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    1 #
    2 # This file is the units database for use with GNU units, a units conversion
    3 # program by Adrian Mariano adrianm@gnu.org
    4 #
    5 # September 2020 Version 3.09
    6 #
    7 # Copyright (C) 1996-2002, 2004-2020
    8 # Free Software Foundation, Inc
    9 #
   10 # This program is free software; you can redistribute it and/or modify
   11 # it under the terms of the GNU General Public License as published by
   12 # the Free Software Foundation; either version 3 of the License, or
   13 # (at your option) any later version.
   14 #
   15 # This program is distributed in the hope that it will be useful,
   16 # but WITHOUT ANY WARRANTY; without even the implied warranty of
   17 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   18 # GNU General Public License for more details.
   19 #
   20 # You should have received a copy of the GNU General Public License
   21 # along with this program; if not, write to the Free Software
   22 # Foundation, Inc., 51 Franklin Street, Fifth Floor,
   23 # Boston, MA  02110-1301  USA
   24 #
   25 ############################################################################
   26 #
   27 # Improvements and corrections are welcome.
   28 #
   29 # Fundamental constants in this file are the 2018 CODATA recommended values.
   30 #
   31 # Most units data was drawn from
   32 #            1. NIST Special Publication 811, Guide for the
   33 #                 Use of the International System of Units (SI).
   34 #                 Barry N. Taylor. 2008
   35 #                 https://www.nist.gov/pml/special-publication-811
   36 #            2. CRC Handbook of Chemistry and Physics 70th edition
   37 #            3. Oxford English Dictionary
   38 #            4. Webster's New Universal Unabridged Dictionary
   39 #            5. Units of Measure by Stephen Dresner
   40 #            6. A Dictionary of English Weights and Measures by Ronald Zupko
   41 #            7. British Weights and Measures by Ronald Zupko
   42 #            8. Realm of Measure by Isaac Asimov
   43 #            9. United States standards of weights and measures, their
   44 #                   creation and creators by Arthur H. Frazier.
   45 #           10. French weights and measures before the Revolution: a
   46 #                   dictionary of provincial and local units by Ronald Zupko
   47 #           11. Weights and Measures: their ancient origins and their
   48 #                   development in Great Britain up to AD 1855 by FG Skinner
   49 #           12. The World of Measurements by H. Arthur Klein
   50 #           13. For Good Measure by William Johnstone
   51 #           14. NTC's Encyclopedia of International Weights and Measures
   52 #                   by William Johnstone
   53 #           15. Sizes by John Lord
   54 #           16. Sizesaurus by Stephen Strauss
   55 #           17. CODATA Recommended Values of Physical Constants available at
   56 #                   http://physics.nist.gov/cuu/Constants/index.html
   57 #           18. How Many?  A Dictionary of Units of Measurement.  Available at
   58 #                   http://www.ibiblio.org/units/
   59 #           19. Numericana.  http://www.numericana.com
   60 #           20. UK history of measurement
   61 #                   http://www.ukmetrication.com/history.htm
   62 #           21. NIST Handbook 44, Specifications, Tolerances, and
   63 #                 Other Technical Requirements for Weighing and Measuring
   64 #                 Devices. 2011
   65 #           22. NIST Special Publication 447, Weights and Measures Standards
   66 #                 of the the United States: a brief history. Lewis V. Judson.
   67 #                 1963; rev. 1976
   68 #           23. CRC Handbook of Chemistry and Physics, 96th edition
   69 #           24. Dictionary of Scientific Units, 6th ed.  H.G.  Jerrard and D.B.
   70 #                 McNeill. 1992
   71 #           25. NIST Special Publication 330, The International System of
   72 #                 Units (SI). ed. Barry N. Taylor and Ambler Thompson. 2008
   73 #                 https://www.nist.gov/pml/special-publication-330
   74 #           26. BIPM Brochure, The International System of Units (SI).
   75 #                 9th ed., 2019
   76 #                 https://www.bipm.org/en/publications/si-brochure/
   77 #
   78 ###########################################################################
   79 #
   80 # If units you use are missing or defined incorrectly, please contact me.
   81 # If your country's local units are missing and you are willing to supply
   82 # them, please send me a list.
   83 #
   84 ###########################################################################
   85 
   86 ###########################################################################
   87 #
   88 # Brief Philosophy of this file
   89 #
   90 # Most unit definitions are made in terms of integers or simple fractions of
   91 # other definitions.  The typical exceptions are when converting between two
   92 # different unit systems, or the values of measured physical constants.  In
   93 # this file definitions are given in the most natural and revealing way in
   94 # terms of integer factors.
   95 #
   96 # If you make changes be sure to run 'units --check' to check your work.
   97 #
   98 # The file is USA-centric, but there is some modest effort to support other
   99 # countries.  This file is now coded in UTF-8.  To support environments where
  100 # UTF-8 is not available, definitions that require this character set are
  101 # wrapped in !utf8 directives.
  102 #
  103 # When a unit name is used in different countries with the different meanings
  104 # the system should be as follows:
  105 #
  106 # Suppose countries ABC and XYZ both use the "foo".  Then globally define
  107 #
  108 #   ABCfoo  <some value>
  109 #   XYZfoo  <different value>
  110 #
  111 # Then, using the !locale directive, define the "foo" appropriately for each of
  112 # the two countries with a definition like
  113 #
  114 # !locale ABC
  115 #    foo  ABCfoo
  116 # !endlocale
  117 #
  118 ###########################################################################
  119 
  120 !locale en_US
  121 !  set UNITS_ENGLISH US
  122 !endlocale
  123 
  124 !locale en_GB
  125 !  set UNITS_ENGLISH GB
  126 !endlocale
  127 
  128 !set UNITS_ENGLISH US   # Default setting for English units
  129 
  130 !set UNITS_SYSTEM default   # Set a default value
  131 
  132 !varnot UNITS_SYSTEM si emu esu gaussian gauss hlu natural natural-gauss hartree planck planck-red default 
  133 !message Unknown unit system given with -u or UNITS_SYSTEM environment variable
  134 !message Valid systems: si, emu, esu, gauss[ian], hlu, natural, natural-gauss
  135 !message                planck, planck-red, hartree
  136 !message Using SI
  137 !prompt (SI)
  138 !endvar
  139 
  140 !var UNITS_SYSTEM si
  141 !message SI units selected
  142 !prompt (SI)
  143 !endvar
  144 
  145 ###########################################################################
  146 #                                                                         #
  147 # Primitive units.  Any unit defined to contain a '!' character is a      #
  148 # primitive unit which will not be reduced any further.  All units should #
  149 # reduce to primitive units.                                              #
  150 #                                                                         #
  151 ###########################################################################
  152 
  153 #
  154 # SI units
  155 #
  156 # On 20 May 2019, the SI was revised to define the units by fixing the
  157 # values of physical constants that depend on those units.
  158 #
  159 # https://www.nist.gov/si-redefinition/
  160 #
  161 # The BIPM--the International Bureau of Weights and Measures--provides a
  162 # succinct description of the new SI in its Concise Summary:
  163 #
  164 # https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN.pdf
  165 #
  166 #     The SI is the system of units in which:
  167 #
  168 #       *  the unperturbed ground state hyperfine transition frequency of the
  169 #          caesium 133 atom is delta nu_Cs = 9 192 631 770 Hz,
  170 #       *  the speed of light in vacuum, c, is 299 792 458 m/s,
  171 #       *  the Planck constant, h, is 6.626 070 15 * 10^-34 J s,
  172 #       *  the elementary charge, e, is 1.602 176 634 * 10^-19 C,
  173 #       *  the Boltzmann constant, k, is 1.380 649 * 10^-23 J/K,
  174 #       *  the Avogadro constant, N_A, is 6.022 140 76 * 10^23 mol^-1,
  175 #       *  the luminous efficacy of monochromatic radiation of frequency
  176 #          540 * 10^12 Hz, K_cd, is 683 lm/W,
  177 #
  178 #     where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz,
  179 #     J, C, lm, and W, respectively, are related to the units second, metre,
  180 #     kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg,
  181 #     A, K, mol, and cd, respectively, according to Hz = s^–1, J = kg m^2 s^–2,
  182 #     C = A s, lm = cd m^2 m^–2 = cd sr, and W = kg m^2 s^–3.
  183 # 
  184 #     These definitions specify the exact numerical value of each constant when
  185 #     its value is expressed in the corresponding SI unit.  By fixing the exact
  186 #     numerical value the unit becomes defined, since the product of the
  187 #     numerical value and the unit has to equal the value of the constant,
  188 #     which is invariant.
  189 # 
  190 #     The defining constants have been chosen such that, when taken together,
  191 #     their units cover all of the units of the SI.  In general, there is no
  192 #     one-to-one correspondence between the defining constants and the SI base
  193 #     units.  Any SI unit is a product of powers of these seven constants and a
  194 #     dimensionless factor.
  195 # 
  196 # Until 2018, the SI was defined in terms of base units and derived units.
  197 # These categories are no longer essential in the SI, but they are maintained
  198 # in view of their convenience and widespread use.  They are arguably more
  199 # intuitive than the new definitions.  (They are also essential to the
  200 # operation of GNU units.)  The definitions of the base units, which follow
  201 # from the definition of the SI in terms of the seven defining constants, are
  202 # given below.
  203 #
  204 
  205 s         !      # The second, symbol s, is the SI unit of time.  It is defined
  206 second    s      # by taking the fixed numerical value of the unperturbed
  207                  # ground-state hyperfine transition frequency of the
  208                  # cesium-133 atom to be 9 192 1631 770 when expressed in the
  209                  # unit Hz, which is equal to 1/s.  
  210                  #
  211                  # This definition is a restatement of the previous one, the
  212                  # duration of 9192631770 periods of the radiation corresponding
  213                  # to the cesium-133 transition. 
  214 
  215 c_SI      299792458
  216 c         299792458 m/s   # speed of light in vacuum (exact)
  217 
  218 m         !      # The metre, symbol m, is the SI unit of length.  It is
  219 meter     m      # defined by taking the fixed numerical value of the speed
  220 metre     m      # of light in vacuum, c, to be 299 792 458 when expressed in
  221                  # units of m/s.
  222                  #
  223                  # This definition is a rewording of the previous one and is
  224                  # equivalent to defining the meter as the distance light
  225                  # travels in 1|299792458 seconds.  The meter was originally
  226                  # intended to be 1e-7 of the length along a meridian from the
  227                  # equator to a pole.
  228 
  229 h_SI      6.62607015e-34
  230 h         6.62607015e-34 J s # Planck constant (exact)
  231 
  232 kg        !      # The kilogram, symbol kg, is the SI unit of mass.  It is
  233 kilogram  kg     # defined by taking the fixed numerical value of the Planck
  234                  # constant, h, to be 6.626 070 15 * 10^-34 when expressed in
  235                  # the unit J s which is equal to kg m^2 / s.
  236                  # 
  237                  # One advantage of fixing h to define the kilogram is that this
  238                  # affects constants used to define the ampere.  If the kg were
  239                  # defined by directly fixing the mass of something, then h
  240                  # would be subject to error.
  241                  #
  242                  # The previous definition of the kilogram was the mass of the
  243                  # international prototype kilogram.  The kilogram was the last
  244                  # unit whose definition relied on reference to an artifact.
  245                  #
  246                  # It is not obvious what this new definition means, or
  247                  # intuitively how fixing Planck's constant defines the
  248                  # kilogram.  To define the kilogram we need to give the mass
  249                  # of some reference in kilograms.  Previously the prototype in
  250                  # France served as this reference, and it weighed exactly 1
  251                  # kg.  But the reference can have any weight as long as you
  252                  # know the weight of the reference.  The new definition uses
  253                  # the "mass" of a photon, or more accurately, the mass
  254                  # equivalent of the energy of a photon.  The energy of a
  255                  # photon depends on its frequency.  If you pick a frequency,
  256                  # f, then the energy of the photon is hf, and hence the mass
  257                  # equivalent is hf/c^2.  If we reduce this expression using
  258                  # the constant defined values for h and c the result is a
  259                  # value in kilograms for the mass-equivalent of a photon of
  260                  # frequency f, which can therefore define the size of the
  261                  # kilogram.
  262                  #
  263                  # For more on the relationship between mass an Planck's
  264                  # constant:
  265                  #
  266                  # https://www.nist.gov/si-redefinition/kilogram-mass-and-plancks-constant
  267                  # This definition may still seem rather abstract: you can't
  268                  # place a "kilogram of radiation" on one side of a balance.
  269                  # Metrologists realize the kilogram using a Kibble Balance, a
  270                  # device which relates mechanical energy to electrical energy
  271                  # and can measure mass with extreme accuracy if h is known.
  272                  #
  273                  # For more on the Kibble Balance see
  274                  #
  275                  # https://www.nist.gov/si-redefinition/kilogram-kibble-balance
  276                  # https://en.wikipedia.org/wiki/Kibble_balance
  277 
  278 k_SI      1.380649e-23
  279 boltzmann 1.380649e-23 J/K   # Boltzmann constant (exact)
  280 k         boltzmann
  281 
  282 K         !      # The kelvin, symbol K, is the SI unit of thermodynamic
  283 kelvin    K      # temperature.  It is defined by taking the fixed numerical
  284                  # value of the Boltzmann constant, k, to be 1.380 649 * 10^-23
  285                  # when expressed in the unit J/K, which is equal to 
  286                  # kg m^2/s^2 K.
  287                  #
  288                  # The boltzmann constant establishes the relationship between
  289                  # energy and temperature.  The average thermal energy carried
  290                  # by each degree of freedom is kT/2.  A monatomic ideal gas
  291                  # has three degrees of freedom corresponding to the three
  292                  # spatial directions, which means its thermal energy is
  293                  # (3/2) k T.
  294                  #
  295                  # The previous definition of the kelvin was based on the
  296                  # triple point of water.  The change in the definition of the
  297                  # kelvin will not have much effect on measurement practice.
  298                  # Practical temperature calibration makes use of two scales,
  299                  # the International Temperature Scale of 1990 (ITS-90), which
  300                  # covers the range of 0.65 K to 1357.77K and the Provisional
  301                  # Low Temperature Scale of 2000 (PLTS-2000), which covers the
  302                  # range of 0.9 mK to 1 K.
  303                  # https://www.bipm.org/en/committees/cc/cct/publications-cc.html
  304                  #
  305                  # The ITS-90 contains 17 reference points including things
  306                  # like the triple point of hydrogen (13.8033 K) or the
  307                  # freezing point of gold (1337.33 K), and of course the triple
  308                  # point of water.  The PLTS-2000 specifies four reference
  309                  # points, all based on properties of helium-3.
  310                  #
  311                  # The redefinition of the kelvin will not affect the values of
  312                  # these reference points, which have been determined by
  313                  # primary thermometry, using thermometers that rely only on
  314                  # relationships that allow temperature to be calculated
  315                  # directly without using any unknown quantities. Examples
  316                  # include acoustic thermometers, which measure the speed of
  317                  # sound in a gas, or electronic thermometers, which measure
  318                  # tiny voltage fluctuations in resistors. Both variables
  319                  # depend directly on temperature.
  320 
  321 e_SI      1.602176634e-19
  322 e         1.602176634e-19 C  # electron charge (exact)
  323 
  324 A         !      # The ampere, symbol A, is the SI unit of electric current.
  325 ampere    A      # It is defined by taking the fixed numerical value of the
  326 amp       ampere # elementary charge, e, to be 1.602 176 634 * 10^-19 when
  327                  # expressed in the unit C, which is equal to A*s.
  328                  #
  329                  # The previous definition was the current which produces a
  330                  # force of 2e-7 N/m between two infinitely long wires a meter
  331                  # apart.  This definition was difficult to realize accurately.
  332                  #
  333                  # The ampere is actually realized by establishing the volt and
  334                  # the ohm, since A = V / ohm.  These measurements can be done
  335                  # using the Josephson effect and the quantum Hall effect,
  336                  # which accurately measure voltage and resistance, respectively,
  337                  # with reference to two fixed constants, the Josephson
  338                  # constant, K_J=2e/h and the von Klitzing constant, R_K=h/e^2.
  339                  # Under the previous SI system, these constants had official
  340                  # fixed values, defined in 1990.  This created a situation
  341                  # where the standard values for the volt and ohm were in some
  342                  # sense outside of SI because they depended primarily on
  343                  # constants different from the ones used to define SI. After
  344                  # the revision, since e and h have exact definitions, the
  345                  # Josephson and von Klitzing constants will also have exact
  346                  # definitions that derive from SI instead of the conventional
  347                  # 1990 values.
  348                  #
  349                  # In fact we know that there is a small offset between the
  350                  # conventional values of the electrical units based on the
  351                  # conventional 1990 values and the SI values.  The new
  352                  # definition, which brings the practical electrical units back
  353                  # into SI, will lead to a one time change of +0.1ppm for
  354                  # voltage values and +0.02ppm for resistance values.
  355                  #
  356                  # The previous definition resulted in fixed exact values for
  357                  # the vacuum permeability (mu0), the impedance of free space
  358                  # (Z0), the vacuum permittivity (epsilon0), and the Coulomb
  359                  # constant. With the new definition, these four values are
  360                  # subject to experimental error.
  361 
  362 avogadro  6.02214076e23 / mol # Size of a mole (exact)
  363 N_A       avogadro
  364 
  365 mol       !      # The mole, symbol mol, is the SI unit of amount of
  366 mole      mol    # substance.  One mole contains exactly 6.022 140 76 * 10^23
  367                  # elementary entities.  This number is the fixed numerical
  368                  # value of the Avogadro constant, N_A, when expressed in the
  369                  # unit 1/mol and is called the Avogadro number.  The amount of
  370                  # substance, symbol n, of a system is a measure of the number
  371                  # of specified elementary entities.  An elementary entity may
  372                  # be an atom, a molecule, an ion, an electron, any other
  373                  # particle or specified group of particles.
  374                  #
  375                  # The atomic mass unit (u) is defined as 1/12 the mass of
  376                  # carbon-12.  Previously the mole was defined so that a mole
  377                  # of carbon-12 weighed exactly 12g, or N_A u = 1 g/mol
  378                  # exactly. This relationship is now an experimental, 
  379                  # approximate relationship.
  380                  #
  381                  # To determine the size of the mole, researchers used spheres
  382                  # of very pure silicon-28 that weighed a kilogram.  They
  383                  # measured the molar mass of Si-28 using mass spectrometry and
  384                  # used X-ray diffraction interferometry to determine the
  385                  # spacing of the silicon atoms in the sphere.  Using the
  386                  # sphere's volume it was then possible to determine the number
  387                  # of silicon atoms in the sphere, and hence determine the
  388                  # Avogadro constant.  The results of this experiment were used to 
  389                  # define N_A, which is henceforth a fixed, unchanging quantity.  
  390                  
  391 cd        !      # The candela, symbol cd, is the SI unit of luminous intensity
  392 candela   cd     # in a given direction.  It is defined by taking the fixed
  393                  # numerical value of the luminous efficacy of monochromatic
  394                  # radiation of the frequency 540e12 Hz to be 683 when
  395                  # expressed in the unit lumen/watt, which is equal to
  396                  # cd sr/W, or cd sr s^3/kg m^2
  397                  #
  398                  # This definition is a rewording of the previous definition.
  399                  # Luminous intensity differs from radiant intensity (W/sr) in
  400                  # that it is adjusted for human perceptual dependence on
  401 		 # wavelength.  The frequency of 540e12 Hz (yellow;
  402 		 # wavelength approximately 555 nm in vacuum) is where human
  403 		 # perception is most efficient.
  404 #
  405 # The radian and steradian are defined as dimensionless primitive units.
  406 # The radian is equal to m/m and the steradian to m^2/m^2 so these units are
  407 # dimensionless.  Retaining them as named units is useful because it allows
  408 # clarity in expressions and makes the meaning of unit definitions more clear.
  409 # These units will reduce to 1 in conversions but not for sums of units or for
  410 # arguments to functions.
  411 #
  412 
  413 radian    !dimensionless   # The angle subtended at the center of a circle by
  414                            #   an arc equal in length to the radius of the
  415                            #   circle
  416 sr        !dimensionless   # Solid angle which cuts off an area of the surface
  417 steradian sr               #   of the sphere equal to that of a square with
  418                            #   sides of length equal to the radius of the
  419                            #   sphere
  420 
  421 #
  422 # A primitive non-SI unit
  423 #
  424 
  425 bit       !      # Basic unit of information (entropy).  The entropy in bits
  426                  #   of a random variable over a finite alphabet is defined
  427                  #   to be the sum of -p(i)*log2(p(i)) over the alphabet where
  428                  #   p(i) is the probability that the random variable takes
  429                  #   on the value i.
  430 
  431 #
  432 # Currency: the primitive unit of currency is defined in currency.units. 
  433 # It is usually the US$ or the euro, but it is user selectable.  
  434 #
  435 
  436 ###########################################################################
  437 #                                                                         #
  438 # Prefixes (longer names must come first)                                 #
  439 #                                                                         #
  440 ###########################################################################
  441 
  442 yotta-                  1e24     # Greek or Latin octo, "eight"
  443 zetta-                  1e21     # Latin septem, "seven"
  444 exa-                    1e18     # Greek hex, "six"
  445 peta-                   1e15     # Greek pente, "five"
  446 tera-                   1e12     # Greek teras, "monster"
  447 giga-                   1e9      # Greek gigas, "giant"
  448 mega-                   1e6      # Greek megas, "large"
  449 myria-                  1e4      # Not an official SI prefix
  450 kilo-                   1e3      # Greek chilioi, "thousand"
  451 hecto-                  1e2      # Greek hekaton, "hundred"
  452 deca-                   1e1      # Greek deka, "ten"
  453 deka-                   deca
  454 deci-                   1e-1     # Latin decimus, "tenth"
  455 centi-                  1e-2     # Latin centum, "hundred"
  456 milli-                  1e-3     # Latin mille, "thousand"
  457 micro-                  1e-6     # Latin micro or Greek mikros, "small"
  458 nano-                   1e-9     # Latin nanus or Greek nanos, "dwarf"
  459 pico-                   1e-12    # Spanish pico, "a bit"
  460 femto-                  1e-15    # Danish-Norwegian femten, "fifteen"
  461 atto-                   1e-18    # Danish-Norwegian atten, "eighteen"
  462 zepto-                  1e-21    # Latin septem, "seven"
  463 yocto-                  1e-24    # Greek or Latin octo, "eight"
  464 
  465 quarter-                1|4
  466 semi-                   0.5
  467 demi-                   0.5
  468 hemi-                   0.5
  469 half-                   0.5
  470 double-                 2
  471 triple-                 3
  472 treble-                 3
  473 
  474 kibi-                   2^10     # In response to the convention of illegally
  475 mebi-                   2^20     # and confusingly using metric prefixes for
  476 gibi-                   2^30     # powers of two, the International
  477 tebi-                   2^40     # Electrotechnical Commission aproved these
  478 pebi-                   2^50     # binary prefixes for use in 1998.  If you
  479 exbi-                   2^60     # want to refer to "megabytes" using the
  480 Ki-                     kibi     # binary definition, use these prefixes.
  481 Mi-                     mebi
  482 Gi-                     gibi
  483 Ti-                     tebi
  484 Pi-                     pebi
  485 Ei-                     exbi
  486 
  487 Y-                      yotta
  488 Z-                      zetta
  489 E-                      exa
  490 P-                      peta
  491 T-                      tera
  492 G-                      giga
  493 M-                      mega
  494 k-                      kilo
  495 h-                      hecto
  496 da-                     deka
  497 d-                      deci
  498 c-                      centi
  499 m-                      milli
  500 u-                      micro   # it should be a mu but u is easy to type
  501 n-                      nano
  502 p-                      pico
  503 f-                      femto
  504 a-                      atto
  505 z-                      zepto
  506 y-                      yocto
  507 
  508 #
  509 # Names of some numbers
  510 #
  511 
  512 one                     1
  513 two                     2
  514 double                  2
  515 couple                  2
  516 three                   3
  517 triple                  3
  518 four                    4
  519 quadruple               4
  520 five                    5
  521 quintuple               5
  522 six                     6
  523 seven                   7
  524 eight                   8
  525 nine                    9
  526 ten                     10
  527 eleven                  11
  528 twelve                  12
  529 thirteen                13
  530 fourteen                14
  531 fifteen                 15
  532 sixteen                 16
  533 seventeen               17
  534 eighteen                18
  535 nineteen                19
  536 twenty                  20
  537 thirty                  30
  538 forty                   40
  539 fifty                   50
  540 sixty                   60
  541 seventy                 70
  542 eighty                  80
  543 ninety                  90
  544 hundred                 100
  545 thousand                1000
  546 million                 1e6
  547 
  548 twoscore                two score
  549 threescore              three score
  550 fourscore               four score
  551 fivescore               five score
  552 sixscore                six score
  553 sevenscore              seven score
  554 eightscore              eight score
  555 ninescore               nine score
  556 tenscore                ten score
  557 twelvescore             twelve score
  558 
  559 # These number terms were described by N. Chuquet and De la Roche in the 16th
  560 # century as being successive powers of a million.  These definitions are still
  561 # used in most European countries.  The current US definitions for these
  562 # numbers arose in the 17th century and don't make nearly as much sense.  These
  563 # numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
  564 # W. Weisstein.
  565 
  566 shortbillion               1e9
  567 shorttrillion              1e12
  568 shortquadrillion           1e15
  569 shortquintillion           1e18
  570 shortsextillion            1e21
  571 shortseptillion            1e24
  572 shortoctillion             1e27
  573 shortnonillion             1e30
  574 shortnoventillion          shortnonillion
  575 shortdecillion             1e33
  576 shortundecillion           1e36
  577 shortduodecillion          1e39
  578 shorttredecillion          1e42
  579 shortquattuordecillion     1e45
  580 shortquindecillion         1e48
  581 shortsexdecillion          1e51
  582 shortseptendecillion       1e54
  583 shortoctodecillion         1e57
  584 shortnovemdecillion        1e60
  585 shortvigintillion          1e63
  586 
  587 centillion              1e303
  588 googol                  1e100
  589 
  590 longbillion               million^2
  591 longtrillion              million^3
  592 longquadrillion           million^4
  593 longquintillion           million^5
  594 longsextillion            million^6
  595 longseptillion            million^7
  596 longoctillion             million^8
  597 longnonillion             million^9
  598 longnoventillion          longnonillion
  599 longdecillion             million^10
  600 longundecillion           million^11
  601 longduodecillion          million^12
  602 longtredecillion          million^13
  603 longquattuordecillion     million^14
  604 longquindecillion         million^15
  605 longsexdecillion          million^16
  606 longseptdecillion         million^17
  607 longoctodecillion         million^18
  608 longnovemdecillion        million^19
  609 longvigintillion          million^20
  610 
  611 # These numbers fill the gaps left by the long system above.
  612 
  613 milliard                1000 million
  614 billiard                1000 million^2
  615 trilliard               1000 million^3
  616 quadrilliard            1000 million^4
  617 quintilliard            1000 million^5
  618 sextilliard             1000 million^6
  619 septilliard             1000 million^7
  620 octilliard              1000 million^8
  621 nonilliard              1000 million^9
  622 noventilliard           nonilliard
  623 decilliard              1000 million^10
  624 
  625 # For consistency
  626 
  627 longmilliard              milliard
  628 longbilliard              billiard
  629 longtrilliard             trilliard
  630 longquadrilliard          quadrilliard
  631 longquintilliard          quintilliard
  632 longsextilliard           sextilliard
  633 longseptilliard           septilliard
  634 longoctilliard            octilliard
  635 longnonilliard            nonilliard
  636 longnoventilliard         noventilliard
  637 longdecilliard            decilliard
  638 
  639 # The long centillion would be 1e600.  The googolplex is another
  640 # familiar large number equal to 10^googol.  These numbers give overflows.
  641 
  642 #
  643 # The short system prevails in English speaking countries
  644 #
  645 
  646 billion                 shortbillion
  647 trillion                shorttrillion
  648 quadrillion             shortquadrillion
  649 quintillion             shortquintillion
  650 sextillion              shortsextillion
  651 septillion              shortseptillion
  652 octillion               shortoctillion
  653 nonillion               shortnonillion
  654 noventillion            shortnoventillion
  655 decillion               shortdecillion
  656 undecillion             shortundecillion
  657 duodecillion            shortduodecillion
  658 tredecillion            shorttredecillion
  659 quattuordecillion       shortquattuordecillion
  660 quindecillion           shortquindecillion
  661 sexdecillion            shortsexdecillion
  662 septendecillion         shortseptendecillion
  663 octodecillion           shortoctodecillion
  664 novemdecillion          shortnovemdecillion
  665 vigintillion            shortvigintillion
  666 
  667 #
  668 # Numbers used in India 
  669 #
  670 
  671 lakh                    1e5
  672 crore                   1e7
  673 arab                    1e9
  674 kharab                  1e11
  675 neel                    1e13
  676 padm                    1e15
  677 shankh                  1e17
  678 
  679 #############################################################################
  680 #                                                                           #
  681 # Derived units which can be reduced to the primitive units                 #
  682 #                                                                           #
  683 #############################################################################
  684 
  685 
  686 
  687 #
  688 # Named SI derived units (officially accepted)
  689 #
  690 
  691 newton                  kg m / s^2   # force
  692 N                       newton
  693 pascal                  N/m^2        # pressure or stress
  694 Pa                      pascal
  695 joule                   N m          # energy
  696 J                       joule
  697 watt                    J/s          # power
  698 W                       watt
  699 coulomb                 A s          # charge
  700 C                       coulomb
  701 volt                    W/A          # potential difference
  702 V                       volt
  703 ohm                     V/A          # electrical resistance
  704 siemens                 A/V          # electrical conductance
  705 S                       siemens
  706 farad                   C/V          # capacitance
  707 F                       farad
  708 weber                   V s          # magnetic flux
  709 Wb                      weber
  710 henry                   V s / A      # inductance
  711 H                       henry
  712 tesla                   Wb/m^2       # magnetic flux density
  713 T                       tesla
  714 hertz                   /s           # frequency
  715 Hz                      hertz
  716 
  717 #
  718 # Dimensions.  These are here to help with dimensional analysis and
  719 # because they will appear in the list produced by hitting '?' at the
  720 # "You want:" prompt to tell the user the dimension of the unit.
  721 #
  722 
  723 LENGTH                  meter
  724 AREA                    LENGTH^2
  725 VOLUME                  LENGTH^3
  726 MASS                    kilogram
  727 AMOUNT                  mole
  728 ANGLE                   radian
  729 SOLID_ANGLE             steradian
  730 MONEY                   US$
  731 FORCE                   newton
  732 PRESSURE                FORCE / AREA
  733 STRESS                  FORCE / AREA
  734 FREQUENCY               hertz
  735 VELOCITY                LENGTH / TIME
  736 ACCELERATION            VELOCITY / TIME
  737 DENSITY                 MASS / VOLUME
  738 LINEAR_DENSITY          MASS / LENGTH
  739 VISCOSITY               FORCE TIME / AREA
  740 KINEMATIC_VISCOSITY     VISCOSITY / DENSITY
  741 CURRENT                 ampere
  742 CHARGE                  coulomb
  743 CAPACITANCE             farad
  744 RESISTANCE              ohm
  745 CONDUCTANCE             siemens
  746 # It may be easier to understand the relationship by considering
  747 # an object with specified dimensions and resistivity, whose
  748 # resistance is given by the resistivity * length / area. 
  749 RESISTIVITY             RESISTANCE AREA / LENGTH
  750 CONDUCTIVITY            CONDUCTANCE LENGTH / AREA
  751 INDUCTANCE              henry
  752 E_FIELD                 ELECTRIC_POTENTIAL / LENGTH
  753 B_FIELD                 tesla
  754 # The D and H fields are related to the E and B fields by factors of
  755 # epsilon and mu respectively, so their units can be found by
  756 # multiplying/dividing by the epsilon0 and mu0.  The more complex
  757 # definitions below make it possible to use D_FIELD and E_FIELD to
  758 # convert between SI and CGS units for these dimensions.
