foo(x) [1; kg] kg m x /hour ; 34 hour / day kg foo # From: lrclause@shasta.cs.uiuc.edu # # Danish units #tomme 26.1545 mm #tommer tomme # Plural form #fod 12 tomme #alen 2 fod #danishmil 7.5325 km #danskmil danishmil # Danish form #tøndeland 5516.23 m^2 # The amount of land that can be sown with one # # barrel of seed #tønderland tøndeland # Plural form #pot .9661 l #kvint 5.0 g #pund 0.5 kg # # wind chill index (WCI) a measurement of the combined cooling effect of low # air temperature and wind on the human body. The index was first defined # by the American Antarctic explorer Paul Siple in 1939. As currently used # by U.S. meteorologists, the wind chill index is computed from the # temperature T (in °F) and wind speed V (in mi/hr) using the formula: WCI # = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4. The metric # equivalent, for T in °C and V in km/hr, is: WCI = 0.045(5.27 sqrt(V) + # 10.45 - 0.28V)(T - 33) + 33. For very low wind speeds, below 4 mi/hr or # 6 km/hr, the WCI is actually higher than the air temperature, but for # higher wind speeds it is lower than the air temperature. # # heat index (HI or HX) a measure of the combined effect of heat and # humidity on the human body. U.S. meteorologists compute the index # from the temperature T (in °F) and the relative humidity H (as a # fraction; that is, H = 0.65 if the relative humidity is 65%). The # formula used is HI = -42.379 + 2.04901523 T + 1014.333127 H - # 22.475541 TH - .00683783 T2 - 548.1717 H2 + 0.122874 T2H + 8.5282 # TH2 - 0.0199 T2H2. # ########################## ########################## #### Working area ######## ########################## ########################## # These definitions are here for testing of the error checking facilities # of the units program. All of them are somehow bogus. # ev100n(x) 2^x / (m2/cd); log2(ev100 m^2/cd) # bogusunit 1 # bogusunit(x) x+1 # foo meter** # baz bleganarf # wronginv(x) 2 x ; 2 x # boo(x) x+1 # bug(x) boo(x)+x # bbb(x) boo(12) # test(x) x^2 ; \ # sqrt(x) # recur(x) [1] 1+recur(x) # fezle[kg] 3 4 4 5 5 4 6 3 # foobiz(x) x x ) ; 3 # testa- (3/4) # testb- (3/4)/(3/4) # testc- m/kg/hr # testt(x) [kg;m] x^2-3 ; sqrt(testt+3) # # # # # Sugar information # from Food Science by Norman Potter # # boiling pt = 1000+100 (0.52) / W (s/M) (boiling pt elevation as in books) # # 1000 (.512) x / (100-x) 342.3 # # Degrees brix measures sugar concentration by weigh as a percentage, so a # solution that is 3 degrees brix is 3% sugar by weight. This unit was named # after Adolf Brix who invented a hydrometer that read this percentage # directly. This table converts brix to density at 20 degrees Celsius. brix[g/cm^3] \ 0.0 0.9982, 0.5 1.0002, 1.0 1.0021 \ 1.5 1.0040, 2.0 1.0060, 2.5 1.0079 \ 3.0 1.0099, 3.5 1.0119, 4.0 1.0139 \ 5.0 1.0178, 5.5 1.0198, 6.0 1.0218 \ 6.5 1.0238, 7.0 1.0259, 7.5 1.0279 \ 8.0 1.0299, 8.5 1.0320, 9.0 1.0340 \ 9.5 1.0361, 10.0 1.0381, 11.0 1.0423 \ 12.0 1.0465, 13.0 1.0507, 14.0 1.0549 \ 15.0 1.0592, 16.0 1.0635, 17.0 1.0678 \ 18.0 1.0722, 19.0 1.0766, 20.0 1.0810 \ 22.0 1.0899, 24.0 1.0990, 26.0 1.1082 \ 28.0 1.1175, 30.0 1.1270, 32.0 1.1366 \ 34.0 1.1464, 36.0 1.1562, 38.0 1.1663 \ 40.0 1.1765, 42.0 1.1868, 44.0 1.1972 \ 46.0 1.2079, 48.0 1.2186, 50.0 1.2295 \ 52.0 1.2406, 54.0 1.2518, 56.0 1.2632 \ 58.0 1.2747, 60.0 1.2864, 62.0 1.2983 \ 64.0 1.3103, 66.0 1.3224, 68.0 1.3348 \ 70.0 1.3472, 72.0 1.3599, 74.0 1.3726 \ 76.0 1.3855, 78.0 1.3986, 80.0 1.4117 \ 82.0 1.4250, 84.0 1.4383 # # #Boiling points of sugar syrups # #conc tempC # #30 100 #40 101 #50 102 #60 103 #70 106 #80 112 #90 123 #95 140 #97 151 #98.2 160 #99.5 166 #99.6 171 # # The boiling point elevation formula is valid for ideal solutions, i.e., # solutions in which the ideal laws hold. In case of boiling point # elevation, the book is referring to what is called the colligative # effect, in which the basic effect is the reduction in the mole fraction # of water. The boiling point of the solution should be linear in the mole # fraction of water. The higher the molecular weight of the solute, the # more in terms of weight concentration it takes to affect the boiling # point. # # As the concentration gets higher, the solutes begin to interact with # each other. Sometimes the interaction is positive, sometimes negative. # The result is that the ideal laws, which ignore these interactions, no # longer hold. The boiling point become nonlinear in mole fraction. # Unfortunately, science hasn't progressed far enough to enable # calculation from first principles the magnitude of this nonideality. # Thus, tables! # # It is difficult to predict where on the concentration scale nonideal # behavior can be detected. However, consider the molar concentration of a # sucrose solution. The molecular weight of sucrose is 342 and that of # water 18. # # wt% sucrose mole fraction of sucrose # 10% .006 # 20% .013 # 30% .022 # 40% .034 # 