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 <