  759 D_FIELD                 E_FIELD epsilon0 / epsilon0_SI  #   mu0_SI c^2 F / m
  760 H_FIELD                 B_FIELD / (mu0/mu0_SI)
  761 ELECTRIC_DIPOLE_MOMENT  C m
  762 MAGNETIC_DIPOLE_MOMENT  J / T
  763 POLARIZATION            ELECTRIC_DIPOLE_MOMENT / VOLUME
  764 MAGNETIZATION           MAGNETIC_DIPOLE_MOMENT / VOLUME
  765 ELECTRIC_POTENTIAL      ENERGY / CHARGE #volt
  766 VOLTAGE                 ELECTRIC_POTENTIAL
  767 E_FLUX                  E_FIELD AREA	
  768 D_FLUX                  D_FIELD AREA
  769 B_FLUX                  B_FIELD AREA	
  770 H_FLUX                  H_FIELD AREA
  771 
  772 #
  773 # units derived easily from SI units
  774 #
  775 
  776 gram                    millikg
  777 gm                      gram
  778 g                       gram
  779 tonne                   1000 kg
  780 t                       tonne
  781 metricton               tonne
  782 sthene                  tonne m / s^2
  783 funal                   sthene
  784 pieze                   sthene / m^2
  785 quintal                 100 kg
  786 bar                     1e5 Pa     # About 1 atm
  787 b                       bar
  788 vac                     millibar
  789 micron                  micrometer # One millionth of a meter
  790 bicron                  picometer  # One brbillionth of a meter
  791 cc                      cm^3
  792 are                     100 m^2
  793 a                       are
  794 liter                   1000 cc       # The liter was defined in 1901 as the
  795 oldliter                1.000028 dm^3 # space occupied by 1 kg of pure water at
  796 L                       liter         # the temperature of its maximum density
  797 l                       liter         # under a pressure of 1 atm.  This was
  798                                       # supposed to be 1000 cubic cm, but it
  799                                       # was discovered that the original
  800                                       # measurement was off.  In 1964, the
  801                                       # liter was redefined to be exactly 1000
  802                                       # cubic centimeters.
  803 mho                     siemens    # Inverse of ohm, hence ohm spelled backward
  804 galvat                  ampere     # Named after Luigi Galvani
  805 angstrom                1e-10 m    # Convenient for describing molecular sizes
  806 xunit                   xunit_cu      # Used for measuring x-ray wavelengths.
  807 siegbahn                xunit         # Originally defined to be 1|3029.45 of
  808 xunit_cu             1.00207697e-13 m # the spacing of calcite planes at 18
  809 xunit_mo             1.00209952e-13 m # degC.  It was intended to be exactly
  810                                       # 1e-13 m, but was later found to be
  811                                       # slightly off.  Current usage is with
  812                                       # reference to common x-ray lines, either
  813                                       # the K-alpha 1 line of copper or the
  814                                       # same line of molybdenum.
  815 angstromstar   1.00001495 angstrom # Defined by JA Bearden in 1965 to replace 
  816                                    #   the X unit.  The wavelength of the
  817                                    #   tungsten K alpha1 line was defined as
  818                                    #   exactly 0.20901 angstrom star, with the
  819                                    #   valule chosen to try to make the new
  820                                    #   unit close to the angstrom.  
  821 silicon_d220     1.920155716e-10 m # Silicon lattice spacing
  822 siliconlattice sqrt(8) silicon_d220# Silicon lattice parameter, (a), the side
  823                                    #   length of the unit cell for the diamond
  824                                    #   centered cubic structure of silicon.
  825 fermi                   1e-15 m    # Convenient for describing nuclear sizes
  826                                    #   Nuclear radius is from 1 to 10 fermis
  827 barn                    1e-28 m^2  # Used to measure cross section for
  828                                    #   particle physics collision, said to
  829                                    #   have originated in the phrase "big as
  830                                    #   a barn".
  831 shed                    1e-24 barn # Defined to be a smaller companion to the
  832                                    #   barn, but it's too small to be of
  833                                    #   much use.
  834 brewster                micron^2/N # measures stress-optical coef
  835 diopter                 /m         # measures reciprocal of lens focal length
  836 fresnel                 1e12 Hz    # occasionally used in spectroscopy
  837 shake                   1e-8 sec
  838 svedberg                1e-13 s    # Used for measuring the sedimentation
  839                                    # coefficient for centrifuging.
  840 gamma                   microgram  # Also used for 1e-9 tesla
  841 lambda                  microliter
  842 spat                    1e12 m     # Rarely used for astronomical measurements
  843 preece                  1e13 ohm m # resistivity
  844 planck                  J s        # action of one joule over one second
  845 sturgeon                /henry     # magnetic reluctance
  846 daraf                   1/farad    # elastance (farad spelled backwards)
  847 leo                     10 m/s^2
  848 poiseuille              N s / m^2  # viscosity
  849 mayer                   J/g K      # specific heat
  850 mired                   / microK   # reciprocal color temperature.  The name
  851                                    #   abbreviates micro reciprocal degree.
  852 crocodile               megavolt   # used informally in UK physics labs
  853 metricounce             25 g
  854 mounce                  metricounce
  855 finsenunit              1e5 W/m^2  # Measures intensity of ultraviolet light
  856                                    # with wavelength 296.7 nm.
  857 fluxunit                1e-26 W/m^2 Hz # Used in radio astronomy to measure
  858                                        #   the energy incident on the receiving
  859                                        #   body across a specified frequency
  860                                        #   bandwidth.  [12]
  861 jansky                  fluxunit   # K. G. Jansky identified radio waves coming
  862 Jy                      jansky     # from outer space in 1931.
  863 flick       W / cm^2 sr micrometer # Spectral radiance or irradiance
  864 pfu                    / cm^2 sr s # particle flux unit -- Used to measure
  865                                    #   rate at which particles are received by
  866                                    #   a spacecraft as particles per solid
  867                                    #   angle per detector area per second. [18]
  868 pyron            cal_IT / cm^2 min # Measures heat flow from solar radiation,
  869                                    #   from Greek work "pyr" for fire.
  870 katal                   mol/sec    # Measure of the amount of a catalyst.  One
  871 kat                     katal      #   katal of catalyst enables the reaction
  872                                    #   to consume or produce on mol/sec.
  873 solarluminosity         382.8e24 W # A common yardstick for comparing the
  874                                    #   output of different stars.
  875                 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
  876 # at mean earth-sun distance
  877 solarirradiance		solarluminosity / (4 pi sundist^2)
  878 solarconstant		solarirradiance
  879 TSI			solarirradiance		# total solar irradiance
  880 
  881 #
  882 # time
  883 #
  884 
  885 sec                     s
  886 minute                  60 s
  887 min                     minute
  888 hour                    60 min
  889 hr                      hour
  890 day                     24 hr
  891 d                       day
  892 da                      day
  893 week                    7 day
  894 wk                      week
  895 sennight                7 day
  896 fortnight               14 day
  897 blink                   1e-5 day   # Actual human blink takes 1|3 second
  898 ce                      1e-2 day
  899 cron                    1e6 years
  900 watch                   4 hours    # time a sentry stands watch or a ship's
  901                                    # crew is on duty.
  902 bell                    1|8 watch  # Bell would be sounded every 30 minutes.
  903 
  904 # French Revolutionary Time or Decimal Time.  It was Proposed during
  905 # the French Revolution.  A few clocks were made, but it never caught
  906 # on.  In 1998 Swatch defined a time measurement called ".beat" and
  907 # sold some watches that displayed time in this unit.
  908 
  909 decimalhour             1|10 day            
  910 decimalminute           1|100 decimalhour   
  911 decimalsecond           1|100 decimalminute 
  912 beat                    decimalminute          # Swatch Internet Time
  913 
  914 #
  915 # angular measure
  916 #
  917 
  918 circle                  2 pi radian
  919 degree                  1|360 circle
  920 deg                     degree
  921 arcdeg                  degree
  922 arcmin                  1|60 degree
  923 arcminute               arcmin
  924 '                       arcmin
  925 arcsec                  1|60 arcmin
  926 arcsecond               arcsec
  927 "                       arcsec
  928 ''                      "
  929 rightangle              90 degrees
  930 quadrant                1|4 circle
  931 quintant                1|5 circle
  932 sextant                 1|6 circle
  933 
  934 sign                    1|12 circle # Angular extent of one sign of the zodiac
  935 turn                    circle
  936 revolution              turn
  937 rev                     turn
  938 pulsatance              radian / sec
  939 gon                     1|100 rightangle  # measure of grade
  940 grade                   gon
  941 centesimalminute        1|100 grade
  942 centesimalsecond        1|100 centesimalminute
  943 milangle                1|6400 circle     # Official NIST definition.
  944                                           # Another choice is 1e-3 radian.
  945 pointangle              1|32 circle  # Used for reporting compass readings
  946 centrad                 0.01 radian  # Used for angular deviation of light
  947                                      # through a prism.
  948 mas                     milli arcsec # Used by astronomers
  949 seclongitude            circle (seconds/day) # Astronomers measure longitude
  950                                      # (which they call right ascension) in
  951                                      # time units by dividing the equator into
  952                                      # 24 hours instead of 360 degrees.
  953 #
  954 # Some geometric formulas
  955 #
  956 
  957 circlearea(r)   units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
  958 spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
  959                                          cuberoot(spherevolume/4|3 pi)
  960 spherevol()     spherevolume
  961 square(x)       range=[0,)          x^2 ; sqrt(square)
  962 
  963 #
  964 # Solid angle measure
  965 #
  966 
  967 sphere                  4 pi sr
  968 squaredegree            1|180^2 pi^2 sr
  969 squareminute            1|60^2 squaredegree
  970 squaresecond            1|60^2 squareminute
  971 squarearcmin            squareminute
  972 squarearcsec            squaresecond
  973 sphericalrightangle     0.5 pi sr
  974 octant                  0.5 pi sr
  975 
  976 #
  977 # Concentration measures
  978 #
  979 
  980 percent                 0.01
  981 %                       percent
  982 mill                    0.001     # Originally established by Congress in 1791
  983                                   # as a unit of money equal to 0.001 dollars,
  984                                   # it has come to refer to 0.001 in general.
  985                                   # Used by some towns to set their property
  986                                   # tax rate, and written with a symbol similar
  987                                   # to the % symbol but with two 0's in the
  988                                   # denominator.  [18]
  989 proof                   1|200     # Alcohol content measured by volume at
  990                                   # 60 degrees Fahrenheit.  This is a USA
  991                                   # measure.  In Europe proof=percent.
  992 ppm                     1e-6
  993 partspermillion         ppm
  994 ppb                     1e-9
  995 partsperbillion         ppb       # USA billion
  996 ppt                     1e-12
  997 partspertrillion        ppt       # USA trillion
  998 karat                   1|24      # measure of gold purity
  999 caratgold               karat
 1000 gammil                  mg/l
 1001 basispoint              0.01 %    # Used in finance
 1002 fine                    1|1000    # Measure of gold purity
 1003 
 1004 # The pH scale is used to measure the concentration of hydronium (H3O+) ions in
 1005 # a solution.  A neutral solution has a pH of 7 as a result of dissociated
 1006 # water molecules.
 1007 
 1008 pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
 1009 
 1010 
 1011 #
 1012 # Temperature
 1013 #
 1014 # Two types of units are defined: units for converting temperature differences
 1015 # and functions for converting absolute temperatures.  Conversions for
 1016 # differences start with "deg" and conversions for absolute temperature start
 1017 # with "temp".
 1018 #
 1019 # If the temperature inside is 72 degrees Fahrenheit and you want to
 1020 # convert this to degrees Celsius then you need absolute temperature:
 1021 #
 1022 # You have: tempF(72)
 1023 # You want: tempC
 1024 #         22.222222
 1025 #
 1026 # If the temperature rose 72 degrees Fahrenheit during the chemical reaction
 1027 # then this is a temperature difference:
 1028 #
 1029 # You have: 72 degF
 1030 # You want: degC
 1031 #        * 40
 1032 #        / 0.025
 1033 #
 1034 
 1035 TEMPERATURE             kelvin
 1036 TEMPERATURE_DIFFERENCE  kelvin
 1037 
 1038 # In 1741 Anders Celsius introduced a temperature scale with water boiling at
 1039 # 0 degrees and freezing at 100 degrees at standard pressure. After his death
 1040 # the fixed points were reversed and the scale was called the centigrade
 1041 # scale.  Due to the difficulty of accurately measuring the temperature of
 1042 # melting ice at standard pressure, the centigrade scale was replaced in 1954
 1043 # by the Celsius scale which is defined by subtracting 273.15 from the
 1044 # temperature in Kelvins.  This definition differed slightly from the old
 1045 # centigrade definition, but the Kelvin scale depends on the triple point of
 1046 # water rather than a melting point, so it can be measured accurately.
 1047 
 1048 tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
 1049                              x K + stdtemp ; (tempC +(-stdtemp))/K
 1050 tempcelsius() tempC
 1051 degcelsius              K
 1052 degC                    K
 1053 
 1054 # Fahrenheit defined his temperature scale by setting 0 to the coldest
 1055 # temperature he could produce in his lab with a salt water solution and by
 1056 # setting 96 degrees to body heat.  In Fahrenheit's words:
 1057 #
 1058 #    Placing the thermometer in a mixture of sal ammoniac or sea
 1059 #    salt, ice, and water a point on the scale will be found which
 1060 #    is denoted as zero. A second point is obtained if the same
 1061 #    mixture is used without salt. Denote this position as 30. A
 1062 #    third point, designated as 96, is obtained if the thermometer
 1063 #    is placed in the mouth so as to acquire the heat of a healthy
 1064 #    man."  (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
 1065 
 1066 tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
 1067                 (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
 1068 tempfahrenheit() tempF
 1069 degfahrenheit           5|9 degC
 1070 degF                    5|9 degC
 1071 
 1072 
 1073 degreesrankine          degF              # The Rankine scale has the
 1074 degrankine              degreesrankine    # Fahrenheit degree, but its zero
 1075 degreerankine           degF              # is at absolute zero.
 1076 degR                    degrankine
 1077 tempR                   degrankine
 1078 temprankine             degrankine
 1079 
 1080 tempreaumur(x)    units=[1;K] domain=[-218.52,) range=[0,) \
 1081                   x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
 1082 degreaumur              10|8 degC # The Reaumur scale was used in Europe and
 1083                                   # particularly in France.  It is defined
 1084                                   # to be 0 at the freezing point of water
 1085                                   # and 80 at the boiling point.  Reaumur
 1086                                   # apparently selected 80 because it is
 1087                                   # divisible by many numbers.
 1088 
 1089 degK                    K         # "Degrees Kelvin" is forbidden usage.
 1090 tempK                   K         # For consistency
 1091 
 1092 # Gas mark is implemented below but in a terribly ugly way.  There is
 1093 # a simple formula, but it requires a conditional which is not
 1094 # presently supported.
 1095 #
 1096 # The formula to convert to degrees Fahrenheit is:
 1097 #
 1098 # 25 log2(gasmark) + k_f   gasmark<=1
 1099 # 25 (gasmark-1) + k_f     gasmark>=1
 1100 #
 1101 # k_f = 275
 1102 #
 1103 gasmark[degR] \
 1104   .0625    634.67 \
 1105   .125     659.67 \
 1106   .25      684.67 \
 1107   .5       709.67 \
 1108   1        734.67 \
 1109   2        759.67 \
 1110   3        784.67 \
 1111   4        809.67 \
 1112   5        834.67 \
 1113   6        859.67 \
 1114   7        884.67 \
 1115   8        909.67 \
 1116   9        934.67 \
 1117   10       959.67
 1118 
 1119 
 1120 # The Beaufort wind force scale was developed from 1805-1807 by Sir Francis
 1121 # Beaufort to categorize wind conditions at sea. It is normally defined from
 1122 # Beaufort 0, also called "Force 0," through Beaufort 12. Beaufort numbers
 1123 # 13-17 were later defined for tropical cyclones but are rarely used. The
 1124 # original Beaufort scale was qualitative and did not relate directly to wind
 1125 # speed. In 1906, George Simpson of the British Met Office fit wind-speed
 1126 # measurements to visual Beaufort estimates made from five coastal and inland
 1127 # stations in Britain. Simpson's formula was adopted by the World Meterological
 1128 # Organization in 1946 to produce a table, known as WMO Code 1100, giving mean
 1129 # (and min/max) wind speed equivalents at a height of 10 meters for each
 1130 # Beaufort number. This is the "operational" Beaufort scale that mariners
 1131 # use. Meterological and climatic researchers typically use a "scientific"
 1132 # Beaufort scale based on more recent and comprehensive fits. See Wallbrink and
 1133 # Cook, Historical Wind Speed Equivalents Of The Beaufort Scale, 1850-1950, at
 1134 # https://icoads.noaa.gov/reclaim/pdf/Hisklim13.pdf
 1135 #
 1136 beaufort_WMO1100(B) units=[1;m/s] domain=[0,17] range=[0,) \
 1137                     0.836 B^3|2 m/s; (beaufort_WMO1100 s / 0.836 m)^2|3
 1138 
 1139 beaufort(B) units=[1;m/s] domain=[0,17] range=[0,) \
 1140             beaufort_WMO1100(B); ~beaufort_WMO1100(beaufort)
 1141 
 1142 # Units cannot handle wind chill or heat index because they are two-variable
 1143 # functions, but they are included here for your edification.  Clearly these
 1144 # equations are the result of a model fitting operation.
 1145 #
 1146 # wind chill index (WCI) a measurement of the combined cooling effect of low
 1147 #      air temperature and wind on the human body. The index was first defined
 1148 #      by the American Antarctic explorer Paul Siple in 1939. As currently used
 1149 #      by U.S. meteorologists, the wind chill index is computed from the
 1150 #      temperature T (in °F) and wind speed V (in mi/hr) using the formula:
 1151 #          WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
 1152 #      For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
 1153 #      the air temperature, but for higher wind speeds it is lower than the air
 1154 #      temperature.
 1155 #
 1156 # heat index (HI or HX) a measure of the combined effect of heat and
 1157 #      humidity on the human body. U.S. meteorologists compute the index
 1158 #      from the temperature T (in °F) and the relative humidity H (as a
 1159 #      value from 0 to 1).
 1160 #        HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
 1161 #             - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
 1162 #             - 0.0199 T^2 H^2.
 1163 
 1164 #
 1165 # Physical constants
 1166 #
 1167 
 1168 # Basic constants
 1169 
 1170 pi                      3.14159265358979323846
 1171 light                   c
 1172 mu0_SI        2 alpha h_SI / e_SI^2 c_SI # Vacuum magnetic permeability
 1173 mu0                    2 alpha h / e^2 c #   Gets overridden in CGS modes
 1174 epsilon0_SI             1/mu0_SI c_SI^2  # Vacuum electric permittivity
 1175 epsilon0                1/mu0 c^2        #   Also overridden in CGS modes
 1176 Z0                      mu0 c            # Free space impedance
 1177 energy                  c^2              # Convert mass to energy
 1178 hbar                    h / 2 pi
 1179 hbar_SI                 h_SI / 2 pi
 1180 spin                    hbar
 1181 G_SI            6.67430e-11
 1182 G               6.67430e-11 N m^2 / kg^2 # Newtonian gravitational constant
 1183 coulombconst            1/4 pi epsilon0  # Listed as k or k_C sometimes
 1184 k_C                     coulombconst
 1185 
 1186 # Physico-chemical constants
 1187 
 1188 atomicmassunit_SI   1.66053906660e-27    # Unified atomic mass unit, defined as
 1189 atomicmassunit      1.66053906660e-27 kg # Unified atomic mass unit, defined as
 1190 u                       atomicmassunit   #   1|12 of the mass of carbon 12.
 1191 amu                     atomicmassunit   #   The relationship N_A u = 1 g/mol
 1192 dalton                  u                #   is approximately, but not exactly 
 1193 Da                      dalton           #   true (with the 2019 SI).
 1194                                          #   Previously the mole was defined to
 1195                                          #   make this relationship exact.
 1196 amu_chem                1.66026e-27 kg   # 1|16 of the weighted average mass of
 1197                                          #   the 3 naturally occuring neutral
 1198                                          #   isotopes of oxygen
 1199 amu_phys                1.65981e-27 kg   # 1|16 of the mass of a neutral
 1200                                          #   oxygen 16 atom
 1201 gasconstant             k N_A            # Molar gas constant (exact)
 1202 R                       gasconstant
 1203 kboltzmann              boltzmann
 1204 molarvolume         mol R stdtemp / atm  # Volume occupied by one mole of an
 1205                                          #   ideal gas at STP.
 1206 loschmidt     avogadro mol / molarvolume # Molecules per cubic meter of an
 1207                                          #   ideal gas at STP.  Loschmidt did
 1208                                          #   work similar to Avogadro.
 1209 molarvolume_si  N_A siliconlattice^3 / 8 # Volume of a mole of crystalline
 1210                                          #   silicon. The unit cell contains 8
 1211                                          #   silicon atoms and has a side
 1212                                          #   length of siliconlattice.
 1213 stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
 1214 sigma                   stefanboltzmann  #   blackbody at temperature T is
 1215                                          #   given by sigma T^4. (exact)
 1216 wiendisplacement     (h c/k)/4.9651142317442763  # Wien's Displacement Law gives
 1217                                          #   the frequency at which the the
 1218                                          #   Planck spectrum has maximum
 1219                                          #   intensity.  The relation is lambda
 1220                                          #   T = b where lambda is wavelength,
 1221                                          #   T is temperature and b is the Wien
 1222                                          #   displacement.  This relation is
 1223                                          #   used to determine the temperature
 1224                                          #   of stars.  The constant is the
 1225                                          #   solution to x=5(1-exp(-x)).
 1226                                          #   This expression has no experimental
 1227                                          #   error, and x is defined exactly
 1228                                          #   by the equation above, so it is
 1229                                          #   an exact definition.  
 1230 K_J90 483597.9 GHz/V    # Direct measurement of the volt is difficult.  Until
 1231 K_J   2e/h              #   recently, laboratories kept Weston cadmium cells as
 1232                         #   a reference, but they could drift.  In 1987 the
 1233                         #   CGPM officially recommended the use of the
 1234                         #   Josephson effect as a laboratory representation of
 1235                         #   the volt.  The Josephson effect occurs when two
 1236                         #   superconductors are separated by a thin insulating
 1237                         #   layer.  A "supercurrent" flows across the insulator
 1238                         #   with a frequency that depends on the potential
 1239                         #   applied across the superconductors.  This frequency
 1240                         #   can be very accurately measured.  The Josephson
 1241                         #   constant K_J relates the measured frequency to the
 1242                         #   potential.  Two values given, the conventional
 1243                         #   (exact) value from 1990, which was used until the
 1244                         #   2019 SI revision, and the current exact value.
 1245 R_K90 25812.807 ohm     # Measurement of the ohm also presents difficulties.
 1246 R_K   h/e^2             #   The old approach involved maintaining resistances
 1247                         #   that were subject to drift.  The new standard is
 1248                         #   based on the Hall effect.  When a current carrying
 1249                         #   ribbon is placed in a magnetic field, a potential
 1250                         #   difference develops across the ribbon.  The ratio
 1251                         #   of the potential difference to the current is
 1252                         #   called the Hall resistance.  Klaus von Klitzing
 1253                         #   discovered in 1980 that the Hall resistance varies
 1254                         #   in discrete jumps when the magnetic field is very
 1255                         #   large and the temperature very low.  This enables
 1256                         #   accurate realization of the resistance h/e^2 in the
 1257                         #   lab.  The 1990 value was an exact conventional 
 1258                         #   value used until the SI revision in 2019. This value
 1259                         #   did not agree with measurements.  The new value
 1260                         #   is exact.
 1261 
 1262 # The 2019 update to SI gives exact definitions for R_K and K_J.  Previously
 1263 # the electromagnetic units were realized using the 1990 conventional values
 1264 # for these constants, and as a result, the standard definitions were in some
 1265 # sense outside of SI.  The revision corrects this problem.  The definitions
 1266 # below give the 1990 conventional values for the electromagnetic units in
 1267 # terms of 2019 SI.  
 1268 
 1269 ampere90 (K_J90 R_K90 / K_J R_K) A
 1270 coulomb90 (K_J90 R_K90 / K_J R_K) C
 1271 farad90 (R_K90/R_K) F
 1272 henry90 (R_K/R_K90) H
 1273 ohm90 (R_K/R_K90) ohm
 1274 volt90 (K_J90/K_J) V
 1275 watt90 (K_J90^2 R_K90 / K_J^2 R_K) W
 1276 
 1277 # Various conventional values
 1278 
 1279 gravity                 9.80665 m/s^2    # std acceleration of gravity (exact)
 1280 force                   gravity          # use to turn masses into forces
 1281 atm                     101325 Pa        # Standard atmospheric pressure
 1282 atmosphere              atm
 1283 Hg             13.5951 gram force / cm^3 # Standard weight of mercury (exact)
 1284 water                   gram force/cm^3  # Standard weight of water (exact)
 1285 waterdensity            gram / cm^3      # Density of water
 1286 H2O                     water
 1287 wc                      water            # water column
 1288 mach                    331.46 m/s       # speed of sound in dry air at STP
 1289 standardtemp            273.15 K         # standard temperature
 1290 stdtemp                 standardtemp
 1291 normaltemp              tempF(70)        # for gas density, from NIST
 1292 normtemp                normaltemp       # Handbook 44
 1293 
 1294 # Weight of mercury and water at different temperatures using the standard
 1295 # force of gravity.
 1296 
 1297 Hg10C         13.5708 force gram / cm^3  # These units, when used to form
 1298 Hg20C         13.5462 force gram / cm^3  # pressure measures, are not accurate
 1299 Hg23C         13.5386 force gram / cm^3  # because of considerations of the
 1300 Hg30C         13.5217 force gram / cm^3  # revised practical temperature scale.
 1301 Hg40C         13.4973 force gram / cm^3
 1302 Hg60F         13.5574 force gram / cm^3
 1303 H2O0C         0.99987 force gram / cm^3
 1304 H2O5C         0.99999 force gram / cm^3
 1305 H2O10C        0.99973 force gram / cm^3
 1306 H2O15C        0.99913 force gram / cm^3
 1307 H2O18C        0.99862 force gram / cm^3
 1308 H2O20C        0.99823 force gram / cm^3
 1309 H2O25C        0.99707 force gram / cm^3
 1310 H2O50C        0.98807 force gram / cm^3
 1311 H2O100C       0.95838 force gram / cm^3
 1312 
 1313 # Atomic constants
 1314 
 1315 
 1316 
 1317 Rinfinity            m_e c alpha^2 / 2 h # The wavelengths of a spectral series
 1318 R_H                     10967760 /m      #   can be expressed as
 1319                                          #     1/lambda = R (1/m^2 - 1/n^2).
 1320                                          #   where R is a number that various
 1321                                          #   slightly from element to element.
 1322                                          #   For hydrogen, R_H is the value,
 1323                                          #   and for heavy elements, the value
 1324                                          #   approaches Rinfinity. 
 1325 alpha                    7.2973525693e-3 # The fine structure constant was
 1326                                          #   introduced to explain fine
 1327                                          #   structure visible in spectral
 1328                                          #   lines.  
 1329 bohrradius              alpha / 4 pi Rinfinity
 1330 prout                   185.5 keV        # nuclear binding energy equal to 1|12
 1331                                          #   binding energy of the deuteron
 1332 conductancequantum      2 e^2 / h
 1333 
 1334 
 1335 # Particle radius
 1336 
 1337 electronradius    coulombconst e^2 / electronmass c^2   # Classical
 1338 deuteronchargeradius    2.12799e-15 m
 1339 protonchargeradius      0.8751e-15 m
 1340 
 1341 # Masses of elementary particles
 1342 
 1343 electronmass_SI         electronmass_u atomicmassunit_SI
 1344 electronmass_u          5.48579909065e-4
 1345 electronmass            5.48579909065e-4 u
 1346 m_e                     electronmass
 1347 muonmass                0.1134289259 u
 1348 m_mu                    muonmass
 1349 taumass                 1.90754 u
 1350 m_tau                   taumass
 1351 protonmass              1.007276466621 u
 1352 m_p                     protonmass
 1353 neutronmass             1.00866491595 u
 1354 m_n                     neutronmass
 1355 deuteronmass            2.013553212745 u    # Nucleus of deuterium, one
 1356 m_d                     deuteronmass        #   proton and one neutron
 1357 alphaparticlemass       4.001506179127 u    # Nucleus of He, two protons
 1358 m_alpha                 alphaparticlemass   #   and two neutrons
 1359 tritonmass              3.01550071621 u     # Nucleius of H3, one proton
 1360 m_t                     tritonmass          #   and two neutrons
 1361 helionmass              3.014932247175 u    # Nucleus of He3, two protons
 1362 m_h                     helionmass          #   and one neutron
 1363 
 1364 # particle wavelengths: the compton wavelength of a particle is
 1365 # defined as h / m c where m is the mass of the particle.
 1366 
 1367 electronwavelength      h / m_e c
 1368 lambda_C                electronwavelength
 1369 protonwavelength        h / m_p c
 1370 lambda_C,p              protonwavelength
 1371 neutronwavelength       h / m_n c
 1372 lambda_C,n              neutronwavelength
 1373 muonwavelength          h / m_mu c
 1374 lambda_C,mu             muonwavelength
 1375 
 1376 # The g-factor or dimensionless magnetic moment is a quantity that
 1377 # characterizes the magnetic moment of a particle.  The electron g-factor is
 1378 # one of the most precisely measured values in physics, with a relative
 1379 # uncertainty of 1.7e-13.  
 1380 
 1381 g_d                     0.8574382338       # Deuteron g-factor
 1382 g_e                    -2.00231930436256   # Electron g-factor
 1383 g_h                    -4.255250615        # Helion g-factor
 1384 g_mu                   -2.0023318418       # Muon g-factor
 1385 g_n                    -3.82608545         # Neutron g-factor
 1386 g_p                     5.5856946893       # Proton g-factor
 1387 g_t                     5.957924931        # Triton g-factor
 1388 
 1389 fermicoupling           1.1663787e-5 / GeV^2
 1390 
 1391 # Magnetic moments (derived from the more accurate g-factors)
 1392 #
 1393 # The magnetic moment is g * mu_ref * spin where in most cases
 1394 # the reference is the nuclear magneton, and all of the particles
 1395 # except the deuteron have spin 1/2.  
 1396 
 1397 bohrmagneton            e hbar / 2 electronmass  # Reference magnetic moment for
 1398 mu_B                    bohrmagneton             #   the electron
 1399 nuclearmagneton         e hbar /  2 protonmass   # Convenient reference magnetic
 1400 mu_N                    nuclearmagneton          #   moment for heavy particles
 1401 mu_e                    g_e mu_B / 2             # Electron spin magnet moment
 1402 mu_mu                   g_mu e hbar / 4 muonmass # Muon spin magnetic moment
 1403 mu_p                    g_p mu_N / 2             # Proton magnetic moment
 1404 mu_n                    g_n mu_N / 2             # Neutron magnetic moment
 1405 mu_t                    g_t mu_N / 2             # Triton magnetic moment
 1406 mu_d                    g_d mu_N            # Deuteron magnetic moment, spin 1
 1407 mu_h                    g_h mu_N / 2             # Helion magnetic moment
 1408 
 1409 #
 1410 # Units derived from physical constants
 1411 #
 1412 
 1413 kgf                     kg force
 1414 technicalatmosphere     kgf / cm^2
 1415 at                      technicalatmosphere
 1416 hyl                     kgf s^2 / m   # Also gram-force s^2/m according to [15]
 1417 mmHg                    mm Hg
 1418 torr                    atm / 760  # The torr, named after Evangelista
 1419                                    # Torricelli, and is very close to the mm Hg
 1420 tor                     Pa         # Suggested in 1913 but seldom used [24].
 1421                                    # Eventually renamed the Pascal.  Don't 
 1422                                    # confuse the tor with the torr.  
