# This file is derived directly from units.dat - the database for use with # GNU units (a units conversion program by Adrian Mariano # adrian@cam.cornell.edu) # # This file was derived from the 27 July 1999 Version 1.24 of units.dat - # Copyright (C) 1996, 1997, 1998 Free Software Foundation, Inc # # Like the original units program, this version is free software; you can # redistribute it and/or modify it under the terms of the GNU General Public # License as published by the Free Software Foundation; either version 2 of # the License, or (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA # ############################################################################ # # Improvements and corrections are welcome. (Corrections should also be # posted to the maintainers of the units.dat database) # # Most units data was drawn from # 1. NIST Special Publication 811, 1995 Edition # 2. CRC Handbook of Chemistry and Physics 70th edition # 3. Oxford English Dictionary # 4. Websters New Universal Unabridged Dictionary # 5. Units of Measure by Stephen Dresner # 6. A Dictionary of English Weights and Measures by Ronald Zupko # 7. British Weights and Measures by Ronald Zupko # 8. Realm of Measure by Isaac Asimov # 9. United States standards of weights and measures, their # creation and creators by Arthur H. Frazier. # 10. French weights and measures before the Revolution: a # dictionary of provincial and local units by Ronald Zupko # 11. Weights and Measures: their ancient origins and their # development in Great Britain up to AD 1855 by FG Skinner # 12. The World of Measurements by H. Arthur Klein # 13. For Good Measure by William Johnstone # 14. NTC's Encyclopedia of International Weights and Measures # by William Johnstone # 15. Sizes by John Lord # 16. Sizesaurus by Stephen Strauss # 17. CODATA Recommended Values of Physical Constants available at # http://physics.nist.gov/cuu/Constants/index.html # # ########################################################################### { prefix yotta = 1e24; # Greek or Latin octo, "eight" prefix Y = 1e24; prefix zetta = 1e21; # Latin septem, "seven" prefix Z = 1e21; prefix exa = 1e18; # Greek hex, "six" prefix E = 1e18; prefix peta = 1e15; # Greek pente, "five" prefix P = 1e15; prefix tera = 1e12; # Greek teras, "monster" prefix T = 1e12; prefix giga = 1e9; # Greek gigas, "giant" prefix G = 1e9; prefix mega = 1e6; # Greek megas, "large" prefix M = 1e6; prefix myria = 1e4; # Not an official SI prefix prefix kilo = 1e3; # Greek chilioi, "thousand" prefix k = 1e3; prefix hecto = 1e2; # Greek hekaton, "hundred" prefix h = 1e2; prefix deca = 1e1; # Greek deka, "ten" prefix deka = 1e1; prefix da = 1e1; prefix deci = 1e-1; # Latin decimus, "tenth" prefix d = 1e-1; prefix centi = 1e-2; # Latin centum, "hundred" prefix c = 1e-2; prefix milli = 1e-3; # Latin mille, "thousand" prefix m = 1e-3; prefix micro = 1e-6; # Latin micro or Greek mikros, "small" //prefix µ = 1e-6; prefix nano = 1e-9; # Latin nanus or Greek nanos, "dwarf" prefix n = 1e-9; prefix pico = 1e-12; # Spanish pico, "a bit" prefix p = 1e-12; prefix femto = 1e-15; # Danish-Norwegian femten, "fifteen" prefix f = 1e-15; prefix atto = 1e-18; # Danish-Norwegian atten, "eighteen" prefix a = 1e-18; prefix zepto = 1e-21; # Latin septem, "seven" prefix z = 1e-21; prefix yocto = 1e-24; # Greek or Latin octo, "eight" prefix y = 1e-24; prefix quarter = 1 / 4; prefix semi = 0.5; prefix demi = 0.5; prefix hemi = 0.5; prefix half = 0.5; prefix double = 2; prefix triple = 3; prefix treble = 3; # # SI units # # Mass of the international prototype # primitive kg; kilogram = kg; # Duration of 9192631770 periods of the radiation # corresponding to the transition between the two hyperfine # levels of the ground state of the cesium-133 atom # primitive s; second = s; sec = s; # Length of the path traveled by light in a vacuum # during 1 / 299792458 seconds. Originally meant to be # 1e-7 of the length along a meridian from the equator # to a pole. # primitive m; meter = m; metre = meter; # The current which produces a force of 2e-7 N/m between two # infinitely long wires that are 1 meter apart # primitive A; ampere = A; amp = ampere; # Luminous intensity in a given direction of a source which # emits monochromatic radiation at 540e9 Hz with radiant # intensity 1 / 683 W/steradian. (This differs from radiant # intensity (W/sr) in that it is adjusted for human # perceptual dependence on wavelength. The frequency of # 540e9 Hz (yellow) is where human perception is most # efficient.) # primitive cd; candela = cd; # The amount of substance of a system which contains as many # elementary entities as there are atoms in 0.012 kg of # carbon 12. The elementary entities must be specified and # may be atoms, molecules, ions, electrons, or other # particles or groups of particles. It is understood that # unbound atoms of carbon 12, at rest and in the ground # state, are referred to. # primitive mol; mole = mol; # 1 / 273.16 of the thermodynamic temperature of the triple # point of water # primitive K; kelvin = K; degK = K; # "Degrees Kelvin" is forbidden usage. //°K = K; # °K is incorrect notation as well! # # The radian and steradian are defined to be unitless. They are included # as primitive units here because, for the most part, it is less confusing # if they are irreducible than if they reduce to 1. # # The angle subtended at the center of a circle by an arc # equal in length to the radius of the circle # primitive radian; # Solid angle which cuts off an area of the surface of # the sphere equal to that of a square with sides of # length equal to the radius of the sphere # primitive sr; steradian = sr; ############################################################################# # # # Derived units which can be reduced to the primitive units # # # ############################################################################# # # Named SI derived units (officially accepted) # newton = kg m / s^2; # force N = newton; pascal = N/m^2; # pressure or stress Pa = pascal; joule = N m; # energy J = joule; watt = J/s; # power W = watt; coulomb = A s; # charge C = coulomb; volt = W/A; # potential difference V = volt; ohm = V/A; # electrical resistance siemens = A/V; # electrical conductance S = siemens; farad = C/V; # capacitance F = farad; weber = V s; # magnetic flux Wb = weber; henry = Wb/A; # inductance H = henry; tesla = Wb/m^2; # magnetic flux density T = tesla; hertz = 1 / s; # frequency Hz = hertz; # # units derived easily from SI units # gram = millikg; gm = gram; g = gram; gramme = gram; tonne = 1000 kg; t = tonne; metricton = tonne; sthene = tonne m / s^2; funal = sthene; pieze = sthene / m^2; quintal = 100 kg; bar = 1e5 Pa; # About 1 atm vac = millibar; micron = micrometer; # One millionth of a meter bicron = picometer; # One brbillionth of a meter cc = cm^3; are = 100 m^2; liter = 1000 cc; # The liter was defined in 1901 as the litre = liter; oldliter = 1.000028 dm^3; # space occupied by 1 kg of pure water at l = liter; # the temperature of its maximum density # under a pressure of 1 atm. This was # supposed to be 1000 cubic cm, but it # was discovered that the original # measurement was off. In 1964, the # liter was redefined to be exactly 1000 # cubic centimeters. mho = siemens; # Inverse of ohm, hence ohm spelled backward galvat = ampere; # Named after Luigi Galvani angstrom = 1e-10 m; # Convenient for describing molecular sizes //ångström = angstrom; //Å = angstrom; xunit = 1.00202e-13 meter; # Used for measuring wavelengths siegbahn = xunit; # of X-rays. It is defined to be # 1 / 3029.45 of the spacing of calcite # planes at 18 degC. It was intended # to be exactly 1e-13 m, but was # later found to be off slightly. fermi = 1e-15 m; # Convenient for describing nuclear sizes # Nuclear radius is from 1 to 10 fermis barn = 1e-28 m^2; # Used to measure cross section for # particle physics collision, said to # have originated in the phrase "big as # a barn". shed = 1e-24 barn; # Defined to be a smaller companion to the # barn, but it's too small to be of # much use. brewster = micron^2/N; # measures stress-optical coef diopter = 1 / m; # measures reciprocal of lens focal length dioptre = diopter; fresnel = 1e12 Hz; # occasionally used in spectroscopy shake = 1e-8 sec; svedberg = 1e-13 s; # Used for measuring the sedimentation # coefficient for centrifuging. gamma = microgram; lambda = microliter; spat = 1e12 m; # Rarely used for astronomical measurements preece = 1e13 ohm m; # resistivity planck = J s; # action of one joule over one second sturgeon = 1 / henry; # magnetic reluctance daraf = 1 / farad; # elastance (farad spelled backwards) leo = 10 m/s^2; poiseuille = N s / m^2; # viscosity mayer = J/(g K); # specific heat mired = 1 / microK; # reciprocal color temperature. The name # abbreviates micro reciprocal degree. crocodile = megavolt; # used informally in UK physics labs metricounce = 25 g; mounce = metricounce; finsenunit = 1e5 W/m^2; # Measures intensity of ultraviolet light # with wavelength 296.7 nm. fluxunit = 1e-26 W/(m^2 Hz); # Used in radio astronomy to measure # the energy incident on the receiving # body across a specified frequency # bandwidth. [12] jansky = fluxunit; # K. G. Jansky identified radio waves coming Jy = jansky; # from outer space in 1931. # # time # minute = 60 s; min = minute; hour = 60 min; hr = hour; day = 24 hr; d = day; da = day; week = 7 day; wk = week; sennight = 7 day; fortnight = 14 day; blink = 1e-5 day; # Actual human blink takes 1 / 3 second ce = 1e-2 day; cron = 1e6 year; # # angular measure # circle = 2 pi radian; degree = (1 / 360) circle; //° = degree; arcdeg = degree; arcmin = (1 / 60) degree; ' = arcmin; arcsec = (1 / 60) arcmin; " = arcsec; '' = "; rightangle = 90 degree; quadrant = (1 / 4) circle; quintant = (1 / 5) circle; sextant = (1 / 6) circle; sign = (1 / 12) circle; # Angular extent of one sign of the zodiac turn = circle; revolution = turn; rev = turn; pulsatance = radian / sec; gon = (1 / 100) rightangle; # measure of grade grade = gon; centesimalminute = (1 / 100) grade; centesimalsecond = (1 / 100) centesimalminute; milangle = (1 / 6400) circle; # Official NIST definition. # Another choice is 1e-3 radian. pointangle = (1 / 32) circle; centrad = 0.01 radian; # Used for angular deviation of light # through a prism. # # Solid angle measure # sphere = 4 pi sr; squaredegree = (1 / 180^2) pi^2 sr; squareminute = (1 / 60^2) squaredegree; squaresecond = (1 / 60^2) squareminute; squarearcmin = squareminute; squarearcsec = squaresecond; sphericalrightangle = 0.5 pi sr; octant = 0.5 pi sr; # # Concentration measures # percent = 0.01; % = percent; proof = 1 / 200; # Alcohol content measured by volume at # 60 degrees Fahrenheit. This is a USA # measure. In Europe proof=percent. ppm = 1e-6; partspermillion = ppm; ppb = 1e-9; partsperbillion = ppb; # USA billion ppt = 1e-12; partspertrillion = ppt; # USA trillion karat = 1 / 24; # measure of gold purity caratgold = karat; gammil = mg/l; basispoint = 0.01 %; # Used in finance # # Temperature difference (we can't handle the shift required for conversion # of absolute temperatures) degcelsius = K; # In 1741 Anders Celsius introduced a degC = K; # temperature scale with water boiling at 0 //°C = degC; # degrees and freezing at 100 degrees at # standard pressure. After his death the # fixed points were reversed and the scale # was called the centigrade scale. Due to # the difficulty of accurately measuring the # temperature of melting ice at standard # pressure, the centigrade scale was replaced # in 1954 by the Celsius scale which is # defined by subtracting 273.15 from the # temperature in Kelvins. This definition # differed slightly from the old centigrade # definition, but the Kelvin scale depends on # the triple point of water rather than a # melting point, so it can be measured # accurately. degfahrenheit = (5 / 9) degC; # Fahrenheit defined his temperature scale degF = degfahrenheit; # by setting 0 to the coldest temperature //°F = degfahrenheit; # he could produce and by setting 96 degrees # to body heat (for reasons unknown). degreesrankine = degF; # The Rankine scale has the degrankine = degreesrankine; # Fahrenheit degree, but it's zero degreerankine = degF; # is at absolute zero. degR = degrankine; //°R = degrankine; degreaumur = (10 / 8) degC; # The Reaumur scale was used in Europe and # particularly in France. It is defined # to be 0 at the freezing point of water # and 80 at the boiling point. Reaumur # apparently selected 80 because it is # divisible by many numbers. # # Units