurf/steradian

Radial
Prefix
Forms

radua- (R↑-)

′radiel1 ×

′Lgℓ rad−1 ×

*8.202083d mm/rad
*0.322916d inch/rad
~ 4 biciaGrafut/radian

radia- (R↓-)

′radiel−1 ×

′Lgℓ−1 rad ×

*121.920243840488d rad/m
37.1612903225806d rad/ft
3.09677419354839d rad/in
~ 3z rad/unciaGrafut

steradua- (R2↑-)

′steradiel ×

′Lgℓ2 rad−2 ×

*67.27417100694d mm2/sr
*0.10427517361d in2/sr
~ 14z quadciaSurf/steradian

steradia- (R2↓-)

′steradiel−1 ×

′Lgℓ−2 rad2 ×

*14864.545858124d sr/m2
1380.96149843913d sr/ft2
9.59001040582726d sr/in2
~ 9z sr/biciaSurf

RECIPROCAL UNITS (see ISO 31)
Physical Quantity Primel Unit (Abbrev)
Colloquialism (Abbrev)
Derivation or Decomposition SI, USC, & TGM

Equivalents
(* = exact)
(~ = approximate)

Specific-
= Massic-
′massic-

′massiquel  (′Mqℓ)

1 ÷ ′massel

′Msℓ−1

1.81233980112d per g
1812.33980112d per kg
51.3790302046d per oz
822.064483274d per lb
~ 23z quadqua per Maz

Volumic Density
= Volumic-

′volumic-
′volumiquel (′Vqℓ)

1 ÷ ′volumel

′Lgℓ−3

*1.81228905560059d per ml (cc)
29.6980967406264d per in3
8.93263066026653d per tsp
~ 23z per triciaVolm

Surface Density
= Areic-

′areic-
′areiquel (′Aqℓ)

1 ÷ ′areanel

′Lgℓ−2

*14864.545858124d per m2
1380.96149843913d per ft2
9.59001040582726d per in2
~ 9z per biciaSurf

Linear Density
= Lineic-

′lineic-
′lineiquel (′Lqℓ)

1 ÷ ′lengthel


′Lgℓ−1

*121.920243840488d per m
37.1612903225806d per ft
3.09677419354839d per in
~ 3z per unciaGrafut

HEAT AND THERMODYNAMICS
Physical Quantity Primel Unit (Abbrev)
Colloquialism (Abbrev)
Derivation SI, USC, & TGM

Equivalents
(* = exact)
(~ = approximate)

Specific
Heat
Capacity
′massic-heatcapacitel
(′MqHcpℓ)
Specific heat
capacity of water
("calorie")

′Lgℓ2 ′Tmℓ−2 ′Tpℓ−1

4198.762864d J/K/kg
~1 Calsp

Heat
Capacity
′heatcapacitel

 (′Hcpℓ)

′MqHcpℓ × ′Msℓ

′Msℓ ′Lgℓ2 ′Tmℓ−2 ′Tpℓ−1

2.316763589981d J/K
~54z hexciaCalkap

Temperature ′temperaturel

 (′Tpℓ)

′Wkℓ ÷ ′Hcpℓ

19.13702738879d μK
~4 biciaCalg

quadqua-
′temperaturel (q↑′Tpℓ)
′stadigrade (′Ϛ°)

104z ′Tpℓ

*25/63d = 0.396825397d K (or °C)
*5/7d = 0.71428571d R (or °F)
~4 biquaCalg

′stadigrade
crystallic
scale (′Ϛ°c)

absolute zero =
water freezes =
room temp =
body temp =
water boils =

−494.4z ′Ϛ°c
0z ′Ϛ°c
41z ′Ϛ°c
79.3z ′Ϛ°c
190z ′Ϛ°c

′stadigrade
familiar
scale (′Ϛ°f)

absolute zero =
water freezes =
room temp =
body temp =
water boils =

−454.4z ′Ϛ°f
40z ′Ϛ°f
81z ′Ϛ°f
Ɛ9.3z ′Ϛ°f
210z ′Ϛ°f

′stadigrade
absolute
scale (′Ϛ°a)

absolute zero =
water freezes =
room temp =
body temp =
water boils =

0z ′Ϛ°a
494.4z ′Ϛ°a
515.4z ′Ϛ°a
551.7z ′Ϛ°a
664.4z ′Ϛ°a

ELECTROMAGNETISM
Physical Quantity Primel Unit (Abbrev)
Colloquialism (Abbrev)
Derivation

SI, USC, & TGM
Equivalents
(* = exact)
(~ = approximate)

Electric
Impedance
Resistance
Reactance

′impedancel (′Imℓ)
′resistancel (′Rsℓ)
′reactancel (′Rcℓ)