 1423 inHg                    inch Hg    
 1424 inH2O                   inch water
 1425 mmH2O                   mm water
 1426 eV                      e V      # Energy acquired by a particle with charge e
 1427 electronvolt            eV       #   when it is accelerated through 1 V
 1428 lightyear               c julianyear # The 365.25 day year is specified in
 1429 ly                      lightyear    # NIST publication 811
 1430 lightsecond             c s
 1431 lightminute             c min
 1432 parsec                  au / tan(arcsec)    # Unit of length equal to distance
 1433 pc                      parsec              #   from the sun to a point having
 1434                                             #   heliocentric parallax of 1
 1435                                             #   arcsec (derived from parallax
 1436                                             #   second).  A distant object with
 1437                                             #   parallax theta will be about
 1438                                             #   (arcsec/theta) parsecs from the
 1439                                             #   sun (using the approximation
 1440                                             #   that tan(theta) = theta).
 1441 rydberg                 h c Rinfinity       # Rydberg energy
 1442 crith                   0.089885 gram       # The crith is the mass of one
 1443                                             #   liter of hydrogen at standard
 1444                                             #   temperature and pressure.
 1445 amagatvolume            molarvolume
 1446 amagat                  mol/amagatvolume    # Used to measure gas densities
 1447 lorentz                 bohrmagneton / h c  # Used to measure the extent
 1448                                             #   that the frequency of light
 1449                                             #   is shifted by a magnetic field.
 1450 cminv                   h c / cm            # Unit of energy used in infrared
 1451 invcm                   cminv               #   spectroscopy.
 1452 wavenumber              cminv
 1453 kcal_mol                kcal_th / mol N_A   # kcal/mol is used as a unit of
 1454                                             #   energy by physical chemists.
 1455 #
 1456 # CGS system based on centimeter, gram and second
 1457 #
 1458 
 1459 dyne                    cm gram / s^2   # force
 1460 dyn                     dyne
 1461 erg                     cm dyne         # energy
 1462 poise                   gram / cm s     # viscosity, honors Jean Poiseuille
 1463 P                       poise
 1464 rhe                     /poise          # reciprocal viscosity
 1465 stokes                  cm^2 / s        # kinematic viscosity
 1466 St                      stokes
 1467 stoke                   stokes
 1468 lentor                  stokes          # old name
 1469 Gal                     cm / s^2        # acceleration, used in geophysics
 1470 galileo                 Gal             # for earth's gravitational field
 1471                                         # (note that "gal" is for gallon
 1472                                         # but "Gal" is the standard symbol
 1473                                         # for the gal which is evidently a
 1474                                         # shortened form of "galileo".)
 1475 barye                   dyne/cm^2       # pressure
 1476 barad                   barye           # old name
 1477 kayser                  1/cm            # Proposed as a unit for wavenumber
 1478 balmer                  kayser          # Even less common name than "kayser"
 1479 kine                    cm/s            # velocity
 1480 bole                    g cm / s        # momentum
 1481 pond                    gram force
 1482 glug                gram force s^2 / cm # Mass which is accelerated at
 1483                                         #   1 cm/s^2 by 1 gram force
 1484 darcy           centipoise cm^2 / s atm # Measures permeability to fluid flow.
 1485                                         #   One darcy is the permeability of a
 1486                                         #   medium that allows a flow of cc/s
 1487                                         #   of a liquid of centipoise viscosity
 1488                                         #   under a pressure gradient of
 1489                                         #   atm/cm.  Named for H. Darcy.
 1490 mobileohm               cm / dyn s      # mobile ohm, measure of mechanical
 1491                                         #   mobility
 1492 mechanicalohm           dyn s / cm      # mechanical resistance
 1493 acousticalohm           dyn s / cm^5    # ratio of the sound pressure of
 1494                                         #   1 dyn/cm^2 to a source of strength
 1495                                         #   1 cm^3/s
 1496 ray                     acousticalohm
 1497 rayl                    dyn s / cm^3    # Specific acoustical resistance
 1498 eotvos                  1e-9 Gal/cm     # Change in gravitational acceleration
 1499                                         #   over horizontal distance
 1500 #
 1501 # Electromagnetic CGS Units
 1502 # 
 1503 # For measuring electromagnetic quantities in SI, we introduce the new base
 1504 # dimension of current, define the ampere to measure current, and derive the
 1505 # other electromagnetic units from the ampere.  With the CGS units one approach
 1506 # is to use the basic equations of electromagnetism to define units that
 1507 # eliminate constants from those equations.  Coulomb's law has the form
 1508 #
 1509 #          F = k_C q1 q2 / r^2
 1510 #
 1511 # where k_C is the Coulomb constant equal to 1|4 pi epsilon0 in SI units.
 1512 # Ampere's force law takes the form
 1513 #
 1514 #          dF/dl = 2 k_A I1 I2 / r
 1515 #
 1516 # where k_A is the ampere constant.  In the CGS system we force either k_C or
 1517 # k_A to 1 which then defines either a unit for charge or a unit for current.
 1518 # The other unit then becomes a derived unit.  When k_C is 1 the ESU system
 1519 # results.  When k_A is 1 the EMU system results.  Note that these parameters
 1520 # are not independent of each other: Maxwell's equations indicate that
 1521 #         
 1522 #           k_C / k_A = c^2
 1523 #
 1524 # where c is the speed of light. 
 1525 #
 1526 # One more choice is needed to define a complete system.  Using Coulomb's law
 1527 # we define the electric field as the force per unit charge
 1528 #
 1529 #           E = k_C 1 / r^2.
 1530 #
 1531 # But what about the magnetic field?  It is derived from Ampere's law but we
 1532 # have the option of adding a proportionality constant, k_B, that may have
 1533 # dimensions:
 1534 #
 1535 #           B = 2 k_A k_B I / r
 1536 #
 1537 # We can choose k_B = 1, which is done in the SI, ESU and EMU systems.  But if
 1538 # instead we give k_B units of length/time then the magnetic field has
 1539 # the same units as the electric field.  This choice leads to the Gaussian
 1540 # and Heaviside-Lorentz systems.
 1541 #
 1542 # The relations above are used to determine the dimensions, but the units are
 1543 # derived from the base units of CGS, not directly from those formulas.  We
 1544 # will use the notation [unit] to refer to the dimension of the unit in
 1545 # brackets.  This same process gives rise to the SI units such as the tesla, 
 1546 # which is defined by
 1547 #
 1548 #         [tesla] = [2 (1/4 pi c^2 epsilon0) amp / m] = [(mu0 / 2) amp / m]
 1549 #
 1550 # which gives kg / A s^2 as expected.  
 1551 #
 1552 # References:
 1553 #
 1554 # Classical Electrodynamics by John David Jackson, 3rd edition. 
 1555 # Cardarelli, Francois. 1999.  Scientific Unit Conversion. 2nd ed.  Trans.
 1556 #     M.J.  Shields.  London: Springer-Verlag. ISBN 1-85233-043-0
 1557 #
 1558 #
 1559 # All of the CGS systems result in electromagnetic units that involve the square
 1560 # roots of the centimeter and gram.  This requires a change in the primitive
 1561 # units.
 1562 # 
 1563 
 1564 !var UNITS_SYSTEM esu emu gaussian gauss hlu
 1565 sqrt_cm                 ! 
 1566 sqrt_centimeter         sqrt_cm
 1567 +m                      100 sqrt_cm^2
 1568 sqrt_g                  !
 1569 sqrt_gram               sqrt_g
 1570 +kg                     kilo sqrt_g^2
 1571 !endvar
 1572 
 1573 # Electrostatic CGS (ESU)
 1574 #
 1575 # This system uses the statcoulomb as the fundamental unit of charge, with
 1576 # derived units that parallel the conventional terminology but use the stat-
 1577 # prefix.  The statcoulomb is designed by setting k_C=1, which means
 1578 #
 1579 #                      dyne = statcoulomb^2 / cm^2. 
 1580 #
 1581 # The statcoulomb is also called the franklin or esu.
 1582 #
 1583 # The ESU system was specified by a committee report in 1873 and rarely used.
 1584 
 1585 statcoulomb             10 coulomb cm / s c   # Charge such that two charges 
 1586 esu                     statcoulomb           # of 1 statC separated by 1 cm
 1587 statcoul                statcoulomb           # exert a force of 1 dyne
 1588 statC                   statcoulomb
 1589 stC                     statcoulomb
 1590 franklin                statcoulomb
 1591 Fr                      franklin
 1592 
 1593 !var UNITS_SYSTEM esu
 1594 !message CGS-ESU units selected
 1595 !prompt (ESU)
 1596 +statcoulomb            sqrt(dyne) cm
 1597 +A                      10 c_SI statamp
 1598 +mu0                    1/c^2
 1599 +coulombconst           1
 1600 !endvar
 1601 
 1602 statampere              statcoulomb / s
 1603 statamp                 statampere
 1604 statA                   statampere
 1605 stA                     statampere
 1606 statvolt                dyne cm / statamp sec
 1607 statV                   statvolt
 1608 stV                     statvolt
 1609 statfarad               statamp sec / statvolt
 1610 statF                   statfarad
 1611 stF                     statfarad
 1612 cmcapacitance           statfarad
 1613 stathenry               statvolt sec / statamp
 1614 statH                   stathenry
 1615 stH                     stathenry
 1616 statohm                 statvolt / statamp
 1617 stohm                   statohm
 1618 statmho                 /statohm
 1619 stmho                   statmho
 1620 statweber               statvolt sec
 1621 statWb                  statweber
 1622 stWb                    statweber
 1623 stattesla               statWb/cm^2   # Defined by analogy with SI; rarely
 1624 statT                   stattesla     #   if ever used
 1625 stT                     stattesla
 1626 debye                   1e-10 statC angstrom # unit of electrical dipole moment
 1627 helmholtz               debye/angstrom^2     # Dipole moment per area
 1628 jar                     1000 statfarad       # approx capacitance of Leyden jar
 1629 
 1630 # Electromagnetic CGS (EMU)
 1631 #
 1632 # The abampere is the fundamental unit of this system, with the derived units
 1633 # using the ab- prefix.  The dimensions of the abampere are defined by assuming
 1634 # that k_A=1, which 
 1635 #
 1636 #            [dyne / cm]  = [2 abampere^2 / cm]
 1637 #
 1638 # where the brackets indicate taking the dimension of the unit in base units
 1639 # and discarding any constant factors.  This results in the definition from
 1640 # base CGS units of:
 1641 #
 1642 #            abampere = sqrt(dyne). 
 1643 #
 1644 # The abampere is also called the biot.  The magnetic field unit (the gauss)
 1645 # follows from the assumption that k_B=1, which means
 1646 #
 1647 #            B = 2 I / r,
 1648 #
 1649 # and hence the dimensions of the gauss are given by
 1650 #
 1651 #            [gauss] = [2 abampere / cm]
 1652 #
 1653 # or rewriting in terms of the base units
 1654 #
 1655 #            gauss = abampere / cm.
 1656 #
 1657 # The definition given below is different because it is in a form that
 1658 # gives a valid reduction for SI and ESU and still gives the correct 
 1659 # result in EMU.  (It can be derived from Faraday's law.)  
 1660 #
 1661 # The EMU system was developed by Gauss and Weber and formalized as a system in
 1662 # a committee report by the British Association for the Advancement of Science
 1663 # in 1873.  
 1664 
 1665 abampere                10 A            # Current which produces a force of
 1666 abamp                   abampere        #   2 dyne/cm between two infinitely
 1667 aA                      abampere        #   long wires that are 1 cm apart
 1668 abA                     abampere
 1669 biot                    abampere
 1670 Bi                      biot
 1671 
 1672 !var UNITS_SYSTEM emu
 1673 !message CGS-EMU units selected
 1674 !prompt (EMU)
 1675 +abampere               sqrt(dyne)
 1676 +A                      0.1 abamp
 1677 +mu0                    1
 1678 +coulombconst           c^2
 1679 !endvar
 1680 
 1681 abcoulomb               abamp sec
 1682 abcoul                  abcoulomb
 1683 abC                     abcoulomb
 1684 abfarad                 abampere sec / abvolt
 1685 abF                     abfarad
 1686 abhenry                 abvolt sec / abamp
 1687 abH                     abhenry
 1688 abvolt                  dyne cm  / abamp sec
 1689 abV                     abvolt
 1690 abohm                   abvolt / abamp
 1691 abmho                   /abohm
 1692 gauss                   abvolt sec / cm^2 # The magnetic field 2 cm from a wire
 1693 Gs                      gauss             # carrying a current of 1 abampere
 1694 maxwell                 gauss cm^2        # Also called the "line"
 1695 Mx                      maxwell
 1696 oersted                 gauss / mu0   # From the relation H = B / mu
 1697 Oe                      oersted      
 1698 gilbert                 gauss cm / mu0
 1699 Gb                      gilbert
 1700 Gi                      gilbert
 1701 unitpole                4 pi maxwell	# unit magnetic pole
 1702 emu                     erg/gauss  # "electro-magnetic unit", a measure of
 1703                                    # magnetic moment, often used as emu/cm^3
 1704                                    # to specify magnetic moment density.
 1705 
 1706 # Electromagnetic CGS (Gaussian)
 1707 #
 1708 # The Gaussian system uses the statcoulomb and statamp from the ESU system
 1709 # derived by setting k_C=1, but it defines the magnetic field unit differently
 1710 # by taking k_B=c instead of k_B=1.  As noted above, k_C and k_A are not
 1711 # independent.  With k_C=1 we must have k_A=c^-2.  This results in the magnetic
 1712 # field unit, the gauss, having dimensions give by:
 1713 #
 1714 #         [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm]
 1715 #
 1716 # We then define the gauss using base CGS units to obtain
 1717 #
 1718 #         gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2.
 1719 #
 1720 # Note that this definition happens to give the same result as the definition
 1721 # for the EMU system, so the definitions of the gauss are consistent.
 1722 #
 1723 # This definition gives the same dimensions for the E and B fields and was also
 1724 # known as the "symmetric system".  This system was proposed by Hertz in 1888.
 1725 
 1726 !var UNITS_SYSTEM gaussian gauss
 1727 !message CGS-Gaussian units selected
 1728 !prompt (Gaussian)
 1729 !endvar
 1730 !var UNITS_SYSTEM gaussian gauss natural-gauss 
 1731 +statcoulomb            sqrt(dyne) cm
 1732 +A                      10 c_SI statamp
 1733 +mu0                    1
 1734 +epsilon0               1
 1735 +coulombconst           1                  # The gauss is the B field produced
 1736 +gauss                  statcoulomb / cm^2 # 1 cm from a wire carrying a current
 1737 +weber                  1e8 maxwell        # of 0.5*(c/(cm/s)) stA = 1.5e10 stA
 1738 +bohrmagneton           e hbar / 2 electronmass c
 1739 +nuclearmagneton        e hbar / 2 protonmass c
 1740 !endvar
 1741 
 1742 # Electromagnetic CGS (Heaviside-Lorentz)
 1743 
 1744 # The Heaviside-Lorentz system is similar to the Gaussian system, but it is
 1745 # "rationalized" so that factors of 4 pi do not appear in Maxwell's equations.
 1746 # The SI system is similarly rationalized, but the other CGS systems are not.
 1747 #
 1748 # The factor of 4 pi appears instead in Coulomb's law, so in this system
 1749 # k_C = 1 / 4 pi, which means the charge unit is defined by
 1750 #
 1751 #                      dyne = (1 / 4 pi) hlu_charge^2 / cm^2.
 1752 # 
 1753 # Since we have the leading constant of (1 / 4pi) the numerical value of the
 1754 # charge number is larger by sqrt(4pi), which in turns means that the HLU
 1755 # charge unit is smaller by this multiple.  But note that the dimensions of the
 1756 # charge unit are the same as the Gaussian system, so both systems measure
 1757 # charge with cm^(3/2) g^(1/2) / s, but the amount of charge for this dimension
 1758 # differs by a factor of sqrt(4pi) between the two systems.
 1759 #
 1760 # Ampere's law for the Heaviside-Lorentz system has the form
 1761 #
 1762 #                B = 1/(2 pi c) * I/r
 1763 
 1764 # The Heaviside-Lorentz system does not appear to have any named units, so we
 1765 # use "hlu" for "Heaviside-Lorentz unit" so we can define values for the basic
 1766 # units in this system.
 1767 
 1768 hlu_charge    statcoulomb / sqrt(4 pi) 
 1769 hlu_current   hlu_charge / sec
 1770 hlu_volt      erg / hlu_charge
 1771 hlu_efield    hlu_volt / cm
 1772 hlu_bfield    sqrt(4 pi) gauss
 1773 
 1774 !var UNITS_SYSTEM hlu
 1775 !message CGS-Heaviside-Lorentz Units selected
 1776 !prompt (HLU)
 1777 !endvar
 1778 !var UNITS_SYSTEM hlu natural planck planck-red
 1779 +statcoulomb            sqrt(dyne) cm sqrt(4 pi)
 1780 +A                      10 c_SI statamp 
 1781 +mu0                    1
 1782 +epsilon0               1
 1783                    # The gauss is the B field produced 1 cm from a wire carrying
 1784                    # a current of 0.5*(c/(cm/s)) stA, derived from Ampere's law
 1785 +gauss                  (1/2 pi c) (0.5 c/(cm/s)) statamp / cm
 1786 +weber                  1e8 maxwell
 1787 +bohrmagneton           e hbar / 2 electronmass c
 1788 +nuclearmagneton        e hbar / 2 protonmass c
 1789 !endvar
 1790 
 1791 # "Natural units" (high energy physics and cosmology)
 1792 #
 1793 # In particle physics "natural units" (which don't seem to have a more specific
 1794 # name) are defined by setting hbar = c = boltzmann = 1.  In this system the
 1795 # electron volt is the only base unit.  The electromagnetic units can be 
 1796 # derived from the rationalized Heaviside-Lorentz units or from Gaussian units.
 1797 # The default form is the rationalized HLU derived version.  
 1798 
 1799 # These are the Heaviside-Lorentz natural units
 1800 
 1801 natural_length          hbar c / eV
 1802 natural_mass            eV / c^2
 1803 natural_time            hbar / eV
 1804 natural_temp            eV / boltzmann
 1805 natural_charge          e / sqrt(4 pi alpha)
 1806 natural_current         natural_charge / natural_time
 1807 natural_force           natural_mass natural_length / natural_time^2
 1808 natural_energy          natural_force natural_length
 1809 natural_power           natural_energy / natural_time
 1810 natural_volt            natural_energy / natural_charge
 1811 natural_Efield          natural_volt / natural_length
 1812 natural_Bfield          natural_volt natural_time / natural_length^2
 1813 
 1814 !var UNITS_SYSTEM natural
 1815 !message Natural units selected (Heaviside-Lorentz based)
 1816 !prompt (natural)
 1817 +eV                     !
 1818 +h                      2 pi
 1819 +c                      1
 1820 +boltzmann              1
 1821 +m                      e_SI / hbar_SI c_SI eV
 1822 +kg                     (c_SI^2 / e_SI) eV
 1823 +s                      e_SI / hbar_SI eV
 1824 +K                      (k_SI / e_SI) eV
 1825 !endvar
 1826 
 1827 !var UNITS_SYSTEM natural-gauss
 1828 !message Natural units selected (Gaussian based)
 1829 !prompt (natgauss)
 1830 +eV                     !
 1831 +h                      2 pi
 1832 +c                      1
 1833 +boltzmann              1
 1834 +m                      e_SI / (h_SI / 2 pi) c_SI eV
 1835 +kg                     (c_SI^2 / e_SI) eV
 1836 +s                      e_SI / (h_SI / 2 pi) eV
 1837 +K                      (k_SI / e_SI) eV
 1838 !endvar
 1839 
 1840 #
 1841 # Planck units
 1842 #
 1843 # Planck units are a set of "natural" units based on physical constants c, G,
 1844 # hbar, boltzmann's constant, and epsilon0, often used when working with
 1845 # gravitational theory.  In planck units, all quantities are dimensionless.
 1846 # Some variations are possible for exactly how the units are defined.  We
 1847 # provide two variations, the rationalized planck units and the
 1848 # rationalized-reduced planck units.
 1849 #
 1850 # In both forms the units are defined by c = hbar = boltzmann = 1. 
 1851 # But the choice of rationalized and reduced affects how epsilon0 and G
 1852 # are treated.  
 1853 #
 1854 # In the "rationalized" units, factors of 4 pi do not appear in Maxwell's 
 1855 # equation, and Coulomb's law bears a factor of 1/4 pi.  See the section on
 1856 # the Heaviside-Lorentz units for more about this.  The choice of rationalized 
 1857 # units means that epsilon0 = 1.  (In the unrationalized case, which is not
 1858 # supported, 1/(4 pi epsilon0) = 1.)  
 1859 #
 1860 # The "reduced" units similarly are defined to eliminate factors of 8 pi
 1861 # from the Einstein field equations for gravitation.  With reduced units
 1862 # we set 8 pi G = 1 and with the unreduced units, simply G = 1.
 1863 
 1864 # Rationalized, unreduced planck units
 1865 
 1866 planckmass              sqrt(hbar c / G)
 1867 m_P                     planckmass
 1868 plancktime              hbar / planckmass c^2
 1869 t_P                     plancktime
 1870 plancklength            plancktime c
 1871 l_P                     plancklength
 1872 plancktemperature       hbar / k plancktime
 1873 T_P                     plancktemperature
 1874 planckenergy            planckmass plancklength^2 / plancktime^2
 1875 E_P                     planckenergy
 1876 planckcharge            sqrt(epsilon0 hbar c)
 1877 planckcurrent           planckcharge / plancktime
 1878 planckvolt              planckenergy / planckcharge
 1879 planckEfield            planckvolt / plancklength
 1880 planckBfield            planckvolt plancktime / plancklength^2
 1881 
 1882 # Rationalized, reduced planck units
 1883 
 1884 planckmass_red          sqrt(hbar c / 8 pi G)
 1885 plancktime_red          hbar / planckmass_red c^2
 1886 plancklength_red        plancktime_red c
 1887 plancktemperature_red   hbar / k plancktime_red
 1888 planckenergy_red        planckmass_red plancklength_red^2 / plancktime_red^2
 1889 planckcharge_red        sqrt(epsilon0 hbar c)
 1890 planckcurrent_red       planckcharge_red / plancktime_red
 1891 planckvolt_red          planckenergy_red / planckcharge_red
 1892 planckEfield_red        planckvolt_red / plancklength_red
 1893 planckBfield_red        planckvolt_red plancktime_red / plancklength_red^2
 1894 
 1895 
 1896 !var UNITS_SYSTEM planck
 1897 !message Planck units selected
 1898 !prompt (planck)
 1899 +c 1
 1900 +h 2 pi
 1901 +G 1
 1902 +boltzmann 1
 1903 +kg sqrt(G_SI / hbar_SI c_SI)
 1904 +s  c_SI^2 / hbar_SI kg 
 1905 +m  s / c_SI            
 1906 +K  k_SI / hbar_SI s    
 1907 !endvar
 1908 
 1909 
 1910 !var UNITS_SYSTEM planck-red
 1911 !message Reduced planck units selected
 1912 !prompt (planck reduced)
 1913 +c 1
 1914 +h 2 pi
 1915 +G 1/8 pi
 1916 +boltzmann 1
 1917 +kg sqrt(8 pi G_SI / hbar_SI c_SI)
 1918 +s  c_SI^2 / hbar_SI kg
 1919 +m  s / c_SI           
 1920 +K  k_SI / hbar_SI s   
 1921 !endvar
 1922 
 1923 #
 1924 # Some historical electromagnetic units
 1925 #
 1926 
 1927 intampere               0.999835 A    # Defined as the current which in one
 1928 intamp                  intampere     #   second deposits .001118 gram of
 1929                                       #   silver from an aqueous solution of
 1930                                       #   silver nitrate.
 1931 intfarad                0.999505 F
 1932 intvolt                 1.00033 V
 1933 intohm                  1.000495 ohm  # Defined as the resistance of a
 1934                                       #   uniform column of mercury containing
 1935                                       #   14.4521 gram in a column 1.063 m
 1936                                       #   long and maintained at 0 degC.
 1937 daniell                 1.042 V       # Meant to be electromotive force of a
 1938                                       #   Daniell cell, but in error by .04 V
 1939 faraday                 N_A e mol     # Charge that must flow to deposit or
 1940 faraday_phys            96521.9 C     #   liberate one gram equivalent of any
 1941 faraday_chem            96495.7 C     #   element.  (The chemical and physical
 1942                                       #   values are off slightly from what is
 1943                                       #   obtained by multiplying by amu_chem
 1944                                       #   or amu_phys.  These values are from
 1945                                       #   a 1991 NIST publication.)  Note that
 1946                                       #   there is a Faraday constant which is
 1947                                       #   equal to N_A e and hence has units of
 1948                                       #   C/mol.
 1949 kappline                6000 maxwell  # Named by and for Gisbert Kapp
 1950 siemensunit             0.9534 ohm    # Resistance of a meter long column of
 1951                                       #   mercury with a 1 mm cross section.
 1952 #
 1953 # Printed circuit board units.  
 1954 #
 1955 # http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm.  
 1956 #
 1957 # Conductivity is often expressed as a percentage of IACS.  A copper wire a
 1958 # meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at 
 1959 # 20 deg C.  Copper density also has a standard IACS value at that temperature.
 1960 #
 1961 
 1962 copperconductivity      58 siemens m / mm^2     # A wire a meter long with
 1963 IACS                    copperconductivity      #   a 1 mm^2 cross section
 1964 copperdensity           8.89 g/cm^3             # The "ounce" measures the     
 1965 ouncecopper             oz / ft^2 copperdensity #   thickness of copper used   
 1966 ozcu                    ouncecopper             #   in circuitboard fabrication
 1967                                                 
 1968 #
 1969 # Photometric units
 1970 #
 1971 
 1972 LUMINOUS_INTENSITY      candela
 1973 LUMINOUS_FLUX           lumen
 1974 LUMINOUS_ENERGY         talbot
 1975 ILLUMINANCE             lux
 1976 EXITANCE                lux
 1977 
 1978 candle                  1.02 candela  # Standard unit for luminous intensity
 1979 hefnerunit              0.9 candle    #   in use before candela
 1980 hefnercandle            hefnerunit    #
 1981 violle                  20.17 cd      # luminous intensity of 1 cm^2 of
 1982                                       #   platinum at its temperature of
 1983                                       #   solidification (2045 K)
 1984 
 1985 lumen                   cd sr         # Luminous flux (luminous energy per
 1986 lm                      lumen         #    time unit)
 1987 
 1988 talbot                  lumen s       # Luminous energy
 1989 lumberg                 talbot        # References give these values for
 1990 lumerg                  talbot        #    lumerg and lumberg both.  Note that
 1991                                       #    a paper from 1948 suggests that
 1992                                       #    lumerg should be 1e-7 talbots so
 1993                                       #    that lumergs/erg = talbots/joule.
 1994                                       #    lumerg = luminous erg
 1995 lux                     lm/m^2        # Illuminance or exitance (luminous
 1996 lx                      lux           #   flux incident on or coming from
 1997 phot                    lumen / cm^2  #   a surface)
 1998 ph                      phot          #
 1999 footcandle              lumen/ft^2    # Illuminance from a 1 candela source
 2000                                       #    at a distance of one foot
 2001 metercandle             lumen/m^2     # Illuminance from a 1 candela source
 2002                                       #    at a distance of one meter
 2003 
 2004 mcs                     metercandle s # luminous energy per area, used to
 2005                                       #    measure photographic exposure
 2006 
 2007 nox                     1e-3 lux      # These two units were proposed for
 2008 skot                    1e-3 apostilb # measurements relating to dark adapted
 2009                                       # eyes.
 2010 # Luminance measures
 2011 
 2012 LUMINANCE               nit
 2013 
 2014 nit                     cd/m^2        # Luminance: the intensity per projected
 2015 stilb                   cd / cm^2     # area of an extended luminous source.
 2016 sb                      stilb         # (nit is from latin nitere = to shine.)
 2017 
 2018 apostilb                cd/pi m^2
 2019 asb                     apostilb
 2020 blondel                 apostilb      # Named after a French scientist.
 2021 
 2022 # Equivalent luminance measures.  These units are units which measure
 2023 # the luminance of a surface with a specified exitance which obeys
 2024 # Lambert's law.  (Lambert's law specifies that luminous intensity of
 2025 # a perfectly diffuse luminous surface is proportional to the cosine
 2026 # of the angle at which you view the luminous surface.)
 2027 
 2028 equivalentlux           cd / pi m^2   # luminance of a 1 lux surface
 2029 equivalentphot          cd / pi cm^2  # luminance of a 1 phot surface
 2030 lambert                 cd / pi cm^2
 2031 footlambert             cd / pi ft^2
 2032 
 2033 # The bril is used to express "brilliance" of a source of light on a
 2034 # logarithmic scale to correspond to subjective perception.  An increase of 1
 2035 # bril means doubling the luminance.  A luminance of 1 lambert is defined to
 2036 # have a brilliance of 1 bril.
 2037 
 2038 bril(x) units=[1;lambert]  2^(x+-100) lamberts ;log2(bril/lambert)+100
 2039 
 2040 # Some luminance data from the IES Lighting Handbook, 8th ed, 1993
 2041 
 2042 sunlum                  1.6e9 cd/m^2  # at zenith
 2043 sunillum                100e3 lux     # clear sky
 2044 sunillum_o              10e3 lux      # overcast sky
 2045 sunlum_h                6e6 cd/m^2    # value at horizon
 2046 skylum                  8000 cd/m^2   # average, clear sky
 2047 skylum_o                2000 cd/m^2   # average, overcast sky
 2048 moonlum                 2500 cd/m^2
 2049 
 2050 #
 2051 # Photographic Exposure Value
 2052 # This section by Jeff Conrad (jeff_conrad@msn.com)
 2053 #
 2054 # The Additive system of Photographic EXposure (APEX) proposed in ASA
 2055 # PH2.5-1960 was an attempt to simplify exposure determination for people who
 2056 # relied on exposure tables rather than exposure meters.  Shortly thereafter,
 2057 # nearly all cameras incorporated exposure meters, so the APEX system never
 2058 # caught on, but the concept of exposure value remains in use.  Though given as
 2059 # 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'.  EV is
 2060 # related to exposure parameters by
 2061 #
 2062 #            A^2   LS   ES
 2063 #     2^EV = --- = -- = --
 2064 #             t    K    C
 2065 #
 2066 # Where
 2067 #     A = Relative aperture (f-number)
 2068 #     t = Exposure time in seconds
 2069 #     L = Scene luminance in cd/m2
 2070 #     E = Scene illuminance in lux
 2071 #     S = Arithmetic ISO speed
 2072 #     K = Reflected-light meter calibration constant
 2073 #     C = Incident-light meter calibration constant
 2074 #
 2075 # Strictly, an exposure value is a combination of aperture and exposure time,
 2076 # but it's also commonly used to indicate luminance (or illuminance).
 2077 # Conversion to luminance or illuminance units depends on the ISO speed and the
 2078 # meter calibration constant.  Common practice is to use an ISO speed of 100.
 2079 # Calibration constants vary among camera and meter manufacturers: Canon,
 2080 # Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
 2081 # Kenko (formerly Minolta) and Pentax use a value of 14.  Kenko and Sekonic use
 2082 # a value of 250 for incident-light meters with flat receptors.
 2083 #
 2084 # The values for in-camera meters apply only averaging, weighted-averaging, or
 2085 # spot metering--the multi-segment metering incorporated in most current
 2086 # cameras uses proprietary algorithms that evaluate many factors related to the
 2087 # luminance distribution of what is being metered; they are not amenable to
 2088 # simple conversions, and are usually not disclosed by the manufacturers.