50% .050 # 60% .073 # 70% .109 # # Even at 50% weight concentration, only one of 20 molecules is sucrose. # >From this point of view, the solution isn't as concentrated as you # think! # # According to your data, the boiling point starts to deviate seriously # from the calculation at 70%. We can see that when 1 of 10 molecules is # sucrose, interactions become significant. # # I hope that this way of looking at solutions helps your perspective. # # Guy Bradley # ################################# ################################# ################################# ## Permanent stuff after this ## ################################# ################################# ################################# # # This file is the units database for use with GNU units, a units conversion # program by Adrian Mariano adrian@cam.cornell.edu # # 12 February 2000 Version 1.27 # # Copyright (C) 1996, 1997, 1998, 1999, 2000 Free Software Foundation, Inc # # This program 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. # # 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 # 18. How Many? A Dictionary of Units of Measurement. Available at # http://www.unc.edu/~rowlett/units/index.html # # Thanks to Jeff Conrad for assistance in ferreting out unit definitions. # ########################################################################### # # If units you use are missing or defined incorrectly, please contact me. # # If you know anything about the use of or the reason for these units # please contact me. These appeared in the original unix data file # but don't seem to appear anywhere else (they are not defined below): # # bottommeasure 1|40 in # imaginarycubicfoot 1.4 ft^3 # sigma microsec # ########################################################################### ########################################################################### # # # Primitive units. Any unit defined to contain a '!' character is a # # primitive unit which will not be reduced any further. All units should # # reduce to primitive units. # # # ########################################################################### # # SI units # kg ! # Mass of the international prototype kilogram kg s ! # Duration of 9192631770 periods of the radiation second s # corresponding to the transition between the two hyperfine # levels of the ground state of the cesium-133 atom m ! # Length of the path traveled by light in a vacuum meter m # during 1|299792458 seconds. Originally meant to be # 1e-7 of the length along a meridian from the equator # to a pole. A ! # The current which produces a force of 2e-7 N/m between two ampere A # infinitely long wires that are 1 meter apart amp ampere cd ! # Luminous intensity in a given direction of a source which candela cd # 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.) mol ! # The amount of substance of a system which contains as many mole mol # 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. K ! # 1|273.16 of the thermodynamic temperature of the triple kelvin K # point of water # # 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. # radian ! # The angle subtended at the center of a circle by an arc # equal in length to the radius of the circle sr ! # Solid angle which cuts off an area of the surface of steradian sr # the sphere equal to that of a square with sides of # length equal to the radius of the sphere # # Some primitive non-SI units # dollar ! # The US dollar is chosen arbitrarily to be the primitive $ dollar # unit of money. bit ! # 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. ########################################################################### # # # Prefixes (longer names must come first) # # # ########################################################################### yotta- 1e24 # Greek or Latin octo, "eight" zetta- 1e21 # Latin septem, "seven" exa- 1e18 # Greek hex, "six" peta- 1e15 # Greek pente, "five" tera- 1e12 # Greek teras, "monster" giga- 1e9 # Greek gigas, "giant" mega- 1e6 # Greek megas, "large" myria- 1e4 # Not an official SI prefix kilo- 1e3 # Greek chilioi, "thousand" hecto- 1e2 # Greek hekaton, "hundred" deca- 1e1 # Greek deka, "ten" deka- deca deci- 1e-1 # Latin decimus, "tenth" centi- 1e-2 # Latin centum, "hundred" milli- 1e-3 # Latin mille, "thousand" micro- 1e-6 # Latin micro or Greek mikros, "small" nano- 1e-9 # Latin nanus or Greek nanos, "dwarf" pico- 1e-12 # Spanish pico, "a bit" femto- 1e-15 # Danish-Norwegian femten, "fifteen" atto- 1e-18 # Danish-Norwegian atten, "eighteen" zepto- 1e-21 # Latin septem, "seven" yocto- 1e-24 # Greek or Latin octo, "eight" quarter- 1|4 semi- 0.5 demi- 0.5 hemi- 0.5 half- 0.5 double- 2 triple- 3 treble- 3 kibi- 2^10 # In response to the convention of illegally mebi- 2^20 # and confusingly using metric prefixes for gibi- 2^30 # powers of two, the International tebi- 2^40 # Electrotechnical Commission aproved these pebi- 2^50 # binary