derived from physical constants # kgf = kg force; technicalatmosphere = kgf / cm^2; at = technicalatmosphere; hyl = kgf s^2 / m; # Also gram-force s^2/m according to [15] mmHg = mm Hg; torr = mmHg; # These units, both named after Evangelista tor = Pa; # Torricelli, should not be confused. # Acording to [15] the torr is actually # atm/760 which is slightly different. inHg = inch Hg; inH2O = inch water; mmH2O = mm water; eV = e V; # Energy acquired by a particle with charge e electronvolt = eV; # when it is accelerated through 1 V lightyear = c 365.25 d; # The 365.25 day year is specified in # NIST publication 811 lightsecond = c s; lightminute = c min; parsec = au radian / arcsec; # Unit of length equal to distance pc = parsec; # from the sun to a point having # heliocentric parallax of 1 # arcsec (derived from parallax # second) The formula should use # tangent, but the error is about # 1e-12. rydberg = h c Rinfinity; # Rydberg energy crith = 0.089885 gram; # The crith is the mass of one # liter of hydrogen at standard # temperature and pressure. amagatvolume = molarvolume; lorentz = bohrmagneton /(h c); # Used to measure the extent # that the frequency of light # is shifted by a magnetic field. cminv = h c / cm; # Unit of energy used in infrared invcm = cminv; # spectroscopy. wavenumber = cminv; kcal_mol = kcal /(mol N_A); # kcal/mol is used as a unit of # energy by physical chemists. # # CGS system based on centimeter, gram and second # dyne = cm gram / s^2; # force dyn = dyne; erg = cm dyne; # energy poise = gram /(cm s); # viscosity, honors Jean Poiseuille P = poise; rhe = 1 / poise; # reciprocal viscosity stokes = cm^2 / s; # kinematic viscosity St = stokes; stoke = stokes; lentor = stokes; # old name Gal = cm / s^2; # acceleration, used in geophysics galileo = Gal; # for earth's gravitational field # (note that "gal" is for gallon # but "Gal" is the standard symbol # for the gal which is evidently a # shortened form of "galileo".) barye = dyne/cm^2; # pressure barad = barye; # old name kayser = 1/cm; # Proposed as a unit for wavenumber balmer = kayser; # Even less common name than "kayser" kine = cm/s; # velocity bole = g cm / s; # momentum pond = gram force; glug = gram force s^2 / cm; # Mass which is accelerated at # 1 cm/s^2 by 1 gram force darcy = centipoise cm^2 /(s atm); # Measures permeability to fluid # flow. One darcy is the # permeability of a medium that # allows a flow of cc/s of a liquid # of centipoise viscosity under a # pressure gradient of atm/cm. mohm = cm /(dyn s); # mobile ohm, measure of mechanical mobileohm = mohm; # mobility mechanicalohm = dyn s / cm; # mechanical resistance acousticalohm = dyn s / cm^5; # ratio of the sound pressure of # 1 dyn/cm^2 to a source of strength # 1 cm^3/s ray = acousticalohm; rayl = dyn s / cm^3; # Specific acoustical resistance eotvos = 1e-9 Gal/cm; # Change in gravitational acceleration # over horizontal distance # Electromagnetic units derived from the abampere abampere = 10 A; # Current which produces a force of abamp = abampere; # 2 dyne/cm between two infinitely aA = abampere; # long wires that are 1 cm apart biot = aA; # alternative name for abamp Bi = biot; abcoulomb = abamp sec; abcoul = abcoulomb; abfarad = abampere sec / abvolt; abhenry = abvolt sec / abamp; abvolt = dyne cm / (abamp sec); abohm = abvolt / abamp; abmho = 1 / abohm; gauss = abvolt sec / cm^2; Gs = gauss; maxwell = abvolt sec; # Also called the "line" Mx = maxwell; oersted = gauss / mu0; Oe = oersted; gilbert = gauss cm / mu0; Gb = gilbert; Gi = gilbert; unitpole = 4 pi maxwell; # Gaussian system: electromagnetic units derived from statampere. # # Note that the Gaussian units are often used in such a way that Coulomb's # law has the form F= q1 * q2 / r^2. The constant (1 / 4)*pi*epsilon0 is # incorporated into the units. From this, we can get the relation # force=charge^2/dist^2. This means that the simplification # esu^2 = dyne cm^2 can be used to simplify units in the Gaussian system, # with the curious result that capacitance can be measured in cm, resistance # in sec/cm, and inductance in sec^2/cm. These units are given the names # statfarad, statohm and stathenry below. statampere = 10 A cm / (s c); statamp = statampere; statvolt = dyne cm / (statamp sec); statcoulomb = statamp s; esu = statcoulomb; statcoul = statcoulomb; statfarad = statamp sec / statvolt; cmcapacitance = statfarad; stathenry = statvolt sec / statamp; statohm = statvolt / statamp; statmho = 1 / statohm; statmaxwell = statvolt sec; franklin = statcoulomb; debye = 1e-18 statcoul cm; # unit of electrical dipole moment helmholtz = debye/angstrom^2; # Dipole moment per area jar = 1000 statfarad; # approx capacitance of Leyden jar # # Some historical eletromagnetic units # intampere = 0.999835 A; # Defined as the current which in one intamp = intampere; # second deposits .001118 gram of # silver from an aqueous solution of # silver nitrate. intfarad = 0.999505 F; intvolt = 1.00033 V; intohm = 1.000495 ohm; # Defined as the resistance of a # uniform column of mercury containing # 14.4521 gram in a column 1.063 m # long and maintained at 0 degC. daniell = 1.042 V; # Meant to be electromotive force of a # Daniell cell, but in error by .04 V faraday = N_A e mol; # Charge that must flow to deposit or faraday_phys = 96521.9 C; # liberate one gram equivalent of any faraday_chem = 96495.7 C; # element. (The chemical and physical # values are off slightly from what is # obtained by multiplying by amu_chem # or amu_phys. These values are from # a 1991 NIST publication.) Note that # there is a Faraday constant which is # equal to N_A e and hence has units of # C/mol. kappline = 6000 maxwell; # Named by and for Gisbert Kapp siemensunit = 0.9534 ohm; # Resistance of a meter long column of # mercury with a 1 mm cross section. # # Photometric units # candle = 1.02 candela; # Standard unit for luminous intensity hefnerunit = 0.9 candle; # in use before candela hefnercandle = hefnerunit; # violle = 20.17 cd; # luminous intensity of 1 cm^2 of # platinum at its temperature of # solidification (2045 K) lumen = cd sr; # Luminous flux (luminous energy per lm = lumen; # time unit) talbot = lumen s; # Luminous energy lumberg = talbot; lux = lm/m^2; # Illuminance or exitance (luminous lx = lux; # flux incident on or coming from phot = lumen / cm^2; # a surface) ph = phot; # footcandle = lumen/ft^2; # Illuminance from a 1 candela source # at a distance of one foot metercandle = lumen/m^2; # Illuminance from a 1 candela source # at a distance of one meter mcs = metercandle s; # luminous energy per area, used to # measure photographic exposure nox = 1e-3 lux; # These two units were proposed for skot = 1e-3 apostilb; # measurements relating to dark adapted # eyes. # Luminance measures nit = cd/m^2; # Luminance: the intensity per projected stilb = cd / cm^2; # area of an extended luminous source. sb = stilb; # (nit is from latin nitere = to shine.); apostilb = cd / (pi m^2); asb = apostilb; blondel = apostilb; # Named after a French scientist. # Equivalent luminance measures. These units are units which measure # the luminance of a surface with a specified exitance which obeys # Lambert's law. (Lambert's law specifies that luminous intensity of # a perfectly diffuse luminous surface is proportional to the cosine # of the angle at which you view the luminous surface.) equivalentlux = cd / (pi m^2); # luminance of a 1 lux surface equivalentphot = cd / (pi cm^2); # luminance of a 1 phot surface lambert = cd / (pi cm^2); footlambert = cd / (pi ft^2); # Some luminance data from the IES Lighting Handbook, 8th ed, 1993 sunlum = 1.6e9 cd/m^2; # at zenith sunillum = 100e3 lux; # clear sky sunillum_o = 10e3 lux; # overcast sky sunlum_h = 6e6 cd/m^2; # value at horizon skylum = 8000 cd/m^2; # average, clear sky skylum_o = 2000 cd/m^2; # average, overcast sky moonlum = 2500 cd/m^2; # # Some other astronomical values # sunmass = 1.9891e30 kg; sunradius = 6.96e8 m; earthmass = 5.9742e24 kg; earthradius = 6371331.3 m; # mean earthradius_polar = 6356912.0 m; earthradius_equatorial= 6378388.0 m; landarea = 148.847e6 km^2; oceanarea = 361.254e6 km^2; moonmass = 7.3483e22 kg; moonradius = 1738 km; # mean value sundist = 1.0000010178 au; # mean earth-sun distance moondist = 3.844e8 m; # mean earth-moon distance sundist_near = 1.471e11 m; # earth-sun distance at perihelion sundist_far = 1.521e11 m; # earth-sun distance at aphelion mercurymass = 0.33022e24 kg; venusmass = 4.8690e24 kg; marsmass = 0.64191e24 kg; jupitermass = 1898.8e24 kg; saturnmass = 568.5e24 kg; uranusmass = 86.625e24 kg; neptunemass = 102.78e24 kg; plutomass = 0.015e24 kg; mercuryradius = 2.57 Mm; venusradius = 6.3 Mm; marsradius = 3.43 Mm; jupiterradius = 72 Mm; saturnradius = 60.5 Mm; uranusradius = 26.7 Mm; neptuneradius = 24.9 Mm; moongravity = 1.62 m/s^2; # # The Hartree system of atomic units, derived from fundamental units # of mass (of electron), action (planck's constant), charge, and # the coulomb constant. # Fundamental units atomicmass = electronmass; atomiccharge = e; atomicaction = hbar; # derived units (Warning: accuracy is lost from deriving them this way) atomiclength = bohrradius; atomictime = hbar^3/(coulombconst^2 atomicmass e^4); # Period of first # bohr orbit atomicvelocity = atomiclength / atomictime; atomicenergy = hbar / atomictime; hartree = atomicenergy; Hartree = hartree; # # These thermal units treat entropy as charge, from [5] # thermalcoulomb = J/K; # entropy thermalampere = W/K; # entropy flow thermalfarad = J/K^2; thermalohm = K^2/W; # thermal resistance fourier = thermalohm; thermalhenry = J K^2/W^2; # thermal inductance thermalvolt = K; # thermal potential difference # # United States units # # linear measure # The US Metric Law of 1866 gave the exact relation 1 meter = 39.37 inches.; # From 1893 until 1959, the foot was exactly (1200 / 3937) meters. In 1959 # the definition was changed to bring the US into agreement with other # countries. Since then, the foot has been exactly 0.3048 meters. At the # same time it was decided that any data expressed in feet derived from # geodetic surveys within the US would continue to use the old definition. US = (1200 / 3937) m/ft; # These four values will convert prefix US = US; # international measures to prefix survey = US; # US Survey measures prefix geodetic = US; int = (3937 / 1200) ft/m; # Convert US Survey measures to prefix int = int; # international measures inch = 2.54 cm; in = inch; foot = 12 inch; feet = foot; ft = foot; yard = 3 ft; yd = yard; mile = 5280 ft; line = (1 / 12) inch; # Also defined as '.1 in' or as '1e-8 Wb' rod = 5.5 USyard; perch = rod; furlong = 40 rod; # From "furrow long" statutemile = USmile; league = 3 USmile; # surveyor's measure surveyorschain = 66 surveyft; surveyorspole = (1 / 4) surveyorschain; surveyorslink = (1 / 100) surveyorschain; chain = surveyorschain; surveychain = chain; ch = chain; link = surveyorslink; acre = 10 chain^2; intacre = 43560 ft^2; # Acre based on international ft acrefoot = acre surveyfoot; section = USmile^2; township = 36 section; homestead = 160 acre; # Area of land granted by the 1862 # Homestead Act of the United States # Congress gunterschain = surveyorschain; engineerschain = 100 ft; engineerslink = (1 / 100) engineerschain; ramsdenschain = engineerschain; ramsdenslink = engineerslink; # nautical measure fathom = 6 USft; # Originally defined as the distance from # fingertip to fingertip with arms fully # extended. nauticalmile = 1852 m; # Supposed to be one minute of latitude at # the equator. That value is about 1855 m. # Early estimates of the earth's circumference # were a bit off. The value of 1852 m was # made the international standard in 1929. # The US did not accept this value until # 1954. The UK switched in 1970. cable = (1 / 10) nauticalmile; intcable = cable; # international cable cablelength = cable; UScable = 100 fathom; navycablelength = 720 USft; marineleague = 3 nauticalmile; geographicalmile = brnauticalmile; knot = nauticalmile / hr; # Avoirdupois weight pound = 0.45359237 kg; # The one normally used lb = pound; # From the latin libra grain = (1 / 7000) pound; # The grain is the same in all three # weight systems. It was originally # defined as the weight of a barley # corn taken from the middle of the # ear. ounce = (1 / 16) pound; oz = ounce; dram = (1 / 16) ounce; dr = dram; hundredweight = 100 pound; # This is the USA hundredweight cwt = hundredweight; shorthundredweight = hundredweight; ton = 2000 lb; shortton = ton; quarter = (1 / 4) ton; shortquarter = (1 / 