 2089 
 2090 s100                    100 / lx s            # ISO 100 speed
 2091 iso100                  s100
 2092 
 2093 # Reflected-light meter calibration constant with ISO 100 speed
 2094 
 2095 k1250                   12.5 (cd/m2) / lx s   # For Canon, Nikon, and Sekonic
 2096 k1400                   14   (cd/m2) / lx s   # For Kenko (Minolta) and Pentax
 2097 
 2098 # Incident-light meter calibration constant with ISO 100 film
 2099 
 2100 c250                    250 lx / lx s         # flat-disc receptor
 2101 
 2102 # Exposure value to scene luminance with ISO 100 imaging media
 2103 
 2104 # For Kenko (Minolta) or Pentax
 2105 #ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
 2106 # For Canon, Nikon, or Sekonic
 2107 ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
 2108 EV100()  ev100
 2109 
 2110 # Exposure value to scene illuminance with ISO 100 imaging media
 2111 
 2112 iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
 2113 
 2114 # Other Photographic Exposure Conversions
 2115 # 
 2116 # As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
 2117 # related by
 2118 #
 2119 #    Ev = Av + Tv = Bv + Sv
 2120 #
 2121 # where
 2122 #  Av = log2(A^2)       Aperture value
 2123 #  Tv = log2(1/t)       Time value
 2124 #  Sv = log2(N Sx)      Speed value
 2125 #  Bv = log2(B S / K)   Luminance ("brightness") value
 2126 #  Iv = log2(I S / C)   Illuminance value
 2127 #
 2128 # and
 2129 #  A  = Relative aperture (f-number)
 2130 #  t  = Exposure time in seconds
 2131 #  Sx = Arithmetic ISO speed in 1/lux s
 2132 #  B  = luminance in cd/m2
 2133 #  I  = luminance in lux
 2134 
 2135 # The constant N derives from the arcane relationship between arithmetic
 2136 # and logarithmic speed given in ASA PH2.5-1960.  That relationship
 2137 # apparently was not obvious--so much so that it was thought necessary
 2138 # to explain it in PH2.12-1961.  The constant has had several values
 2139 # over the years, usually without explanation for the changes.  Although
 2140 # APEX had little impact on consumer cameras, it has seen a partial
 2141 # resurrection in the Exif standards published by the Camera & Imaging
 2142 # Products Association of Japan.
 2143 
 2144 #N_apex         2^-1.75 lx s    # precise value implied in ASA PH2.12-1961,
 2145                                 # derived from ASA PH2.5-1960.
 2146 #N_apex         0.30 lx s       # rounded value in ASA PH2.5-1960, 
 2147                                 # ASA PH2.12-1961, and ANSI PH2.7-1986
 2148 #N_apex         0.3162 lx s     # value in ANSI PH2.7-1973
 2149 N_exif          1|3.125 lx s    # value in Exif 2.3 (2010), making Sv(5) = 100
 2150 K_apex1961      11.4 (cd/m2) / lx s    # value in ASA PH2.12-1961
 2151 K_apex1971      12.5 (cd/m2) / lx s    # value in ANSI PH3.49-1971; more common
 2152 C_apex1961      224 lx / lx s   # value in PH2.12-1961 (20.83 for I in 
 2153                                 #   footcandles; flat sensor?)
 2154 C_apex1971      322 lx / lx s   # mean value in PH3.49-1971 (30 +/- 5 for I in
 2155                                 # footcandles; hemispherical sensor?)
 2156 N_speed         N_exif
 2157 K_lum           K_apex1971
 2158 C_illum         C_apex1961
 2159 
 2160 # Units for Photographic Exposure Variables
 2161 #
 2162 # Practical photography sometimes pays scant attention to units for exposure
 2163 # variables.  In particular, the "speed" of the imaging medium is treated as if
 2164 # it were dimensionless when it should have units of reciprocal lux seconds;
 2165 # this practice works only because "speed" is almost invariably given in
 2166 # accordance with international standards (or similar ones used by camera
 2167 # manufacturers)--so the assumed units are invariant.  In calculating
 2168 # logarithmic quantities--especially the time value Tv and the exposure value
 2169 # EV--the units for exposure time ("shutter speed") are often ignored; this
 2170 # practice works only because the units of exposure time are assumed to be in
 2171 # seconds, and the missing units that make the argument to the logarithmic
 2172 # function dimensionless are silently provided.
 2173 #
 2174 # In keeping with common practice, the definitions that follow treat "speeds"
 2175 # as dimensionless, so ISO 100 speed is given simply as '100'.  When
 2176 # calculating the logarithmic APEX quantities Av and Tv, the definitions
 2177 # provide the missing units, so the times can be given with any appropriate
 2178 # units.  For example, giving an exposure time of 1 minute as either '1 min' or
 2179 # '60 s' will result in Tv of -5.9068906.
 2180 #
 2181 # Exposure Value from f-number and Exposure Time
 2182 # 
 2183 # Because nonlinear unit conversions only accept a single quantity,
 2184 # there is no direct conversion from f-number and exposure time to
 2185 # exposure value EV.  But the EV can be obtained from a combination of
 2186 # Av and Tv.  For example, the "sunny 16" rule states that correct
 2187 # exposure for a sunlit scene can achieved by using f/16 and an exposure
 2188 # time equal to the reciprocal of the ISO speed in seconds; this can be
 2189 # calculated as
 2190 #
 2191 #    ~Av(16) + ~Tv(1|100 s),
 2192 #
 2193 # which gives 14.643856.  These conversions may be combined with the
 2194 # ev100 conversion:
 2195 #
 2196 #    ev100(~Av(16) + ~Tv(1|100 s))
 2197 #
 2198 # to yield the assumed average scene luminance of 3200 cd/m^2.
 2199 
 2200 # convert relative aperture (f-number) to aperture value
 2201 Av(A)           units=[1;1] domain=[-2,) range=[0.5,)  2^(A/2); 2 log2(Av)
 2202 # convert exposure time to time value
 2203 Tv(t)           units=[1;s] range=(0,)  2^(-t) s; log2(s / Tv)
 2204 # convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
 2205 # make arithmetic speed dimensionless
 2206 # 'Sv' conflicts with the symbol for sievert; you can uncomment this function
 2207 # definition if you don't need that symbol
 2208 #Sv(S)    units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
 2209 Sval(S)   units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
 2210 
 2211 # convert luminance value Bv in ASA PH2.12-1961 to luminance
 2212 Bv(x)           units=[1;cd/m^2] range=(0,) \
 2213                 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
 2214 
 2215 # convert illuminance value Iv in ASA PH2.12-1961 to illuminance
 2216 Iv(x)           units=[1;lx] range=(0,) \
 2217                 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
 2218 
 2219 # convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in 
 2220 # ASA PH2.5-1960; make arithmetic speed dimensionless
 2221 Sx(S)           units=[1;1] domain=(0,) \
 2222                 log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
 2223 
 2224 # convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
 2225 # for convenience, speed is treated here as if it were dimensionless
 2226 Sdeg(S)         units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
 2227 Sdin()          Sdeg
 2228 
 2229 # Numerical Aperture and f-Number of a Lens
 2230 #
 2231 # The numerical aperture (NA) is given by
 2232 #
 2233 #   NA = n sin(theta)
 2234 #
 2235 # where n is the index of refraction of the medium and theta is half
 2236 # of the angle subtended by the aperture stop from a point in the image
 2237 # or object plane. For a lens in air, n = 1, and
 2238 #
 2239 #   NA = 0.5 / f-number
 2240 #
 2241 # convert NA to f-number
 2242 numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
 2243                      0.5 / x ; 0.5 / numericalaperture
 2244 NA()            numericalaperture
 2245 #
 2246 # convert f-number to itself; restrict values to those possible
 2247 fnumber(x)      units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
 2248 
 2249 # Referenced Photographic Standards
 2250 #
 2251 # ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
 2252 #    Continuous-Tone) Speed of Photographic Negative Materials.
 2253 # ASA PH2.12-1961. American Standard, General-Purpose Photographic
 2254 #    Exposure Meters (photoelectric type).
 2255 # ANSI PH3.49-1971. American National Standard for general-purpose
 2256 #    photographic exposure meters (photoelectric type).
 2257 # ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
 2258 # ANSI PH2.7-1986. American National Standard for Photography --
 2259 #    Photographic Exposure Guide.
 2260 # CIPA DC-008-2010. Exchangeable image file format for digital still
 2261 #    cameras: Exif Version 2.3
 2262 # ISO 6:1993.  International Standard, Photography -- Black-and-white
 2263 #    pictorial still camera negative film/process systems --
 2264 #    Determination of ISO Speed.
 2265 
 2266 
 2267 #
 2268 # Astronomical time measurements
 2269 #
 2270 # Astronomical time measurement is a complicated matter.  The length of the
 2271 # true day at a given place can be 21 seconds less than 24 hours or 30 seconds
 2272 # over 24 hours.  The two main reasons for this are the varying speed of the
 2273 # earth in its elliptical orbit and the fact that the sun moves on the ecliptic
 2274 # instead of along the celestial equator.  To devise a workable system for time
 2275 # measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun".
 2276 # Consider a first fictitious sun traveling along the ecliptic at a constant
 2277 # speed and coinciding with the true sun at perigee and apogee.  Then
 2278 # considering a second fictitious sun traveling along the celestial equator at
 2279 # a constant speed and coinciding with the first fictitious sun at the
 2280 # equinoxes.  The second fictitious sun is the "mean sun".  From this equations
 2281 # can be written out to determine the length of the mean day, and the tropical
 2282 # year.  The length of the second was determined based on the tropical year
 2283 # from such a calculation and was officially used from 1960-1967 until atomic
 2284 # clocks replaced astronomical measurements for a standard of time.  All of the
 2285 # values below give the mean time for the specified interval.
 2286 #
 2287 # See "Mathematical Astronomy Morsels" by Jean Meeus for more details
 2288 # and a description of how to compute the correction to mean time.
 2289 #
 2290 
 2291 TIME                    second
 2292 
 2293 anomalisticyear         365.2596 days       # The time between successive
 2294                                             #   perihelion passages of the
 2295                                             #   earth.
 2296 siderealyear            365.256360417 day   # The time for the earth to make
 2297                                             #   one revolution around the sun
 2298                                             #   relative to the stars.
 2299 tropicalyear            365.242198781 day   # The time needed for the mean sun
 2300                                             #   as defined above to increase
 2301                                             #   its longitude by 360 degrees.
 2302                                             #   Most references defined the
 2303                                             #   tropical year as the interval
 2304                                             #   between vernal equinoxes, but
 2305                                             #   this is misleading.  The length
 2306                                             #   of the season changes over time
 2307                                             #   because of the eccentricity of
 2308                                             #   the earth's orbit.  The time
 2309                                             #   between vernal equinoxes is
 2310                                             #   approximately 365.24237 days
 2311                                             #   around the year 2000.  See
 2312                                             #   "Mathematical Astronomy
 2313                                             #   Morsels" for more details.
 2314 eclipseyear             346.62 days         # The line of nodes is the
 2315                                             #   intersection of the plane of
 2316                                             #   Earth's orbit around the sun
 2317                                             #   with the plane of the moon's
 2318                                             #   orbit around earth.  Eclipses
 2319                                             #   can only occur when the moon
 2320                                             #   and sun are close to this
 2321                                             #   line.  The line rotates and
 2322                                             #   appearances of the sun on the
 2323                                             #   line of nodes occur every
 2324                                             #   eclipse year.
 2325 saros                   223 synodicmonth    # The earth, moon and sun appear in
 2326                                             #   the same arrangement every
 2327                                             #   saros, so if an eclipse occurs,
 2328                                             #   then one saros later, a similar
 2329                                             #   eclipse will occur.  (The saros
 2330                                             #   is close to 19 eclipse years.)
 2331                                             #   The eclipse will occur about
 2332                                             #   120 degrees west of the
 2333                                             #   preceding one because the
 2334                                             #   saros is not an even number of
 2335                                             #   days.  After 3 saros, an
 2336                                             #   eclipse will occur at
 2337                                             #   approximately the same place.
 2338 siderealday             86164.09054 s       # The sidereal day is the interval
 2339 siderealhour            1|24 siderealday    #   between two successive transits
 2340 siderealminute          1|60 siderealhour   #   of a star over the meridian,
 2341 siderealsecond          1|60 siderealminute #   or the time required  for the
 2342                                             #   earth to make one rotation
 2343                                             #   relative to the stars.  The
 2344                                             #   more usual solar day is the
 2345                                             #   time required to make a
 2346                                             #   rotation relative to the sun.
 2347                                             #   Because the earth moves in its
 2348                                             #   orbit, it has to turn a bit
 2349                                             #   extra to face the sun again,
 2350                                             #   hence the solar day is slightly
 2351                                             #   longer.
 2352 anomalisticmonth        27.55454977 day     # Time for the moon to travel from
 2353                                             #   perigee to perigee
 2354 nodicalmonth            27.2122199 day      # The nodes are the points where
 2355 draconicmonth           nodicalmonth        #   an orbit crosses the ecliptic.
 2356 draconiticmonth         nodicalmonth        #   This is the time required to
 2357                                             #   travel from the ascending node
 2358                                             #   to the next ascending node.
 2359 siderealmonth           27.321661 day       # Time required for the moon to
 2360                                             #   orbit the earth
 2361 lunarmonth              29 days + 12 hours + 44 minutes + 2.8 seconds
 2362                                             # Mean time between full moons.
 2363 synodicmonth            lunarmonth          #   Full moons occur when the sun
 2364 lunation                synodicmonth        #   and moon are on opposite sides
 2365 lune                    1|30 lunation       #   of the earth.  Since the earth
 2366 lunour                  1|24 lune           #   moves around the sun, the moon
 2367                                             #   has to revolve a bit extra to
 2368                                             #   get into the full moon
 2369                                             #   configuration.
 2370 year                    tropicalyear
 2371 yr                      year
 2372 month                   1|12 year
 2373 mo                      month
 2374 lustrum                 5 years             # The Lustrum was a Roman
 2375                                             #   purification ceremony that took
 2376                                             #   place every five years.
 2377                                             #   Classically educated Englishmen
 2378                                             #   used this term.
 2379 decade                  10 years
 2380 century                 100 years
 2381 millennium              1000 years
 2382 millennia               millennium
 2383 solaryear               year
 2384 lunaryear               12 lunarmonth
 2385 calendaryear            365 day
 2386 commonyear              365 day
 2387 leapyear                366 day
 2388 julianyear              365.25 day
 2389 gregorianyear           365.2425 day
 2390 islamicyear             354 day          # A year of 12 lunar months. They
 2391 islamicleapyear         355 day          # began counting on July 16, AD 622
 2392                                          # when Muhammad emigrated to Medina
 2393                                          # (the year of the Hegira).  They need
 2394                                          # 11 leap days in 30 years to stay in
 2395                                          # sync with the lunar year which is a
 2396                                          # bit longer than the 29.5 days of the
 2397                                          # average month.  The months do not
 2398                                          # keep to the same seasons, but
 2399                                          # regress through the seasons every
 2400                                          # 32.5 years.
 2401 islamicmonth            1|12 islamicyear # They have 29 day and 30 day months.
 2402 
 2403 # The Hebrew year is also based on lunar months, but synchronized to the solar
 2404 # calendar.  The months vary irregularly between 29 and 30 days in length, and
 2405 # the years likewise vary.  The regular year is 353, 354, or 355 days long.  To
 2406 # keep up with the solar calendar, a leap month of 30 days is inserted every
 2407 # 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle.  This
 2408 # gives leap years that last 383, 384, or 385 days.
 2409 
 2410 
 2411 # Sidereal days
 2412 
 2413 mercuryday              58.6462 day
 2414 venusday                243.01 day        # retrograde
 2415 earthday                siderealday
 2416 marsday                 1.02595675 day
 2417 jupiterday              0.41354 day
 2418 saturnday               0.4375 day
 2419 uranusday               0.65 day          # retrograde
 2420 neptuneday              0.768 day
 2421 plutoday                6.3867 day
 2422 
 2423 # Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html.  Data
 2424 # was updated in May 2001 based on the 1992 Explanatory Supplement to the
 2425 # Astronomical Almanac and the mean longitude rates.  Apparently the table of
 2426 # years in that reference is incorrect.
 2427 
 2428 mercuryyear             0.2408467 julianyear
 2429 venusyear               0.61519726 julianyear
 2430 earthyear               siderealyear
 2431 marsyear                1.8808476 julianyear
 2432 jupiteryear             11.862615 julianyear
 2433 saturnyear              29.447498 julianyear
 2434 uranusyear              84.016846 julianyear
 2435 neptuneyear             164.79132 julianyear
 2436 plutoyear               247.92065 julianyear
 2437 
 2438 # Objects on the earth are charted relative to a perfect ellipsoid whose
 2439 # dimensions are specified by different organizations.  The ellipsoid is
 2440 # specified by an equatorial radius and a flattening value which defines the
 2441 # polar radius.  These values are the 1996 values given by the International
 2442 # Earth Rotation Service (IERS) whose reference documents can be found at
 2443 # http://maia.usno.navy.mil/
 2444 
 2445 earthflattening         1|298.25642
 2446 earthradius_equatorial  6378136.49 m
 2447 earthradius_polar       (-earthflattening+1) earthradius_equatorial
 2448 
 2449 landarea                148.847e6 km^2
 2450 oceanarea               361.254e6 km^2
 2451 
 2452 moonradius              1738 km         # mean value
 2453 sunradius               6.96e8 m
 2454 
 2455 # Many astronomical values can be measured most accurately in a system of units
 2456 # using the astronomical unit and the mass of the sun as base units.  The
 2457 # uncertainty in the gravitational constant makes conversion to SI units
 2458 # significantly less accurate.
 2459 
 2460 # The astronomical unit was defined to be the length of the of the semimajor
 2461 # axis of a massless object with the same year as the earth.  With such a
 2462 # definition in force, and with the mass of the sun set equal to one, Kepler's
 2463 # third law can be used to solve for the value of the gravitational constant.
 2464 
 2465 # Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital
 2466 # period, a is the size of the semimajor axis, G is the gravitational constant
 2467 # and M is the mass.  With M = 1 and T and a chosen for the earth's orbit, we
 2468 # find sqrt(G) = (2 pi / T) sqrt(AU^3).  This constant is called the Gaussian
 2469 # gravitational constant, apparently because Gauss originally did the
 2470 # calculations.  However, when the original calculation was done, the value
 2471 # for the length of the earth's year was inaccurate.  The value used is called
 2472 # the Gaussian year.  Changing the astronomical unit to bring it into
 2473 # agreement with more accurate values for the year would have invalidated a
 2474 # lot of previous work, so instead the astronomical unit has been kept equal
 2475 # to this original value.  This is accomplished by using a standard value for
 2476 # the Gaussian gravitational constant.  This constant is called k.
 2477 # Many values below are from http://ssd.jpl.nasa.gov/?constants
 2478 
 2479 gauss_k                 0.01720209895   # This beast has dimensions of
 2480                                         # au^(3|2) / day and is exact.
 2481 gaussianyear      (2 pi / gauss_k) days # Year that corresponds to the Gaussian
 2482                                         # gravitational constant. This is a
 2483                                         # fictional year, and doesn't
 2484                                         # correspond to any celestial event.
 2485 astronomicalunit         149597870700 m # IAU definition from 2012, exact
 2486 au                     astronomicalunit # ephemeris for the above described
 2487                                         # astronomical unit.  (See the NASA
 2488                                         # site listed above.)
 2489 GMsun        1.32712440018e20 m^3 / s^2 # heliocentric gravitational constant
 2490 solarmass                       GMsun/G # with uncertainty 8e9 is known more
 2491 sunmass                       solarmass # accurately than G. 
 2492 
 2493 
 2494 sundist                 1.0000010178 au # mean earth-sun distance
 2495 moondist                3.844e8 m       # mean earth-moon distance
 2496 sundist_near            1.471e11 m      # earth-sun distance at perihelion
 2497 sundist_far             1.521e11 m      # earth-sun distance at aphelion
 2498 moondist_min		3.564e8 m	# approximate least distance at
 2499                                         #    perigee 1901-2300
 2500 moondist_max		4.067e8 m	# approximate greatest distance at
 2501                                         #    apogee 1901-2300
 2502 
 2503 
 2504 # The following are masses for planetary systems, not just the planet itself.
 2505 # The comments give the uncertainty in the denominators.  As noted above,
 2506 # masses are given relative to the solarmass because this is more accurate.
 2507 # The conversion to SI is uncertain because of uncertainty in G, the
 2508 # gravitational constant.
 2509 #
 2510 # Values are from http://ssd.jpl.nasa.gov/astro_constants.html
 2511 
 2512 mercurymass             solarmass / 6023600   # 250
 2513 venusmass               solarmass / 408523.71 # 0.06
 2514 earthmoonmass           solarmass / 328900.56 # 0.02
 2515 marsmass                solarmass / 3098708   # 9
 2516 jupitermass             solarmass / 1047.3486 # 0.0008
 2517 saturnmass              solarmass / 3497.898  # 0.018
 2518 uranusmass              solarmass / 22902.98  # 0.03
 2519 neptunemass             solarmass / 19412.24  # 0.04
 2520 plutomass               solarmass / 1.35e8    # 0.07e8
 2521 
 2522 moonearthmassratio      0.012300034 # uncertainty 3e-9
 2523 earthmass               earthmoonmass / ( 1 + moonearthmassratio)
 2524 moonmass                moonearthmassratio earthmass
 2525 
 2526 # These are the old values for the planetary masses.  They may give
 2527 # the masses of the planets alone.
 2528 
 2529 oldmercurymass             0.33022e24 kg
 2530 oldvenusmass               4.8690e24 kg
 2531 oldmarsmass                0.64191e24 kg
 2532 oldjupitermass             1898.8e24 kg
 2533 oldsaturnmass              568.5e24 kg
 2534 olduranusmass              86.625e24 kg
 2535 oldneptunemass             102.78e24 kg
 2536 oldplutomass               0.015e24 kg
 2537 
 2538 # Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in
 2539 # turn cites Global Earth Physics by CF Yoder, 1995.
 2540 
 2541 mercuryradius           2440 km
 2542 venusradius             6051.84 km
 2543 earthradius             6371.01 km
 2544 marsradius              3389.92 km
 2545 jupiterradius           69911 km
 2546 saturnradius            58232 km
 2547 uranusradius            25362 km
 2548 neptuneradius           24624 km
 2549 plutoradius             1151 km
 2550 
 2551 moongravity             1.62 m/s^2
 2552 
 2553 # The Hubble constant gives the speed at which distance galaxies are moving
 2554 # away from the earth according to v = H0*d, where H0 is the hubble constant
 2555 # and d is the distance to the galaxy.
 2556 
 2557 hubble                  70 km/s/Mpc        # approximate
 2558 H0                      hubble
 2559 
 2560 # Parallax is the angular difference between the topocentric (on Earth's
 2561 # surface) and geocentric (at Earth's center) direction toward a celestial body
 2562 # when the body is at a given altitude.  When the body is on the horizon, the
 2563 # parallax is the horizontal parallax; when the body is on the horizon and the
 2564 # observer is on the equator, the parallax is the equatorial horizontal
 2565 # parallax.  When the body is at zenith, the parallax is zero.
 2566 
 2567 lunarparallax  asin(earthradius_equatorial / moondist) # Moon equatorial 
 2568 moonhp         lunarparallax                           # horizontal parallax
 2569                                                        # at mean distance
 2570 
 2571 # Light from celestial objects is attenuated by passage through Earth's
 2572 # atmosphere.  A body near the horizon passes through much more air than an
 2573 # object at zenith, and is consequently less bright.  Air mass is the ratio of
 2574 # the length of the optical path at a given altitude (angle above the horizon)
 2575 # to the length at zenith.  Air mass at zenith is by definition unity; at the
 2576 # horizon, air mass is approximately 38, though the latter value can vary
 2577 # considerably with atmospheric conditions.  The general formula is # E = E0
 2578 # exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value
 2579 # seen by an observer, X is the air mass and c is the extinction coefficient.
 2580 # A common value for c in reasonably clear air is 0.21, but values can be
 2581 # considerably greater in urban areas.  Apparent altitude is that perceived by
 2582 # an observer; it includes the effect of atmospheric refraction.  There is no
 2583 # shortage of formulas for air mass
 2584 # (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to
 2585 # variations in local atmospheric conditions.  The formula used here is simple
 2586 # and is in good agreement with rigorously calculated values under standard
 2587 # conditions.
 2588 #
 2589 # Extraterrestrial illuminance or luminance of an object at a given altitude
 2590 # determined with vmag() or SB_xxx() below can be multiplied by
 2591 # atm_transmission() or atm_transmissionz() to estimate the terrestrial value.
 2592 #
 2593 # Kasten and Young (1989) air mass formula. alt is apparent altitude
 2594 # Reference:
 2595 # Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables
 2596 #     and Approximation Formula."  Applied Optics.  Vol. 28, 4735–4738.
 2597 #     Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735.
 2598 
 2599 airmass(alt) units=[degree;1] domain=[0,90] noerror \
 2600     1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364)
 2601 
 2602 # zenith is apparent zenith angle (zenith = 90 deg - alt)
 2603 airmassz(zenith) units=[degree;1] domain=[0,90] noerror \
 2604     1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364)
 2605 
 2606 # For reasonably clear air at sea level; values may need adjustment for
 2607 # elevation and local atmospheric conditions
 2608 # for scotopic vision (510 nm), appropriate for the dark-adapted eye
 2609 # extinction_coeff           0.26
 2610 # for photopic vision, appropriate for observing brighter objects such
 2611 # as the full moon
 2612 extinction_coeff	0.21
 2613 
 2614 atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \
 2615     exp(-extinction_coeff airmass(alt))
 2616 
 2617 # in terms of zenith angle (zenith = 90 deg - alt)
 2618 atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \
 2619     exp(-extinction_coeff airmassz(zenith))
 2620 
 2621 # Moon and Sun data at mean distances
 2622 moonvmag	-12.74	# Moon apparent visual magnitude at mean distance
 2623 sunvmag		-26.74	# Sun apparent visual magnitude at mean distance
 2624 moonsd	asin(moonradius / moondist) # Moon angular semidiameter at mean distance
 2625 sunsd	asin(sunradius / sundist)   # Sun angular semidiameter at mean distance
 2626 
 2627 # Visual magnitude of star or other celestial object.  The system of stellar
 2628 # magnitudes, developed in ancient Greece, assigned magnitudes from 1
 2629 # (brightest) to 6 (faintest visible to the naked eye).  In 1856, British
 2630 # astronomer Norman Pogson made the system precise, with a magnitude 1 object
 2631 # 100 times as bright as a magnitude 6 object, and each magnitude differing
 2632 # from the next by a constant ratio; the ratio, sometimes known as Pogson's
 2633 # ratio, is thus 100^0.2, or approximately 2.5119.  The logarithm of 100^0.2 is
 2634 # 0.4, hence the common use of powers of 10 and base-10 logarithms.
 2635 #
 2636 # Reference:
 2637 # Allen, C.W. 1976.  Astrophysical Quantities, 3rd ed. 1973, reprinted
 2638 #     with corrections, 1976.  London: Athlone.
 2639 #
 2640 # The function argument is the (dimensionless) visual magnitude; reference
 2641 # illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside
 2642 # Earth's atmosphere.  Illuminance values can be adjusted to terrestrial values
 2643 # by multiplying by one of the atm_transmission functions above.
 2644 
 2645 # Illuminance from apparent visual magnitude
 2646 vmag(mag) units=[1;lx] domain=[,]  range=(0,] \
 2647     2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx))
 2648 
 2649 # Surface brightness of a celestial object of a given visual magnitude
 2650 # is a logarithmic measure of the luminance the object would have if its
 2651 # light were emitted by an object of specified solid angle; it is
 2652 # expressed in magnitudes per solid angle.  Surface brightness can be
 2653 # obtained from the visual magnitude by
 2654 #    S = m + 2.5 log(pi pi k a b),
 2655 # where k is the phase (fraction illuminated), a is the equatorial
 2656 # radius, and b is the polar radius.  For 100% illumination (e.g., full
 2657 # moon), this is often simplified to
 2658 #    S = m + 2.5 log(pi k s^2),
 2659 # where s is the object's angular semidiameter; the units of s determine
 2660 # the units of solid angle.  The visual magnitude and semidiameter must
 2661 # be appropriate for the object's distance; for other than 100%
 2662 # illumination, the visual magnitude must be appropriate for the phase.
 2663 # Luminance values are for outside Earth's atmosphere; they can be
 2664 # adjusted to terrestrial values by multiplying by one of the atm_transmission
 2665 # functions above.
 2666 
 2667 # luminance from surface brightness in magnitudes per square degree
 2668 SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
 2669     vmag(sb) / squaredegree ; \
 2670     ~vmag(SB_degree squaredegree)
 2671 
 2672 # luminance from surface brightness in magnitudes per square minute
 2673 SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
 2674     vmag(sb) / squareminute ; \
 2675     ~vmag(SB_minute squareminute)
 2676 
 2677 # luminance from surface brightness in magnitudes per square second
 2678 SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
 2679     vmag(sb) / squaresecond ; \
 2680     ~vmag(SB_second squaresecond)
 2681 
 2682 # luminance from surface brightness in magnitudes per steradian
 2683 SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
 2684     vmag(sb) / sr ; \
 2685     ~vmag(SB_sr sr)
 2686 
 2687 SB()		SB_second
 2688 SB_sec()	SB_second
 2689 SB_min()	SB_minute
 2690 SB_deg()	SB_degree
 2691 
 2692 # The brightness of one tenth-magnitude star per square degree outside
 2693 # Earth's atmosphere; often used for night sky brightness.
 2694 S10	SB_degree(10)
 2695 
 2696 # Examples for magnitude and surface brightness functions
 2697 # Sun illuminance from visual magnitude
 2698 #     You have: sunvmag
 2699 #     You want:
 2700 # 	    Definition: -26.74 = -26.74
 2701 #     You have: vmag(sunvmag)
 2702 #     You want: lx
 2703 # 	    * 126134.45
 2704 # 	    / 7.9280482e-06
 2705 #
 2706 # Moon surface brightness from visual magnitude and semidiameter at 100%
 2707 # illumination (full moon):
 2708 #     You have: moonvmag
 2709 #     You want:
 2710 # 	    Definition: -12.74 = -12.74
 2711 #     You have: moonsd
 2712 #     You want: arcsec
 2713 # 	    * 932.59484
 2714 # 	    / 0.001072277
 2715 #     You have: moonvmag + 2.5 log(pi 932.59484^2)
 2716 #     You want:
 2717 # 	    Definition: 3.3513397
 2718 #
 2719 # Similar example with specific data obtained from another source (JPL
 2720 # Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in
 2721 # arcseconds
 2722 #
 2723 #     You have: -12.9 + 2.5 log(pi 2023.201|2^2)
 2724 #     You want:
 2725 # 	    Definition: 3.3679199
 2726 #     You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2))
 2727 #     You want:
 2728 # 	    Definition: 4858.6547 cd / m^2
 2729 #
 2730 # If surface brightness is provided by another source (e.g., Horizons),
 2731 # it can simply be used directly:
 2732 # You have: SB_second(3.3679199)
 2733 # You want: cd/m^2
 2734 #         * 4858.6546
 2735 #         / 0.0002058183
 2736 # The illuminance and luminance values are extraterrestrial (outside
 2737 # Earth's atmosphere).  The values at Earth's surface are less than these
 2738 # because of atmospheric extinction.  For example, in the last example
 2739 # above, if the Moon were at an altitude of 55 degrees, the terrestrial
 2740 # luminance could be calculated with
 2741 #     You have: SB_second(3.3679199)
 2742 #     You want: cd/m^2
 2743 # 	    * 4858.6546
 2744 # 	    / 0.0002058183
 2745 #     You have: _ atm_transmission(55 deg)
 2746 #     You want: cd/m^2
 2747 # 	    * 3760.6356
 2748 # 	    / 0.0002659125
 2749 # If desired, photographic exposure can be determined with EV100(),
 2750 # leading to acceptable combinations of aperture and exposure time.
 2751 # For the example above, but with the Moon at 10 degrees,
 2752 #     You have: SB_second(3.3679199) atm_transmission(10 deg)
 2753 #     You want: EV100
 2754 # 	    13.553962
 2755 
 2756 
 2757 # The Hartree system of atomic units, derived from fundamental units
 2758 # of mass (of electron), action (Planck's constant), charge, and
 2759 # the Coulomb constant.  This system is used in the fields of physical
 2760 # chemistry and condensed matter physics.  