prefixes for use in 1998. If you exbi- 2^60 # want to refer to "megabytes" using the Ki- kibi # binary definition, use these prefixes. Mi- mebi Gi- gibi Ti- tebi Pi- pebi Ei- exbi Y- yotta Z- zetta E- exa P- peta T- tera G- giga M- mega k- kilo h- hecto da- deka d- deci c- centi m- milli n- nano p- pico f- femto a- atto z- zepto y- yocto # # Names of some numbers # one 1 two 2 double 2 couple 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. ############################################################################# # # # 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 /s # frequency Hz hertz # # units derived easily from SI units # gram millikg gm gram g 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 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 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 /m # measures reciprocal of lens focal length 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 /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 / 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. pfu / cm^2 sr s # particle flux unit -- Used to measure # rate at which particles are received by # a spacecraft as particles per solid # angle per detector area per second. [18] katal mol/sec # Measure of the amount of a catalyst. One kat katal # katal of catalyst enables the reaction # to consume or produce on mol/sec. # # time # sec s 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 years watch 4 hours # time a sentry stands watch or a ship's # crew is on duty. bell 1|8 watch # Bell would be sounded every 30 minutes. # # angular measure # circle 2 pi radian degree 1|360 circle arcdeg degree arcmin 1|60 degree arcminute arcmin ' arcmin arcsec 1|60 arcmin arcsecond arcsec " arcsec '' " rightangle 90 degrees 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 # Used for reporting compass readings centrad 0.01 radian # Used for angular deviation of light # through a prism. mas milli-arcsec # Used by astronomers seclongitude circle (seconds/day) # Astronomers measure longitude # (which they call right ascension) in # time units by dividing the equator into # 24 hours instead of 360 degrees. # # Some geometric formulas # circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi) spherevolume(r) [m;m^3] 4|3 pi r^3 ; cuberoot(spherevolume/4|3 pi) spherevol(r) [m;m^3] spherevolume(r) ; ~spherevolume(spherevol) square(x) x^2 ; sqrt(square) # # 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 mill 0.001 # Originally established by Congress in 1791 # as a unit of money equal to 0.001 dollars, # it has come to refer to 0.001 in general. # Used by some towns to set their property # tax rate, and written with a symbol similar # to the % symbol but with two 0's in the # denominator. [18] 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 fine 1|1000 # Measure of gold purity # The pH scale is used to measure the concentration of hydronium (H30+) ions in # a solution. A neutral solution has a pH of 7 as a result of dissociated # water molecules. pH(x) [;mol/liter] 10^(-x) mol/liter ; (-log(pH liters/mol)) # # Temperature # # Two types of units are defined: units for computing temperature differences # and functions for converting absolute temperatures. Conversions for # differences start with "deg" and conversions for absolute temperature start # with "temp". # tempF(x) [;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 tempC(x) [;K] x K + stdtemp ; (tempC +(-stdtemp))/K # In 1741 Anders Celsius tempcelsius(x) [;K] tempC(x); ~tempC(tempcelsius) # introduced a temperature degcelsius K # scale with water boiling at 0 degrees and degC K # 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. tempF(x) [;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 tempfahrenheit(x) [;K] tempF(x) ; ~tempF(tempfahrenheit) degfahrenheit 5|9 degC # Fahrenheit defined his temperature scale degF 5|9 degC # by setting 0 to the coldest temperature # he could produce in his lab with a salt # water solution and by setting 96 degrees to # body heat. In Fahrenheit's words: # # Placing the thermometer in a mixture of # sal ammoniac or sea salt, ice, and water # a point on the scale will be found which # is denoted as zero. A second point is # obtained if the same mixture is used # without salt. Denote this position as # 30. A third point, designated as 96, is # obtained if the thermometer is placed in # the mouth so as to acquire the heat of a # healthy man." (D. G. Fahrenheit, # Phil. Trans. (London) 33, 78, 1724) degreesrankine degF # The Rankine scale has the degrankine degreesrankine # Fahrenheit degree, but it's zero degreerankine degF # is at absolute zero. degR degrankine tempR degrankine temprankine degrankine tempreaumur(x) [;K] x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur 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. degK K # "Degrees Kelvin" is forbidden usage. tempK K # For consistency. # # 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 spin hbar 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 grams/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 per area 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 # Standard weight of mercury (exact) water gram force/cm^3 # Standard weight of water (exact) waterdensity gram / cm^3 # Density of water 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 # # 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 / tan(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). A distant object with # paralax theta will be about # (arcsec/theta) parsecs from the # sun (using the approximation # that tan(theta) = theta). 