4) shortton; # Troy Weight. In 1828 the troy pound was made the first United States # standard weight. It was to be used to regulate coinage. troypound = 5760 grain; troyounce = (1 / 12) troypound; ozt = troyounce; pennyweight = (1 / 20) troyounce; # Abbreviated "d" in reference to a dwt = pennyweight; # Frankish coin called the "denier" # minted in the late 700's. There # were 240 deniers to the pound. assayton = mg ton / troyounce; # mg / assayton = troyounce / ton; # Some other jewelers units metriccarat = 0.2 gram; metricgrain = 50 mg; carat = metriccarat; ct = carat; jewelerspoint = (1 / 100) carat; silversmithpoint = (1 / 4000) inch; # Apothecaries' weight appound = troypound; apounce = troyounce; apdram = (1 / 8) apounce; scruple = (1 / 3) apdram; # Liquid measure gallon = 231 in^3; gal = gallon; quart = (1 / 4) gallon; qt = quart; pint = (1 / 2) qt; pt = pint; gill = (1 / 4) pint; fluidounce = (1 / 16) pint; floz = fluidounce; fluiddram = (1 / 8) floz; fldr = fluiddram; minim = (1 / 60) fldr; liquidbarrel = 31.5 gallon; petroleumbarrel = 42 gallon; # Originated in Pennsylvania oil barrel = petroleumbarrel; # fields, from the winetierce bbl = barrel; hogshead = 63 gallon; firkin = 9 gallon; # Dry measures: The Winchester Bushel was defined by William III in 1702 and # legally adopted in the US in 1836. drybarrel = 7056 in^3; bushel = 2150.42 in^3; # Volume of 8 inch cylinder with 18.5 bu = bushel; # inch diameter (rounded) peck = (1 / 4) bushel; pk = peck; drygallon = (1 / 2) peck; dryquart = (1 / 4) drygallon; drypint = (1 / 2) dryquart; # Grain measures. The bushel as it is used by farmers in the USA is actually # a measure of mass which varies for different commodities. Canada uses the # same bushel masses for most commodities, but not for oats. wheatbushel = 60 lb; soybeanbushel = 60 lb; cornbushel = 56 lb; ryebushel = 56 lb; barleybushel = 48 lb ; oatbushel = 32 lb; ricebushel = 45 lb; canada_oatbushel = 34 lb; # Wine and Spirits measure pony = 1 floz; jigger = 1.5 floz; # Can vary between 1 and 2 floz shot = jigger; # Sometimes 1 floz eushot = 25 ml; # EU standard spirits measure fifth = (1 / 5) gallon; winebottle = 750 ml; # US industry standard, 1979 winesplit = (1 / 4) winebottle; wineglass = 4 floz; magnum = 1.5 liter; # Standardized in 1979, but given # as 2 qt in some references metrictenth = 375 ml; metricfifth = 750 ml; metricquart = 1 liter; # French champagne bottle sizes split = 200 ml; jeroboam = 2 magnum; rehoboam = 3 magnum; methuselah = 4 magnum; salmanazar = 6 magnum; balthazar = 8 magnum; nebuchadnezzar = 10 magnum; # Shoe measures shoeiron = (1 / 48) inch; # Used to measure leather in soles shoeounce = (1 / 64) inch; # Used to measure non-sole shoe leather # # USA slang units # key = kg; # usually of marijuana, 60's lid = 1 oz; # Another 60's weed unit footballfield = 100 yard; marathon = 138435 ft; // 26 miles + 385 yards # # British # UK = (1200000 / 3937014) m/ft; # The UK lengths were defined by prefix british = UK; # a bronze bar manufactured in prefix UK = UK; # 1844. Measurement of that bar # revealed the dimensions given # here. brnauticalmile = 6080 ft; # Used until 1970 when the UK brknot = brnauticalmile / hr; # switched to the international brcable = (1 / 10) brnauticalmile; # nautical mile. admiraltymile = brnauticalmile; admiraltyknot = brknot; admiraltycable = brcable; seamile = 6000 ft; # British Imperial weight is mostly the same as US weight. A few extra # units are added here. clove = 7 lb; stone = 14 lb; brquartermass = (1 / 4) brhundredweight; brhundredweight = 8 stone; longhundredweight = brhundredweight; longton = 20 brhundredweight; brton = longton; brassayton = mg brton / troyounce; # British Imperial volume measures brminim = (1 / 60) brdram; brscruple = (1 / 3) brdram; fluidscruple = brscruple; brdram = (1 / 8) brfloz; brfloz = (1 / 20) brpint; brfluidounce = brfloz; brgill = (1 / 4) brpint; brpint = (1 / 2) brquart; brquart = (1 / 4) brgallon; brgallon = 4.54609 l; # The British Imperial gallon was canadiangallon = brgallon; # defined in 1824 to be the volume of cangallon = brgallon; # water which weighed 10 pounds at 62 # deg F with a pressure of 30 inHg. # In 1963 it was defined to be the space # occupied by 10 pounds of distilled # water of density 0.998859 g/ml weighed # in air of density 0.001217 g/ml # against weights of density 8.136 g/ml. # The value given here is given by [1] # as an exact value. brpeck = 2 brgallon; brbarrel = 36 brgallon; # Used for beer brbushel = 4 brpeck; brquarter = 8 brbushel; brchaldron = 36 brbushel; # Obscure British volume measures. These units are generally traditional # measures whose definitions have fluctuated over the years. Often they # depended on the quantity being measured. They are given here in terms of # British Imperial measures. For example, the puncheon may have historically # been defined relative to the wine gallon or beer gallon or ale gallon # rather than the British Imperial gallon. bag = 4 brbushel; bucket = 4 brgallon; last = 40 brbushel; noggin = brgill; pottle = 0.5 brgallon; pin = 4.5 brgallon; puncheon = 72 brgallon; seam = 8 brbushel; coomb = 4 brbushel; boll = 6 brbushel ; firlot = (1 / 4) boll; brfirkin = 9 brgallon; # Used for ale and beer cran = 37.5 brgallon; # measures herring, about 750 fish brhogshead = 63 brgallon; registerton = 100 ft^3; # Used for internal capacity of ships shippington = 40 ft^3; # Used for ship's cargo freight or timber brshippington = 42 ft^3; # freightton = shippington; # Both register ton and shipping ton derive # from the "tun cask" of wine. displacementton = 35 ft^3; # Approximate volume of a longton weight of # sea water used to measure ship displacement waterton = 224 brgallon; strike = 70.5 l; # 16th century unit, sometimes # defined as .5, 2, or 4 bushels # depending on the location. It # probably doesn't make a lot of # sense to define in terms of imperial # bushels. Zupko gives a value of # 2 Winchester grain bushels or about # 70.5 liters. # obscure British lengths barleycorn = (1 / 3) UKinch; # Given in Realm of Measure as the # difference between successive shoe sizes nail = (1 / 16) UKyard; # Originally the width of the thumbnail, # or (1 / 16) ft. This took on the general # meaning of (1 / 16) and settled on the # nail of a yard or (1 / 16) yards as its # final value. [12] pole = 16.5 UKft; rope = 20 UKft; englishell = 45 UKinch; flemishell = 27 UKinch; ell = englishell; # supposed to be measure from elbow to # fingertips span = 9 UKinch; # supposed to be distance from thumb # to pinky with full hand extension # misc obscure British units rood = (1 / 4) acre; englishcarat = 3.163 grain; # Originally intended to be 4 grain # but this value ended up being # used in the London diamond market mancus = 2 oz; mast = 2.5 lb; basebox = 31360 in^2; # Used in metal plating # # Units derived the human body (may not be very accurate) # geometricpace = 5 ft; # distance between points where the same # foot hits the ground pace = 2.5 ft; # distance between points where alternate # feet touch the ground USmilitarypace = 30 in; # United States official military pace USdoubletimepace = 36 in; # United States official doubletime pace fingerbreadth = (7 / 8) in; # The finger is defined as either the width fingerlength = 4.5 in; # or length of the finger finger = fingerbreadth; palmwidth = hand; # Palm is a unit defined as either the width palmlength = 8 in; # or the length of the hand hand = 4 inch; # width of hand # # Units derived from imperial system # ouncedal = oz ft / s^2; # force which accelerates an ounce # at 1 ft/s^2 poundal = lb ft / s^2; # same thing for a pound tondal = ton ft / s^2; # and for a ton pdl = poundal; psi = pound force / inch^2; psia = psi; # absolute pressure tsi = ton force / inch^2; reyn = psi sec; slug = lbf s^2 / ft; slugf = slug force; slinch = lbf s^2 / inch; # Mass unit derived from inch second slinchf = slinch force; # pound-force system. Used in space # applications where in/sec^2 was a # natural acceleration measure. geepound = slug; lbf = lb force; tonf = ton force; lbm = lb; kip = 1000 lbf; # from kilopound mil = 0.001 inch; thou = 0.001 inch; circularinch = (1 / 4) pi in^2; # area of a one-inch diameter circle circularmil = (1 / 4) pi mil^2; # area of one-mil diameter circle cmil = circularmil; cental = 100 pound; centner = cental; caliber = 0.01 inch; # for measuring bullets duty = ft lbf; celo = ft / s^2; jerk = ft / s^3; australiapoint = 0.01 inch; # The "point" is used to measure rainfall # in Australia sabin = ft^2; # Measure of sound absorption equal to the # absorbing power of one square foot of # a perfectly absorbing material. The # sound absorptivity of an object is the # area times a dimensionless # absorptivity coefficient. standardgauge = 56.5 in; #4 ft + 8.5 in Standard width between railroad track flag = 5 ft^2; # Construction term referring to sidewalk. rollwallpaper = 30 ft^2; # Area of roll of wall paper fillpower = in^3 / ounce; # Density of down at standard pressure. # The best down has 750-800 fillpower. pinlength = (1 / 16) inch; # A #17 pin is (17 / 16) in long in the USA. buttonline = (1 / 40) inch; # The line was used in 19th century USA # to measure width of buttons. scoopnumber = 1 / quart; # Ice cream scoops are labeled with a # number specifying how many scoops # fill a quart. # # Other units of work, energy, power, etc # # Calories: energy to raise a gram of water one degree celsius cal_IT = 4.1868 J; # International Table calorie cal_th = 4.184 J; # Thermochemical calorie cal_fifteen = 4.18580 J; # Energy to go from 14.5 to 15.5 degC cal_twenty = 4.18190 J; # Energy to go from 19.5 to 20.5 degC cal_mean = 4.19002 J; # (1 / 100) energy to go from 0 to 100 degC calorie = cal_IT; cal = calorie; calorie_IT = cal_IT; thermcalorie = cal_th; calorie_th = thermcalorie; Calorie = kilocalorie; # the food Calorie thermie = 1e6 cal_fifteen; # Heat required to raise the # temperature of a tonne of # water from 14.5 to 15.5 degC. # btu definitions: energy to raise a pound of water 1 degF btu = cal lb degF / (gram K); # international table BTU britishthermalunit = btu; btu_IT = btu; btu_th = cal_th lb degF / (gram K); btu_mean = cal_mean lb degF / (gram K); quad = quadrillion btu; ECtherm = 1.05506e8 J; # Exact definition, close to 1e5 btu UStherm = 1.054804e8 J; # Exact definition therm = UStherm; # The horsepower is supposedly the power of one horse pulling. Obviously # different people had different horses. horsepower = 550 foot pound force / sec; # Invented by James Watt hp = horsepower; metrichorsepower = 75 kilogram force meter / sec; electrichorsepower = 746 W; boilerhorsepower = 9809.50 W; waterhorsepower = 746.043 W; brhorsepower = 745.70 W; donkeypower = 250 W; # Thermal insulance: Thermal conductivity has dimension power per area per # (degree per inch thickness) which comes out to W / K m. If the thickness # is fixed, then the conductance will have units of W / K m^2. Thermal # insulance is the reciprocal. Rvalue = degF ft^2 hr / btu; Uvalue = 1/Rvalue; europeanUvalue = watt / (m^2 K); RSI = degC m^2 / W; clo = 0.155 degC m^2 / W; # Supposed to be the insulance # required to keep a resting person # comfortable indoors. The value # given is from NIST and the CRC, # but [5] gives a slightly different # value of 0.875 ft^2 degF hr / btu. # Misc other measures clausius = 1e3 cal/K; # A unit of physical entropy langley = thermcalorie/cm^2; poncelet = 100 kg force m / s; tonrefrigeration = ton 144 btu / (lb day); # One ton refrigeration is # the rate of heat extraction req'd # turn one ton of water to ice in # a day. Ice is defined to have a # latent heat of 144 btu/lb. tonref = tonrefrigeration; refrigeration = tonref / ton; frigorie = 1000 cal_fifteen; # Used in refrigeration engineering. tnt = 4.184e9 J/ton; # So you can write tons-tnt, this # is a defined, not measured, value # # Permeability: The permeability or permeance, n, of a substance determines # how fast vapor flows through the substance. The formula W = n A dP; # holds where W is the rate of flow (in mass/time), n is the permeability, # A is the area of the flow path, and dP is the vapor pressure difference. # perm_0C = grain / (hr ft^2 inHg); perm_zero = perm_0C; perm_0 = perm_0C; perm = perm_0C; perm_23C = grain / (hr ft^2 in Hg23C); perm_twentythree = perm_23C; # # Counting measures # pair = 2; nest = 3; dickers = 10; dozen = 12; bakersdozen = 13; score = 20; flock = 40; timer = 40; shock = 60; gross = 144; greatgross = 12 gross; # Paper counting measure shortquire = 