 2761 #
 2762 # The Hartree energy can be derived from m_e, e, hbar, and coulombconst by
 2763 #    hartree = coulombconst^2 m_e e^4 / hbar^2
 2764 # but due to correlations between the measurements for m_e and coulombconst
 2765 # this results in a significant loss of precision.  So we use an alternate 
 2766 # equivalent definition for the hartree and use energy instead of the
 2767 # Coulomb constant to derive the other units.  This method retains the
 2768 # precision.  
 2769 
 2770 hartree                 2 rydberg  # Approximate electric potential energy of 
 2771                                    # the hydrogen atom in its ground state, 
 2772                                    # and approximately twice its ionization 
 2773                                    # energy.  
 2774 # Fundamental units
 2775 
 2776 atomicmass              electronmass
 2777 atomiccharge            e
 2778 atomicaction            hbar
 2779 atomicenergy            hartree
 2780 
 2781 # Derived units
 2782 
 2783 atomicvelocity          sqrt(atomicenergy / atomicmass)
 2784 atomictime              atomicaction / atomicenergy
 2785 atomiclength            atomicvelocity atomictime
 2786 atomicforce             atomicenergy / atomiclength
 2787 atomicmomentum          atomicenergy / atomicvelocity
 2788 atomiccurrent           atomiccharge / atomictime
 2789 atomicpotential         atomicenergy / atomiccharge   # electrical potential
 2790 atomicvolt              atomicpotential
 2791 atomicEfield            atomicpotential / atomiclength
 2792 atomicBfield            atomicvolt atomictime / atomiclength^2
 2793 atomictemperature       atomicenergy / boltzmann
 2794 
 2795 !var UNITS_SYSTEM hartree
 2796 !message Hartree units selected
 2797 !prompt (hartree)
 2798 +kg           1/electronmass_SI
 2799 +K            k_SI / hbar_SI s 
 2800 +m            alpha c_SI electronmass_SI / hbar_SI
 2801 +s            alpha c_SI m
 2802 +A            1 / s e_SI
 2803 !endvar
 2804 
 2805 #
 2806 # These thermal units treat entropy as charge, from [5]
 2807 #
 2808 
 2809 thermalcoulomb          J/K        # entropy
 2810 thermalampere           W/K        # entropy flow
 2811 thermalfarad            J/K^2
 2812 thermalohm              K^2/W      # thermal resistance
 2813 fourier                 thermalohm
 2814 thermalhenry            J K^2/W^2  # thermal inductance
 2815 thermalvolt             K          # thermal potential difference
 2816 
 2817 
 2818 #
 2819 # United States units
 2820 #
 2821 
 2822 # linear measure
 2823 
 2824 # The US Metric Law of 1866 legalized the metric system in the USA and
 2825 # defined the meter in terms of the British system with the exact
 2826 # 1 meter = 39.37 inches.  On April 5, 1893 Thomas Corwin Mendenhall,
 2827 # Superintendent of Weights and Measures, decided, in what has become
 2828 # known as the "Mendenhall Order" that the meter and kilogram would be the
 2829 # fundamental standards in the USA.  The definition from 1866 was turned
 2830 # around to give an exact definition of the yard as 3600|3937 meters This
 2831 # definition was used until July of 1959 when the definition was changed
 2832 # to bring the US and other English-speaking countries into agreement; the
 2833 # Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it
 2834 # was approximately halfway between the British and US values; it had the
 2835 # added advantage of making 1 inch = 25.4 mm (exactly).  Since 1959, the
 2836 # "international" foot has been exactly 0.3048 meters.  At the same time,
 2837 # it was decided that any data expressed in feet derived from geodetic
 2838 # surveys within the US would continue to use the old definition and call
 2839 # the old unit the "survey foot." The US continues to define the statute
 2840 # mile, furlong, chain, rod, link, and fathom in terms of the US survey
 2841 # foot.
 2842 # Sources:
 2843 # NIST Special Publication 447, Sects. 5, 7, and 8.
 2844 # NIST Handbook 44, 2011 ed., Appendix C.
 2845 # Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014.
 2846 
 2847 US                      1200|3937 m/ft   # These four values will convert
 2848 US-                     US               #   international measures to
 2849 survey-                 US               #   US Survey measures
 2850 geodetic-               US
 2851 int                     3937|1200 ft/m   # Convert US Survey measures to
 2852 int-                    int              #   international measures
 2853 
 2854 inch                    2.54 cm
 2855 in                      inch
 2856 foot                    12 inch
 2857 feet                    foot
 2858 ft                      foot
 2859 yard                    3 ft
 2860 yd                      yard
 2861 mile                    5280 ft          # The mile was enlarged from 5000 ft
 2862                                          # to this number in order to make
 2863                                          # it an even number of furlongs.
 2864                                          # (The Roman mile is 5000 romanfeet.)
 2865 line                    1|12 inch  # Also defined as '.1 in' or as '1e-8 Wb'
 2866 rod                     5.5 yard
 2867 perch                   rod
 2868 furlong                 40 rod           # From "furrow long"
 2869 statutemile             mile
 2870 league                  3 mile           # Intended to be an an hour's walk
 2871 
 2872 # surveyor's measure
 2873 
 2874 surveyorschain          66 surveyft
 2875 surveychain             surveyorschain
 2876 surveyorspole           1|4 surveyorschain
 2877 surveyorslink           1|100 surveyorschain
 2878 chain                   66 ft
 2879 link                    1|100 chain
 2880 ch                      chain
 2881 USacre                  10 surveychain^2
 2882 intacre                 10 chain^2       # Acre based on international ft
 2883 intacrefoot             acre foot
 2884 USacrefoot              USacre surveyfoot
 2885 acrefoot                intacrefoot
 2886 acre                    intacre
 2887 section                 mile^2
 2888 township                36 section
 2889 homestead               160 acre # Area of land granted by the 1862 Homestead
 2890                                  # Act of the United States Congress
 2891 gunterschain            surveyorschain
 2892 
 2893 engineerschain          100 ft
 2894 engineerslink           1|100 engineerschain
 2895 ramsdenschain           engineerschain
 2896 ramsdenslink            engineerslink
 2897 
 2898 gurleychain             33 feet           # Andrew Ellicott chain is the
 2899 gurleylink              1|50 gurleychain  # same length
 2900 
 2901 wingchain               66 feet           # Chain from 1664, introduced by
 2902 winglink                1|80 wingchain    # Vincent Wing, also found in a
 2903                                           # 33 foot length with 40 links.
 2904 # early US length standards
 2905 
 2906 # The US has had four standards for the yard: one by Troughton of London
 2907 # (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent
 2908 # with the definition of the meter in the metric joint resolution of
 2909 # Congress in 1866, but defining the yard in terms of the meter; and the
 2910 # international yard (1959), which standardized definitions for Australia,
 2911 # Canada, New Zealand, South Africa, the UK, and the US.
 2912 # Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com;
 2913 # Lewis E.  Barbrow and Lewis V.  Judson (1976).  NBS Special Publication
 2914 # 447, Weights and Measures Standards of the United States: A Brief
 2915 # History.
 2916 
 2917 troughtonyard           914.42190 mm
 2918 bronzeyard11            914.39980 mm
 2919 mendenhallyard          surveyyard
 2920 internationalyard       yard
 2921 
 2922 # nautical measure
 2923 
 2924 fathom                  6 ft     # Originally defined as the distance from
 2925                                  #   fingertip to fingertip with arms fully
 2926                                  #   extended.
 2927 nauticalmile            1852 m   # Supposed to be one minute of latitude at
 2928                                  # the equator.  That value is about 1855 m.
 2929                                  # Early estimates of the earth's circumference
 2930                                  # were a bit off.  The value of 1852 m was
 2931                                  # made the international standard in 1929.
 2932                                  # The US did not accept this value until
 2933                                  # 1954.  The UK switched in 1970.
 2934 
 2935 cable                   1|10 nauticalmile
 2936 intcable                cable              # international cable
 2937 cablelength             cable
 2938 UScable                 100 USfathom
 2939 navycablelength         720 USft           # used for depth in water
 2940 marineleague            3 nauticalmile
 2941 geographicalmile        brnauticalmile
 2942 knot                    nauticalmile / hr
 2943 click                   km       # US military slang
 2944 klick                   click
 2945 
 2946 # Avoirdupois weight
 2947 
 2948 pound                   0.45359237 kg   # The one normally used
 2949 lb                      pound           # From the latin libra
 2950 grain                   1|7000 pound    # The grain is the same in all three
 2951                                         # weight systems.  It was originally
 2952                                         # defined as the weight of a barley
 2953                                         # corn taken from the middle of the
 2954                                         # ear.
 2955 ounce                   1|16 pound
 2956 oz                      ounce
 2957 dram                    1|16 ounce
 2958 dr                      dram
 2959 ushundredweight         100 pounds
 2960 cwt                     hundredweight
 2961 shorthundredweight      ushundredweight
 2962 uston                   shortton
 2963 shortton                2000 lb
 2964 quarterweight           1|4 uston
 2965 shortquarterweight      1|4 shortton
 2966 shortquarter            shortquarterweight
 2967 
 2968 # Troy Weight.  In 1828 the troy pound was made the first United States
 2969 # standard weight.  It was to be used to regulate coinage.
 2970 
 2971 troypound               5760 grain
 2972 troyounce               1|12 troypound
 2973 ozt                     troyounce
 2974 pennyweight             1|20 troyounce  # Abbreviated "d" in reference to a
 2975 dwt                     pennyweight     #   Frankish coin called the "denier"
 2976                                         #   minted in the late 700's.  There
 2977                                         #   were 240 deniers to the pound.
 2978 assayton                mg ton / troyounce  # mg / assayton = troyounce / ton
 2979 usassayton              mg uston / troyounce
 2980 brassayton              mg brton / troyounce
 2981 fineounce               troyounce       # A troy ounce of 99.5% pure gold
 2982 
 2983 # Some other jewelers units
 2984 
 2985 metriccarat             0.2 gram        # Defined in 1907
 2986 metricgrain             50 mg
 2987 carat                   metriccarat
 2988 ct                      carat
 2989 jewelerspoint           1|100 carat
 2990 silversmithpoint        1|4000 inch
 2991 momme                   3.75 grams      # Traditional Japanese unit based
 2992                                         # on the chinese mace.  It is used for
 2993                                         # pearls in modern times and also for
 2994                                         # silk density.  The definition here
 2995                                         # was adopted in 1891.
 2996 # Apothecaries' weight
 2997 
 2998 appound                 troypound
 2999 apounce                 troyounce
 3000 apdram                  1|8 apounce
 3001 apscruple               1|3 apdram
 3002 
 3003 # Liquid measure
 3004 
 3005 usgallon                231 in^3        # US liquid measure is derived from
 3006 gal                     gallon          # the British wine gallon of 1707.
 3007 quart                   1|4 gallon      # See the "winegallon" entry below
 3008 pint                    1|2 quart       # more historical information.
 3009 gill                    1|4 pint
 3010 usquart                 1|4 usgallon
 3011 uspint                  1|2 usquart
 3012 usgill                  1|4 uspint
 3013 usfluidounce            1|16 uspint
 3014 fluiddram               1|8 usfloz
 3015 minimvolume             1|60 fluiddram
 3016 qt                      quart
 3017 pt                      pint
 3018 floz                    fluidounce
 3019 usfloz                  usfluidounce
 3020 fldr                    fluiddram
 3021 liquidbarrel            31.5 usgallon
 3022 usbeerbarrel            2 beerkegs
 3023 beerkeg                 15.5 usgallon   # Various among brewers
 3024 ponykeg                 1|2 beerkeg
 3025 winekeg                 12 usgallon
 3026 petroleumbarrel         42 usgallon     # Originated in Pennsylvania oil
 3027 barrel                  petroleumbarrel # fields, from the winetierce
 3028 bbl                     barrel
 3029 ushogshead              2 liquidbarrel
 3030 usfirkin                9 usgallon
 3031 
 3032 # Dry measures: The Winchester Bushel was defined by William III in 1702 and
 3033 # legally adopted in the US in 1836.
 3034 
 3035 usbushel                2150.42 in^3  # Volume of 8 inch cylinder with 18.5
 3036 bu                      bushel        # inch diameter (rounded)
 3037 peck                    1|4 bushel
 3038 uspeck                  1|4 usbushel
 3039 brpeck                  1|4 brbushel
 3040 pk                      peck
 3041 drygallon               1|2 uspeck
 3042 dryquart                1|4 drygallon
 3043 drypint                 1|2 dryquart
 3044 drybarrel               7056 in^3     # Used in US for fruits, vegetables,
 3045                                       #   and other dry commodities except for
 3046                                       #   cranberries.
 3047 cranberrybarrel         5826 in^3     # US cranberry barrel
 3048 heapedbushel            1.278 usbushel# The following explanation for this
 3049                                       #   value was provided by Wendy Krieger
 3050                                       #   <os2fan2@yahoo.com> based on
 3051                                       #   guesswork.  The cylindrical vessel is
 3052                                       #   18.5 inches in diameter and 1|2 inch
 3053                                       #   thick.  A heaped bushel includes the
 3054                                       #   contents of this cylinder plus a heap
 3055                                       #   on top.  The heap is a cone 19.5
 3056                                       #   inches in diameter and 6 inches
 3057                                       #   high.  With these values, the volume
 3058                                       #   of the bushel is 684.5 pi in^3 and
 3059                                       #   the heap occupies 190.125 pi in^3.
 3060                                       #   Therefore, the heaped bushel is
 3061                                       #   874.625|684.5 bushels.  This value is
 3062                                       #   approximately 1.2777575 and it rounds
 3063                                       #   to the value listed for the size of
 3064                                       #   the heaped bushel.  Sometimes the
 3065                                       #   heaped bushel is reported as 1.25
 3066                                       #   bushels.  This same explanation gives
 3067                                       #   that value if the heap is taken to
 3068                                       #   have an 18.5 inch diameter.
 3069 
 3070 # Grain measures.  The bushel as it is used by farmers in the USA is actually
 3071 # a measure of mass which varies for different commodities.  Canada uses the
 3072 # same bushel masses for most commodities, but not for oats.
 3073 
 3074 wheatbushel             60 lb
 3075 soybeanbushel           60 lb
 3076 cornbushel              56 lb
 3077 ryebushel               56 lb
 3078 barleybushel            48 lb
 3079 oatbushel               32 lb
 3080 ricebushel              45 lb
 3081 canada_oatbushel        34 lb
 3082 
 3083 # Wine and Spirits measure
 3084 
 3085 ponyvolume              1 usfloz
 3086 jigger                  1.5 usfloz   # Can vary between 1 and 2 usfloz
 3087 shot                    jigger     # Sometimes 1 usfloz
 3088 eushot                  25 ml      # EU standard spirits measure
 3089 fifth                   1|5 usgallon
 3090 winebottle              750 ml     # US industry standard, 1979
 3091 winesplit               1|4 winebottle
 3092 magnum                  1.5 liter  # Standardized in 1979, but given
 3093                                    # as 2 qt in some references
 3094 metrictenth             375 ml
 3095 metricfifth             750 ml
 3096 metricquart             1 liter
 3097 
 3098 # Old British bottle size
 3099 
 3100 reputedquart            1|6 brgallon
 3101 reputedpint             1|2 reputedquart
 3102 brwinebottle            reputedquart       # Very close to 1|5 winegallon
 3103 
 3104 # French champagne bottle sizes
 3105 
 3106 split                   200 ml
 3107 jeroboam                2 magnum
 3108 rehoboam                3 magnum
 3109 methuselah              4 magnum
 3110 imperialbottle          4 magnum
 3111 salmanazar              6 magnum
 3112 balthazar               8 magnum
 3113 nebuchadnezzar          10 magnum
 3114 solomon                 12 magnum
 3115 melchior                12 magnum
 3116 sovereign               17.5 magnum
 3117 primat                  18 magnum
 3118 goliath                 18 magnum
 3119 melchizedek             20 magnum
 3120 midas                   20 magnum
 3121 
 3122 # The wine glass doesn't seem to have an official standard, but the same value
 3123 # is suggested by several organization. 
 3124 
 3125 # https://www.rethinkingdrinking.niaaa.nih.gov/
 3126 # http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/
 3127 # https://www.drinkaware.co.uk/
 3128 # https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf
 3129 # http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide-cnt
 3130 
 3131 wineglass               150 mL     # the size of a "typical" serving
 3132 
 3133 # A unit of alcohol is a specified mass of pure ethyl alcohol.
 3134 # The term is used officially in the UK, but other countries use the same
 3135 # concept but with different values.  For example, the UK value of 8 g is
 3136 # nominally the amount of alcohol that a typical adult can metabolize in
 3137 # one hour.  Values for several countries, converted to a volumetric basis:
 3138 
 3139 alcoholunitus           14 g   / ethanoldensity
 3140 alcoholunitca           13.6 g / ethanoldensity
 3141 alcoholunituk            8 g   / ethanoldensity
 3142 alcoholunitau           10 g   / ethanoldensity
 3143 
 3144 # Example: for 12% ABV (alcohol by volume)
 3145 # alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL.
 3146 
 3147 
 3148 # Coffee 
 3149 #
 3150 # The recommended ratio of coffee to water. Values vary considerably;
 3151 # one is from the  Specialty Coffee Association of America
 3152 # http://scaa.org/?page=resources&d=brewing-best-practices
 3153 
 3154 coffeeratio             55 g/L  # ± 10%
 3155 
 3156 # other recommendations are more loose, e.g.,
 3157 # http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee
 3158 
 3159 
 3160 #
 3161 # Water is "hard" if it contains various minerals, expecially calcium
 3162 # carbonate.
 3163 #
 3164 
 3165 clarkdegree     grains/brgallon # Content by weigh of calcium carbonate
 3166 gpg             grains/usgallon # Divide by water's density to convert to
 3167                                 #   a dimensionless concentration measure
 3168 #
 3169 # Shoe measures
 3170 #
 3171 
 3172 shoeiron                1|48 inch    # Used to measure leather in soles
 3173 shoeounce               1|64 inch    # Used to measure non-sole shoe leather
 3174 
 3175 # USA shoe sizes.  These express the length of the shoe or the length
 3176 # of the "last", the form that the shoe is made on.  But note that
 3177 # this only captures the length.  It appears that widths change 1/4
 3178 # inch for each letter within the same size, and if you change the
 3179 # length by half a size then the width changes between 1/8 inch and
 3180 # 1/4 inch.  But this may not be standard.  If you know better, please
 3181 # contact me.
 3182 
 3183 shoesize_delta          1|3 inch     # USA shoe sizes differ by this amount
 3184 shoe_men0               8.25 inch
 3185 shoe_women0             (7+11|12) inch
 3186 shoe_boys0              (3+11|12) inch
 3187 shoe_girls0             (3+7|12) inch
 3188 
 3189 shoesize_men(n) units=[1;inch]   shoe_men0 + n shoesize_delta ; \
 3190                                 (shoesize_men+(-shoe_men0))/shoesize_delta
 3191 shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
 3192                                 (shoesize_women+(-shoe_women0))/shoesize_delta
 3193 shoesize_boys(n) units=[1;inch]  shoe_boys0 + n shoesize_delta ; \
 3194                                 (shoesize_boys+(-shoe_boys0))/shoesize_delta
 3195 shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
 3196                                 (shoesize_girls+(-shoe_girls0))/shoesize_delta
 3197 
 3198 # European shoe size.  According to
 3199 #      http://www.shoeline.com/footnotes/shoeterm.shtml
 3200 # shoe sizes in Europe are measured with Paris points which simply measure
 3201 # the length of the shoe.
 3202 
 3203 europeshoesize          2|3 cm
 3204 
 3205 #
 3206 # USA slang units
 3207 #
 3208 
 3209 buck                    US$
 3210 fin                     5 US$
 3211 sawbuck                 10 US$
 3212 usgrand                 1000 US$
 3213 greenback               US$
 3214 key                     kg           # usually of marijuana, 60's
 3215 lid                     1 oz         # Another 60's weed unit
 3216 footballfield           usfootballfield
 3217 usfootballfield         100 yards
 3218 canadafootballfield     110 yards    # And 65 yards wide
 3219 marathon                26 miles + 385 yards
 3220 
 3221 #
 3222 # British
 3223 #
 3224 
 3225 # The length measure in the UK was defined by a bronze bar manufactured in
 3226 # 1844.  Various conversions were sanctioned for convenience at different
 3227 # times, which makes conversions before 1963 a confusing matter.  Apparently
 3228 # previous conversions were never explicitly revoked.  Four different
 3229 # conversion factors appear below.  Multiply them times an imperial length
 3230 # units as desired.  The Weights and Measures Act of 1963 switched the UK away
 3231 # from their bronze standard and onto a definition of the yard in terms of the
 3232 # meter.  This happened after an international agreement in 1959 to align the
 3233 # world's measurement systems.
 3234 
 3235 UK                      UKlength_SJJ
 3236 UK-                     UK
 3237 british-                UK
 3238 
 3239 UKlength_B            0.9143992 meter / yard  # Benoit found the yard to be
 3240                                               #   0.9143992 m at a weights and
 3241                                               #   measures conference around
 3242                                               #   1896.   Legally sanctioned
 3243                                               #   in 1898.
 3244 UKlength_SJJ          0.91439841 meter / yard # In 1922, Seers, Jolly and
 3245                                               #   Johnson found the yard to be
 3246                                               #   0.91439841 meters.
 3247                                               #   Used starting in the 1930's.
 3248 UKlength_K              meter / 39.37079 inch # In 1816 Kater found this ratio
 3249                                               #   for the meter and inch.  This
 3250                                               #   value was used as the legal
 3251                                               #   conversion ratio when the
 3252                                               #   metric system was legalized
 3253                                               #   for contract in 1864.
 3254 UKlength_C            meter / 1.09362311 yard # In 1866 Clarke found the meter
 3255                                               #   to be 1.09362311 yards.  This
 3256                                               #   conversion was legalized
 3257                                               #   around 1878.
 3258 brnauticalmile          6080 ft               # Used until 1970 when the UK
 3259 brknot                  brnauticalmile / hr   #   switched to the international
 3260 brcable                 1|10 brnauticalmile   #   nautical mile.
 3261 admiraltymile           brnauticalmile
 3262 admiraltyknot           brknot
 3263 admiraltycable          brcable
 3264 seamile                 6000 ft
 3265 shackle                 15 fathoms            # Adopted 1949 by British navy
 3266 
 3267 # British Imperial weight is mostly the same as US weight.  A few extra
 3268 # units are added here.
 3269 
 3270 clove                   7 lb
 3271 stone                   14 lb
 3272 tod                     28 lb
 3273 brquarterweight         1|4 brhundredweight
 3274 brhundredweight         8 stone
 3275 longhundredweight       brhundredweight
 3276 longton                 20 brhundredweight
 3277 brton                   longton
 3278 
 3279 # British Imperial volume measures
 3280 
 3281 brminim                 1|60 brdram
 3282 brscruple               1|3 brdram
 3283 fluidscruple            brscruple
 3284 brdram                  1|8 brfloz
 3285 brfluidounce            1|20 brpint
 3286 brfloz                  brfluidounce
 3287 brgill                  1|4 brpint
 3288 brpint                  1|2 brquart
 3289 brquart                 1|4 brgallon
 3290 brgallon                4.54609 l      # The British Imperial gallon was
 3291                                        # defined in 1824 to be the volume of
 3292                                        # water which weighed 10 pounds at 62
 3293                                        # deg F with a pressure of 30 inHg.
 3294                                        # It was also defined as 277.274 in^3,
 3295                                        # Which is slightly in error.  In
 3296                                        # 1963 it was defined to be the volume
 3297                                        # occupied by 10 pounds of distilled
 3298                                        # water of density 0.998859 g/ml weighed
 3299                                        # in air of density 0.001217 g/ml
 3300                                        # against weights of density 8.136 g/ml.
 3301                                        # This gives a value of approximately
 3302                                        # 4.5459645 liters, but the old liter
 3303                                        # was in force at this time.  In 1976
 3304                                        # the definition was changed to exactly
 3305                                        # 4.54609 liters using the new
 3306                                        # definition of the liter (1 dm^3).
 3307 brbarrel                36 brgallon    # Used for beer
 3308 brbushel                8 brgallon
 3309 brheapedbushel          1.278 brbushel
 3310 brquarter               8 brbushel
 3311 brchaldron              36 brbushel
 3312 
 3313 # Obscure British volume measures.  These units are generally traditional
 3314 # measures whose definitions have fluctuated over the years.  Often they
 3315 # depended on the quantity being measured.  They are given here in terms of
 3316 # British Imperial measures.  For example, the puncheon may have historically
 3317 # been defined relative to the wine gallon or beer gallon or ale gallon
 3318 # rather than the British Imperial gallon.
 3319 
 3320 bag                     4 brbushel
 3321 bucket                  4 brgallon
 3322 kilderkin               2 brfirkin
 3323 last                    40 brbushel
 3324 noggin                  brgill
 3325 pottle                  0.5 brgallon
 3326 pin                     4.5 brgallon
 3327 puncheon                72 brgallon
 3328 seam                    8 brbushel
 3329 coomb                   4 brbushel
 3330 boll                    6 brbushel
 3331 firlot                  1|4 boll
 3332 brfirkin                9 brgallon     # Used for ale and beer
 3333 cran                    37.5 brgallon  # measures herring, about 750 fish
 3334 brwinehogshead          52.5 brgallon  # This value is approximately equal
 3335 brhogshead              brwinehogshead #   to the old wine hogshead of 63
 3336                                        #   wine gallons.  This adjustment
 3337                                        #   is listed in the OED and in
 3338                                        #   "The Weights and Measures of
 3339                                        #   England" by R. D. Connor
 3340 brbeerhogshead          54 brgallon
 3341 brbeerbutt              2 brbeerhogshead
 3342 registerton             100 ft^3  # Used for internal capacity of ships
 3343 shippington             40 ft^3   # Used for ship's cargo freight or timber
 3344 brshippington           42 ft^3   #
 3345 freightton            shippington # Both register ton and shipping ton derive
 3346                                   # from the "tun cask" of wine.
 3347 displacementton         35 ft^3   # Approximate volume of a longton weight of
 3348                                   # sea water.  Measures water displaced by
 3349                                   # ships.
 3350 waterton                224 brgallon
 3351 strike                  70.5 l    # 16th century unit, sometimes
 3352                                   #   defined as .5, 2, or 4 bushels
 3353                                   #   depending on the location.  It
 3354                                   #   probably doesn't make a lot of
 3355                                   #   sense to define in terms of imperial
 3356                                   #   bushels.  Zupko gives a value of
 3357                                   #   2 Winchester grain bushels or about
 3358                                   #   70.5 liters.
 3359 amber                   4 brbushel# Used for dry and liquid capacity [18]
 3360 
 3361 # British volume measures with "imperial"
 3362 
 3363 imperialminim           brminim
 3364 imperialscruple         brscruple
 3365 imperialdram            brdram
 3366 imperialfluidounce      brfluidounce
 3367 imperialfloz            brfloz
 3368 imperialgill            brgill
 3369 imperialpint            brpint
 3370 imperialquart           brquart
 3371 imperialgallon          brgallon
 3372 imperialbarrel          brbarrel
 3373 imperialbushel          brbushel
 3374 imperialheapedbushel    brheapedbushel
 3375 imperialquarter         brquarter
 3376 imperialchaldron        brchaldron
 3377 imperialwinehogshead    brwinehogshead
 3378 imperialhogshead        brhogshead
 3379 imperialbeerhogshead    brbeerhogshead
 3380 imperialbeerbutt        brbeerbutt
 3381 imperialfirkin          brfirkin
 3382 
 3383 # obscure British lengths
 3384 
 3385 barleycorn              1|3 UKinch   # Given in Realm of Measure as the
 3386                                      # difference between successive shoe sizes
 3387 nail                    1|16 UKyard  # Originally the width of the thumbnail,
 3388                                      #   or 1|16 ft.  This took on the general
 3389                                      #   meaning of 1|16 and settled on the
 3390                                      #   nail of a yard or 1|16 yards as its
 3391                                      #   final value.  [12]
 3392 pole                    16.5 UKft    # This was 15 Saxon feet, the Saxon
 3393 rope                    20 UKft      #   foot (aka northern foot) being longer
 3394 englishell              45 UKinch
 3395 flemishell              27 UKinch
 3396 ell                     englishell   # supposed to be measure from elbow to
 3397                                      #   fingertips
 3398 span                    9 UKinch     # supposed to be distance from thumb
 3399                                      #   to pinky with full hand extension
 3400 goad                    4.5 UKft     # used for cloth, possibly named after the
 3401                                      #   stick used for prodding animals.
 3402 
 3403 # misc obscure British units
 3404 
 3405 hide                    120 acre  # English unit of land area dating to the 7th
 3406                                   #   century, originally the amount of land
 3407                                   #   that a single plowman could cultivate,
 3408                                   #   which varied from 60-180 acres regionally.
 3409                                   #   Standardized at Normon conquest.
 3410 virgate                 1|4 hide
 3411 nook                    1|2 virgate
 3412 rood                    furlong rod  # Area of a strip a rod by a furlong
 3413 englishcarat            troyounce/151.5 # Originally intended to be 4 grain
 3414                                         #   but this value ended up being
 3415                                         #   used in the London diamond market
 3416 mancus                  2 oz
 3417 mast                    2.5 lb
 3418 nailkeg                 100 lbs
 3419 basebox                 31360 in^2      # Used in metal plating
 3420 
 3421 # alternate spellings
 3422 
 3423 gramme                  gram
 3424 litre                   liter
 3425 dioptre                 diopter
 3426 aluminium               aluminum
 3427 sulphur                 sulfur
 3428 
 3429 #
 3430 # Units derived the human body (may not be very accurate)
 3431 #
 3432 
 3433 geometricpace           5 ft   # distance between points where the same
 3434                                # foot hits the ground
 3435 pace                    2.5 ft # distance between points where alternate
 3436                                # feet touch the ground
 3437 USmilitarypace          30 in  # United States official military pace
 3438 USdoubletimepace        36 in  # United States official doubletime pace
 3439 fingerbreadth           7|8 in # The finger is defined as either the width
 3440 fingerlength            4.5 in #   or length of the finger
 3441 finger                  fingerbreadth
 3442 palmwidth               hand   # The palm is a unit defined as either the width
 3443 palmlength              8 in   #   or the length of the hand
 3444 hand                    4 inch # width of hand
 3445 shaftment               6 inch # Distance from tip of outstretched thumb to the
 3446                                #   opposite side of the palm of the hand.  The
 3447                                #   ending -ment is from the old English word
 3448                                #   for hand. [18]
 3449 smoot              5 ft + 7 in # Created as part of an MIT fraternity prank.
 3450                                #   In 1958 Oliver Smoot was used to measure
 3451                                #   the length of the Harvard Bridge, which was
 3452                                #   marked off in Smoot lengths.  These
 3453                                #   markings have been maintained on the bridge
 3454                                #   since then and repainted by subsequent
 3455                                #   incoming fraternity members.  During a
 3456                                #   bridge renovation the new sidewalk was
 3457                                #   scored every Smoot rather than at the
 3458                                #   customary 6 ft spacing.
 3459 tomcruise       5 ft + 7.75 in # Height of Tom Cruise
 3460 
 3461 #
 3462 # Cooking measures
 3463 #
 3464 
 3465 # Common abbreviations
 3466 
 3467 tbl                     tablespoon
 3468 tbsp                    tablespoon
 3469 tblsp                   tablespoon
 3470 Tb                      tablespoon
 3471 tsp                     teaspoon
 3472 saltspoon               1|4 tsp
 3473 
 3474 # US measures
 3475 
 3476 uscup                   8 usfloz
 3477 ustablespoon            1|16 uscup
 3478 usteaspoon              1|3 ustablespoon
 3479 ustbl                   ustablespoon
 3480 ustbsp                  ustablespoon
 3481 ustblsp                 ustablespoon
 3482 ustsp                   usteaspoon
 3483 metriccup               250 ml
 3484 stickbutter             1|4 lb            # Butter in the USA is sold in one
 3485                                           # pound packages that contain four
 3486                                           # individually wrapped pieces.  The
 3487                                           # pieces are marked into tablespoons,
 3488                                           # making it possible to measure out
 3489                                           # butter by volume by slicing the
 3490                                           # butter.