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 amagat mol/amagatvolume # Used to measure gas densities 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 /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. Named for H. Darcy. 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 /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 emu erg/gauss # "electro-magnetic unit", a measure of # magnetic moment, often used as emu/cm^3 # to specify magnetic moment density. # 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 /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 # The bril is used to express "brilliance" of a source of light on a # logarithmic scale to correspond to subjective perception. An increase of 1 # bril means doubling the luminance. A luminance of 1 lambert is defined to # have a brilliance of 1 bril. bril(x) [;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100 # 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 # Photographic Exposure Value # # The Additive Photographic EXposure (APEX) system developed in Germany in # the 1960s was an attempt to simplify exposure determination for people # who relied on exposure tables rather than exposure meters. Shortly # thereafter, nearly all cameras incorporated exposure meters, so the APEX # system never caught on, but the concept of Exposure Value (EV) given by # # A^2 LS ES # 2^EV = --- = -- = -- # T K C # # Where # A = Relative aperture (f-number) # T = Shutter time in seconds # L = Scene luminance in cd/m2 # E = Scene illuminance in lux # S = Arithmetic ISO film speed # K = Reflected-light meter calibration constant # C = Incident-light meter calibration constant # # remains in use. Strictly speaking, an Exposure Value is a combination # of aperture and shutter time, but it's also commonly used to indicate # luminance (or illuminance). Conversion to luminance or illuminance # units depends on the ISO film speed and the meter calibration constant. # Common practice is to use an ISO film speed of 100 (because film speeds # are in even 1/3-step increments, the exact value is 64 * 2^(2|3)). # Calibration constants vary among camera and meter manufacturers: Canon, # Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while # Minolta and Pentax use a value of 14. Minolta and Sekonic use a value # of 250 for incident-light meters with flat receptors. s100 64 * 2^(2|3) / lx s # exact speed for ISO 100 film # Reflected-light meter calibration constant with ISO 100 film k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic k1400 14 (cd/m2) / lx s # For Minolta and Pentax # Incident-light meter calibration constant with ISO 100 film c250 250 lx / lx s # flat-disc receptor # Exposure value to scene luminance with ISO 100 film # For Minolta or Pentax #ev100(x) [;cd/m^2] 2^x k1400 / s100; log2(ev100 s100 / k1400) # For Canon, Nikon or Sekonic ev100(x) [;cd/m^2] 2^x k1250 / s100; log2(ev100 s100 / k1250) # Exposure value to scene illuminance with ISO 100 film iv100(x) [1;lx] 2^x c250 / s100; log2(iv100 s100 / c250) # # Astronomical time measurements # anomalisticyear 365.2596 days # The time between successive # perihelion passages of the # earth. siderealyear 365.256360417 day # The 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 days # The orbital period of a body in # circular orbit at a distance of # 1 au from the sun. Calculated # from Kepler's third law. elipseyear 346.62 days # The line of nodes is the # intersection of the plane of # Earth's orbit around the sun # with the plane of the moon's # orbit around earth. Eclipses # can only occur when the moon # and sun are close to this # line. The line rotates and # appearances of the sun on the # line of nodes occur every # eclipse year. saros 223 synodicmonth # The earth, moon and sun appear in # the same arrangement every # saros, so if an eclipse occurs, # then one saros later, a similar # eclipse will occur. (The saros # is close to 19 eclipse years.) # The eclipse will occur about # 120 degrees west of the # preceeding one because the # saros is not an even number of # days. After 3 saros, an # eclipse will occur at # approximately the same place. 