24; quire = 25; shortream = 480; ream = 500 ; perfectream = 516; bundle = 2 ream; bale = 5 bundle; # # Paper measures # # USA paper sizes lettersize = 8.5 inch 11 inch; legalsize = 8.5 inch 14 inch; ledgersize = 11 inch 17 inch; executivesize = 7.25 inch 10.5 inch; Apaper = 8.5 inch 11 inch; Bpaper = 11 inch 17 inch; Cpaper = 17 inch 22 inch; Dpaper = 22 inch 34 inch; Epaper = 34 inch 44 inch; # The metric paper sizes are defined so that if a sheet is cut in half # along the short direction, the result is two sheets which are # similar to the original sheet. This means that for any metric size, # the long side is close to sqrt(2) times the length of the short # side. Each series of sizes is generated by repeated cuts in half, # with the values rounded down to the nearest millimeter. A0paper = 841 mm 1189 mm; # The basic size in the A series A1paper = 594 mm 841 mm; # is defined to have an area of A2paper = 420 mm 594 mm; # one square meter. A3paper = 297 mm 420 mm; A4paper = 210 mm 297 mm; A5paper = 148 mm 210 mm; A6paper = 105 mm 148 mm; A7paper = 74 mm 105 mm; A8paper = 52 mm 74 mm; A9paper = 37 mm 52 mm; A10paper = 26 mm 37 mm; B0paper = 1000 mm 1414 mm; # The basic B size has an area B1paper = 707 mm 1000 mm; # of sqrt(2) square meters. B2paper = 500 mm 707 mm; B3paper = 353 mm 500 mm; B4paper = 250 mm 353 mm; B5paper = 176 mm 250 mm; B6paper = 125 mm 176 mm; B7paper = 88 mm 125 mm; B8paper = 62 mm 88 mm; B9paper = 44 mm 62 mm; B10paper = 31 mm 44 mm; C0paper = 917 mm 1297 mm; # The basic C size has an area C1paper = 648 mm 917 mm; # of sqrt(sqrt(2)) square meters. C2paper = 458 mm 648 mm; C3paper = 324 mm 458 mm; # Intended for envelope sizes C4paper = 229 mm 324 mm; C5paper = 162 mm 229 mm; C6paper = 114 mm 162 mm; C7paper = 81 mm 114 mm; C8paper = 57 mm 81 mm; C9paper = 40 mm 57 mm; C10paper = 28 mm 40 mm; # gsm (Grams per Square Meter), a sane, metric paper weight measure gsm = gram / meter^2; # In the USA, a collection of crazy historical paper measures are used. # Paper is measured as a weight of a ream of that particular type of paper. # This is sometimes called the "substance" or "basis" (as in "substance 20" # paper). The standard sheet size or "basis size" varies depending on the # type of paper. As a result, 20 pound bond paper and 50 pound text paper # are actually about the same weight. The different sheet sizes were # historically the most convenient for printing or folding in the different # applications. These different basis weights are standards maintained by # American Society for Testing Materials (ASTM) and the American Forest and # Paper Association (AF&PA). poundbookpaper = lb / (25 inch 38 inch ream); lbbook = poundbookpaper; poundtextpaper = poundbookpaper; lbtext = poundtextpaper; poundoffsetpaper = poundbookpaper; # For offset printing lboffset = poundoffsetpaper; poundbiblepaper = poundbookpaper; # Designed to be lightweight, thin, lbbible = poundbiblepaper; # strong and opaque. poundtagpaper = lb / (24 inch 36 inch ream); lbtag = poundtagpaper; poundbagpaper = poundtagpaper; lbbag = poundbagpaper; poundnewsprintpaper = poundtagpaper; lbnewsprint = poundnewsprintpaper; poundposterpaper = poundtagpaper; lbposter = poundposterpaper; poundtissuepaper = poundtagpaper; lbtissue = poundtissuepaper; poundwrappingpaper = poundtagpaper; lbwrapping = poundwrappingpaper; poundwaxingpaper = poundtagpaper; lbwaxing = poundwaxingpaper; poundglassinepaper = poundtagpaper; lbglassine = poundglassinepaper; poundcoverpaper = lb / (20 inch 26 inch ream); lbcover = poundcoverpaper; poundindexpaper = lb / (25.5 inch 30.5 inch ream); lbindex = poundindexpaper; poundindexbristolpaper= poundindexpaper; lbindexbristol = poundindexpaper; poundbondpaper = lb / (17 inch 22 inch ream); # Bond paper is stiff lbbond = poundbondpaper; # and durable for repeated poundwritingpaper = poundbondpaper; # filing, and it resists lbwriting = poundwritingpaper; # ink penetration. poundledgerpaper = poundbondpaper; lbledger = poundledgerpaper; poundcopypaper = poundbondpaper; lbcopy = poundcopypaper; poundblottingpaper = lb / (19 inch 24 inch ream); lbblotting = poundblottingpaper; poundblankspaper = lb / (22 inch 28 inch ream); lbblanks = poundblankspaper; poundpostcardpaper = lb / (22.5 inch 28.5 inch ream); lbpostcard = poundpostcardpaper; poundweddingbristol = poundpostcardpaper; lbweddingbristol = poundweddingbristol; poundbristolpaper = poundweddingbristol; lbbristol = poundbristolpaper; poundboxboard = lb / (1000 ft^2); lbboxboard = poundboxboard; poundpaperboard = poundboxboard; lbpaperboard = poundpaperboard; # When paper is marked in units of M, it means the weight of 1000 sheets of # the given size of paper. To convert this to paper weight, divide by the # size of the paper in question. paperM = lb / 1000; # # Printing # fournierpoint = 0.1648 inch / 12; # First definition of the printers # point made by Pierre Fournier who # defined it in 1737 as (1 / 12) of a # cicero which was 0.1648 inches. olddidotpoint = (1 / 72) frenchinch; # François Ambroise Didot, one of # a family of printers, changed # Fournier's definition around 1770 # to fit to the French units then in # use. bertholdpoint = (1 / 2660) m; # H. Berthold tried to create a # metric version of the didot point # in 1878. INpoint = 0.4 mm; # This point was created by a # group directed by Fermin Didot in # 1881 and is associated with the # imprimerie nationale. It doesn't # seem to have been used much. germandidotpoint = 0.376065 mm; # Exact definition appears in DIN # 16507, a German standards document # of 1954. Adopted more broadly in # 1966 by ??? metricpoint = (3 / 8) mm; # Proposed in 1977 by Eurograf point = (1 / 72.27) inch; # The American point was invented printerspoint = point; # by Nelson Hawks in 1879 and # dominates USA publishing. # It was standardized by the American # Typefounders Association at the # value of 0.013837 inches exactly. # Knuth uses the approximation given # here (which is very close). The # comp.fonts FAQ claims that this # value is supposed to be (1 / 12) of a # pica where 83 picas is equal to 35 # cm. But this value differs from # the standard. texscaledpoint = (1 / 65536) point; # The TeX typesetting system uses texsp = texscaledpoint; # this for all computations. computerpoint = (1 / 72) inch; # The American point was rounded computerpica = 12 computerpoint; # to an even (1 / 72) inch by computer postscriptpoint = computerpoint; # people at some point. pspoint = postscriptpoint; Q = (1 / 4) mm; # Used in Japanese phototypesetting # Q is for quarter frenchprinterspoint = olddidotpoint ; didotpoint = germandidotpoint; # This seems to be the dominant value europeanpoint = didotpoint; # for the point used in Europe cicero = 12 didotpoint; stick = 2 inch; # Type sizes excelsior = 3 point; brilliant = 3.5 point; diamond = 4 point; pearl = 5 point; agate = 5.5 point; ruby = agate; # British nonpareil = 6 point; mignonette = 6.5 point; emerald = mignonette; # British minion = 7 point; brevier = 8 point; bourgeois = 9 point; longprimer = 10 point; smallpica = 11 point; pica = 12 point; english = 14 point; columbian = 16 point; greatprimer = 18 point; paragon = 20 point; meridian = 44 point; canon = 48 point; # German type sizes nonplusultra = 2 didotpoint; brillant = 3 didotpoint; diamant = 4 didotpoint; perl = 5 didotpoint; nonpareille = 6 didotpoint; kolonel = 7 didotpoint; petit = 8 didotpoint; borgis = 9 didotpoint; korpus = 10 didotpoint; corpus = korpus; garamond = korpus; mittel = 14 didotpoint; tertia = 16 didotpoint; text = 18 didotpoint; kleine_kanon = 32 didotpoint; kanon = 36 didotpoint; grobe_kanon = 42 didotpoint; missal = 48 didotpoint; kleine_sabon = 72 didotpoint; grobe_sabon = 84 didotpoint; jiffy = 0.01 sec; # This is defined in the Jargon File jiffies = jiffy; # (http://www.jargon.org) as being the # duration of a clock tick for measuring # wall-clock time. Supposedly the value # used to be (1 / 60) sec or (1 / 50) sec # depending on the frequency of AC power, # but then (1 / 100) sec became more common. # On linux systems, this term is used and # for the Intel based chips, it does have # the value of .01 sec. The Jargon File # also lists two other definitions: # millisecond, and the time taken for # light to travel one foot. # # yarn and cloth measures # # yarn linear density woolyarnrun = 1600 yard/pound; # 1600 yds of "number 1 yarn" weighs # a pound. yarncut = 300 yard/pound; # Less common system used in # Pennsylvania for wool yarn cottonyarncount = 840 yard/pound; linenyarncount = 300 yard/pound; # Also used for hemp and ramie worstedyarncount = 1680 ft/pound; metricyarncount = meter/gram; denier = (1 / 9) tex; # used for silk and rayon manchesteryarnnumber = dram/(1000 yard); # old system used for silk pli = lb/in; typp = 1000 yd/lb; asbestoscut = 100 yd/lb; # used for glass and asbestos yarn tex = gram / km; # rational metric yarn measure, meant drex = 0.1 tex; # to be used for any kind of yarn # yarn and cloth length skeincotton = 80 54 inch; # 80 turns of thread on a reel with a # 54 in circumference (varies for other # kinds of thread) cottonbolt = 120 ft; # cloth measurement woolbolt = 210 ft; bolt = cottonbolt; heer = 600 yard; cut = 300 yard; # used for wet-spun linen yarn lea = 300 yard; # # drug dosage # mcg = microgram; # Frequently used for vitamins iudiptheria = 62.8 microgram; # IU is for international unit iupenicillin = 0.6 microgram; iuinsulin = 41.67 microgram; drop = (1 / 20) ml; # The drop was an old "unit" that was # replaced by the minim. But I was # told by a pharmacist that in his # profession, the conversion of 20 # drops per ml is actually used. # # Units used for measuring volume of wood # cord = 4 4 8 ft^3; # 4 ft by 4 ft by 8 ft bundle of wood facecord = (1 / 2) cord; cordfoot = (1 / 8) cord; # One foot long section of a cord cordfeet = cordfoot; housecord = (1 / 3) cord; # Used to sell firewood for residences # often confusingly called a "cord" boardfoot = ft^2 inch; # Usually 1 inch thick wood boardfeet = boardfoot; fbm = boardfoot; # feet board measure stere = m^3; timberfoot = ft^3; # Used for measuring solid blocks of wood standard = 120 12 ft 11 in 1.5 in; # This is the St Petersburg or # Pittsburg standard. Apparently the # term is short for "std hundred" # which was meant to refer to 100 # pieces of wood (deals). However, # this particular standard is equal # to 120 deals which are 12 ft by 11 # in by 1.5 inches (not the standard # deal). # In Britain, the deal is apparently any piece of wood over 6 feet long, over # 7 wide and 2.5 inches thick. The OED doesn't give a std size. A piece # of wood less than 7 inches wide is called a "batten". Unit is now used # exclusively for fir and pine. deal = 12 ft 11 in 2.5 in; # Standard North American deal [OED] wholedeal = 12 ft 11 in 1.25 in; # If it's half as thick as the standard # deal it's called a "whole deal"! splitdeal = 12 ft 11 in (5 / 8) in; # And half again as thick is a split # deal. # # Gas and Liquid flow units # # Some obvious volumetric gas flow units (cu is short for cubic) cumec = m^3/s; cusec = ft^3/s; # Conventional abbreviations for fluid flow units gph = gal/hr; gpm = gal/min; mgd = megagal/day; cfs = ft^3/s; cfh = ft^3/hour; cfm = ft^3/min; lpm = liter/min; # Miner's inch: This is an old historic unit used in the Western United # States. It is generally defined as the rate of flow through a one square # inch hole at a specified depth such as 4 inches. In the late 19th century, # volume of water was sometimes measured in the "24 hour inch". Values for # miner's inch were fixed by state statues. (This information is from a web # site operated by the Nevada Division of Water Planning: The Water Words # Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.) minersinchAZ = 1.5 ft^3/min; minersinchCA = 1.5 ft^3/min; minersinchMT = 1.5 ft^3/min; minersinchNV = 1.5 ft^3/min; minersinchOR = 1.5 ft^3/min; minersinchID = 1.2 ft^3/min; minersinchKS = 1.2 ft^3/min; minersinchNE = 1.2 ft^3/min; minersinchNM = 1.2 ft^3/min; minersinchND = 1.2 ft^3/min; minersinchSD = 1.2 ft^3/min; minersinchUT = 1.2 ft^3/min; minersinchCO = 1.56 ft^3/min; minersinchBC = 1.68 ft^3/min; # British Columbia # In vacuum science and some other applications, gas flow is measured # as the product of volumetric flow and pressure. This is useful # because it makes it easy to compare with the flow at standard # pressure (one atmosphere). It also directly relates to the number # of gas molecules per unit time, and hence to the mass flow if the # molecular mass is known. sccm = atm cc/min; # 's' is for "standard" to indicate sccs = atm cc/sec; # flow at standard pressure scfh = atm ft^3/hour; scfm = atm ft^3/min; slpm = atm liter/min; slph = atm liter/hour; lusec = liter micron Hg / s; # Used in vacuum science # Wire gauge: this area is a nightmare with huge charts of wire gauge dia. # that usually have no clear origin. There are at least 5 competing wire # gauge systems to add to the confusion. # Use of wire gauge is related to the manufacturing method: a metal rod is # heated and drawn through a hole. The size change can't be too big. To get # smaller wires, the process is repeated with a series of smaller holes. # American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most # important gauge. ASTM B-258 specifies that this gauge is based on geometric # interpolation between gauge 0000, which is 0.46 inches exactly, and gauge # 36 which is 0.005 inches exactly. Therefore, the diameter in inches of a # wire is given by the formula 1 / 200 92^((36-g)/39). Note that 92^(1/39) # is close to 2^(1/6), so diameter is approximately halved for every # 6 gauges. For the repeated zero values, use negative numbers in the # formula. The same document also specifies rounding rules which seem to be # ignored by makers of tables. Gauges up to 44 are to be specified with up to # 4 significant figures, but no closer than 0.0001 inch. Gauges from 44 to # 56 are to be rounded to the nearest 0.00001 inch. The table below gives # 4 significant figures for all gauges. # # In addition to being used to measure wire thickness, this gauge is used to # measure the thickness of sheets of aluminum, copper, and most metals other # than steel, iron and zinc. wire0000gauge = 0.4600 in; wire000gauge = 0.4096 in; wire00gauge = 0.3648 in; wire0gauge = 0.3249 in; wire1gauge = 0.2893 in; wire2gauge = 0.2576 in; wire3gauge = 0.2294 in; wire4gauge = 0.2043 in; wire5gauge = 0.1819 in; wire6gauge = 0.1620 in; wire7gauge = 0.1443 in; wire8gauge = 0.1285 in; wire9gauge = 0.1144 in; wire10gauge = 0.1019 in; wire11gauge = 0.09074 in; wire12gauge = 0.08081 in; wire13gauge = 0.07196 in; wire14gauge = 0.06408 in; wire15gauge = 0.05707 in; wire16gauge = 0.05082 in; wire17gauge = 0.04526 in; wire18gauge = 0.04030 in; wire19gauge = 0.03589 in; wire20gauge = 0.03196 in; wire21gauge = 0.02846 in; wire22gauge = 0.02535 in; wire23gauge = 0.02257 in; wire24gauge = 0.02010 in; wire25gauge = 0.01790 in; wire26gauge = 0.01594 in; wire27gauge = 0.01420 in; wire28gauge = 0.01264 in; wire29gauge = 0.01126 in; wire30gauge = 0.01003 in; wire31gauge = 0.008928 in; wire32gauge = 0.007950 in; wire33gauge = 0.007080 in; wire34gauge = 0.006305 in; wire35gauge = 0.005615 in; wire36gauge = 0.005000 in; wire37gauge = 0.004453 in; wire38gauge = 0.003965 in; wire39gauge = 0.003531 in; wire40gauge = 0.003145 in; wire41gauge = 0.002800 in; wire42gauge = 0.002494 in; wire43gauge = 0.002221 in; wire44gauge = 0.001978 in; wire45gauge = 0.001761 in; wire46gauge = 0.001568 in; wire47gauge = 0.001397 in; wire48gauge = 0.001244 in; wire49gauge = 0.001108 in; wire50gauge = 0.0009863 in; wire51gauge = 0.0008783 in; wire52gauge = 0.0007822 in; wire53gauge = 0.0006966 in; wire54gauge = 0.0006203 in; wire55gauge = 0.0005524 in; wire56gauge = 0.0004919 in; # Next we have the SWG, the Imperial or British Standard Wire Gauge. This # one is piecewise linear, so it is not generated by a simple formula. It # was used for aluminum sheets. brwire0000000gauge = 0.500 in; brwire000000gauge = 0.464 in; brwire00000gauge = 0.432 in; brwire0000gauge = 0.400 in; brwire000gauge = 0.372 in; brwire00gauge = 0.348 in ; brwire0gauge = 0.324 in; brwire1gauge = 0.300 in; brwire2gauge = 0.276 in; brwire3gauge = 0.252 in; brwire4gauge = 0.232 in; brwire5gauge = 0.212 in; brwire6gauge = 0.192 in; brwire7gauge = 0.176 in; brwire8gauge = 0.160 in; brwire9gauge = 0.144 in; brwire10gauge = 0.128 in; brwire11gauge = 0.116 in; brwire12gauge = 0.104 in; brwire13gauge = 0.092 in; brwire14gauge = 0.080 in; brwire15gauge = 0.072 in; brwire16gauge = 0.064 in; brwire17gauge = 0.056 in; brwire18gauge = 0.048 in; brwire19gauge = 0.040 in; brwire20gauge = 0.036 in; brwire21gauge = 0.032 in; brwire22gauge = 0.028 in; brwire23gauge = 0.024 in; brwire24gauge = 0.022 in; brwire25gauge = 0.0200 in; brwire26gauge = 0.0180 in; brwire27gauge = 0.0164 in; brwire28gauge = 0.0149 in; brwire29gauge = 0.0136 in; brwire30gauge = 0.0124 in; brwire31gauge = 0.0116 in; brwire32gauge = 0.0108 in; brwire33gauge = 0.0100 in; brwire34gauge = 0.0092 in; brwire35gauge = 0.0084 in; brwire36gauge = 0.0076 in; brwire37gauge = 0.0068 in; brwire38gauge = 0.0060 in; brwire39gauge = 0.0052 in; brwire40gauge = 0.0048 in; brwire41gauge = 0.0044 in; brwire42gauge = 0.0040 in; brwire43gauge = 0.0036 in; brwire44gauge = 0.0032 in; brwire45gauge = 0.0028 in; brwire46gauge = 0.0024 in; brwire47gauge = 0.0020 in; brwire48gauge = 0.0016 in; brwire49gauge = 0.0012 in; brwire50gauge = 0.0010 in; # The following is from the Appendix to ASTM B 258 # # For example, in U.S. gage, the standard for sheet metal is based on the # weight of the metal, not on the thickness. 16-gage is listed as approx. # .0625 inch thick and 40 ounces per square foot (the original standard was # based on wrought iron at .2778 pounds per cubic inch; steel has almost # entirely superseded wrought iron for sheet use, at .2833 pounds per cubic # inch). Smaller numbers refer to greater thickness. There is no formula for # converting gage to thickness or weight. # # It's rather unclear from the passage above whether the plate gauge values # are therefore wrong if steel is being used. Reference [15] states that # steel is in fact measured using this gauge (under the name Manufacturers' # Standard Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for # steel. But this doesn't seem to be the correct density of steel # (.2833 lb/in3 is closer), and nobody else lists these values. # # This gauge was established in 1893 for purposes of taxation. plate000000gauge = (15 / 32) in; # 300 oz / ft^2 plate00000gauge = (14 / 32) in; # 280 oz / ft^2 plate0000gauge = (13 / 32) in; # 260 oz / ft^2 plate000gauge = (12 / 32) in; # 240 oz / ft^2 plate00gauge = (11 / 32) in; # 220 oz / ft^2 plate0gauge = (10 / 32) in; # 200 oz / ft^2 plate1gauge = (9 / 32) in; # 180 oz / ft^2 plate2gauge = (17 / 64) in; # 170 oz / ft^2 plate3gauge = (16 / 64) in; # 160 oz / ft^2 plate4gauge = (15 / 64) in; # 150 oz / ft^2 plate5gauge = (14 / 64) in; # 140 oz / ft^2 plate6gauge = (13 / 64) in; # 130 oz / ft^2 plate7gauge = (12 / 64) in; # 120 oz / ft^2 plate8gauge = (11 / 64) in; # 110 oz / ft^2 plate9gauge = (10 / 64) in; # 100 oz / ft^2 plate10gauge = (9 / 64) in; # 90 oz / ft^2 plate11gauge = (8 / 64) in; # 80 oz / ft^2 plate12gauge = (7 / 64) in; # 70 oz / ft^2 plate13gauge = (6 / 64) in; # 60 oz / ft^2 plate14gauge = (5 / 64) in; # 50 oz / ft^2 plate15gauge = (9 / 128) in; # 45 oz / ft^2 plate16gauge = (8 / 128) in; # 40 oz / ft^2 plate17gauge = (9 / 160) in; # 36 oz / ft^2 plate18gauge = (8 / 160) in; # 32 oz / ft^2 plate19gauge = (7 / 160) in; # 28 oz / ft^2 plate20gauge = (6 / 160) in; # 24 oz / ft^2 plate21gauge = (11 / 320) in; # 22 oz / ft^2 plate22gauge = (10 / 320) in; # 20 oz / ft^2 plate23gauge = (9 / 320) in; # 18 oz / ft^2 plate24gauge = (8 / 320) in; # 16 oz / ft^2 plate25gauge = (7 / 320) in; # 14 oz / ft^2 plate26gauge = (6 / 320) in; # 12 oz / ft^2 plate27gauge = (11 / 640) in; # 11 oz / ft^2 plate28gauge = (10 / 640) in; # 10 oz / ft^2 plate29gauge = (9 / 640) in; # 9 oz / ft^2 plate30gauge = (8 / 640) in; # 8 oz / ft^2 plate31gauge = (7 / 640) in; # 7 oz / ft^2 plate32gauge = (13 / 1280) in; # 6.5 oz / ft^2 plate33gauge = (12 / 1280) in; # 6 oz / ft^2 plate34gauge = (11 / 1280) in; # 5.5 oz / ft^2 plate35gauge = (10 / 1280) in; # 5 oz / ft^2 plate36gauge = (9 / 1280) in; # 4.5 oz / ft^2 plate37gauge = (17 / 2560) in; # 4.25 oz / ft^2 plate38gauge = (16 / 2560) in; # 4 oz / ft^2 # Zinc sheet metal gauge zinc1gauge = 0.002 in; zinc2gauge = 0.004 in; zinc3gauge = 0.006 in; zinc4gauge = 0.008 in; zinc5gauge = 0.010 in; zinc6gauge = 0.012 in; zinc7gauge = 0.014 in; zinc8gauge = 0.016 in; zinc9gauge = 0.018 in; zinc10gauge = 0.020 in; zinc11gauge = 0.024 in; zinc12gauge = 0.028 in; zinc13gauge = 0.032 in; zinc14gauge = 0.036 in; zinc15gauge = 0.040 in; zinc16gauge = 0.045 in; zinc17gauge = 0.050 in; zinc18gauge = 0.055 in; zinc19gauge = 0.060 in; zinc20gauge = 0.070 in; zinc21gauge = 0.080 in; zinc22gauge = 0.090 in; zinc23gauge = 0.100 in; zinc24gauge = 0.125 in; zinc25gauge = 0.250 in; zinc26gauge = 0.375 in; zinc27gauge = 0.500 in; zinc28gauge = 1.000 in; # USA ring sizes. Several slightly different definitions seem to be in # circulation. According to [15], the interior diameter of size n ring in # inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The # size 2 ring is inconsistently 0.538in and no 2.5 size is listed. # # However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the # diameter and list no special case for size 2. (Or alternatively they are # 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) # One reference claimed that the original system was that each size was # 1 / 10 inch circumference, but that source doesn't have an explanation for # the modern system which is somewhat different. # # This table gives circumferences as listed in [15]. size2ring = 0.538 in pi; size3ring = 0.554 in pi; size3.5ring = 0.570 in pi; size4ring = 0.586 in pi; size4.5ring = 0.602 in pi; size5ring = 0.618 in pi; size5.5ring = 0.634 in pi; size6ring = 0.650 in pi; size6.5ring = 0.666 in pi; size7ring = 0.682 in pi; size7.5ring = 0.698 in pi; size8ring = 0.714 in pi; size8.5ring = 0.730 in pi; size9ring = 0.746 in pi; size9.5ring = 0.762 in pi; size10ring = 0.778 in pi; size10.5ring = 0.794 in pi; size11ring = 0.810 in pi; size11.5ring = 0.826 in pi; size12ring = 0.842 in pi; size12.5ring = 0.858 in pi; size13ring = 0.874 in pi; size13.5ring = 0.890 in pi; # Old practice in the UK measured rings using the "Wheatsheaf gauge" with sz # specified alphabetically and based on the ring inside diameter in steps of # 1 / 64 in. This system was replaced in 1987 by British Standard 6820 which # specifies sizes based on circumference. Each size is 1.25 mm different # from the preceding size. The baseline is size C which is 40 mm # circumference. The new sizes are close to the old ones. Sometimes it's # necessary to go beyond size Z to Z+1, Z+2, etc. sizeAring = 37.50 mm; sizeBring = 38.75 mm; sizeCring = 40.00 mm; sizeDring = 41.25 mm; sizeEring = 42.50 mm; sizeFring = 43.75 mm; sizeGring = 45.00 mm; sizeHring = 46.25 mm; sizeIring = 47.50 mm; sizeJring = 48.75 mm; sizeKring = 50.00 mm; sizeLring = 51.25 mm; sizeMring = 52.50 mm; sizeNring = 53.75 mm; sizeOring = 55.00 mm; sizePring = 56.25 mm; sizeQring = 57.50 mm; sizeRring = 58.75 mm; sizeSring = 60.00 mm; sizeTring = 61.25 mm; sizeUring = 62.50 mm; sizeVring = 63.75 mm; sizeWring = 65.00 mm; sizeXring = 66.25 mm; sizeYring = 67.50 mm; sizeZring = 68.75 mm; # Japanese sizes start with size 1 at a 13mm inside diameter and each size is # 1 / 3 mm larger in diameter than the previous one. They are multiplied by # pi to give circumference. jpsize1ring = (39 / 3) pi mm; jpsize2ring = (40 / 3) pi mm; jpsize3ring = (41 / 3) pi mm; jpsize4ring = (42 / 3) pi mm; jpsize5ring = (43 / 3) pi mm; jpsize6ring = (44 / 3) pi mm; jpsize7ring = (45 / 3) pi mm; jpsize8ring = (46 / 3) pi mm; jpsize9ring = (47 / 3) pi mm; jpsize10ring = (48 / 3) pi mm; jpsize11ring = (49 / 3) pi mm; jpsize12ring = (50 / 3) pi mm; jpsize13ring = (51 / 3) pi mm; jpsize14ring = (52 / 3) pi mm; jpsize15ring = (53 / 3) pi mm; jpsize16ring = (54 / 3) pi mm; jpsize17ring = (55 / 3) pi mm; jpsize18ring = (56 / 3) pi mm; jpsize19ring = (57 / 3) pi mm; jpsize20ring = (58 / 3) pi mm; jpsize21ring = (59 / 3) pi mm; jpsize22ring = (60 / 3) pi mm; jpsize23ring = (61 / 3) pi mm; jpsize24ring = (62 / 3) pi mm; jpsize25ring = (63 / 3) pi mm; jpsize26ring = (64 / 3) pi mm; jpsize27ring = (65 / 3) pi mm; jpsize28ring = (66 / 3) pi mm; jpsize29ring = (67 / 3) pi mm; jpsize30ring = (68 / 3) pi mm; # The European ring sizes are the length of the circumference in mm minus 40. eusize1ring = 41 mm; eusize2ring = 42 mm; eusize3ring = 43 mm; eusize4ring = 44 mm; eusize5ring = 45 mm; eusize6ring = 46 mm; eusize7ring = 47 mm; eusize8ring = 48 mm; eusize9ring = 49 mm; eusize10ring = 50 mm; eusize11ring = 51 mm; eusize12ring = 52 mm; eusize13ring = 53 mm; eusize14ring = 54 mm; eusize15ring = 55 mm; eusize16ring = 56 mm; eusize17ring = 57 mm; eusize18ring = 58 mm; eusize19ring = 59 mm; eusize20ring = 60 mm; eusize21ring = 61 mm; eusize22ring = 62 mm; eusize23ring = 63 mm; eusize24ring = 64 mm; eusize25ring = 65 mm; eusize26ring = 66 mm; eusize27ring = 67 mm; eusize28ring = 68 mm; eusize29ring = 69 mm; eusize30ring = 70 mm; # # Abbreviations # mph = mile/hr; mpg = mile/gal; kph = km/hr; fL = footlambert; fpm = ft/min; fps = ft/s; rpm = rev/min; rps = rev/sec; mi = mile; mbh = 1e3 btu/hour; mcm = 1e3 circularmil; # # Compatibility units with unix version # pa = Pa; ev = eV; hg = Hg; oe = Oe; mh = mH; us = microsec; rd = rod; pf = pF; gr = grain; nt = N; hz = Hz; hd = hogshead; dry = drygallon/gallon; imperial = brgallon/gallon; # This is a dubious definition # since it fails for fluid ounces # and all units derived from fluid # ounces. nmile = nauticalmile; beV = GeV; bev = beV; coul = C; # # Radioactivity units # becquerel = 1 /s; # Activity of radioactive source Bq = becquerel; # curie = 3.7e10 Bq; # Defined in 1910 as the radioactivity Ci = curie; # emitted by the amount of radon that is # in equilibrium with 1 gram of radium. rutherford = 1e6 Bq; # gray = J/kg; # Absorbed dose of radiation Gy = gray; # rad = 1e-2 Gy; # From Radiation Absorbed Dose rep = 8.38 mGy; # Roentgen Equivalent Physical, the amount # of radiation which , absorbed in the # body, would liberate the same amount # of energy as 1 roentgen of X rays # would, or 97 ergs. sievert = J/kg; # Dose equivalent: dosage that has the Sv = sievert; # same effect on human tissues as 200 rem = 1e-2 Sv; # keV X-rays. Different types of # radiation are weighted by the # Relative Biological Effectiveness # (RBE). # # Radiation type RBE # X-ray, gamma ray 1 # beta rays, > 1 MeV 1 # beta rays, < 1 MeV 1.08 # neutrons, < 1 MeV 4-5 # neutrons, 1-10 MeV 10 # protons, 1 MeV 8.5 # protons, .1 MeV 10 # alpha, 5 MeV 15 # alpha, 1 MeV 20 # # The energies are the kinetic energy # of the particles. Slower particles # interact more, so they are more # effective ionizers, and hence have # higher RBE values. # # rem stands for Roentgen Equivalent # Mammal roentgen = 2.58e-4 C / kg; # Ionizing radiation that produces # 1 statcoulomb of charge in 1 cc of # dry air at stp. rontgen = roentgen; # Sometimes it appears spelled this way //röntgen = roentgen; sievertunit = 8.38 rontgen; # Unit of gamma ray dose delivered in one # hour at a distance of 1 cm from a # point source of 1 mg of radium # enclosed in platinum .5 mm thick. eman = 1e-7 Ci/m^3; # radioactive concentration mache = 3.7e-7 Ci/m^3; } { # # fixup units for times when prefix handling doesn't do the job # hectare = hectoare; megohm = megaohm; kilohm = kiloohm; microhm = microohm; usec = microsec; } { # # Some primitive non-SI units # # Basic unit of information (entropy). The entropy in bits # of a random variable over a finite alphabet is defined # to be the sum of -p(i)*log2(p(i)) over the alphabet where # p(i) is the probability that the random variable takes # on the value i. # primitive bit; prefix yotta = 2^80; # Greek or Latin octo, "eight" prefix Y = 2^80; prefix zetta = 2^70; # Latin septem, "seven" prefix Z = 2^70; prefix exa = 2^60; # Greek hex, "six" prefix E = 2^60; prefix peta = 2^50; # Greek pente, "five" prefix P = 2^50; prefix tera = 2^40; # Greek teras, "monster" prefix T = 2^40; prefix giga = 2^30; # Greek gigas, "giant" prefix G = 2^30; prefix mega = 2^20; # Greek megas, "large" prefix M = 2^20; prefix kilo = 2^10; # Greek chilioi, "thousand" prefix k = 2^10; # # Information theory units # nat = 0.69314718056 bit; # Entropy measured base e hartley = 3.32192809488 bit; # log2(10) bits, or the entropy # of a uniformly distributed # random variable over 10 # symbols. # # Computer # bps = bit/sec; # Sometimes the term "baud" is # incorrectly used to refer to # bits per second. Baud refers # to symbols per second. Modern # modems transmit several bits # per symbol. byte = 8 bit; # Not all machines had 8 bit # bytes, but these days most of # them do. But beware: for # transmission over modems, a # few extra bits are used so # there are actually 10 bits per # byte. nybble = 4 bit; # Half of a byte. Sometimes # equal to different lengths # such as 3 bits. nibble = nybble; } { # # fixup units for times when prefix handling doesn't do the job # meg = megabyte; gig = gigabyte; KB = kilobyte; MB = megabyte; GB = gigabyte; TB = terabyte; PB = petabyte; EB = exabyte; ZB = zettabyte; YB = yottabyte; } { # # Names of some numbers # one = 1; two = 2; double = 2; three = 3; triple = 3; four = 4; quadruple = 4; five = 5; quintuple = 5; six = 6; seven = 7; eight = 8; nine = 9; ten = 10; twenty = 20; thirty = 30; forty = 40; fifty = 50; sixty = 60; seventy = 70; eighty = 80; ninety = 90; hundred = 100; thousand = 1000; million = 1e6; # These number terms were described by N. Chuquet and De la Roche in the 16th # century as being successive powers of a million. These definitions are # still used in most European countries. The current US definitions for # these numbers arose in the 17th century and don't make nearly as much # sense. These numbers are listed in the CRC Concise Encyclopedia of # Mathematics by Eric W. Weisstein. billion = 1e9; trillion = 1e12; quadrillion = 1e15; quintillion = 1e18; sextillion = 1e21; septillion = 1e24; octillion = 1e27; nonillion = 1e30; noventillion = nonillion; decillion = 1e33; undecillion = 1e36; duodecillion = 1e39; tredecillion = 1e42; quattuordecillion = 1e45; quindecillion = 1e48; sexdecillion = 1e51; septendecillion = 1e54; octodecillion = 1e57; novemdecillion = 1e60; vigintillion = 1e63; centillion = 1e303; googol = 1e100; brbillion = million^2; brtrillion = million^3; brquadrillion = million^4; brquintillion = million^5; brsextillion = million^6; brseptillion = million^7; broctillion = million^8; brnonillion = million^9; brnoventillion = brnonillion; brdecillion = million^10; brundecillion = million^11; brduodecillion = million^12; brtredecillion = million^13; brquattuordecillion = million^14; brquindecillion = million^15; brsexdecillion = million^16; brseptdecillion = million^17; broctodecillion = million^18; brnovemdecillion = million^19; brvigintillion = million^20; # These numbers fill the gaps left by the European system above. milliard = 1000 million; billiard = 1000 million^2; trilliard = 1000 million^3; quadrilliard = 1000 million^4; quintilliard = 1000 million^5; sextilliard = 1000 million^6; septilliard = 1000 million^7; octilliard = 1000 million^8; nonilliard = 1000 million^9; noventilliard = nonilliard; decilliard = 1000 million^10; # For consistency brmilliard = milliard; brbilliard = billiard; brtrilliard = trilliard; brquadrilliard = quadrilliard; brquintilliard = quintilliard; brsextilliard = sextilliard; brseptilliard = septilliard; broctilliard = octilliard; brnonilliard = nonilliard; brnoventilliard = noventilliard; brdecilliard = decilliard; # The British Centillion would be 1e600. The googolplex is another # familiar large number equal to 10^googol. These numbers give overflows. } { # # Physical constants # # Basic constants pi = 3.14159265358979323846; c = 2.99792458e8 m/s; # speed of light in vacuum (exact) light = c; mu0 = 4 pi 1e-7 H/m; # permeability of vacuum (exact) epsilon0 = 1/(mu0 c^2); # permittivity of vacuum (exact) energy = c^2; # convert mass to energy e = 1.602176462e-19 C; # electron charge h = 6.62606876e-34 J s; # Planck constant hbar = h / (2 pi); G = 6.673e-11 N m^2 / kg^2; # Newtonian gravity const coulombconst = 1 / (4 pi epsilon0); # listed as "k" sometimes au = 1.49597871e11 m; # astronomical unit astronomicalunit = au; # Physico-chemical constants atomicmassunit = 1.66053873e-27 kg; # atomic mass unit (defined to be u = atomicmassunit; # 1 / 12 of the mass of carbon 12) amu = atomicmassunit; amu_chem = 1.66026e-27 kg; # 1/16 of the weighted average mass of # the 3 naturally occuring neutral # isotopes of oxygen amu_phys = 1.65981e-27 kg; # 1 / 16 of the mass of a neutral # oxygen 16 atom dalton = u; # Maybe this should be amu_chem? avogadro = gram / (amu mol); # size of a mole N_A = avogadro; gasconstant = 8.314472 J / (mol K); # molar gas constant R = gasconstant; boltzmann = R / N_A; # Boltzmann constant k = boltzmann; molarvolume = mol R stdtemp / atm; # Volume occupied by one mole of an # ideal gas at STP. loschmidt = avogadro mol / molarvolume; # Molecules per cubic meter of # an ideal gas at STP. # Loschmidt did work similar # to Avogadro. stefanboltzmann = pi^2 k^4 / (60 hbar^3 c^2); # The power radiated by a sigma = stefanboltzmann; # blackbody at temperature T # is given by sigma T^4. wiendisplacement = 2.8977686e-3 m K; # Wien's Displacement Law gives the # frequency at which the the Planck # spectrum has maximum intensity. # The relation is lambda T = b where; # lambda is wavelength, T is # temperature and b is the Wien # displacement. This relation is # used to determine the temperature # of stars. K_J = 483597.9 GHz/V; # Direct measurement of the volt is # difficult. Until recently, laboratories # kept Weston cadmium cells as a reference, # but they could drift. In 1987 the CGPM # officially recommended the use of the # Josephson effect as a laboratory # representation of the volt. The Josephson # effect occurs when two superconductors are # separated by a thin insulating layer. A # "supercurrent" flows across the insulator # with a frequency that depends on the # potential applied across the # superconductors. This frequency can be # very accurately measured. The Josephson # constant K_J, which is equal to 2e/h, # relates the measured frequency to the # potential. The value given here is the # officially specified value for use # beginning in 1990. The 1998 recommended # value of the constant is 483597.898 GHz/V. R_K = 25812.807 ohm; # Measurement of the ohm also presents # difficulties. The old approach involved # maintaining resistances that were subject # to drift. The new standard is based on the # Hall effect. When a current carrying # ribbon is placed in a magnetic field, a # potential difference develops across the # ribbon. The ratio of the potential # difference to the current is called the # Hall resistance. Klaus von Klitzing # discovered in 1980 that the Hall resistance # varies in discrete jumps when the magnetic # field is very large and the temperature # very low. This enables accurate # realization of the resistance h/e^2 in the # lab. The value given here is the # officially specified value for use # beginning in 1990. # Various conventional values gravity = 9.80665 m/s^2; # std acceleration of gravity (exact) force = gravity; # use to turn masses into forces atm = 101325 Pa; # Standard atmospheric pressure atmosphere = atm; Hg = 13.5951 gram force / cm^3; # Std weight of mercury (exact) water = gram force/cm^3; # Standard weight of water (exact) H2O = water; wc = water; # water column mach = 331.46 m/s; # speed of sound in dry air at STP standardtemp = 273.15 K; # standard temperature stdtemp = standardtemp; # Weight of mercury and water at different temperatures using the standard # force of gravity. Hg10C = 13.5708 force gram / cm^3; # These units, when used to form Hg20C = 13.5462 force gram / cm^3; # pressure measures, are not accurate Hg23C = 13.5386 force gram / cm^3; # because of considerations of the Hg30C = 13.5217 force gram / cm^3; # revised practical temperature scale. Hg40C = 13.4973 force gram / cm^3; Hg60F = 13.5574 force gram / cm^3; H2O0C = 0.99987 force gram / cm^3; H2O5C = 0.99999 force gram / cm^3; H2O10C = 0.99973 force gram / cm^3; H2O15C = 0.99913 force gram / cm^3; H2O18C = 0.99862 force gram / cm^3; H2O20C = 0.99823 force gram / cm^3; H2O25C = 0.99707 force gram / cm^3; H2O50C = 0.98807 force gram / cm^3; H2O100C = 0.95838 force gram / cm^3; # Atomic constants Rinfinity = 10973731.568 /m; # The wavelengths of a spectral series R_H = 10967760 / m; # can be expressed as # 1/lambda = R (1/m^2 - 1/n^2). # where R is a number that various # slightly from element to element. # For hydrogen, R_H is the value, # and for heavy elements, the value # approaches Rinfinity, which can be # computed from # m_e c alpha^2 / 2 h # with a loss of 5 digits # of precision. alpha = 7.297352533e-3; # The fine structure constant was # introduced to explain fine # structure visible in spectral # lines. It can be computed from # mu0 c e^2 / 2 h # with a loss of 3 digits precision # and loss of precision in derived # values which use alpha. bohrradius = alpha / (4 pi Rinfinity); prout = 185.5 keV; # nuclear binding energy equal to 1 / 12 # binding energy of the deuteron # Planck