 3491 
 3492 legalcup                240 ml            # The cup used on nutrition labeling
 3493 legaltablespoon         1|16 legalcup
 3494 legaltbsp               legaltablespoon
 3495 
 3496 # Scoop size.  Ice cream scoops in the US are marked with numbers
 3497 # indicating the number of scoops required to fill a US quart.
 3498 
 3499 scoop(n)  units=[1;cup] domain=[4,100] range=[0.04,1] \
 3500            32 usfloz / n ; 32 usfloz / scoop
 3501 
 3502 
 3503 # US can sizes.
 3504 
 3505 number1can              10 usfloz
 3506 number2can              19 usfloz
 3507 number2.5can            3.5 uscups
 3508 number3can              4 uscups
 3509 number5can              7 uscups
 3510 number10can             105 usfloz
 3511 
 3512 # British measures
 3513 
 3514 brcup                   1|2 brpint
 3515 brteacup                1|3 brpint
 3516 brtablespoon            15 ml             # Also 5|8 brfloz, approx 17.7 ml
 3517 brteaspoon              1|3 brtablespoon  # Also 1|4 brtablespoon
 3518 brdessertspoon          2 brteaspoon
 3519 dessertspoon            brdessertspoon
 3520 dsp                     dessertspoon
 3521 brtsp                   brteaspoon
 3522 brtbl                   brtablespoon
 3523 brtbsp                  brtablespoon
 3524 brtblsp                 brtablespoon
 3525 
 3526 # Australian
 3527 
 3528 australiatablespoon     20 ml
 3529 austbl                  australiatablespoon
 3530 austbsp                 australiatablespoon
 3531 austblsp                australiatablespoon
 3532 australiateaspoon       1|4 australiatablespoon
 3533 austsp                  australiateaspoon
 3534 
 3535 # Italian
 3536 
 3537 etto                    100 g          # Used for buying items like meat and
 3538 etti                    etto           #   cheese.
 3539 
 3540 # Chinese
 3541 
 3542 catty                   0.5 kg
 3543 oldcatty                4|3 lbs        # Before metric conversion.
 3544 tael                    1|16 oldcatty  # Should the tael be defined both ways?
 3545 mace                    0.1 tael
 3546 oldpicul                100 oldcatty
 3547 picul                   100 catty      # Chinese usage
 3548 
 3549 # Indian
 3550 
 3551 seer                    14400 grain    # British Colonial standard
 3552 ser                     seer
 3553 maund                   40 seer
 3554 pakistanseer            1 kg
 3555 pakistanmaund           40 pakistanseer
 3556 chittak                 1|16 seer
 3557 tola                    1|5 chittak
 3558 ollock                  1|4 liter      # Is this right?
 3559 
 3560 # Japanese
 3561 
 3562 japancup                200 ml
 3563 
 3564 # densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
 3565 # so you can convert '2 cups sugar' to grams, for example, or in the other
 3566 # direction grams could be converted to 'cup flour_scooped'.
 3567 
 3568 butter                  8 oz/uscup
 3569 butter_clarified        6.8 oz/uscup
 3570 cocoa_butter            9 oz/uscup
 3571 shortening              6.75 oz/uscup   # vegetable shortening
 3572 oil                     7.5 oz/uscup
 3573 cakeflour_sifted        3.5 oz/uscup    # The density of flour depends on the
 3574 cakeflour_spooned       4 oz/uscup      # measuring method.  "Scooped",  or
 3575 cakeflour_scooped       4.5 oz/uscup    # "dip and sweep" refers to dipping a
 3576 flour_sifted            4 oz/uscup      # measure into a bin, and then sweeping
 3577 flour_spooned           4.25 oz/uscup   # the excess off the top.  "Spooned"
 3578 flour_scooped           5 oz/uscup      # means to lightly spoon into a measure
 3579 breadflour_sifted       4.25 oz/uscup   # and then sweep the top.  Sifted means
 3580 breadflour_spooned      4.5 oz/uscup    # sifting the flour directly into a
 3581 breadflour_scooped      5.5 oz/uscup    # measure and then sweeping the top.
 3582 cornstarch              120 grams/uscup
 3583 dutchcocoa_sifted       75 g/uscup      # These are for Dutch processed cocoa
 3584 dutchcocoa_spooned      92 g/uscup
 3585 dutchcocoa_scooped      95 g/uscup
 3586 cocoa_sifted            75 g/uscup      # These are for nonalkalized cocoa
 3587 cocoa_spooned           82 g/uscup
 3588 cocoa_scooped           95 g/uscup
 3589 heavycream              232 g/uscup
 3590 milk                    242 g/uscup
 3591 sourcream               242 g/uscup
 3592 molasses                11.25 oz/uscup
 3593 cornsyrup               11.5 oz/uscup
 3594 honey                   11.75 oz/uscup
 3595 sugar                   200 g/uscup
 3596 powdered_sugar          4 oz/uscup
 3597 brownsugar_light        217 g/uscup     # packed
 3598 brownsugar_dark         239 g/uscup
 3599 
 3600 baking_powder           4.6 grams / ustsp
 3601 salt                    6 g / ustsp
 3602 koshersalt              2.8 g / ustsp   # Diamond Crystal kosher salt
 3603 koshersalt_morton       4.8 g / ustsp   # Morton kosher salt
 3604                                         # Values are from the nutrition info
 3605                                         # on the packages
 3606 
 3607 
 3608 # Egg weights and volumes for a USA large egg
 3609 
 3610 egg                     50 grams        # without shell
 3611 eggwhite                30 grams
 3612 eggyolk                 18.6 grams
 3613 eggvolume               3 ustablespoons + 1|2 ustsp
 3614 eggwhitevolume          2 ustablespoons
 3615 eggyolkvolume           3.5 ustsp
 3616 
 3617 # Alcohol density
 3618 
 3619 ethanoldensity          0.7893 g/cm^3   # From CRC Handbook, 91st Edition
 3620 alcoholdensity          ethanoldensity
 3621 
 3622 #
 3623 # Density measures.  Density has traditionally been measured on a variety of
 3624 # bizarre nonlinear scales.
 3625 #
 3626 
 3627 # Density of a sugar syrup is frequently measured in candy making procedures.
 3628 # In the USA the boiling point of the syrup is measured.  Some recipes instead
 3629 # specify the density using degrees Baume.  Conversion between degrees Baume
 3630 # and the boiling point measure has proved elusive.  This table appeared in one
 3631 # text, and provides a fragmentary relationship to the concentration.
 3632 #
 3633 # temp(C)  conc (%)
 3634 #   100      30
 3635 #   101      40
 3636 #   102      50
 3637 #   103      60
 3638 #   106      70
 3639 #   112      80
 3640 #   123      90
 3641 #   140      95
 3642 #   151      97
 3643 #   160      98.2
 3644 #   166      99.5
 3645 #   171      99.6
 3646 #
 3647 # The best source identified to date came from "Boiling point elevation of
 3648 # technical sugarcane solutions and its use in automatic pan boiling" by
 3649 # Michael Saska.  International Sugar Journal, 2002, 104, 1247, pp 500-507.
 3650 #
 3651 # But I'm using equation (3) which is credited to Starzak and Peacock,
 3652 # "Water activity coefficient in aqueous solutions of sucrose--A comprehensive
 3653 # data analysis.  Zuckerindustrie, 122, 380-387.  (I couldn't find this
 3654 # document.)
 3655 #
 3656 # Note that the range of validity is uncertain, but answers are in agreement
 3657 # with the above table all the way to 99.6.
 3658 #
 3659 # The original equation has a parameter for the boiling point of water, which
 3660 # of course varies with altitude.  It also includes various other model
 3661 # parameters.  The input is the molar concentration of sucrose in the solution,
 3662 # (moles sucrose) / (total moles).
 3663 #
 3664 # Bsp 3797.06 degC
 3665 # Csp 226.28 degC
 3666 # QQ -17638 J/mol
 3667 # asp -1.0038
 3668 # bsp -0.24653
 3669 # tbw 100 degC     # boiling point of water
 3670 # sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \
 3671 #           /(tbw+stdtemp)) /  (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp)
 3672 #
 3673 # To convert mass concentration (brix) to molar concentration
 3674 #
 3675 # sc(x)  (x / 342.3) / (( x/342.3) + (100-x)/18.02); \
 3676 #        100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1)
 3677 #
 3678 # Here is a simplified version of this equation where the temperature of boiling
 3679 # water has been fixed at 100 degrees Celsius and the argument is now the
 3680 # concentration (brix).
 3681 #
 3682 # sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \
 3683 #                   / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K
 3684 #
 3685 #
 3686 # The formula is not invertible, so to implement it in units we unfortunately
 3687 # must turn it into a table.
 3688 
 3689 # This table gives the boiling point elevation as a function of the sugar syrup
 3690 # concentration expressed as a percentage.
 3691 
 3692 sugar_conc_bpe[K] \
 3693  0 0.0000   5 0.0788  10 0.1690  15 0.2729  20 0.3936  25 0.5351  \
 3694 30 0.7027  35 0.9036  40 1.1475  42 1.2599  44 1.3825  46 1.5165  \
 3695 48 1.6634  50 1.8249  52 2.0031  54 2.2005  56 2.4200  58 2.6651  \
 3696 60 2.9400  61 3.0902  62 3.2499  63 3.4198  64 3.6010  65 3.7944  \
 3697 66 4.0012  67 4.2227  68 4.4603  69 4.7156  70 4.9905  71 5.2870  \
 3698 72 5.6075  73 5.9546  74 6.3316  75 6.7417  76 7.1892  77 7.6786  \
 3699 78.0  8.2155  79.0  8.8061  80.0  9.4578  80.5  9.8092  81.0 10.1793  \
 3700 81.5 10.5693  82.0 10.9807  82.5 11.4152  83.0 11.8743  83.5 12.3601  \
 3701 84.0 12.8744  84.5 13.4197  85.0 13.9982  85.5 14.6128  86.0 15.2663  \
 3702 86.5 15.9620  87.0 16.7033  87.5 17.4943  88.0 18.3391  88.5 19.2424  \
 3703 89.0 20.2092  89.5 21.2452  90.0 22.3564  90.5 23.5493  91.0 24.8309  \
 3704 91.5 26.2086  92.0 27.6903  92.5 29.2839  93.0 30.9972  93.5 32.8374  \
 3705 94.0 34.8104  94.5 36.9195  95.0 39.1636  95.5 41.5348  96.0 44.0142  \
 3706 96.5 46.5668  97.0 49.1350  97.5 51.6347  98.0 53.9681  98.1 54.4091  \
 3707 98.2 54.8423  98.3 55.2692  98.4 55.6928  98.5 56.1174  98.6 56.5497  \
 3708 98.7 56.9999  98.8 57.4828  98.9 58.0206  99.0 58.6455  99.1 59.4062  \
 3709 99.2 60.3763  99.3 61.6706  99.4 63.4751  99.5 66.1062  99.6 70.1448  \
 3710 99.7 76.7867
 3711 
 3712 # Using the brix table we can use this to produce a mapping from boiling point
 3713 # to density which makes all of the units interconvertible.  Because the brix
 3714 # table stops at 95 this approach works up to a boiling point elevation of 39 K
 3715 # or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy
 3716 # making.  The "hard crack" stage continues up to 310 F.
 3717 
 3718 # Boiling point elevation
 3719 sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \
 3720                brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe))
 3721 # Absolute boiling point (produces an absolute temperature)
 3722 sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \
 3723                                          range=[0.99717,1.5144619] \
 3724                         brix(~sugar_conc_bpe(T-tempC(100))) ;\
 3725                         sugar_conc_bpe(~brix(sugar_bp))+tempC(100)
 3726 
 3727 # In practice dealing with the absolute temperature is annoying because it is
 3728 # not possible to convert to a nested function, so you're stuck retyping the
 3729 # absolute temperature in Kelvins to convert to celsius or Fahrenheit.  To
 3730 # prevent this we supply definitions that build in the temperature conversion
 3731 # and produce results in the Fahrenheit and Celsius scales.  So using these
 3732 # measures, to convert 46 degrees Baume to a Fahrenheit boiling point:
 3733 #
 3734 #      You have: baume(45)
 3735 #      You want: sugar_bpF
 3736 #              239.05647
 3737 #
 3738 sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\
 3739                         brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\
 3740                         ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100))
 3741 sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\
 3742                         brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\
 3743                         ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100))
 3744 
 3745 # Degrees Baume is used in European recipes to specify the density of a sugar
 3746 # syrup.  An entirely different definition is used for densities below
 3747 # 1 g/cm^3.  An arbitrary constant appears in the definition.  This value is
 3748 # equal to 145 in the US, but was according to [], the old scale used in
 3749 # Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
 3750 
 3751 baumeconst 145      # US value
 3752 baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
 3753                           (baumeconst/(baumeconst+-d)) g/cm^3 ; \
 3754                           (baume+((-g)/cm^3)) baumeconst / baume
 3755 
 3756 # It's not clear if this value was ever used with negative degrees.
 3757 twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
 3758                              (1 + 0.005 x) g / cm^3 ; \
 3759                              200 (twaddell / (g/cm^3) +- 1)
 3760 
 3761 # The degree quevenne is a unit for measuring the density of milk.
 3762 # Similarly it's unclear if negative values were allowed here.
 3763 quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
 3764                              (1 + 0.001 x) g / cm^3 ; \
 3765                              1000 (quevenne / (g/cm^3) +- 1)
 3766 
 3767 # Degrees brix measures sugar concentration by weigh as a percentage, so a
 3768 # solution that is 3 degrees brix is 3% sugar by weight.  This unit was named
 3769 # after Adolf Brix who invented a hydrometer that read this percentage
 3770 # directly.  This data is from Table 114 of NIST Circular 440, "Polarimetry,
 3771 # Saccharimetry and the Sugars".  It gives apparent specific gravity at 20
 3772 # degrees Celsius of various sugar concentrations.  As rendered below this
 3773 # data is converted to apparent density at 20 degrees Celsius using the
 3774 # density figure for water given in the same NIST reference.  They use the
 3775 # word "apparent" to refer to measurements being made in air with brass
 3776 # weights rather than vacuum.
 3777 
 3778 brix[0.99717g/cm^3]\
 3779     0 1.00000  1 1.00390  2 1.00780  3 1.01173  4 1.01569  5 1.01968 \
 3780     6 1.02369  7 1.02773  8 1.03180  9 1.03590 10 1.04003 11 1.04418 \
 3781    12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \
 3782    18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \
 3783    24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \
 3784    30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \
 3785    36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \
 3786    42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \
 3787    48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \
 3788    54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \
 3789    60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \
 3790    66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \
 3791    72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \
 3792    78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \
 3793    84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \
 3794    90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876
 3795 
 3796 # Density measure invented by the American Petroleum Institute.  Lighter
 3797 # petroleum products are more valuable, and they get a higher API degree.
 3798 #
 3799 # The intervals of range and domain should be open rather than closed.
 3800 #
 3801 apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
 3802                               141.5 g/cm^3 / (x+131.5) ; \
 3803                               141.5 (g/cm^3) / apidegree + (-131.5)
 3804 #
 3805 # Average densities of various woods (dried)
 3806 # Data from The Wood Database https://www.wood-database.com
 3807 #
 3808 
 3809 # North American Hardwoods
 3810 
 3811 wood_cherry             35 lb/ft^3
 3812 wood_redoak             44 lb/ft^3
 3813 wood_whiteoak           47 lb/ft^3
 3814 wood_blackwalnut        38 lb/ft^3
 3815 wood_walnut             wood_blackwalnut
 3816 wood_birch              43 lb/ft^3
 3817 wood_hardmaple          44 lb/ft^3
 3818 
 3819 wood_bigleafmaple       34 lb/ft^3
 3820 wood_boxeldermaple      30 lb/ft^3
 3821 wood_redmaple           38 lb/ft^3
 3822 wood_silvermaple        33 lb/ft^3
 3823 wood_stripedmaple       32 lb/ft^3
 3824 wood_softmaple         (wood_bigleafmaple \
 3825                       + wood_boxeldermaple \
 3826                       + wood_redmaple \
 3827                       + wood_silvermaple \
 3828                       + wood_stripedmaple) / 5
 3829 wood_poplar             29 lb/ft^3
 3830 wood_beech              45 lb/ft^3
 3831 
 3832 # North American Softwoods
 3833 
 3834 wood_jeffreypine        28 lb/ft^3
 3835 wood_ocotepine	        44 lb/ft^3
 3836 wood_ponderosapine      28 lb/ft^3
 3837 
 3838 wood_loblollypine       35 lb/ft^3
 3839 wood_longleafpine       41 lb/ft^3
 3840 wood_shortleafpine      35 lb/ft^3
 3841 wood_slashpine    	41 lb/ft^3
 3842 wood_yellowpine        (wood_loblollypine \
 3843                       + wood_longleafpine \
 3844                       + wood_shortleafpine \
 3845                       + wood_slashpine) / 4
 3846 wood_redpine            34 lb/ft^3
 3847 
 3848 wood_easternwhitepine   25 lb/ft^3
 3849 wood_westernwhitepine   27 lb/ft^3
 3850 wood_whitepine         (wood_easternwhitepine + wood_westernwhitepine) / 2
 3851 
 3852 wood_douglasfir         32 lb/ft^3
 3853 
 3854 wood_blackspruce        28 lb/ft^3
 3855 wood_engelmannspruce    24 lb/ft^3
 3856 wood_redspruce          27 lb/ft^3
 3857 wood_sitkaspruce        27 lb/ft^3
 3858 wood_whitespruce        27 lb/ft^3
 3859 wood_spruce            (wood_blackspruce \
 3860                       + wood_engelmannspruce \
 3861                       + wood_redspruce \
 3862                       + wood_sitkaspruce \
 3863                       + wood_whitespruce) / 5
 3864 
 3865 # Other woods 
 3866 
 3867 wood_basswood           26 lb/ft^3
 3868 wood_balsa               9 lb/ft^3
 3869 wood_ebony_gaboon       60 lb/ft^3
 3870 wood_ebony_macassar     70 lb/ft^3
 3871 wood_mahogany           37 lb/ft^3   # True (Honduran) mahogany,
 3872                                      # Swietenia macrophylla
 3873 wood_teak               41 lb/ft^3   
 3874 wood_rosewood_brazilian 52 lb/ft^3
 3875 wood_rosewood_honduran  64 lb/ft^3
 3876 wood_rosewood_indian    52 lb/ft^3
 3877 wood_cocobolo           69 lb/ft^3          
 3878 wood_bubinga            56 lb/ft^3
 3879 wood_zebrawood          50 lb/ft^3
 3880 wood_koa                38 lb/ft^3
 3881 wood_snakewood          75.7 lb/ft^3
 3882 wood_lignumvitae        78.5 lb/ft^3
 3883 wood_blackwood          79.3 lb/ft^3
 3884 wood_blackironwood      84.5 lb/ft^3 # Krugiodendron ferreum, listed
 3885                                      #   in database as the heaviest wood
 3886 
 3887 #
 3888 # Modulus of elasticity of selected woods.
 3889 # Data from The Wood Database https://www.wood-database.com
 3890 #
 3891 
 3892 # North American Hardwoods
 3893 
 3894 wood_mod_beech              1.720e6 lbf/in^2
 3895 wood_mod_birchyellow        2.010e6 lbf/in^2
 3896 wood_mod_birch              wood_mod_birchyellow
 3897 wood_mod_cherry             1.490e6 lbf/in^2
 3898 wood_mod_hardmaple          1.830e6 lbf/in^2
 3899 
 3900 wood_mod_bigleafmaple       1.450e6 lbf/in^2
 3901 wood_mod_boxeldermaple      1.050e6 lbf/in^2
 3902 wood_mod_redmaple           1.640e6 lbf/in^2
 3903 wood_mod_silvermaple        1.140e6 lbf/in^2
 3904 wood_mod_softmaple         (wood_mod_bigleafmaple \
 3905                           + wood_mod_boxeldermaple \
 3906 			  + wood_mod_redmaple \
 3907                           + wood_mod_silvermaple) / 4
 3908 
 3909 wood_mod_redoak             1.761e6 lbf/in^2
 3910 wood_mod_whiteoak           1.762e6 lbf/in^2
 3911 wood_mod_poplar             1.580e6 lbf/in^2
 3912 wood_mod_blackwalnut        1.680e6 lbf/in^2
 3913 wood_mod_walnut             wood_mod_blackwalnut
 3914 
 3915 # North American Softwoods
 3916 
 3917 wood_mod_jeffreypine        1.240e6 lbf/in^2
 3918 wood_mod_ocotepine          2.209e6 lbf/in^2
 3919 wood_mod_ponderosapine      1.290e6 lbf/in^2
 3920 
 3921 wood_mod_loblollypine	    1.790e6 lbf/in^2
 3922 wood_mod_longleafpine       1.980e6 lbf/in^2
 3923 wood_mod_shortleafpine      1.750e6 lbf/in^2
 3924 wood_mod_slashpine	    1.980e6 lbf/in^2
 3925 wood_mod_yellowpine        (wood_mod_loblollypine \
 3926                           + wood_mod_longleafpine \
 3927                           + wood_mod_shortleafpine \
 3928                           + wood_mod_slashpine) / 4
 3929 
 3930 wood_mod_redpine            1.630e6 lbf/in^2
 3931 
 3932 wood_mod_easternwhitepine   1.240e6 lbf/in^2
 3933 wood_mod_westernwhitepine   1.460e6 lbf/in^2
 3934 wood_mod_whitepine         (wood_mod_easternwhitepine + \
 3935                             wood_mod_westernwhitepine) / 2
 3936 
 3937 wood_mod_douglasfir         1.765e6  lbf/in^2
 3938 
 3939 wood_mod_blackspruce        1.523e6 lbf/in^2
 3940 wood_mod_englemannspruce    1.369e6 lbf/in^2
 3941 wood_mod_redspruce          1.560e6 lbf/in^2
 3942 wood_mod_sitkaspruce        1.600e6 lbf/in^2
 3943 wood_mod_whitespruce        1.315e6 lbf/in^2
 3944 wood_mod_spruce            (wood_mod_blackspruce \
 3945                           + wood_mod_englemannspruce \
 3946                           + wood_mod_redspruce + wood_mod_sitkaspruce \
 3947 		          + wood_mod_whitespruce) / 5
 3948 
 3949 # Other woods 
 3950 
 3951 wood_mod_balsa              0.538e6 lbf/in^2
 3952 wood_mod_basswood           1.460e6 lbf/in^2
 3953 wood_mod_blackwood          2.603e6 lbf/in^2  # African, Dalbergia melanoxylon
 3954 wood_mod_bubinga            2.670e6 lbf/in^2
 3955 wood_mod_cocobolo           2.712e6 lbf/in^2
 3956 wood_mod_ebony_gaboon       2.449e6 lbf/in^2
 3957 wood_mod_ebony_macassar     2.515e6 lbf/in^2
 3958 wood_mod_blackironwood      2.966e6 lbf/in^2  # Krugiodendron ferreum
 3959 wood_mod_koa                1.503e6 lbf/in^2
 3960 wood_mod_lignumvitae        2.043e6 lbf/in^2
 3961 wood_mod_mahogany           1.458e6 lbf/in^2  # True (Honduran) mahogany,
 3962                                               # Swietenia macrophylla
 3963 wood_mod_rosewood_brazilian 2.020e6 lbf/in^2
 3964 wood_mod_rosewood_honduran  3.190e6 lbf/in^2
 3965 wood_mod_rosewood_indian    1.668e6 lbf/in^2
 3966 wood_mod_snakewood          3.364e6 lbf/in^2
 3967 wood_mod_teak               1.781e6 lbf/in^2
 3968 wood_mod_zebrawood          2.374e6 lbf/in^2
 3969 
 3970 #
 3971 # Area of countries and other regions.  This is the "total area" which
 3972 # includes land and water areas within international boundaries and
 3973 # coastlines.  Data from January, 2019.  