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 lustrum 5 years # The Lustrum was a Roman # purification ceremony that took # place every five years. # Classically educated Englishmen # used this term. decade 10 years century 100 years millennium 1000 years 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. The months do not # keep to the same seasons, but # regress through the seasons every # 32.5 years. islamicmonth 1|12 islamicyear # They have 29 day and 30 day months. # The Hewbrew year is also based on lunar months, but synchronized to the solar # calendar. The months vary irregularly between 29 and 30 days in length, and # the years likewise vary. The regular year is 353, 354, or 355 days long. To # keep up with the solar calendar, a leap month of 30 days is inserted every # 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This # gives leap years that last 383, 384, or 385 days. # 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 # # 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 # Could be wrong? 6378136.3 m better? 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 US- US # international measures to survey- US # US Survey measures geodetic- US int 3937|1200 ft/m # Convert US Survey measures to 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 click km # 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 pounds # 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 # Defined in 1907 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. 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 drybarrel 7056 in^3 # Used in US for fruits, vegetables, # and other dry commodities except for # cranberries. cranberrybarrel 5826 in^3 # US cranberry barrel heapedbushel 1.278 bushel # Why this particular value? Often # rounded to 1.25 bushels. # 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 # # Water is "hard" if it contains various minerals, expecially calcium # carbonate. # clarkdegree 1|70000 # Content by weigh of calcium carbonate gpg grains/gallon # Divide by water's density to convert to # a dimensionless concentration measure # # 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 # buck dollar fin 5 dollar sawbuck 10 dollar key kg # usually of marijuana, 60's lid 1 oz # Another 60's weed unit footballfield 100 yards marathon 26 miles + 385 yards # # British # UK 1200000|3937014 m/ft # The UK lengths were defined by british- UK # a bronze bar manufactured in 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 shackle 15 fathoms # Adopted 1949 by British navy # British Imperial weight is mostly the same as US weight. A few extra # units are added here. clove 7 lb stone 14 lb tod 28 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 volume # 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. # This gives a value of approximately # 4.5459645 liters, but the old liter # was in force at this time. In 1976 # the definition was changed to exactly # 4.54609 liters using the new # definition of the liter (1 dm^3). brpeck 2 brgallon brbarrel 36 brgallon # Used for beer brbushel 4 brpeck brheapedbushel 1.278 brbushel 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. Measures water displaced by # ships. 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. amber 4 bushel # Used for dry and liquid capacity [18] # 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 goad 4.5 UKft # used for cloth, possibly named after the # stick used for prodding animals. # 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 # alternate spellings metre meter gramme gram litre liter dioptre diopter aluminium aluminum sulphur sulfur # # 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 # The palm is a unit defined as either the width palmlength 8 in # or the length of the hand hand 4 inch # width of hand shaftment 6 inch # Distance from tip of outstretched thumb to the # opposite side of the palm of the hand. The # ending -ment is from the old English word # for hand. [18] # # Cooking measures # # US measures cup 8 floz tablespoon 1|16 cup tbl tablespoon tbsp tablespoon teaspoon 1|3 tbsp tsp teaspoon saltspoon 1|4 tsp metriccup 250 ml stickbutter 1|4 lb # Butter in the USA is sold in one # pound packages that contain four # individually wrapped pieces. The # pieces are marked into tablespoons, # making it possible to measure out # butter by volume by slicing the # butter. # US can sizes. number1can 10 floz number2can 19 floz number2.5can 3.5 cups number3can 4 cups number5can 7 cups 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 lbs # Before metric conversion. tael 1|16 oldcatty # Should the tael be defined both ways? mace 0.1 tael oldpicul 100 oldcatty picul 100 catty # Chinese usage # 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 grams/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 grams / 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 grams eggwhite 30 grams eggyolk 