Z0 = μ0c0 = vacuum impedance
′Msℓ ′Lgℓ2 ′Tmℓ−1 ′Chℓ−2
′Msℓ ′Lgℓ2 ′Tmℓ−3 ′Crℓ−2

*29.9792458d·2τ Ω (exact)
~376.730313462d Ω (approx)
~0.26Ӿ489595z Og

Electric
Admittance
Conductance
Susceptance

′admittancel (′Adℓ)
′conductancel (′Cdℓ)
′susceptancel (′Scℓ)

Y0 = 1/Z0 = ε0c0

 = vacuum admittance
′Msℓ−1 ′Lgℓ−2 ′Tmℓ ′Chℓ2
′Msℓ−1 ′Lgℓ−2 ′Tmℓ3 ′Crℓ2

2.65441872944d mS
4.7Ɛ977404Ɛ2z Go

Electric
Current
′currentel

 (′Crℓ)

(′powerel ÷ ′impedancel)1/2

′Chℓ ′Tmℓ−1

2.01673892448d mA
7.043Ӿ0397436z triciaKur

Electric
Charge
′chargel

 (′Chℓ)

′currentel × ′timel

58.3547142499d μC
1.2087807727Ӿz triciaQuel

Electric
Alternation
′alternationel

 (′Altℓ)

′currentel ÷ ′timel

69.6984972299d mA/s
3.621Ɛ01Ӿ9819z biciaKur/Tim

Electric
Potential
′potentialel

 (′Ptℓ)

′powerel ÷ ′currentel

′Msℓ ′Lgℓ2 ′Tmℓ−2 ′Chℓ−1
′Msℓ ′Lgℓ2 ′Tmℓ−3 ′Crℓ−1

0.759766687189d V
1.60ƐӾ55Ɛ6Ӿ6Ӿ9z triciaPel

Electric
Capacitance
′capacitancel

 (′Cpℓ)

′chargel ÷ ′potentialel

′Msℓ−1 ′Lgℓ−2 ′Tmℓ2 ′Chℓ2
′Msℓ−1 ′Lgℓ−2 ′Tmℓ4 ′Crℓ2

76.806097495315d μF
0.93Ɛ732809Ӿ634z Kap

Electric
Permittivity
′permittivitel

 (′Pmtℓ)

′capacitel ÷ ′lengthel

′Msℓ−1 ′Lgℓ−3 ′Tmℓ2 ′Chℓ2
′Msℓ−1 ′Lgℓ−3 ′Tmℓ4 ′Crℓ2

9.36421813507d mF/m
24.044763457Ӿz Mit

vacuum
permittivity

 (ε0)

′Pmtℓ ÷ (c0 / ′Veℓ)

4.Ӿ665888366Ɛ e↓′Pmtℓ
8.85418781762d pF/m
Ɛ4.9061498144z enciaMit

Magneto-Motive
Force
′magnetomotivel

 (′Ctℓ)

′currentel × turn

′Chℓ ′Tmℓ−1
′Crℓ ⊙

2.01673892448d mAT
7.043Ӿ0397436z triciaKurn

Magnetic
Flux
′fluxel

 (′Fxℓ)

′potentialel × ′timel

′Msℓ ′Lgℓ2 ′Tmℓ−1 ′Chℓ−1
′Msℓ ′Lgℓ2 ′Tmℓ−2 ′Crℓ−1

21.9839897913d mWb
0.301Ɛ8ӾƐƐ1919z Flum

Magnetic
Flux
Density
′fluxdensitel

 (′Fdℓ)

′fluxel ÷ ′areael

′Msℓ ′Tmℓ−1 ′Chℓ−1
′Msℓ ′Tmℓ−2 ′Crℓ−1

326.782024398d T
0.23247336207Ɛz Flenz

Magnetic
Inductance
′inductancel

 (′Idℓ)

′fluxel ÷ ′currentel

′Msℓ ′Lgℓ2 ′Chℓ−2
′Msℓ ′Lgℓ2 ′Tmℓ−2 ′Crℓ−2

10.9007613849d H
51.8956Ɛ6Ӿ0Ӿ8z triciaGen

Magnetic
Reluctance
′reluctancel

 (′Reℓ)

′currentel ÷ ′fluxel

′Msℓ−1 ′Lgℓ−2 ′Tmℓ2 ′Chℓ2

91.7367112894d 1/H
23.ƐӾ99802586z Lukt

Magnetic
Permeability
′permeabilitel

 (′Pmbℓ)

′inductancel ÷ ′lengthel

′Msℓ ′Lgℓ ′Tmℓ−2 ′Chℓ−2

1329.02348609d H/m
1.35552Ӿ09Ӿ57z Meab

vacuum
permeability

 (μ0)

′Pmbℓ ÷ (c0 / ′Veℓ)

4.Ӿ665888366Ɛ e↓′Pmbℓ
1.2566370614359d μH/m
6.349416967Ɛ64z e↓Meab


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