 3974 #
 3975 # except as noted, sources are
 3976 # https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area
 3977 # https://www.cia.gov/library/publications/the-world-factbook)
 3978 
 3979 area_russia              17098246 km^2
 3980 area_antarctica          14000000 km^2
 3981 # area_canada is covered below as sum of province and territory areas
 3982 area_china                9596961 km^2
 3983 # area_unitedstates is covered below as sum of state areas
 3984 # includes only the 50 states and District of Columbia
 3985 area_us                   area_unitedstates
 3986 area_brazil               8515767 km^2
 3987 area_australia            7692024 km^2
 3988 # area_europeanunion is covered below as sum of member areas
 3989 area_india                3287263 km^2
 3990 area_argentina            2780400 km^2
 3991 area_kazakhstan           2724900 km^2
 3992 area_algeria              2381741 km^2
 3993 area_drcongo              2344858 km^2
 3994 area_greenland            2166086 km^2
 3995 area_saudiarabia          2149690 km^2
 3996 area_mexico               1964375 km^2
 3997 area_indonesia            1910931 km^2
 3998 area_sudan                1861484 km^2
 3999 area_libya                1759540 km^2
 4000 area_iran                 1648195 km^2
 4001 area_mongolia             1564110 km^2
 4002 area_peru                 1285216 km^2
 4003 area_chad                 1284000 km^2
 4004 area_niger                1267000 km^2
 4005 area_angola               1246700 km^2
 4006 area_mali                 1240192 km^2
 4007 area_southafrica          1221037 km^2
 4008 area_colombia             1141748 km^2
 4009 area_ethiopia             1104300 km^2
 4010 area_bolivia              1098581 km^2
 4011 area_mauritania           1030700 km^2
 4012 area_egypt                1002450 km^2
 4013 area_tanzania              945087 km^2
 4014 area_nigeria               923768 km^2
 4015 area_venezuela             916445 km^2
 4016 area_pakistan              881912 km^2
 4017 area_namibia               825615 km^2
 4018 area_mozambique            801590 km^2
 4019 area_turkey                783562 km^2
 4020 area_chile                 756102 km^2
 4021 area_zambia                752612 km^2
 4022 area_myanmar               676578 km^2
 4023 area_burma                area_myanmar
 4024 area_afghanistan           652230 km^2
 4025 area_southsudan            644329 km^2
 4026 area_france                640679 km^2
 4027 area_somalia               637657 km^2
 4028 area_centralafrica         622984 km^2
 4029 area_ukraine               603500 km^2
 4030 area_crimea		    27000 km^2	# occupied by Russia; included in
 4031                                         # (Encyclopedia Britannica)
 4032 area_madagascar            587041 km^2
 4033 area_botswana              581730 km^2
 4034 area_kenya                 580367 km^2
 4035 area_yemen                 527968 km^2
 4036 area_thailand              513120 km^2
 4037 area_spain                 505992 km^2
 4038 area_turkmenistan          488100 km^2
 4039 area_cameroon              475422 km^2
 4040 area_papuanewguinea        462840 km^2
 4041 area_sweden                450295 km^2
 4042 area_uzbekistan            447400 km^2
 4043 area_morocco               446550 km^2
 4044 area_iraq                  438317 km^2
 4045 area_paraguay              406752 km^2
 4046 area_zimbabwe              390757 km^2
 4047 area_japan                 377973 km^2
 4048 area_germany               357114 km^2
 4049 area_congorepublic         342000 km^2
 4050 area_finland               338424 km^2
 4051 area_vietnam               331212 km^2
 4052 area_malaysia              330803 km^2
 4053 area_norway                323802 km^2
 4054 area_ivorycoast            322463 km^2
 4055 area_poland                312696 km^2
 4056 area_oman                  309500 km^2
 4057 area_italy                 301339 km^2
 4058 area_philippines           300000 km^2
 4059 area_ecuador               276841 km^2
 4060 area_burkinafaso           274222 km^2
 4061 area_newzealand            270467 km^2
 4062 area_gabon                 267668 km^2
 4063 area_westernsahara         266000 km^2
 4064 area_guinea                245857 km^2
 4065 # area_unitedkingdom is covered below
 4066 area_uganda                241550 km^2
 4067 area_ghana                 238533 km^2
 4068 area_romania               238397 km^2
 4069 area_laos                  236800 km^2
 4070 area_guyana                214969 km^2
 4071 area_belarus               207600 km^2
 4072 area_kyrgyzstan            199951 km^2
 4073 area_senegal               196722 km^2
 4074 area_syria                 185180 km^2
 4075 area_golanheights	     1150 km^2	# occupied by Israel; included in 
 4076                                         # Syria (Encyclopedia Britannica)
 4077 area_cambodia              181035 km^2
 4078 area_uruguay               176215 km^2
 4079 area_somaliland            176120 km^2
 4080 area_suriname              163820 km^2
 4081 area_tunisia               163610 km^2
 4082 area_bangladesh            147570 km^2
 4083 area_nepal                 147181 km^2
 4084 area_tajikistan            143100 km^2
 4085 area_greece                131990 km^2
 4086 area_nicaragua             130373 km^2
 4087 area_northkorea            120540 km^2
 4088 area_malawi                118484 km^2
 4089 area_eritrea               117600 km^2
 4090 area_benin                 114763 km^2
 4091 area_honduras              112492 km^2
 4092 area_liberia               111369 km^2
 4093 area_bulgaria              110879 km^2
 4094 area_cuba                  109884 km^2
 4095 area_guatemala             108889 km^2
 4096 area_iceland               103000 km^2
 4097 area_southkorea            100210 km^2
 4098 area_hungary                93028 km^2
 4099 area_portugal               92090 km^2
 4100 area_jordan                 89342 km^2
 4101 area_serbia                 88361 km^2
 4102 area_azerbaijan             86600 km^2
 4103 area_austria                83871 km^2
 4104 area_uae                    83600 km^2
 4105 area_czechia                78865 km^2
 4106 area_czechrepublic         area_czechia
 4107 area_panama                 75417 km^2
 4108 area_sierraleone            71740 km^2
 4109 area_ireland                70273 km^2
 4110 area_georgia                69700 km^2
 4111 area_srilanka               65610 km^2
 4112 area_lithuania              65300 km^2
 4113 area_latvia                 64559 km^2
 4114 area_togo                   56785 km^2
 4115 area_croatia                56594 km^2
 4116 area_bosnia                 51209 km^2
 4117 area_costarica              51100 km^2
 4118 area_slovakia               49037 km^2
 4119 area_dominicanrepublic      48671 km^2
 4120 area_estonia                45227 km^2
 4121 area_denmark                43094 km^2
 4122 area_netherlands            41850 km^2
 4123 area_switzerland            41284 km^2
 4124 area_bhutan                 38394 km^2
 4125 area_taiwan                 36193 km^2
 4126 area_guineabissau           36125 km^2
 4127 area_moldova                33846 km^2
 4128 area_belgium                30528 km^2
 4129 area_lesotho                30355 km^2
 4130 area_armenia                29743 km^2
 4131 area_solomonislands         28896 km^2
 4132 area_albania                28748 km^2
 4133 area_equitorialguinea       28051 km^2
 4134 area_burundi                27834 km^2
 4135 area_haiti                  27750 km^2
 4136 area_rwanda                 26338 km^2
 4137 area_northmacedonia         25713 km^2
 4138 area_djibouti               23200 km^2
 4139 area_belize                 22966 km^2
 4140 area_elsalvador             21041 km^2
 4141 area_israel                 20770 km^2
 4142 area_slovenia               20273 km^2
 4143 area_fiji                   18272 km^2
 4144 area_kuwait                 17818 km^2
 4145 area_eswatini               17364 km^2
 4146 area_easttimor              14919 km^2
 4147 area_bahamas                13943 km^2
 4148 area_montenegro             13812 km^2
 4149 area_vanatu                 12189 km^2
 4150 area_qatar                  11586 km^2
 4151 area_gambia                 11295 km^2
 4152 area_jamaica                10991 km^2
 4153 area_kosovo                 10887 km^2
 4154 area_lebanon                10452 km^2
 4155 area_cyprus                  9251 km^2
 4156 area_puertorico              9104 km^2	# United States territory; not included
 4157                                         #   in United States area
 4158 area_westbank                5860 km^2	# (CIA World Factbook)
 4159 area_hongkong                2755 km^2
 4160 area_luxembourg              2586 km^2
 4161 area_singapore                716 km^2
 4162 area_gazastrip                360 km^2	# (CIA World Factbook)
 4163 area_malta                    316 km^2  # smallest EU country
 4164 area_liechtenstein            160 km^2
 4165 area_monaco                     2.02 km^2
 4166 area_vaticancity                0.44 km^2
 4167 
 4168 # Members as of 1 Feb 2020
 4169 area_europeanunion        area_austria + area_belgium + area_bulgaria \
 4170 			+ area_croatia + area_cyprus + area_czechia + area_denmark \
 4171                         + area_estonia + area_finland + area_france + area_germany \
 4172                         + area_greece + area_hungary + area_ireland + area_italy \
 4173                         + area_latvia + area_lithuania + area_luxembourg \
 4174                         + area_malta + area_netherlands + area_poland \
 4175                         + area_portugal + area_romania + area_slovakia \
 4176                         + area_slovenia + area_spain + area_sweden
 4177 area_eu                   area_europeanunion
 4178 
 4179 #
 4180 # Areas of the individual US states
 4181 #
 4182 # https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area
 4183 #
 4184 # United States Summary: 2010, Population and Housing Unit Counts, Table 18, p. 41
 4185 # Issued September 2012
 4186 
 4187 area_alaska               1723336.8 km^2
 4188 area_texas                 695661.6 km^2
 4189 area_california            423967.4 km^2
 4190 area_montana               380831.1 km^2
 4191 area_newmexico             314917.4 km^2
 4192 area_arizona               295233.5 km^2
 4193 area_nevada                286379.7 km^2
 4194 area_colorado              269601.4 km^2
 4195 area_oregon                254799.2 km^2
 4196 area_wyoming               253334.5 km^2
 4197 area_michigan              250486.8 km^2
 4198 area_minnesota             225162.8 km^2
 4199 area_utah                  219881.9 km^2
 4200 area_idaho                 216442.6 km^2
 4201 area_kansas                213100.0 km^2
 4202 area_nebraska              200329.9 km^2
 4203 area_southdakota           199728.7 km^2
 4204 area_washington            184660.8 km^2
 4205 area_northdakota           183107.8 km^2
 4206 area_oklahoma              181037.2 km^2
 4207 area_missouri              180540.3 km^2
 4208 area_florida               170311.7 km^2
 4209 area_wisconsin             169634.8 km^2
 4210 area_georgia_us            153910.4 km^2
 4211 area_illinois              149995.4 km^2
 4212 area_iowa                  145745.9 km^2
 4213 area_newyork               141296.7 km^2
 4214 area_northcarolina         139391.0 km^2
 4215 area_arkansas              137731.8 km^2
 4216 area_alabama               135767.4 km^2
 4217 area_louisiana             135658.7 km^2
 4218 area_mississippi           125437.7 km^2
 4219 area_pennsylvania          119280.2 km^2
 4220 area_ohio                  116097.7 km^2
 4221 area_virginia              110786.6 km^2
 4222 area_tennessee             109153.1 km^2
 4223 area_kentucky              104655.7 km^2
 4224 area_indiana                94326.2 km^2
 4225 area_maine                  91633.1 km^2
 4226 area_southcarolina          82932.7 km^2
 4227 area_westvirginia           62755.5 km^2
 4228 area_maryland               32131.2 km^2
 4229 area_hawaii                 28313.0 km^2
 4230 area_massachusetts          27335.7 km^2
 4231 area_vermont                24906.3 km^2
 4232 area_newhampshire           24214.2 km^2
 4233 area_newjersey              22591.4 km^2
 4234 area_connecticut            14357.4 km^2
 4235 area_delaware                6445.8 km^2
 4236 area_rhodeisland             4001.2 km^2
 4237 area_districtofcolumbia       177.0 km^2
 4238 
 4239 area_unitedstates          area_alabama + area_alaska + area_arizona \
 4240                          + area_arkansas + area_california + area_colorado \
 4241                          + area_connecticut + area_delaware \
 4242                          + area_districtofcolumbia + area_florida \
 4243                          + area_georgia_us + area_hawaii + area_idaho \
 4244                          + area_illinois + area_indiana + area_iowa \
 4245                          + area_kansas + area_kentucky + area_louisiana \
 4246                          + area_maine + area_maryland + area_massachusetts \
 4247                          + area_michigan + area_minnesota + area_mississippi \
 4248                          + area_missouri + area_montana + area_nebraska \
 4249                          + area_nevada + area_newhampshire + area_newjersey \
 4250                          + area_newmexico + area_newyork + area_northcarolina \
 4251                          + area_northdakota + area_ohio + area_oklahoma \
 4252                          + area_oregon + area_pennsylvania + area_rhodeisland \
 4253                          + area_southcarolina + area_southdakota \
 4254                          + area_tennessee + area_texas + area_utah \
 4255                          + area_vermont + area_virginia + area_washington \
 4256                          + area_westvirginia + area_wisconsin + area_wyoming
 4257 
 4258 # Total area of Canadian province and territories
 4259 #
 4260 # Statistics Canada, "Land and freshwater area, by province and territory",
 4261 # 2016-10-07:
 4262 #
 4263 # https://www150.statcan.gc.ca/n1/pub/11-402-x/2012000/chap/geo/tbl/tbl06-eng.htm
 4264 
 4265 area_ontario                    1076395 km^2    # confederated 1867-Jul-01
 4266 area_quebec                     1542056 km^2    # confederated 1867-Jul-01
 4267 area_novascotia                 55284 km^2      # confederated 1867-Jul-01
 4268 area_newbrunswick               72908 km^2      # confederated 1867-Jul-01
 4269 area_canada_original            area_ontario + area_quebec + area_novascotia \
 4270                                              + area_newbrunswick
 4271 area_manitoba                   647797 km^2     # confederated 1870-Jul-15
 4272 area_britishcolumbia            944735 km^2     # confederated 1871-Jul-20
 4273 area_princeedwardisland         5660 km^2       # confederated 1873-Jul-01
 4274 area_canada_additional          area_manitoba + area_britishcolumbia \
 4275                                               + area_princeedwardisland
 4276 area_alberta                    661848 km^2     # confederated 1905-Sep-01
 4277 area_saskatchewan               651036 km^2     # confederated 1905-Sep-01
 4278 area_newfoundlandandlabrador    405212 km^2     # confederated 1949-Mar-31
 4279 area_canada_recent              area_alberta + area_saskatchewan \
 4280                                              + area_newfoundlandandlabrador
 4281 area_canada_provinces           area_canada_original + area_canada_additional \
 4282                                                      + area_canada_recent
 4283 area_northwestterritories       1346106 km^2    # NT confederated 1870-Jul-15
 4284 area_yukon                      482443 km^2     # YT confederated 1898-Jun-13
 4285 area_nunavut                    2093190 km^2    # NU confederated 1999-Apr-01
 4286 area_canada_territories         area_northwestterritories + area_yukon \
 4287                                               + area_nunavut
 4288 area_canada                     area_canada_provinces + area_canada_territories
 4289 
 4290 # area-uk-countries.units - UK country (/province) total areas
 4291 # https://en.wikipedia.org/wiki/Countries_of_the_United_Kingdom#Statistics
 4292 # GB is official UK country code for some purposes but internally is a Kingdom
 4293 #
 4294 # areas from A Beginners Guide to UK Geography 2019 v1.0, Office for National Statistics
 4295 # England: country; 0927-Jul-12 united; 1603-Mar-24 union of crowns
 4296 area_england            132947.76 km^2
 4297 #
 4298 # Wales: 1282 conquered; 1535 union; principality until 2011
 4299 area_wales              21224.48 km^2
 4300 #
 4301 # England and Wales: nation; 1535 union
 4302 area_englandwales       area_england + area_wales
 4303 #
 4304 # Scotland: country; ~900 united; 1603-Mar-24 union of crowns
 4305 area_scotland           80226.36 km^2
 4306 #
 4307 # Great Britain: kingdom; excludes NI;
 4308 # 1707 Treaty and Acts of Union: union of parliaments
 4309 area_greatbritain       area_england + area_wales + area_scotland
 4310 area_gb                 area_greatbritain
 4311 #
 4312 # Northern Ireland: province; Ireland: 1177 Henry II lordship;
 4313 # 1542 Henry VIII kingdom; 1652 Cromwell commonwealth;
 4314 # 1691 William III kingdom; 1800 Acts of Union: UK of GB & Ireland;
 4315 # 1921 Irish Free State independent of UK
 4316 area_northernireland    14133.38 km^2
 4317 #
 4318 # United Kingdom of GB & NI: 1800 Acts of Union: UK of GB & Ireland;
 4319 # 1921 Irish Free State independent of UK
 4320 area_unitedkingdom      area_greatbritain + area_northernireland
 4321 area_uk                 area_unitedkingdom
 4322 
 4323 #
 4324 # Units derived from imperial system
 4325 #
 4326 
 4327 ouncedal                oz ft / s^2     # force which accelerates an ounce
 4328                                         #    at 1 ft/s^2
 4329 poundal                 lb ft / s^2     # same thing for a pound
 4330 tondal                  longton ft / s^2    # and for a ton
 4331 pdl                     poundal
 4332 osi                     ounce force / inch^2   # used in aviation
 4333 psi                     pound force / inch^2
 4334 psia                    psi             # absolute pressure
 4335                                         #   Note that gauge pressure can be given
 4336                                         #   using the gaugepressure() and
 4337                                         #   psig() nonlinear unit definitions
 4338 tsi                     ton force / inch^2
 4339 reyn                    psi sec
 4340 slug                    lbf s^2 / ft
 4341 slugf                   slug force
 4342 slinch                  lbf s^2 / inch  # Mass unit derived from inch second
 4343 slinchf                 slinch force    #   pound-force system.  Used in space
 4344                                         #   applications where in/sec^2 was a
 4345                                         #   natural acceleration measure.
 4346 geepound                slug
 4347 lbf                     lb force
 4348 tonf                    ton force
 4349 lbm                     lb
 4350 kip                     1000 lbf     # from kilopound
 4351 ksi                     kip / in^2
 4352 mil                     0.001 inch
 4353 thou                    0.001 inch
 4354 tenth                   0.0001 inch  # one tenth of one thousandth of an inch
 4355 millionth               1e-6 inch    # one millionth of an inch
 4356 circularinch            1|4 pi in^2  # area of a one-inch diameter circle
 4357 circleinch              circularinch #    A circle with diameter d inches has
 4358                                      #    an area of d^2 circularinches
 4359 cylinderinch         circleinch inch # Cylinder h inch tall, d inches diameter
 4360                                      #    has volume d^2 h cylinder inches
 4361 circularmil             1|4 pi mil^2 # area of one-mil diameter circle
 4362 cmil                    circularmil
 4363 
 4364 cental                  100 pound
 4365 centner                 cental
 4366 caliber                 0.01 inch    # for measuring bullets
 4367 duty                    ft lbf
 4368 celo                    ft / s^2
 4369 jerk                    ft / s^3
 4370 australiapoint          0.01 inch    # The "point" is used to measure rainfall
 4371                                      #   in Australia
 4372 sabin                   ft^2         # Measure of sound absorption equal to the
 4373                                      #   absorbing power of one square foot of
 4374                                      #   a perfectly absorbing material.  The
 4375                                      #   sound absorptivity of an object is the
 4376                                      #   area times a dimensionless
 4377                                      #   absorptivity coefficient.
 4378 standardgauge          4 ft + 8.5 in # Standard width between railroad track
 4379 flag                   5 ft^2        # Construction term referring to sidewalk.
 4380 rollwallpaper          30 ft^2       # Area of roll of wall paper
 4381 fillpower              in^3 / ounce  # Density of down at standard pressure.
 4382                                      #   The best down has 750-800 fillpower.
 4383 pinlength              1|16 inch     # A #17 pin is 17/16 in long in the USA.
 4384 buttonline             1|40 inch     # The line was used in 19th century USA
 4385                                      #   to measure width of buttons.
 4386 beespace               1|4 inch      # Bees will fill any space that is smaller
 4387                                      #   than the bee space and leave open
 4388                                      #   spaces that are larger.  The size of
 4389                                      #   the space varies with species.
 4390 diamond                8|5 ft        # Marking on US tape measures that is
 4391                                      #   useful to carpenters who wish to place
 4392                                      #   five studs in an 8 ft distance.  Note
 4393                                      #   that the numbers appear in red every
 4394                                      #   16 inches as well, giving six
 4395                                      #   divisions in 8 feet.
 4396 retmaunit              1.75 in       # Height of rack mountable equipment.
 4397 U                      retmaunit     #   Equipment should be 1|32 inch narrower
 4398 RU                     U             #   than its U measurement indicates to
 4399                                      #   allow for clearance, so 4U=(6+31|32)in
 4400                                      #   RETMA stands for the former name of
 4401                                      #   the standardizing organization, Radio
 4402                                      #   Electronics Television Manufacturers
 4403                                      #   Association.  This organization is now
 4404                                      #   called the Electronic Industries
 4405                                      #   Alliance (EIA) and the rack standard
 4406                                      #   is specified in EIA RS-310-D.
 4407 count                  per pound     # For measuring the size of shrimp
 4408 flightlevel            100 ft        # Flight levels are used to ensure safe
 4409 FL                     flightlevel   #   vertical separation between aircraft
 4410                                      #   despite variations in local air
 4411                                      #   pressure.  Flight levels define
 4412                                      #   altitudes based on a standard air
 4413                                      #   pressure so that altimeter calibration
 4414                                      #   is not needed.  This means that
 4415                                      #   aircraft at separated flight levels
 4416                                      #   are guaranteed to be separated.
 4417                                      #   Hence the definition of 100 feet is
 4418                                      #   a nominal, not true, measure.
 4419                                      #   Customarily written with no space in
 4420                                      #   the form FL290, which will not work in
 4421                                      #   units.  But note "FL 290" will work.  
 4422 
 4423 #
 4424 # Other units of work, energy, power, etc
 4425 #
 4426 
 4427 ENERGY                  joule
 4428 WORK                    joule
 4429 
 4430 # Calorie: approximate energy to raise a gram of water one degree celsius
 4431 
 4432 calorie                 cal_th       # Default is the thermochemical calorie
 4433 cal                     calorie
 4434 calorie_th              4.184 J      # Thermochemical calorie, defined in 1930
 4435 thermcalorie            calorie_th   #   by Frederick Rossini as 4.1833 J to 
 4436 cal_th                  calorie_th   #   avoid difficulties associated with the 
 4437                                      #   uncertainty in the heat capacity of 
 4438                                      #   water.  In 1948 the value of the joule 
 4439                                      #   was changed, so the thermochemical
 4440                                      #   calorie was redefined to 4.184 J.
 4441                                      #   This kept the energy measured by this
 4442                                      #   unit the same. 
 4443 calorie_IT              4.1868 J     # International (Steam) Table calorie,
 4444 cal_IT                  calorie_IT   #   defined in 1929 as watt-hour/860 or
 4445                                      #   equivalently 180|43 joules.  At this
 4446                                      #   time the international joule had a
 4447                                      #   different value than the modern joule,
 4448                                      #   and the values were different in the
 4449                                      #   USA and in Europe.  In 1956 at the
 4450                                      #   Fifth International Conference on
 4451                                      #   Properties of Steam the exact
 4452                                      #   definition given here was adopted. 
 4453 calorie_15              4.18580 J    # Energy to go from 14.5 to 15.5 degC
 4454 cal_15                  calorie_15
 4455 calorie_fifteen         cal_15
 4456 calorie_20              4.18190 J    # Energy to go from 19.5 to 20.5 degC
 4457 cal_20                  calorie_20
 4458 calorie_twenty          calorie_20
 4459 calorie_4               4.204 J      # Energy to go from 3.5 to 4.5 degC
 4460 cal_4                   calorie_4
 4461 calorie_four            calorie_4
 4462 cal_mean                4.19002 J    # 1|100 energy to go from 0 to 100 degC
 4463 Calorie                 kilocalorie  # the food Calorie
 4464 thermie              1e6 cal_15      # Heat required to raise the
 4465                                      # temperature of a tonne of
 4466                                      # water from 14.5 to 15.5 degC.
 4467 
 4468 # btu definitions: energy to raise a pound of water 1 degF
 4469 
 4470 btu                     btu_IT       # International Table BTU is the default
 4471 britishthermalunit      btu
 4472 btu_IT                  cal_IT lb degF / gram K
 4473 btu_th                  cal_th lb degF / gram K
 4474 btu_mean                cal_mean lb degF / gram K
 4475 btu_15                  cal_15 lb degF / gram K
 4476 btu_ISO                 1055.06 J    # Exact, rounded ISO definition based
 4477                                      #    on the IT calorie
 4478 quad                    quadrillion btu
 4479 
 4480 ECtherm                 1e5 btu_ISO    # Exact definition
 4481 UStherm                 1.054804e8 J   # Exact definition, 
 4482 therm                   UStherm
 4483 
 4484 # Water latent heat from [23]
 4485 
 4486 water_fusion_heat       6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
 4487 water_vaporization_heat 2256.4 J/g  # At saturation, 100 deg C, 101.42 kPa
 4488 
 4489 # Specific heat capacities of various substances
 4490 
 4491 specificheat_water      calorie / g K
 4492 water_specificheat      specificheat_water
 4493      # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
 4494 specificheat_aluminum   0.91 J/g K
 4495 specificheat_antimony   0.21 J/g K
 4496 specificheat_barium     0.20 J/g K
 4497 specificheat_beryllium  1.83 J/g K
 4498 specificheat_bismuth    0.13 J/g K
 4499 specificheat_cadmium    0.23 J/g K
 4500 specificheat_cesium     0.24 J/g K
 4501 specificheat_chromium   0.46 J/g K
 4502 specificheat_cobalt     0.42 J/g K
 4503 specificheat_copper     0.39 J/g K
 4504 specificheat_gallium    0.37 J/g K
 4505 specificheat_germanium  0.32 J/g K
 4506 specificheat_gold       0.13 J/g K
 4507 specificheat_hafnium    0.14 J/g K
 4508 specificheat_indium     0.24 J/g K
 4509 specificheat_iridium    0.13 J/g K
 4510 specificheat_iron       0.45 J/g K
 4511 specificheat_lanthanum  0.195 J/g K
 4512 specificheat_lead       0.13 J/g K
 4513 specificheat_lithium    3.57 J/g K
 4514 specificheat_lutetium   0.15 J/g K
 4515 specificheat_magnesium  1.05 J/g K
 4516 specificheat_manganese  0.48 J/g K
 4517 specificheat_mercury    0.14 J/g K
 4518 specificheat_molybdenum 0.25 J/g K
 4519 specificheat_nickel     0.44 J/g K
 4520 specificheat_osmium     0.13 J/g K
 4521 specificheat_palladium  0.24 J/g K
 4522 specificheat_platinum   0.13 J/g K
 4523 specificheat_plutonum   0.13 J/g K
 4524 specificheat_potassium  0.75 J/g K
 4525 specificheat_rhenium    0.14 J/g K
 4526 specificheat_rhodium    0.24 J/g K
 4527 specificheat_rubidium   0.36 J/g K
 4528 specificheat_ruthenium  0.24 J/g K
 4529 specificheat_scandium   0.57  J/g K
 4530 specificheat_selenium   0.32 J/g K
 4531 specificheat_silicon    0.71 J/g K
 4532 specificheat_silver     0.23 J/g K
 4533 specificheat_sodium     1.21 J/g K
 4534 specificheat_strontium  0.30 J/g K
 4535 specificheat_tantalum   0.14 J/g K
 4536 specificheat_thallium   0.13 J/g K
 4537 specificheat_thorium    0.13 J/g K
 4538 specificheat_tin        0.21 J/g K
 4539 specificheat_titanium   0.54 J/g K
 4540 specificheat_tungsten   0.13 J/g K
 4541 specificheat_uranium    0.12 J/g K
 4542 specificheat_vanadium   0.39 J/g K
 4543 specificheat_yttrium    0.30 J/g K
 4544 specificheat_zinc       0.39 J/g K
 4545 specificheat_zirconium  0.27 J/g K
 4546 specificheat_ethanol    2.3  J/g K
 4547 specificheat_ammonia    4.6 J/g K
 4548 specificheat_freon      0.91 J/g K   # R-12 at 0 degrees Fahrenheit
 4549 specificheat_gasoline   2.22 J/g K
 4550 specificheat_iodine     2.15 J/g K
 4551 specificheat_oliveoil   1.97 J/g K
 4552 
 4553 #  en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
 4554 specificheat_hydrogen   14.3 J/g K
 4555 specificheat_helium     5.1932 J/g K
 4556 specificheat_argon      0.5203 J/g K
 4557 specificheat_tissue     3.5 J/g K
 4558 specificheat_diamond    0.5091 J/g K
 4559 specificheat_granite    0.79 J/g K
 4560 specificheat_graphite   0.71 J/g K
 4561 specificheat_ice        2.11 J/g K
 4562 specificheat_asphalt    0.92 J/g K
 4563 specificheat_brick      0.84 J/g K
 4564 specificheat_concrete   0.88 J/g K
 4565 specificheat_glass_silica 0.84 J/g K
 4566 specificheat_glass_flint  0.503 J/g K
 4567 specificheat_glass_pyrex  0.753 J/g K
 4568 specificheat_gypsum     1.09 J/g K
 4569 specificheat_marble     0.88 J/g K
 4570 specificheat_sand       0.835 J/g K
 4571 specificheat_soil       0.835 J/g K
 4572 specificheat_wood       1.7 J/g K
 4573 
 4574 specificheat_sucrose    1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
 4575 
 4576 
 4577 # Energy densities of various fuels
 4578 #
 4579 # Most of these fuels have varying compositions or qualities and hence their
 4580 # actual energy densities vary.  These numbers are hence only approximate.
 4581 #
 4582 # E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html
 4583 # E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm
 4584 # E3. http://www.ior.com.au/ecflist.html
 4585 
 4586 tonoil                  1e10 cal_IT    # Ton oil equivalent.  A conventional
 4587                                        # value for the energy released by
 4588 toe                     tonoil         # burning one metric ton of oil. [18,E2]
 4589                                        # Note that energy per mass of petroleum
 4590                                        # products is fairly constant.
 4591                                        # Variations in volumetric energy
 4592                                        # density result from variations in the
 4593                                        # density (kg/m^3) of different fuels.
 4594                                        # This definition is given by the
 4595                                        # IEA/OECD.
 4596 toncoal                 7e9 cal_IT     # Energy in metric ton coal from [18].
 4597                                        # This is a nominal value which
 4598                                        # is close to the heat content
 4599                                        # of coal used in the 1950's
 4600 barreloil               5.8 Mbtu       # Conventional value for barrel of crude
 4601                                        # oil [E2].  Actual range is 5.6 - 6.3.
 4602 naturalgas_HHV          1027 btu/ft3   # Energy content of natural gas.  HHV
 4603 naturalgas_LHV          930 btu/ft3    # is for Higher Heating Value and
 4604 naturalgas              naturalgas_HHV # includes energy from condensation
 4605                                        # combustion products.  LHV is for Lower
 4606                                        # Heating Value and excludes these.
 4607                                        # American publications typically report
 4608                                        # HHV whereas European ones report LHV.
 4609 charcoal                30 GJ/tonne
 4610 woodenergy_dry          20 GJ/tonne    # HHV, a cord weights about a tonne
 4611 woodenergy_airdry       15 GJ/tonne    # 20% moisture content
 4612 coal_bituminous         27 GJ / tonne
 4613 coal_lignite            15 GJ / tonne
 4614 coal_US                 22 GJ / uston  # Average for US coal (short ton), 1995
 4615 ethanol_HHV         84000 btu/usgallon
 4616 ethanol_LHV         75700 btu/usgallon
 4617 diesel             130500 btu/usgallon
 4618 gasoline_LHV       115000 btu/usgallon
 4619 gasoline_HHV       125000 btu/usgallon
 4620 gasoline                gasoline_HHV
 4621 heating                 37.3 MJ/liter
 4622 fueloil                 39.7 MJ/liter  # low sulphur
 4623 propane                 93.3 MJ/m^3
 4624 butane                  124 MJ/m^3
 4625 
 4626 # These values give total energy from uranium fission.  Actual efficiency
 4627 # of nuclear power plants is around 30%-40%.  Note also that some reactors
 4628 # use enriched uranium around 3% U-235.  Uranium during processing or use
 4629 # may be in a compound of uranium oxide or uranium hexafluoride, in which
 4630 # case the energy density would be lower depending on how much uranium is
 4631 # in the compound.
 4632 
 4633 uranium_pure     200 MeV avogadro / (235.0439299 g/mol)  # Pure U-235
 4634 uranium_natural         0.7% uranium_pure        # Natural uranium: 0.7% U-235
 4635 
 4636 # Celsius heat unit: energy to raise a pound of water 1 degC
 4637 
 4638 celsiusheatunit         cal lb degC / gram K
 4639 chu                     celsiusheatunit
 4640 
 4641 POWER                   watt
 4642 
 4643 # "Apparent" average power in an AC circuit, the product of rms voltage
 4644 # and rms current, equal to the true power in watts when voltage and
 4645 # current are in phase.  In a DC circuit, always equal to the true power.
 4646 
 4647 VA                      volt ampere
 4648 
 4649 kWh                     kilowatt hour
 4650 
 4651 # The horsepower is supposedly the power of one horse pulling.   Obviously
 4652 # different people had different horses.
 4653 
 4654 horsepower              550 foot pound force / sec    # Invented by James Watt
 4655 mechanicalhorsepower    horsepower
 4656 hp                      horsepower
 4657 metrichorsepower        75 kilogram force meter / sec # PS=Pferdestaerke in
 4658 electrichorsepower      746 W                         # Germany
 4659 boilerhorsepower        9809.50 W
 4660 waterhorsepower         746.043 W
 4661 brhorsepower            horsepower   # Value corrected Dec, 2019.  Was 745.7 W.
 4662 donkeypower             250 W
 4663 chevalvapeur            metrichorsepower
 4664 
 4665 #
 4666 # Heat Transfer
 4667 #
 4668 # Thermal conductivity, K, measures the rate of heat transfer across
 4669 # a material.  The heat transfered is
 4670 #     Q = K dT A t / L
 4671 # where dT is the temperature difference across the material, A is the
 4672 # cross sectional area, t is the time, and L is the length (thickness).
 4673 # Thermal conductivity is a material property.
 4674 
 4675 THERMAL_CONDUCTIVITY    POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH)
 4676 THERMAL_RESISTIVITY     1/THERMAL_CONDUCTIVITY
 4677 
 4678 # Thermal conductance is the rate at which heat flows across a given
 4679 # object, so the area and thickness have been fixed.  It depends on
 4680 # the size of the object and is hence not a material property.
 4681 
 4682 THERMAL_CONDUCTANCE     POWER / TEMPERATURE_DIFFERENCE
 4683 THERMAL_RESISTANCE      1/THERMAL_CONDUCTANCE
 4684 
 4685 # Thermal admittance is the rate of heat flow per area across an
 4686 # object whose thickness has been fixed.  Its reciprocal, thermal
 4687 # insulation, is used to for measuring the heat transfer per area
 4688 # of sheets of insulation or cloth that are of specified thickness.
 4689 
 4690 THERMAL_ADMITTANCE      THERMAL_CONDUCTIVITY / LENGTH
 4691 THERMAL_INSULANCE       THERMAL_RESISTIVITY LENGTH
 4692 THERMAL_INSULATION      THERMAL_RESISTIVITY LENGTH
 4693 
 4694 Rvalue                  degF ft^2 hr / btu
 4695 Uvalue                  1/Rvalue
 4696 europeanUvalue          watt / m^2 K
 4697 RSI                     degC m^2 / W
 4698 clo                     0.155 degC m^2 / W # Supposed to be the insulance
 4699                                            # required to keep a resting person
 4700                                            # comfortable indoors.  The value
 4701                                            # given is from NIST and the CRC,
 4702                                            # but [5] gives a slightly different
 4703                                            # value of 0.875 ft^2 degF hr / btu.
 4704 tog                     0.1 degC m^2 / W   # Also used for clothing.
 4705 
 4706 
 4707 # Thermal Conductivity of a few materials
 4708 
 4709 diamond_natural_thermal_conductivity    2200 W / m K
 4710 diamond_synthetic_thermal_conductivity  3320 W / m K  # 99% pure C12
 4711 silver_thermal_conductivity             406 W / m K
 4712 aluminum_thermal_conductivity           205 W / m K
 4713 copper_thermal_conductivity             385 W / m K
 4714 gold_thermal_conductivity               314 W / m K
 4715 iron_thermal_conductivity               79.5 W / m K
 4716 stainless_304_thermal_conductivity      15.5 W / m K  # average value
 4717 
 4718 # The bel was defined by engineers of Bell Laboratories to describe the
 4719 # reduction in audio level over a length of one mile. It was originally
 4720 # called the transmission unit (TU) but was renamed around 1923 to honor
 4721 # Alexander Graham Bell. The bel proved inconveniently large so the decibel
 4722 # has become more common.  The decibel is dimensionless since it reports a
 4723 # ratio, but it is used in various contexts to report a signal's power
 4724 # relative to some reference level.
 4725 
 4726 bel(x)     units=[1;1] range=(0,) 10^(x);    log(bel)    # Basic bel definition
 4727 decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
 4728 dB()       decibel                                           # Abbreviation
 4729 dBW(x)     units=[1;W] range=(0,) dB(x) W ;  ~dB(dBW/W)      # Reference = 1 W
 4730 dBk(x)     units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW)     # Reference = 1 kW
 4731 dBf(x)     units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW)     # Reference = 1 fW
 4732 dBm(x)     units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW)     # Reference = 1 mW
 4733 dBmW(x)    units=[1;W] range=(0,) dBm(x) ;   ~dBm(dBmW)      # Reference = 1 mW
 4734 dBJ(x)     units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J)        # Energy relative
 4735                                      # to 1 joule.  Used for power spectral
 4736                                      # density since W/Hz = J
 4737 
 4738 # When used to measure amplitude, voltage, or current the signal is squared
 4739 # because power is proportional to the square of these measures.  The root
 4740 # mean square (RMS) voltage is typically used with these units.
 4741 
 4742 dBV(x)  units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
 4743 dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
 4744 dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
 4745                                    # Reference = 1 microvolt
 4746 
 4747 # Here are dB measurements for current.  Be aware that dbA is also 
 4748 # a unit for frequency weighted sound pressure.  
 4749 dBA(x)  units=[1;A] range=(0,) dB(0.5 x) A;~dB(dBA^2 / A^2) # Reference = 1 A
 4750 dBmA(x) units=[1;A] range=(0,) dB(0.5 x) mA;~dB(dBmA^2/mA^2)# Reference = 1 mA
 4751 dBuA(x) units=[1;A] range=(0,) dB(0.5 x) microA ; ~dB(dBuA^2 / microA^2)
 4752                                                     # Reference = 1 microamp
 4753 
 4754 # Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
 4755 # Originally defined as dBv but changed to prevent confusion with dBV.
 4756 # The "u" is for unloaded.
 4757 dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
 4758                               ~dB(dBu^2 / mW 600 ohm)
 4759 dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv)  # Synonym for dBu
 4760 
 4761 # Measurements for sound in air, referenced to the threshold of human hearing
 4762 # Note that sound in other media typically uses 1 micropascal as a reference
 4763 # for sound pressure.  Units dBA, dBB, dBC, refer to different frequency
 4764 # weightings meant to approximate the human ear's response.