18.6 grams eggvolume 3 tablespoons + 1|2 tsp eggwhitevolume 2 tablespoons eggyolkvolume 3.5 tsp # # Density measures. Density has traditionally been measured on a variety of # bizarre nonlinear scales. # # Often used in European recipes to specify the density of a sugar syrup. # An entirely different definition is used for densities below 1 g/cm^3. # An arbitrary constant appears in the definition. This value is equal to 145 # in the US, but was according to [], the old scale used in Holland had a value # of 144, and the new scale or Gerlach scale used 146.78. baumeconst 145 # US value baume(d) [1;g/cm^3] (baumeconst/(baumeconst+-d)) g/cm^3 ; \ (baume+((-g)/cm^3)) baumeconst / baume twaddell(x) [1;g/cm^3] (1 + 0.005 x) g / cm^3 ; 200 (twaddell / (g/cm^3) +- 1) # Density measure invented by the American Petroleum Institute. Lighter # petroleum products are more valuable, and they get a higher API degree. apidegree(x) [1;g/cm^3] 141.5 g/cm^3 / (x+131.5) ; \ 141.5 (g/cm^3) / apidegree + (-131.5) # # 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 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 /quart # Ice cream scoops are labeled with a # number specifying how many scoops # fill a quart. beespace 1|4 inch # Bees will fill any space that is smaller # than the bee space and leave open # spaces that are larger. The size of # the space varies with species. diamond 8|5 ft # Marking on US tape measures that is # useful to carpenters who wish to place # five studs in an 8 ft distance. # # 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 toe 41.868 GJ # ton oil equivalent. Energy released # by burning one metric ton of oil. [18] tonscoal 1|2.3 toe # Energy in metric ton coal from [18]. naturalgas toe / 1270 m^3 # Energy released from natural gas # from [18]. (At what pressure?) # Celsius heat unit: energy to raise a pound of water 1 degC celsiusheatunit cal lb degC / gram K chu celsiusheatunit # 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 # (temperature difference per length 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. tog 0.1 degC m^2 / W # Also used for clothing. # 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 required # 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. airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as # pressure times air flow. # # 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 brace 2 nest 3 # often used for items like bowls that # nest together hattrick 3 # Used in sports, especially cricket and ice # hockey to report the number of goals. dicker 10 dozen 12 bakersdozen 13 score 20 flock 40 timer 40 shock 60 gross 144 greatgross 12 gross tithe 1|10 # From Anglo-Saxon word for tenth # Paper counting measure shortquire 24 quire 25 shortream 480 ream 500 perfectream 516 bundle 2 reams bale 5 bundles # # 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 pointthickness mil # 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 grams / 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 and lbbond poundbondpaper # 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 inches # Type sizes excelsior 3 point brilliant 3.5 point diamondtype 4 point pearl 5 point agate 5.5 point # Originally agate type was 14 lines per # inch, giving a value of 1|14 in. 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 # # Information theory units # nat ln(2) bits # Entropy measured base e hartley log2(10) bits # 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 B byte # 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 bits # Half of a byte. Sometimes # equal to different lengths # such as 3 bits. nibble nybble meg megabyte # Sometimse 2^20 bytes gig gigabyte # Sometimes 2^30 bytes # See the prefix section above # for binary prefixes analagous to # the metric ones. 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. # # Musical measures. Musical intervals expressed as ratios. Multiply # two intervals together to get the sum of the interval. The function # musicalcent can be used to convert ratios to cents. # # Perfect intervals octave 2 majorsecond musicalfifth^2 / octave majorthird 5|4 minorthird 6|5 musicalfourth 4|3 musicalfifth 3|2 majorsixth musicalfourth majorthird minorsixth musicalfourth minorthird majorseventh musicalfifth majorthird minorseventh musicalfifth minorthird pythagoreanthird majorsecond musicalfifth^2 / octave syntoniccomma pythagoreanthird / majorthird pythagoreancomma musicalfifth^12 / octave^7 # Equal tempered definitions semitone octave^(1|12) musicalcent(x) [1;1] semitone^(x/100) ; 100 log(musicalcent)/log(semitone) # # 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 drams/1000 yards # 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 yards cut 300 yards # used for wet-spun linen yarn lea 300 yards # # 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. bloodunit 450 ml # For whole blood. For blood # components, a