constants planckmass = 2.1767e-8 kg; # sqrt(hbar c / G) m_P = planckmass; plancktime = hbar / (planckmass c^2); t_P = plancktime; plancklength = plancktime c; l_P = plancklength; # Masses of elementary particles electronmass = 5.485799110e-4 u; m_e = electronmass; protonmass = 1.00727646688 u; m_p = protonmass; neutronmass = 1.00866491578 u; m_n = neutronmass; muonmass = 0.1134289168 u; m_mu = muonmass; deuteronmass = 2.01355321271 u; m_d = deuteronmass; alphaparticlemass = 4.0015061747 u; m_alpha = alphaparticlemass; # particle wavelengths: the compton wavelength of a particle is # defined as h / m c where m is the mass of the particle. electronwavelength = h / (m_e c); lambda_C = electronwavelength; protonwavelength = h / (m_p c); lambda_C,p = protonwavelength; neutronwavelength = h / (m_n c); lambda_C,n = neutronwavelength; # Magnetic moments bohrmagneton = e hbar / (2 electronmass); mu_B = bohrmagneton; nuclearmagneton = e hbar / (2 protonmass); mu_N = nuclearmagneton; mu_mu = 4.49044813e-26 J/T; # Muon magnetic moment mu_p = 1.410606633e-26 J/T; # Proton magnetic moment mu_e = 928.476362e-26 J/T; # Electron magnetic moment mu_n = 0.96623640e-26 J/T; # Neutron magnetic moment mu_d = 0.433073457e-26 J/T; # Deuteron magnetic moment } { # # Astronomical time measurements # anomalisticyear = 365.2596 day; # The time between successive # perihelion passages of the # earth. siderealyear = 365.256360417 day; # Time for the earth to make # one revolution around the sun # relative to the stars. tropicalyear = 365.242198781 day; # The mean interval between vernal # equinoxes. Differs from the # sidereal year by 1 part in # 26000 due to precession of the # earth about its rotational axis # combined with precession of the # perihelion of the earth's # orbit. gaussianyear = 365.2690 day; # The orbital period of a body in # circular orbit at a distance of # 1 au from the sun. Calculated # from Kepler's third law. siderealday = 23.934469444 hour; # The sidereal day is the interval siderealhour = (1 / 24) siderealday; # between two successive transits siderealminute = (1 / 60) siderealhour; # of a star over the meridian, siderealsecond = (1 / 60) siderealminute; # or the time required for the # earth to make one rotation # relative to the stars. The # more usual solar day is the # time required to make a # rotation relative to the sun. # Because the earth moves in its # orbit, it has to turn a bit # extra to face the sun again, # hence the solar day is slightly # longer. anomalisticmonth = 27.55454977 day; # Time from perigee to perigee nodicalmonth = 27.2122199 day; # The nodes are the points where draconicmonth = nodicalmonth; # an orbit crosses the ecliptic. draconiticmonth = nodicalmonth; # This is the time required to # travel from the ascending node # to the next ascending node. siderealmonth = 27.321661 day; # Time required for the moon to # orbit the earth lunarmonth = 29.5305555 day; # Time between full moons. Full synodicmonth = lunarmonth; # moon occur when the sun and lunation = synodicmonth; # moon are on opposite sides of lune = (1 / 30) lunation; # the earth. Since the earth lunour = (1 / 24) lune; # moves around the sun, the moon # has to revolve a bit farther to # get into the full moon # configuration. year = tropicalyear; yr = year; month = (1 / 12) year; mo = month; decade = 10 year; century = 100 year; millennium = 1000 year; millennia = millennium; solaryear = year; lunaryear = 12 lunarmonth; calendaryear = 365 day; commonyear = 365 day; leapyear = 366 day; julianyear = 365.25 day; gregorianyear = 365.2425 day; islamicyear = 354 day; # A year of 12 lunar months. They islamicleapyear = 355 day; # began counting on July 16, AD 622 # when Muhammad emigrated to Medina # (the year of the Hegira). They need # 11 leap days in 30 years to stay in # sync with the lunar year which is a # bit longer than the 29.5 days of the # average month. islamicmonth = (1 / 12) islamicyear; # They have 29 day and 30 day months. # Sidereal days mercuryday = 58.6462 day; venusday = 243.01 day; # retrograde earthday = siderealday; marsday = 1.02595675 day; jupiterday = 0.41354 day; saturnday = 0.4375 day; uranusday = 0.65 day; # retrograde neptuneday = 0.768 day; plutoday = 6.3867 day; # Planetary sidereal years mercuryyear = 86.96 day; venusyear = 224.68 day; earthyear = siderealyear; marsyear = 686.95 day; jupiteryear = 11.862 tropicalyear; saturnyear = 29.458 tropicalyear; uranusyear = 84.012 tropicalyear; neptuneyear = 164.798 tropicalyear; plutoyear = 248.5 tropicalyear; } { # # Cooking measures # # US measures cup = 8 floz; tablespoon = (1 / 16) cup; tbl = tablespoon; tbsp = tablespoon; teaspoon = (1 / 3) tbsp; tsp = teaspoon; metriccup = 250 ml; # US can sizes. number1can = 10 floz; number2can = 19 floz; number2.5can = 3.5 cup; number3can = 4 cup; number5can = 7 cup; number10can = 105 floz; # British measures brcup = (1 / 2) brpint; brteacup = (1 / 3) brpint; brtablespoon = 15 ml; # Also 5 / 8 brfloz, approx 17.7 ml brteaspoon = (1 / 3) brtablespoon; # Also 1 / 4 brtablespoon dessertspoon = 2 brteaspoon; brtsp = brteaspoon; brtbl = brtablespoon; dsp = dessertspoon; # Australian australiatablespoon = 20 ml; austbl = australiatablespoon; # Chinese catty = 0.5 kg; oldcatty = (4 / 3) lb; # Before metric conversion. tael = (1 / 16) oldcatty; # Should the tael be defined both ways? # Japanese japancup = 200 ml; # densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum # so you can convert '2 cups sugar' to grams, for example, or in the other # direction grams could be converted to 'cup flour_scooped'. butter = 8 oz/cup; butter_clarified = 6.8 oz/cup; cocoa_butter = 9 oz/cup; shortening = 6.75 oz/cup; # vegetable shortening oil = 7.5 oz/cup; cakeflour_sifted = 3.5 oz/cup; # The density of flour depends on the cakeflour_spooned = 4 oz/cup; # measuring method. "Scooped", or cakeflour_scooped = 4.5 oz/cup; # "dip and sweep" refers to dipping a flour_sifted = 4 oz/cup; # measure into a bin, and then sweeping flour_spooned = 4.25 oz/cup; # the excess off the top. "Spooned" flour_scooped = 5 oz/cup; # means to lightly spoon into a measure breadflour_sifted = 4.25 oz/cup; # and then sweep the top. Sifted means breadflour_spooned = 4.5 oz/cup; # sifting the flour directly into a breadflour_scooped = 5.5 oz/cup; # measure and then sweeping the top. cornstarch = 120 gram/cup; dutchcocoa_sifted = 75 g/cup; # These are for Dutch processed cocoa dutchcocoa_spooned = 92 g/cup; dutchcocoa_scooped = 95 g/cup; cocoa_sifted = 75 g/cup; # These are for nonalkalized cocoa cocoa_spooned = 82 g/cup; cocoa_scooped = 95 g/cup; heavycream = 232 g/cup; milk = 242 g/cup; sourcream = 242 g/cup; molasses = 11.25 oz/cup; cornsyrup = 11.5 oz/cup; honey = 11.75 oz/cup; sugar = 200 g/cup; powdered_sugar = 4 oz/cup; brownsugar_light = 217 g/cup; # packed brownsugar_dark = 239 g/cup; baking_powder = 4.6 gram / tsp; salt = 6 g / tsp; koshersalt = 2.8 g / tsp; # Diamond Crystal salt, from package # Note that Morton kosher salt is # much denser. # Egg weights and volumes for a USA large egg egg = 50 gram; eggwhite = 30 gram; eggyolk = 18.6 gram; eggvolume = 9.5 tsp; // 3 tablespoons + 1 / 2 tsp eggwhitevolume = 2 tablespoon; eggyolkvolume = 3.5 tsp; } { # # Old French distance measures, from French Weights and Measures # Before the Revolution by Zupko # frenchfoot = (4500 / 13853) m; # pied de roi, the standard of Paris. pied = frenchfoot; # Half of the hashimicubit, frenchfeet = frenchfoot; # instituted by Charlemagne. frenchinch = (1 / 12) frenchfoot; # This exact definition comes from frenchthumb = frenchinch; # a law passed on 10 Dec 1799 which pouce = frenchthumb; # fixed the meter at # 3 frenchfeet + 11.296 lignes. frenchline = (1 / 12) frenchinch; # This is supposed to be the size ligne = frenchline; # of the average barleycorn frenchpoint = (1 / 12) frenchline; toise = 6 frenchfeet; arpent = 180^2 pied^2; # The arpent is 100 square perches, # but the perche seems to vary a lot # and can be 18 feet, 20 feet, or 22 # feet. This measure was described # as being in common use in Canada in # 1934 (Websters 2nd). The value # given here is the Paris standard # arpent. # # Before the Imperial Weights and Measures Act of 1824, various different # weights and measures were in use in different places. # # Scots linear measure scotsinch = 1.00540054 UKinch; scotslink = (1 / 100) scotschain; scotsfoot = 12 scotsinch; scotsfeet = scotsfoot; scotsell = 37 scotsinch; scotsfall = 6 scotsell; scotschain = 4 scotsfall; scotsfurlong = 10 scotschain; scotsmile = 8 scotsfurlong; # Scots area measure scotsrood = 40 scotsfall^2; scotsacre = 4 scotsrood; # Irish linear measure irishinch = UKinch; irishpalm = 3 irishinch; irishspan = 3 irishpalm; irishfoot = 12 irishinch; irishfeet = irishfoot; irishcubit = 18 irishinch; irishyard = 3 irishfeet; irishpace = 5 irishfeet; irishfathom = 6 irishfeet; irishpole = 7 irishyard; # Only these values irishperch = irishpole; # are different from irishchain = 4 irishperch; # the British Imperial irishlink = (1 / 100) irishchain; # or English values for irishfurlong = 10 irishchain; # these lengths. irishmile = 8 irishfurlong; # # Irish area measure irishrood = 40 irishpole^2; irishacre = 4 irishrood; # English wine capacity measures (Winchester measures) winepint = (1 / 2) winequart; winequart = (1 / 4) winegallon; winegallon = 231 UKinch^3; # Sometimes called the Winchester Wine Gallon, # it was legalized in 1707 by Queen Anne, and # given the definition of 231 cubic inches. It # had been in use for a while as 8 pounds of # wine using a merchant's pound of 7200 grains # or 15 troy ounces. (The old mercantile # pound had been 15 tower ounces.) winerundlet = 18 winegallon; winebarrel = 31.5 winegallon; winetierce = 42 winegallon; winehogshead = 2 winebarrel; winepuncheon = 2 winetierce; winebutt = 2 winehogshead; winepipe = winebutt; winetun = 2 winebutt; # English beer and ale measures used 1803-1824 and used for beer before 1688 beerpint = (1 / 2) beerquart; beerquart = (1 / 4) beergallon; beergallon = 282 UKinch^3; beerbarrel = 36 beergallon; beerhogshead = 1.5 beerbarrel; # English ale measures used from 1688-1803 for both ale and beer alepint = (1 / 2) alequart; alequart = (1 / 4) alegallon; alegallon = beergallon; alebarrel = 34 alegallon; alehogshead = 1.5 alebarrel; # Scots capacity measure scotsgill = (1 / 4) mutchkin; mutchkin = (1 / 2) choppin; choppin = (1 / 2) scotspint; scotspint = (1 / 2) scotsquart; scotsquart = (1 / 4) scotsgallon; scotsgallon = 827.232 UKinch^3; scotsbarrel = 8 scotsgallon; # Scots dry capacity measure scotswheatlippy = 137.333 UKinch^3; # Also used for peas, beans, rye, salt scotswheatlippies = scotswheatlippy; scotswheatpeck = 4 scotswheatlippy; scotswheatfirlot = 4 scotswheatpeck; scotswheatboll = 4 scotswheatfirlot; scotswheatchalder = 16 scotswheatboll; scotsoatlippy = 200.345 UKinch^3; # Also used for barley and malt scotsoatlippies = scotsoatlippy; scotsoatpeck = 4 scotsoatlippy; scotsoatfirlot = 4 scotsoatpeck; scotsoatboll = 4 scotsoatfirlot; scotsoatchalder = 16 scotsoatboll; # Scots Tron weight trondrop = (1 / 16) tronounce; tronounce = (1 / 20) tronpound; tronpound = 9520 grain; tronstone = 16 tronpound; # Irish liquid capacity measure irishnoggin = (1 / 4) irishpint; irishpint = (1 / 2) irishquart; irishquart = (1 / 2) irishpottle; irishpottle = (1 / 2) irishgallon; irishgallon = 217.6 UKinch^3; irishrundlet = 18 irishgallon; irishbarrel = 31.5 irishgallon; irishtierce = 42 irishgallon; irishhogshead = 2 irishbarrel; irishpuncheon = 2 irishtierce; irishpipe = 2 irishhogshead; irishtun = 2 irishpipe; # Irish dry capacity measure irishpeck = 2 irishgallon; irishbushel = 4 irishpeck; irishstrike = 2 irishbushel; irishdrybarrel = 2 irishstrike; irishquarter = 2 irishbarrel; # English Tower weights, abolished in 1528 towerpound = 5400 grain; towerounce = (1 / 12) towerpound; towerpennyweight = (1 / 20) towerounce; # English Mercantile weights, used since the late 12th century mercpound = 6750 grain; mercounce = (1 / 15) mercpound; mercpennyweight = (1 / 20) mercounce; # English weights for lead leadstone = 12.5 lb; fotmal = 70 lb; leadwey = 14 leadstone; fothers = 12 leadwey; # English Hay measure newhaytruss = 60 lb; # New and old here seem to refer to "new" newhayload = 36 newhaytruss; # hay and "old" hay rather than a new unit oldhaytruss = 56 lb; # and an old unit. oldhayload = 36 oldhaytruss; # English wool measure woolclove = 7 lb; woolstone = 2 woolclove; wooltod = 2 woolstone; woolwey = 13 woolstone; woolsack = 2 