blood unit is the # quanity of the component found in a # blood unit of whole blood. The # human body contains about 12 blood # units of whole blood. # # fixup units for times when prefix handling doesn't do the job # hectare hectoare megohm megaohm kilohm kiloohm microhm microohm megalerg megaerg # 'L' added to make it pronounceable [18]. # # Exchange rates from the New York Times, 27 July 1999 # # Some European currencies have permanent fixed exchange rates with # the Euro. These rates were taken from the EC's web site: # http://europa.eu.int/eurobirth/rates.html # cent $ .01 argentinapeso $ 1.0010 # Financial rate australiadollar 0.6483 $ austriaschilling 1|13.7603 euro belgiumfranc 1|40.3399 euro brazilreal 0.5488 $ britainpound 1.5906 $ canadadollar 0.6625 $ chilepeso 0.001932 $ # Official rate chinayuan 0.1208 $ colombiapeso 0.000545 $ czechkoruna 0.0287 $ denmarkkrone 0.1439 $ euro 1.061 $ # 27 July 1999 rate from Yahoo ecuadorsucre 0.000086 $ egyptpound 0.2930 $ finlandmarkka 1|5.94573 euro francefranc 1|6.55957 euro germanymark 1|1.95583 euro greatbritainpound britainpound greecedrachma 0.003282 $ hongkongdollar 0.1288 $ hungaryforint 0.0042 $ indiarupee 0.0231 $ # official rate indonesiarupiah 0.000143 $ irelandpunt 1|0.787564 euro israelshekel 0.2439 $ italylira 1|1936.27 euro japanyen 0.008576 $ jordandinar 1.4104 $ lebanonpound 0.000663 $ malaysiaringgit 0.2632 $ mexicopeso 0.106373 $ netherlandsguilder 1|2.20371 euro newzealanddollar 0.5275 $ norwaykrone 0.1283 $ pakistanrupee 0.0195 $ perunewsol 0.3008 $ philippinespeso 0.0261 $ polandzloty 0.2604 $ portugalescudo 1|200.482 euro russiaruble 0.0413 $ # Moscow Interbank Currency Exchange saudiarabiariyal 0.2666 $ singaporedollar 0.5936 $ slovakiakoruna 0.0235 $ southafricarand 0.1630 $ southkoreawon 0.000828 $ spainpeseta 1|166.386 euro swedenkrona 0.1210 $ switzerlandfranc 0.6644 $ taiwandollar 0.0310 $ thailandbaht 0.02675 $ turkeylira 0.000002 $ unitedarabdirham 0.2723 $ unitedkingdompound britainpound unitedstatesdollar $ uruguaynewpeso 0.0870 $ venezuelabolivar 0.0016 $ mark germanymark bolivar venezuelabolivar peseta spainpeseta rand southafricarand escudo portugalescudo sol perunewsol guilder netherlandsguilder hollandguilder netherlandsguilder peso mexicopeso yen japanyen lira italylira rupee indiarupee drachma greecedrachma franc francefranc markka finlandmarkka sucre ecuadorsucre poundsterling britainpound # ISO currency codes AED unitedarabdirham ATS austriaschilling AUD australiadollar BEF belgiumfranc BRR brazilreal CAD canadadollar CHF switzerlandfranc CLP chilepeso COP colombiapeso CZK czechkoruna DEM germanymark DKK denmarkkrone ECS ecuadorsucre EGP egyptpound ESP spainpeseta EUR euro FIM finlandmarkka FRF francefranc GBP britainpound GRD greecedrachma HKD hongkongdollar HUF hungaryforint IDR indonesiarupiah IEP irelandpunt ILS israelshekel IND indiarupee ITL italylira JOD jordandinar JPY japanyen KRW southkoreawon LBP lebanonpound MYR malaysiaringgit MXP mexicopeso NLG netherlandsguilder NOK norwaykrone NZD newzealanddollar PEN perunewsol PHP philippinespeso PLZ polandzloty PTE portugalescudo RUR russiaruble SAR saudiarabiariyal SEK swedenkrona SGD singaporedollar SKK slovakiakoruna THB thailandbaht TRL turkeylira TWD taiwandollar USD $ VEB venezuelabolivar XEU euro ZAR southafricarand UKP GBP # Not an ISO code, but looks like one, and # sometimes used on usenet. # Precious metals (27 Nov 1996 NY Times) goldprice $ 379 / troyounce silverprice $ 4.70 / troyounce # Money on the gold standard, used in the late 19th century and early # 20th century. olddollargold 23.22 grains goldprice # Used until 1934 newdollargold 96|7 grains goldprice # After Jan 31, 1934 dollargold newdollargold poundgold 113 grains goldprice # British currency shilling 1|20 britainpound # Before decimalisation, there oldpence 1|12 shilling # were 20 shillings to a pound, # each of twelve old pence quid britainpound # Slang names fiver 5 quid tenner 10 quid # # 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 stack 4 yard^3 # British, used for firewood and coal [18] rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly # sometimes called a face cord, but this # value is equal to 1|3 cord. Name # comes from an old Norse word for a # stack of wood. 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 "standard 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 standard size. A piece # of wood less than 7 inches wide is called a "batten". This unit is now used # exclusively for fir and pine. deal 12 ft 11 in 2.5 in # The 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 the # 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 # Oceanographic flow sverdrup 1e6 m^3 / sec # Used to express flow of ocean # currents. Named after Norwegian # oceanographer H. Sverdrup. # 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 diameters # that usually have no clear origin. There are at least 5 competing wire gauge # systems to add to the confusion. The 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. Generally larger gauges mean smaller wires. # The gauges often have values such as "00" and "000" which are larger sizes # than simply "0" gauge. In the tables that appear below, these gauges must be # specified as negative numbers (e.g. "00" is -1, "000" is -2, etc). # Alternatively, you can use the following units: # g00 (-1) g000 (-2) g0000 (-3) g00000 (-4) g000000 (-5) g0000000 (-6) # 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. # # 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. wiregauge(g) [;m] 1|200 92^((36+(-g))/39) in;36+(-39)ln(200 wiregauge/in)/ln(92) # Next we have the SWG, the Imperial or British Standard Wire Gauge. This one # is piecewise linear. It was used for aluminum sheets. brwiregauge[in] \ -6 0.5 \ -5 0.464 \ -3 0.4 \ -2 0.372 \ 3 0.252 \ 6 0.192 \ 10 0.128 \ 14 0.08 \ 19 0.04 \ 23 0.024 \ 26 0.018 \ 28 0.0148 \ 30 0.0124 \ 39 0.0052 \ 49 0.0012 \ 50 0.001 # 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 # approximately .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). # # This gauge was established in 1893 for purposes of taxation. # Old plate gauge for iron plategauge[(oz/ft^2)/(480*lb/ft^3)] \ -5 300 \ 1 180 \ 14 50 \ 16 40 \ 17 36 \ 20 24 \ 26 12 \ 31 7 \ 36 4.5 \ 38 4 # Manufacturers Standard Gage stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \ -5 300 \ 1 180 \ 14 50 \ 16 40 \ 17 36 \ 20 24 \ 26 12 \ 31 7 \ 36 4.5 \ 38 4 # A special gauge is used for zinc sheet metal. Notice that larger gauges # indicate thicker sheets. zincgauge[in] \ 1 0.002 \ 10 0.02 \ 15 0.04 \ 19 0.06 \ 23 0.1 \ 24 0.125 \ 27 0.5 \ 28 1 # 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]. ringsize(n) [;in] (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018 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 sizes # specified alphabetically and based on the ring inside diameter in steps of # 1|64 inch. 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. jpringsize(n) [;mm] (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38) # The European ring sizes are the length of the circumference in mm minus 40. euringsize(n) [;mm] (n+40) mm ; euringsize/mm + (-40) # # 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 ipy inch/year # used for corrosion rates ccf 100 ft^3 # used for selling water [18] Mcf 1000 ft^3 # not million cubic feet [18] # # 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 /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 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 # # 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 Standard 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 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 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 # # A few German units as currently in use. # zentner 50 kg doppelzentner 2 zentner pfund 500 g # # 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 nook 20 acres # Given in [18] with English acres; apparently # developed after the switch to Imperial units. # 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 jug scotspint # 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 # This value appears in numerous sources. In "The pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm. romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the romandigit 1|16 romanfoot # same names as the subdivisions of the pound, romanpalm 1|4 romanfoot # but we can't have the names for different romancubit 18 romaninch # units. romanpace 5 romanfeet # Roman double pace (basic military unit) passus romanpace romanperch 10 romanfeet stade 125 romanpaces 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^2 # 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 egyptiandigit 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 greekfingers # Elbow to end of knuckles. shortgreekcubit 18 greekfingers # 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 aeginastaters aeginatalent 60 aeginamina atticstater 135 grain # Varies 134-138 grain atticdrachmae 1|2 atticstater atticobol 1|6 atticdrachmae atticmina 50 atticstaters 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 # The 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 barabictradepound 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 # # Some definitions using ISO 8859-1 characters # ¼- 1|4 ½- 1|2 ¾- 3|4 µ- micro ¢ cent £ britainpound ¥ japanyen ångström angstrom Å angstrom röntgen roentgen °C degC °F degF °K K # °K is incorrect notation °R degR ° degree ############################################################################ # # 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 # # 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. # ############################################################################