woolwey; woolsarpler = 2 woolsack; woollast = 6 woolsarpler; # # Ancient history units: There tends to be uncertainty in the definitions # of the units in this section # These units are from [11] # Roman measure. The Romans had a well defined distance measure, but their # measures of weight were poor. They adopted local weights in different # regions without distinguishing among them so that there are half a dozen # different Roman "standard" weight systems. romanfoot = 296 mm; # There is some uncertainty in this definition romanfeet = romanfoot; # from which all the other units are derived. pes = romanfoot; # Value appears in numerous sources. In "The pedes = romanfoot; # Roman Land Surveyors", Dilke gives 295.7 mm. romaninch = (1 / 12) romanfoot; # The subdiv of the Roman foot have the romandigit = (1 / 16) romanfoot; # same names as the subdivisions of romanpalm = (1 / 4) romanfoot; # the pound, but we can't have the romancubit = 18 romaninch; # name for differemt units. romanpace = 5 romanfeet; # Roman double pace (basic military unit) passus = romanpace; romanperch = 10 romanfeet; stade = 125 romanpace; stadia = stade; stadium = stade; romanmile = 8 stadia; # 1000 paces romanleague = 1.5 romanmile; schoenus = 4 romanmile; # Other values for the Roman foot (from Dilke) earlyromanfoot = 29.73 cm; pesdrusianus = 33.3 cm; # or 33.35 cm, used in Gaul & Germany in 1st c BC lateromanfoot = 29.42 cm; # Roman areas actuslength = 120 romanfeet; # length of a Roman furrow actus = 120 4 romanfeet; # area of the furrow squareactus = 120^2 romanfeet^2; # actus quadratus acnua = squareactus; iugerum = 2 squareactus; iugera = iugerum; jugerum = iugerum; jugera = iugerum; heredium = 2 iugera; # heritable plot heredia = heredium; centuria = 100 heredia; centurium = centuria; # Roman volumes sextarius = 35.4 in^3; # Basic unit of Roman volume. As always, sextarii = sextarius; # there is uncertainty. Six large Roman # measures survive with volumes ranging from # 34.4 in^3 to 39.55 in^3. Three of them # cluster around the size given here. # # But the values for this unit vary wildly # in other sources. One reference gives 0.547 # liters, but then says the amphora is a # cubic Roman foot. This gives a value for the # sextarius of 0.540 liters. And the # encyclopedia Brittanica lists 0.53 liters for # this unit. Both [7] and [11], which were # written by scholars of weights and measures, # give the value of 35.4 cubic inches. cochlearia = (1 / 48) sextarius; cyathi = (1 / 12) sextarius; acetabula = (1 / 8) sextarius; quartaria = (1 / 4) sextarius; quartarius = quartaria; heminae = (1 / 2) sextarius; hemina = heminae; cheonix = 1.5 sextarii; # Dry volume measures (usually) semodius = 8 sextarius; semodii = semodius; modius = 16 sextarius; modii = modius; # Liquid volume measures (usually) congius = 12 heminae; congii = congius; amphora = 8 congii; amphorae = amphora; # Also a dry volume measure culleus = 20 amphorae; quadrantal = amphora; # Roman weights libra = 5052 grain; # The Roman pound varied significantly librae = libra; # from 4210 grains to 5232 grains. Most of romanpound = libra; # the standards were obtained from the weight uncia = (1 / 12) libra; # of particular coins. The one given here is unciae = uncia; # based on the Gold Aureus of Augustus which romanounce = uncia; # was in use from BC 27 to AD 296. deunx = 11 uncia; dextans = 10 uncia; dodrans = 9 uncia; bes = 8 uncia; seprunx = 7 uncia; semis = 6 uncia; quincunx = 5 uncia; triens = 4 uncia; quadrans = 3 uncia; sextans = 2 uncia; sescuncia = 1.5 uncia; semuncia = (1 / 2) uncia; siscilius = (1 / 4) uncia; sextula = (1 / 6) uncia; semisextula = (1 / 12) uncia; scriptulum = (1 / 24) uncia; scrupula = scriptulum; romanobol = (1 / 2) scrupula; romanaspound = 4210 grain; # Old pound based on bronze coinage, the # earliest money of Rome BC 338 to BC 268. # Egyptian length measure egyptianroyalcubit = 20.63 in; # plus or minus .2 in egyptianpalm = (1 / 7) egyptianroyalcubit; epyptiandigit = (1 / 4) egyptianpalm; egyptianshortcubit = 6 egyptianpalm; doubleremen = 29.16 in; # Length of the diagonal of a square with remendigit = (1 / 40) doubleremen; # side length of 1 royal egyptian cubit # This is divided into 40 digits which # are not the same size as the digits # based on the royal cubit. # Greek length measures greekfoot = 12.45 in; # Listed as being derived from the greekfeet = greekfoot; # Egyptian Royal cubit in [11]. It is greekcubit = 1.5 greekfoot; # said to be 3 / 5 of a 20.75 in cubit. pous = greekfoot; podes = greekfoot; orguia = 6 greekfoot; greekfathom = orguia; stadion = 100 orguia; akaina = 10 greekfeet; plethron = 10 akaina; greekfinger = (1 / 16) greekfoot; homericcubit = 20 greekfinger; # Elbow to end of knuckles. shortgreekcubit = 18 greekfinger; # Elbow to start of fingers. ionicfoot = 296 mm ; doricfoot = 326 mm; olympiccubit = 25 remendigit; # These olympic measures were not as olympicfoot = (2 / 3) olympiccubit; # common as the other greek measures. olympicfinger = (1 / 16) olympicfoot; # They were used in agriculture. olympicfeet = olympicfoot; olympicdakylos = olympicfinger; olympicpalm = (1 / 4) olympicfoot; olympicpalestra = olympicpalm; olympicspithame = (3 / 4) foot; olympicspan = olympicspithame; olympicbema = 2.5 olympicfeet; olympicpace = olympicbema; olympicorguia = 6 olympicfeet; olympicfathom = olympicorguia; olympiccord = 60 olympicfeet; olympicamma = olympiccord; olympicplethron = 100 olympicfeet; olympicstadion = 600 olympicfeet; # Greek capacity measure greekkotyle = 270 ml; # This approximate value is obtained xestes = 2 greekkotyle; # from two earthenware vessels that khous = 12 greekkotyle; # were reconstructed from fragments. metretes = 12 khous; # The kotyle is a day's corn ration choinix = 4 greekkotyle; # for one man. hekteos = 8 choinix; medimnos = 6 hekteos; # Greek weight. Two weight standards were used, an Aegina standard based # on the Beqa shekel and an Athens (attic) standard. aeginastater = 192 grain; # Varies up to 199 grain aeginadrachmae = (1 / 2) aeginastater; aeginaobol = (1 / 6) aeginadrachmae; aeginamina = 50 aeginastater; aeginatalent = 60 aeginamina; atticstater = 135 grain; # Varies 134-138 grain atticdrachmae = (1 / 2) atticstater; atticobol = (1 / 6) atticdrachmae; atticmina = 50 atticstater; attictalent = 60 atticmina; # "Northern" cubit and foot. This was used by the pre-Aryan civilization in # the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China, # central and Western Europe until modern times when it was displaced by # the metric system. northerncubit = 26.6 in; # plus/minus .2 in northernfoot = (1 / 2) northerncubit; sumeriancubit = 495 mm; kus = sumeriancubit; sumerianfoot = (2 / 3) sumeriancubit; assyriancubit = 21.6 in; assyrianfoot = (1 / 2) assyriancubit; assyrianpalm = (1 / 3) assyrianfoot; assyriansusi = (1 / 20) assyrianpalm; susi = assyriansusi; persianroyalcubit = 7 assyrianpalm; # Arabic measures. The arabic standards were meticulously kept. Glass # weights accurate to .2 grains were made during AD 714-900. hashimicubit = 25.56 in; # Standard of linear measure used # in Persian dominions of the Arabic # empire 7-8th cent. Is equal to two # French feet. blackcubit = 21.28 in; arabicfeet = (1 / 2) blackcubit; arabicfoot = arabicfeet; arabicinch = (1 / 12) arabicfoot; arabicmile = 4000 blackcubit; silverdirhem = 45 grain; # Weights were derived from these two tradedirhem = 48 grain; # units with two identically named # systems used for silver and used for # trade purposes. silverkirat = (1 / 16) silverdirhem; silverwukiyeh = 10 silverdirhem; silverrotl = 12 silverwukiyeh; arabicsilverpound = silverrotl; tradekirat = (1 / 16) tradedirhem; tradewukiyeh = 10 tradedirhem; traderotl = 12 tradewukiyeh; arabictradepound = traderotl; # Miscellaneous ancient units parasang = 3.5 mile; # Persian unit of length usually thought # to be between 3 and 3.5 miles biblicalcubit = 21.8 in; hebrewcubit = 17.58 in; li = (10 / 27.8) mile; # Chinese unit of length # 100 li is considered a day's march liang = (11 / 3) oz; # Chinese weight unit # Medieval time units. According to the OED, these appear in Du Cange # by Papias. timepoint = (1 / 5) hour; # also given as 1 / 4 timeminute = (1 / 10) hour; timeostent = (1 / 60) hour; timeounce = (1 / 8) timeostent; timeatom = (1 / 47) timeounce; # Given in [15], these subdivisions of the grain were supposedly used # by jewelers. The mite may have been used but the blanc could not # have been accurately measured. mite = (1 / 20) grain; droit = (1 / 24) mite; periot = (1 / 20) droit; blanc = (1 / 24) periot ; } { # # Atomic weights. The atomic weight of an element is the ratio of the mass # of a mole of the element to 1 / 12 of a mole of Carbon 12. The Std Atomic # Weights apply to the elements as they occur naturally on earth. Elements # which do not occur naturally or which occur with wide isotopic variability # do not have Standard Atomic Weights. For these elements, the atomic weight # is based on the longest lived isotope, as marked in the comments. In some # cases, the comment for these entries also gives a number which is an atomic # weight for a different isotope that may be of more interest than the # longest lived isotope. # actinium = 227.0278; aluminum = 26.981539; aluminium = aluminum; americium = 243.0614; # Longest lived. 241.06 antimony = 121.760; argon = 39.948; arsenic = 74.92159; astatine = 209.9871; # Longest lived barium = 137.327; berkelium = 247.0703; # Longest lived. 249.08 beryllium = 9.012182; bismuth = 208.98037; boron = 10.811; bromine = 79.904; cadmium = 112.411; calcium = 40.078; californium = 251.0796; # Longest lived. 252.08 carbon = 12.011; cerium = 140.115; cesium = 132.90543; chlorine = 35.4527; chromium = 51.9961; cobalt = 58.93320; copper = 63.546; curium = 247.0703; dysprosium = 162.50; einsteinium = 252.083; # Longest lived erbium = 167.26; europium = 151.965; fermium = 257.0951; # Longest lived fluorine = 18.9984032; francium = 223.0197; # Longest lived gadolinium = 157.25; gallium = 69.723; germanium = 72.61; gold = 196.96654; hafnium = 178.49; helium = 4.002602; holmium = 164.93032; hydrogen = 1.00794; indium = 114.818; iodine = 126.90447; iridium = 192.217; iron = 55.845; krypton = 83.80; lanthanum = 138.9055; lawrencium = 262.11; # Longest lived lead = 207.2; lithium = 6.941; lutetium = 174.967; magnesium = 24.3050; manganese = 54.93805; mendelevium = 258.10; # Longest lived mercury = 200.59; molybdenum = 95.94; neodymium = 144.24; neon = 20.1797; neptunium = 237.0482; nickel = 58.6934; niobium = 92.90638; nitrogen = 14.00674; nobelium = 259.1009; # Longest lived osmium = 190.23; oxygen = 15.9994; palladium = 106.42; phosphorus = 30.973762; platinum = 195.08; plutonium = 244.0642; # Longest lived. 239.05 polonium = 208.9824; # Longest lived. 209.98 potassium = 39.0983; praseodymium = 140.90765; promethium = 144.9127; # Longest lived. 146.92 protactinium = 231.03588; radium = 226.0254; radon = 222.0176; # Longest lived rhenium = 186.207; rhodium = 102.90550; rubidium = 85.4678; ruthenium = 101.07; samarium = 150.36; scandium = 44.955910; selenium = 78.96; silicon = 28.0855; silver = 107.8682; sodium = 22.989768; strontium = 87.62; sulfur = 32.066; sulphur = sulfur; tantalum = 180.9479; technetium = 97.9072; # Longest lived. 98.906 tellurium = 127.60; terbium = 158.92534; thallium = 204.3833; thorium = 232.0381; thullium = 168.93421; tin = 118.710; titanium = 47.867; tungsten = 183.84; uranium = 238.0289; vanadium = 50.9415; xenon = 131.29; ytterbium = 173.04; yttrium = 88.90585; zinc = 65.39; zirconium = 91.224; } ############################################################################ # # The following units were in the unix units database but do not appear in # this file: # # wey used for cheese, salt and other goods. Measured mass or # waymass volume depending on what was measured and where the measuring # took place. A wey of cheese ranged from 200 to 324 pounds. # # sack No precise definition # # spindle The length depends on the type of yarn # # doppelzentner The 'units' program doesn't need to get into the # translating business (and I don't know German). # # block Defined variously on different computer systems # # erlang A unit of telephone traffic defined variously. # Omitted because there are no other units for this # dimension. Is this true? What about CCS = 1/36 erlang? # Erlang is supposed to be dimensionless. One erlang means # a single channel occupied for one hour. # ############################################################################