 4765 
 4766 dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ;  \
 4767                                  ~dB(dBSPL^2 / (20 microPa)^2) # pressure
 4768 dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
 4769                                     ~dB(dBSIL / (1e-12 W/m^2)) # intensity
 4770 dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
 4771 
 4772 
 4773 # Misc other measures
 4774 
 4775 ENTROPY                 ENERGY / TEMPERATURE
 4776 clausius                1e3 cal/K       # A unit of physical entropy
 4777 langley                 thermcalorie/cm^2    # Used in radiation theory
 4778 poncelet                100 kg force m / s
 4779 tonrefrigeration        uston 144 btu / lb day # One ton refrigeration is
 4780                                         # the rate of heat extraction required
 4781                                         # turn one ton of water to ice in
 4782                                         # a day.  Ice is defined to have a
 4783                                         # latent heat of 144 btu/lb.
 4784 tonref                  tonrefrigeration
 4785 refrigeration           tonref / ton
 4786 frigorie                1000 cal_15     # Used in refrigeration engineering.
 4787 tnt                     1e9 cal_th / ton# So you can write tons tnt. This
 4788                                         # is a defined, not measured, value.
 4789 airwatt                 8.5 (ft^3/min) inH2O # Measure of vacuum power as
 4790                                              # pressure times air flow.
 4791 
 4792 # Nuclear weapon yields 
 4793 
 4794 davycrocket             10 ton tnt         # lightest US tactical nuclear weapon
 4795 hiroshima               15.5 kiloton tnt   # Uranium-235 fission bomb
 4796 nagasaki                21 kiloton tnt     # Plutonium-239 fission bomb
 4797 fatman                  nagasaki
 4798 littleboy               hiroshima
 4799 ivyking                 500 kiloton tnt    # most powerful fission bomb
 4800 castlebravo             15 megaton tnt     # most powerful US test
 4801 tsarbomba		50 megaton tnt     # most powerful test ever: USSR,
 4802                                            # 30 October 1961
 4803 b53bomb                 9 megaton tnt
 4804                  # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/
 4805 trinity                 18 kiloton tnt     # July 16, 1945
 4806 gadget                  trinity
 4807 
 4808 #
 4809 # Permeability: The permeability or permeance, n, of a substance determines
 4810 # how fast vapor flows through the substance.  The formula W = n A dP
 4811 # holds where W is the rate of flow (in mass/time), n is the permeability,
 4812 # A is the area of the flow path, and dP is the vapor pressure difference.
 4813 #
 4814 
 4815 perm_0C                 grain / hr ft^2 inHg
 4816 perm_zero               perm_0C
 4817 perm_0                  perm_0C
 4818 perm                    perm_0C
 4819 perm_23C                grain / hr ft^2 in Hg23C
 4820 perm_twentythree        perm_23C
 4821 
 4822 #
 4823 # Counting measures
 4824 #
 4825 
 4826 pair                    2
 4827 brace                   2
 4828 nest                    3     # often used for items like bowls that
 4829                               #   nest together
 4830 hattrick                3     # Used in sports, especially cricket and ice
 4831                               #   hockey to report the number of goals.
 4832 dicker                  10
 4833 dozen                   12
 4834 bakersdozen             13
 4835 score                   20
 4836 flock                   40
 4837 timer                   40
 4838 shock                   60
 4839 toncount                100   # Used in sports in the UK
 4840 longhundred             120   # From a germanic counting system
 4841 gross                   144
 4842 greatgross              12 gross
 4843 tithe                   1|10  # From Anglo-Saxon word for tenth
 4844 
 4845 # Paper counting measure
 4846 
 4847 shortquire              24
 4848 quire                   25
 4849 shortream               480
 4850 ream                    500
 4851 perfectream             516
 4852 bundle                  2 reams
 4853 bale                    5 bundles
 4854 
 4855 #
 4856 # Paper measures
 4857 #
 4858 
 4859 # USA paper sizes
 4860 
 4861 lettersize              8.5 inch 11 inch
 4862 legalsize               8.5 inch 14 inch
 4863 ledgersize              11 inch 17 inch
 4864 executivesize           7.25 inch 10.5 inch
 4865 Apaper                  8.5 inch 11 inch
 4866 Bpaper                  11 inch 17 inch
 4867 Cpaper                  17 inch 22 inch
 4868 Dpaper                  22 inch 34 inch
 4869 Epaper                  34 inch 44 inch
 4870 
 4871 # Correspondence envelope sizes.  #10 is the standard business
 4872 # envelope in the USA. 
 4873 
 4874 envelope6_25size        3.5 inch 6 inch
 4875 envelope6_75size        3.625 inch 6.5 inch
 4876 envelope7size           3.75 inch 6.75 inch
 4877 envelope7_75size        3.875 inch 7.5 inch
 4878 envelope8_625size       3.625 inch 8.625 inch
 4879 envelope9size           3.875 inch 8.875 inch
 4880 envelope10size          4.125 inch 9.5 inch
 4881 envelope11size          4.5 inch 10.375 inch
 4882 envelope12size          4.75 inch 11 inch
 4883 envelope14size          5 inch 11.5 inch
 4884 envelope16size          6 inch 12 inch
 4885 
 4886 # Announcement envelope sizes (no relation to metric paper sizes like A4)
 4887 
 4888 envelopeA1size          3.625 inch 5.125 inch  # same as 4bar
 4889 envelopeA2size          4.375 inch 5.75 inch
 4890 envelopeA6size          4.75 inch 6.5 inch
 4891 envelopeA7size          5.25 inch 7.25 inch
 4892 envelopeA8size          5.5 inch 8.125 inch   
 4893 envelopeA9size          5.75 inch 8.75 inch
 4894 envelopeA10size         6 inch 9.5 inch
 4895 
 4896 # Baronial envelopes
 4897 
 4898 envelope4bar            3.625 inch 5.125 inch  # same as A1
 4899 envelope5_5bar          4.375 inch 5.75 inch
 4900 envelope6bar            4.75 inch 6.5 inch
 4901 
 4902 # Coin envelopes
 4903 
 4904 envelope1baby           2.25 inch 3.5 inch     # same as #1 coin
 4905 envelope00coin          1.6875 inch 2.75 inch
 4906 envelope1coin           2.25 inch 3.5 inch
 4907 envelope3coin           2.5 inch 4.25 inch
 4908 envelope4coin           3 inch 4.5 inch
 4909 envelope4_5coin         3 inch 4.875 inch
 4910 envelope5coin           2.875 inch 5.25 inch
 4911 envelope5_5coin         3.125 inch 5.5 inch
 4912 envelope6coin           3.375 inch 6 inch
 4913 envelope7coin           3.5 inch 6.5 inch
 4914 
 4915 # The metric paper sizes are defined so that if a sheet is cut in half
 4916 # along the short direction, the result is two sheets which are
 4917 # similar to the original sheet.  This means that for any metric size,
 4918 # the long side is close to sqrt(2) times the length of the short
 4919 # side.  Each series of sizes is generated by repeated cuts in half,
 4920 # with the values rounded down to the nearest millimeter.
 4921 
 4922 A0paper                 841 mm 1189 mm   # The basic size in the A series
 4923 A1paper                 594 mm  841 mm   # is defined to have an area of
 4924 A2paper                 420 mm  594 mm   # one square meter.
 4925 A3paper                 297 mm  420 mm
 4926 A4paper                 210 mm  297 mm
 4927 A5paper                 148 mm  210 mm
 4928 A6paper                 105 mm  148 mm
 4929 A7paper                  74 mm  105 mm
 4930 A8paper                  52 mm   74 mm
 4931 A9paper                  37 mm   52 mm
 4932 A10paper                 26 mm   37 mm
 4933 
 4934 B0paper                1000 mm 1414 mm   # The basic B size has an area
 4935 B1paper                 707 mm 1000 mm   # of sqrt(2) square meters.
 4936 B2paper                 500 mm  707 mm
 4937 B3paper                 353 mm  500 mm
 4938 B4paper                 250 mm  353 mm
 4939 B5paper                 176 mm  250 mm
 4940 B6paper                 125 mm  176 mm
 4941 B7paper                  88 mm  125 mm
 4942 B8paper                  62 mm   88 mm
 4943 B9paper                  44 mm   62 mm
 4944 B10paper                 31 mm   44 mm
 4945 
 4946 C0paper                 917 mm 1297 mm   # The basic C size has an area
 4947 C1paper                 648 mm  917 mm   # of sqrt(sqrt(2)) square meters.
 4948 C2paper                 458 mm  648 mm
 4949 C3paper                 324 mm  458 mm   # Intended for envelope sizes
 4950 C4paper                 229 mm  324 mm
 4951 C5paper                 162 mm  229 mm
 4952 C6paper                 114 mm  162 mm
 4953 C7paper                  81 mm  114 mm
 4954 C8paper                  57 mm   81 mm
 4955 C9paper                  40 mm   57 mm
 4956 C10paper                 28 mm   40 mm
 4957 
 4958 # gsm (Grams per Square Meter), a sane, metric paper weight measure
 4959 
 4960 gsm                     grams / meter^2
 4961 
 4962 # In the USA, a collection of crazy historical paper measures are used.  Paper
 4963 # is measured as a weight of a ream of that particular type of paper.  This is
 4964 # sometimes called the "substance" or "basis" (as in "substance 20" paper).
 4965 # The standard sheet size or "basis size" varies depending on the type of
 4966 # paper.  As a result, 20 pound bond paper and 50 pound text paper are actually
 4967 # about the same weight.  The different sheet sizes were historically the most
 4968 # convenient for printing or folding in the different applications.  These
 4969 # different basis weights are standards maintained by American Society for
 4970 # Testing Materials (ASTM) and the American Forest and Paper Association
 4971 # (AF&PA).
 4972 
 4973 poundbookpaper          lb / 25 inch 38 inch ream
 4974 lbbook                  poundbookpaper
 4975 poundtextpaper          poundbookpaper
 4976 lbtext                  poundtextpaper
 4977 poundoffsetpaper        poundbookpaper    # For offset printing
 4978 lboffset                poundoffsetpaper
 4979 poundbiblepaper         poundbookpaper    # Designed to be lightweight, thin,
 4980 lbbible                 poundbiblepaper   # strong and opaque.
 4981 poundtagpaper           lb / 24 inch 36 inch ream
 4982 lbtag                   poundtagpaper
 4983 poundbagpaper           poundtagpaper
 4984 lbbag                   poundbagpaper
 4985 poundnewsprintpaper     poundtagpaper
 4986 lbnewsprint             poundnewsprintpaper
 4987 poundposterpaper        poundtagpaper
 4988 lbposter                poundposterpaper
 4989 poundtissuepaper        poundtagpaper
 4990 lbtissue                poundtissuepaper
 4991 poundwrappingpaper      poundtagpaper
 4992 lbwrapping              poundwrappingpaper
 4993 poundwaxingpaper        poundtagpaper
 4994 lbwaxing                poundwaxingpaper
 4995 poundglassinepaper      poundtagpaper
 4996 lbglassine              poundglassinepaper
 4997 poundcoverpaper         lb / 20 inch 26 inch ream
 4998 lbcover                 poundcoverpaper
 4999 poundindexpaper         lb / 25.5 inch 30.5 inch ream
 5000 lbindex                 poundindexpaper
 5001 poundindexbristolpaper  poundindexpaper
 5002 lbindexbristol          poundindexpaper
 5003 poundbondpaper          lb / 17 inch 22 inch ream  # Bond paper is stiff and
 5004 lbbond                  poundbondpaper             # durable for repeated
 5005 poundwritingpaper       poundbondpaper             # filing, and it resists
 5006 lbwriting               poundwritingpaper          # ink penetration.
 5007 poundledgerpaper        poundbondpaper
 5008 lbledger                poundledgerpaper
 5009 poundcopypaper          poundbondpaper
 5010 lbcopy                  poundcopypaper
 5011 poundblottingpaper      lb / 19 inch 24 inch ream
 5012 lbblotting              poundblottingpaper
 5013 poundblankspaper        lb / 22 inch 28 inch ream
 5014 lbblanks                poundblankspaper
 5015 poundpostcardpaper      lb / 22.5 inch 28.5 inch ream
 5016 lbpostcard              poundpostcardpaper
 5017 poundweddingbristol     poundpostcardpaper
 5018 lbweddingbristol        poundweddingbristol
 5019 poundbristolpaper       poundweddingbristol
 5020 lbbristol               poundbristolpaper
 5021 poundboxboard           lb / 1000 ft^2
 5022 lbboxboard              poundboxboard
 5023 poundpaperboard         poundboxboard
 5024 lbpaperboard            poundpaperboard
 5025 
 5026 # When paper is marked in units of M, it means the weight of 1000 sheets of the
 5027 # given size of paper.  To convert this to paper weight, divide by the size of
 5028 # the paper in question.
 5029 
 5030 paperM                  lb / 1000
 5031 
 5032 # In addition paper weight is reported in "caliper" which is simply the
 5033 # thickness of one sheet, typically in inches.  Thickness is also reported in
 5034 # "points" where a point is 1|1000 inch.  These conversions are supplied to
 5035 # convert these units roughly (using an approximate density) into the standard
 5036 # paper weight values.
 5037 
 5038 pointthickness          0.001 in
 5039 paperdensity            0.8 g/cm^3        # approximate--paper densities vary!
 5040 papercaliper            in paperdensity
 5041 paperpoint              pointthickness paperdensity
 5042 
 5043 #
 5044 # Printing
 5045 #
 5046 
 5047 fournierpoint           0.1648 inch / 12  # First definition of the printers
 5048                                           # point made by Pierre Fournier who
 5049                                           # defined it in 1737 as 1|12 of a
 5050                                           # cicero which was 0.1648 inches.
 5051 olddidotpoint           1|72 frenchinch   # François Ambroise Didot, one of
 5052                                           # a family of printers, changed
 5053                                           # Fournier's definition around 1770
 5054                                           # to fit to the French units then in
 5055                                           # use.
 5056 bertholdpoint           1|2660 m          # H. Berthold tried to create a
 5057                                           # metric version of the didot point
 5058                                           # in 1878.
 5059 INpoint                 0.4 mm            # This point was created by a
 5060                                           # group directed by Fermin Didot in
 5061                                           # 1881 and is associated with the
 5062                                           # imprimerie nationale.  It doesn't
 5063                                           # seem to have been used much.
 5064 germandidotpoint        0.376065 mm       # Exact definition appears in DIN
 5065                                           # 16507, a German standards document
 5066                                           # of 1954.  Adopted more broadly  in
 5067                                           # 1966 by ???
 5068 metricpoint             3|8 mm            # Proposed in 1977 by Eurograf
 5069 oldpoint                1|72.27 inch      # The American point was invented
 5070 printerspoint           oldpoint          # by Nelson Hawks in 1879 and
 5071 texpoint                oldpoint          # dominates USA publishing.
 5072                                           # It was standardized by the American
 5073                                           # Typefounders Association at the
 5074                                           # value of 0.013837 inches exactly.
 5075                                           # Knuth uses the approximation given
 5076                                           # here (which is very close).  The
 5077                                           # comp.fonts FAQ claims that this
 5078                                           # value is supposed to be 1|12 of a
 5079                                           # pica where 83 picas is equal to 35
 5080                                           # cm.  But this value differs from
 5081                                           # the standard.
 5082 texscaledpoint          1|65536 texpoint  # The TeX typesetting system uses
 5083 texsp                   texscaledpoint    # this for all computations.
 5084 computerpoint           1|72 inch         # The American point was rounded
 5085 point                   computerpoint
 5086 computerpica            12 computerpoint  # to an even 1|72 inch by computer
 5087 postscriptpoint         computerpoint     # people at some point.
 5088 pspoint                 postscriptpoint
 5089 twip                    1|20 point        # TWentieth of an Imperial Point
 5090 Q                       1|4 mm            # Used in Japanese phototypesetting
 5091                                           # Q is for quarter
 5092 frenchprinterspoint     olddidotpoint
 5093 didotpoint              germandidotpoint  # This seems to be the dominant value
 5094 europeanpoint           didotpoint        # for the point used in Europe
 5095 cicero                  12 didotpoint
 5096 
 5097 stick                   2 inches
 5098 
 5099 # Type sizes
 5100 
 5101 excelsior               3 oldpoint
 5102 brilliant               3.5 oldpoint
 5103 diamondtype             4 oldpoint
 5104 pearl                   5 oldpoint
 5105 agate                   5.5 oldpoint  # Originally agate type was 14 lines per
 5106                                       #   inch, giving a value of 1|14 in.
 5107 ruby                    agate         # British
 5108 nonpareil               6 oldpoint
 5109 mignonette              6.5 oldpoint
 5110 emerald                 mignonette    # British
 5111 minion                  7 oldpoint
 5112 brevier                 8 oldpoint
 5113 bourgeois               9 oldpoint
 5114 longprimer              10 oldpoint
 5115 smallpica               11 oldpoint
 5116 pica                    12 oldpoint
 5117 english                 14 oldpoint
 5118 columbian               16 oldpoint
 5119 greatprimer             18 oldpoint
 5120 paragon                 20 oldpoint
 5121 meridian                44 oldpoint
 5122 canon                   48 oldpoint
 5123 
 5124 # German type sizes
 5125 
 5126 nonplusultra            2 didotpoint
 5127 brillant                3 didotpoint
 5128 diamant                 4 didotpoint
 5129 perl                    5 didotpoint
 5130 nonpareille             6 didotpoint
 5131 kolonel                 7 didotpoint
 5132 petit                   8 didotpoint
 5133 borgis                  9 didotpoint
 5134 korpus                  10 didotpoint
 5135 corpus                  korpus
 5136 garamond                korpus
 5137 mittel                  14 didotpoint
 5138 tertia                  16 didotpoint
 5139 text                    18 didotpoint
 5140 kleine_kanon            32 didotpoint
 5141 kanon                   36 didotpoint
 5142 grobe_kanon             42 didotpoint
 5143 missal                  48 didotpoint
 5144 kleine_sabon            72 didotpoint
 5145 grobe_sabon             84 didotpoint
 5146 
 5147 #
 5148 # Information theory units.  Note that the name "entropy" is used both
 5149 # to measure information and as a physical quantity.
 5150 #
 5151 
 5152 INFORMATION             bit
 5153 
 5154 nat                     (1/ln(2)) bits       # Entropy measured base e
 5155 hartley                 log2(10) bits        # Entropy of a uniformly
 5156 ban                     hartley              #   distributed random variable
 5157                                              #   over 10 symbols.
 5158 dit                     hartley              # from Decimal digIT
 5159 
 5160 #
 5161 # Computer
 5162 #
 5163 
 5164 bps                     bit/sec              # Sometimes the term "baud" is
 5165                                              #   incorrectly used to refer to
 5166                                              #   bits per second.  Baud refers
 5167                                              #   to symbols per second.  Modern
 5168                                              #   modems transmit several bits
 5169                                              #   per symbol.
 5170 byte                    8 bit                # Not all machines had 8 bit
 5171 B                       byte                 #   bytes, but these days most of
 5172                                              #   them do.  But beware: for
 5173                                              #   transmission over modems, a
 5174                                              #   few extra bits are used so
 5175                                              #   there are actually 10 bits per
 5176                                              #   byte.
 5177 octet                   8 bits               # The octet is always 8 bits
 5178 nybble                  4 bits               # Half of a byte. Sometimes
 5179                                              #   equal to different lengths
 5180                                              #   such as 3 bits.
 5181 nibble                  nybble
 5182 nyp                     2 bits               # Donald Knuth asks in an exercise
 5183                                              #   for a name for a 2 bit
 5184                                              #   quantity and gives the "nyp"
 5185                                              #   as a solution due to Gregor
 5186                                              #   Purdy.  Not in common use.
 5187 meg                     megabyte             # Some people consider these
 5188                                              # units along with the kilobyte
 5189 gig                     gigabyte             # to be defined according to
 5190                                              # powers of 2 with the kilobyte
 5191                                              # equal to 2^10 bytes, the
 5192                                              # megabyte equal to 2^20 bytes and
 5193                                              # the gigabyte equal to 2^30 bytes
 5194                                              # but these usages are forbidden
 5195                                              # by SI.  Binary prefixes have
 5196                                              # been defined by IEC to replace
 5197                                              # the SI prefixes.  Use them to
 5198                                              # get the binary values: KiB, MiB,
 5199                                              # and GiB.
 5200 jiffy                   0.01 sec     # This is defined in the Jargon File
 5201 jiffies                 jiffy        # (http://www.jargon.org) as being the
 5202                                      # duration of a clock tick for measuring
 5203                                      # wall-clock time.  Supposedly the value
 5204                                      # used to be 1|60 sec or 1|50 sec
 5205                                      # depending on the frequency of AC power,
 5206                                      # but then 1|100 sec became more common.
 5207                                      # On linux systems, this term is used and
 5208                                      # for the Intel based chips, it does have
 5209                                      # the value of .01 sec.  The Jargon File
 5210                                      # also lists two other definitions:
 5211                                      # millisecond, and the time taken for
 5212                                      # light to travel one foot.
 5213 cdaudiospeed      44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2
 5214                                      # samples of sixteen bits each.
 5215 cdromspeed       75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read
 5216                                      # each second with 2048 bytes per sector.
 5217                                      # Audio CDs do not have sectors, but
 5218                                      # people sometimes divide the bit rate by
 5219                                      # 75 and claim a sector length of 2352.
 5220                                      # Data CDs have a lower rate due to
 5221                                      # increased error correction overhead.
 5222                                      # There is a rarely used mode (mode2) with
 5223                                      # 2336 bytes per sector that has fewer
 5224                                      # error correction bits than mode1.
 5225 dvdspeed                 1385 kB/s   # This is the "1x" speed of a DVD using
 5226                                      # constant linear velocity (CLV) mode.
 5227                                      # Modern DVDs may vary the linear velocity
 5228                                      # as they go from the inside to the
 5229                                      # outside of the disc.
 5230                        # See http://www.osta.org/technology/dvdqa/dvdqa4.htm
 5231 
 5232 FIT         / 1e9 hour # Failures In Time, number of failures per billion hours
 5233 
 5234 #
 5235 # The IP address space is divided into subnets.  The number of hosts
 5236 # in a subnet depends on the length of the subnet prefix.  This is
 5237 # often written as /N where N is the number of bits in the prefix.
 5238 #
 5239 # https://en.wikipedia.org/wiki/Subnetwork
 5240 #
 5241 # These definitions gives the number of hosts for a subnet whose
 5242 # prefix has the specified length in bits.
 5243 #
 5244 
 5245 ipv4subnetsize(prefix_len) units=[1;1]  domain=[0,32] range=[1,4294967296] \
 5246                          2^(32-prefix_len) ; 32-log2(ipv4subnetsize)
 5247 ipv4classA               ipv4subnetsize(8)
 5248 ipv4classB               ipv4subnetsize(16)
 5249 ipv4classC               ipv4subnetsize(24)
 5250 
 5251 ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \
 5252                          range=[1,340282366920938463463374607431768211456] \
 5253                          2^(128-prefix_len) ; 128-log2(ipv6subnetsize)
 5254 
 5255 #
 5256 # Musical measures.  Musical intervals expressed as ratios.  Multiply
 5257 # two intervals together to get the sum of the interval.  The function
 5258 # musicalcent can be used to convert ratios to cents.
 5259 #
 5260 
 5261 # Perfect intervals
 5262 
 5263 octave                  2
 5264 majorsecond             musicalfifth^2 / octave
 5265 majorthird              5|4
 5266 minorthird              6|5
 5267 musicalfourth           4|3
 5268 musicalfifth            3|2
 5269 majorsixth              musicalfourth majorthird
 5270 minorsixth              musicalfourth minorthird
 5271 majorseventh            musicalfifth majorthird
 5272 minorseventh            musicalfifth minorthird
 5273 
 5274 pythagoreanthird        majorsecond musicalfifth^2 / octave
 5275 syntoniccomma           pythagoreanthird / majorthird
 5276 pythagoreancomma        musicalfifth^12 / octave^7
 5277 
 5278 # Equal tempered definitions
 5279 
 5280 semitone                octave^(1|12)
 5281 musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
 5282                                       100 log(musicalcent)/log(semitone)
 5283 
 5284 #
 5285 # Musical note lengths.
 5286 #
 5287 
 5288 wholenote               !
 5289 MUSICAL_NOTE_LENGTH     wholenote
 5290 halfnote                1|2 wholenote
 5291 quarternote             1|4 wholenote
 5292 eighthnote              1|8 wholenote
 5293 sixteenthnote           1|16 wholenote
 5294 thirtysecondnote        1|32 wholenote
 5295 sixtyfourthnote         1|64 wholenote
 5296 dotted                  3|2
 5297 doubledotted            7|4
 5298 breve                   doublewholenote
 5299 semibreve               wholenote
 5300 minimnote               halfnote
 5301 crotchet                quarternote
 5302 quaver                  eighthnote
 5303 semiquaver              sixteenthnote
 5304 demisemiquaver          thirtysecondnote
 5305 hemidemisemiquaver      sixtyfourthnote
 5306 semidemisemiquaver      hemidemisemiquaver
 5307 
 5308 #
 5309 # yarn and cloth measures
 5310 #
 5311 
 5312 # yarn linear density
 5313 
 5314 woolyarnrun             1600 yard/pound # 1600 yds of "number 1 yarn" weighs
 5315                                         # a pound.
 5316 yarncut                 300 yard/pound  # Less common system used in
 5317                                         # Pennsylvania for wool yarn
 5318 cottonyarncount         840 yard/pound
 5319 linenyarncount          300 yard/pound  # Also used for hemp and ramie
 5320 worstedyarncount        1680 ft/pound
 5321 metricyarncount         meter/gram
 5322 denier                  1|9 tex            # used for silk and rayon
 5323 manchesteryarnnumber    drams/1000 yards   # old system used for silk
 5324 pli                     lb/in
 5325 typp                    1000 yd/lb   # abbreviation for Thousand Yard Per Pound
 5326 asbestoscut             100 yd/lb    # used for glass and asbestos yarn
 5327 
 5328 tex                     gram / km    # rational metric yarn measure, meant
 5329 drex                    0.1 tex      # to be used for any kind of yarn
 5330 poumar                  lb / 1e6 yard
 5331 
 5332 # yarn and cloth length
 5333 
 5334 skeincotton             80*54 inch   # 80 turns of thread on a reel with a
 5335                                      #  54 in circumference (varies for other
 5336                                      #  kinds of thread)
 5337 cottonbolt              120 ft       # cloth measurement
 5338 woolbolt                210 ft
 5339 bolt                    cottonbolt
 5340 heer                    600 yards
 5341 cut                     300 yards    # used for wet-spun linen yarn
 5342 lea                     300 yards
 5343 
 5344 sailmakersyard          28.5 in
 5345 sailmakersounce         oz / sailmakersyard 36 inch
 5346 
 5347 silkmomme               momme / 25 yards 1.49 inch  # Traditional silk weight
 5348 silkmm                  silkmomme        # But it is also defined as
 5349                                          # lb/100 yd 45 inch.  The two
 5350                                          # definitions are slightly different
 5351                                          # and neither one seems likely to be
 5352                                          # the true source definition.
 5353 
 5354 #
 5355 # drug dosage
 5356 #
 5357 
 5358 mcg                     microgram        # Frequently used for vitamins
 5359 iudiptheria             62.8 microgram   # IU is for international unit
 5360 iupenicillin            0.6 microgram
 5361 iuinsulin               41.67 microgram
 5362 drop                    1|20 ml          # The drop was an old "unit" that was
 5363                                          # replaced by the minim.  But I was
 5364                                          # told by a pharmacist that in his
 5365                                          # profession, the conversion of 20
 5366                                          # drops per ml is actually used.
 5367 bloodunit               450 ml           # For whole blood.  For blood
 5368                                          # components, a blood unit is the
 5369                                          # quanity of the component found in a
 5370                                          # blood unit of whole blood.  The
 5371                                          # human body contains about 12 blood
 5372                                          # units of whole blood.
 5373 
 5374 #
 5375 # misc medical measure
 5376 #
 5377 
 5378 frenchcathetersize      1|3 mm           # measure used for the outer diameter
 5379                                          # of a catheter
 5380 charriere               frenchcathetersize
 5381 
 5382 
 5383 #
 5384 # fixup units for times when prefix handling doesn't do the job
 5385 #
 5386 
 5387 hectare                 hectoare
 5388 megohm                  megaohm
 5389 kilohm                  kiloohm
 5390 microhm                 microohm
 5391 megalerg                megaerg    # 'L' added to make it pronounceable [18].
 5392 
 5393 #
 5394 # Money
 5395 #
 5396 # Note that US$ is the primitive unit so other currencies are
 5397 # generally given in US$.
 5398 #
 5399 
 5400 unitedstatesdollar      US$
 5401 usdollar                US$
 5402 $                       dollar
 5403 mark                    germanymark
 5404 #bolivar                 venezuelabolivar       # Not all databases are 
 5405 #venezuelabolivarfuerte  1e-5 bolivar           #    supplying these
 5406 #bolivarfuerte           1e-5 bolivar           # The currency was revalued 
 5407 #oldbolivar              1|1000 bolivarfuerte   # twice
 5408 peseta                  spainpeseta
 5409 rand                    southafricarand
 5410 escudo                  portugalescudo
 5411 guilder                 netherlandsguilder
 5412 hollandguilder          netherlandsguilder
 5413 peso                    mexicopeso
 5414 yen                     japanyen
 5415 lira                    italylira
 5416 rupee                   indiarupee
 5417 drachma                 greecedrachma
 5418 franc                   francefranc
 5419 markka                  finlandmarkka
 5420 britainpound            unitedkingdompound
 5421 greatbritainpound       unitedkingdompound
 5422 unitedkingdompound      ukpound
 5423 poundsterling           britainpound
 5424 yuan                    chinayuan
 5425 
 5426 # Unicode Currency Names
 5427 
 5428 !utf8
 5429 icelandkróna            icelandkrona
 5430 polandzłoty             polandzloty
 5431 tongapa’anga            tongapa'anga
 5432 #venezuelabolívar        venezuelabolivar
 5433 vietnamđồng             vietnamdong
 5434 mongoliatögrög          mongoliatugrik
 5435 sãotomé&príncipedobra   saotome&principedobra
 5436 !endutf8
 5437 
 5438 UKP                     GBP        # Not an ISO code, but looks like one, and
 5439                                    # sometimes used on usenet.
 5440 
 5441 !include currency.units
 5442 
 5443 # Money on the gold standard, used in the late 19th century and early
 5444 # 20th century.
 5445 
 5446 olddollargold           23.22 grains goldprice  # Used until 1934
 5447 newdollargold           96|7 grains goldprice   # After Jan 31, 1934
 5448 dollargold              newdollargold
 5449 poundgold               113 grains goldprice    # British pound
 5450 
 5451 # Precious metals
 5452 
 5453 goldounce               goldprice troyounce
 5454 silverounce             silverprice troyounce
 5455 platinumounce           platinumprice troyounce
 5456 XAU                     goldounce
 5457 XPT                     platinumounce
 5458 XAG                     silverounce
 5459 
 5460 # Nominal masses of US coins.  Note that dimes, quarters and half dollars
 5461 # have weight proportional to value.  Before 1965 it was $40 / kg.
 5462 
 5463 USpennyweight           2.5 grams         # Since 1982, 48 grains before
 5464 USnickelweight          5 grams
 5465 USdimeweight            US$ 0.10 / (20 US$ / lb)   # Since 1965
 5466 USquarterweight         US$ 0.25 / (20 US$ / lb)   # Since 1965
 5467 UShalfdollarweight      US$ 0.50 / (20 US$ / lb)   # Since 1971
 5468 USdollarweight          8.1 grams         # Weight of Susan B. Anthony and
 5469                                           #   Sacagawea dollar coins
 5470 
 5471 # British currency
 5472 
 5473 quid                    britainpound        # Slang names
 5474 fiver                   5 quid
 5475 tenner                  10 quid
 5476 monkey                  500 quid
 5477 brgrand                 1000 quid
 5478 bob                     shilling
 5479 
 5480 shilling                1|20 britainpound   # Before decimalisation, there
 5481 oldpence                1|12 shilling       # were 20 shillings to a pound,
 5482 farthing                1|4 oldpence        # each of twelve old pence
 5483 guinea                  21 shilling         # Still used in horse racing
 5484 crown                   5 shilling
 5485 florin                  2 shilling
 5486 groat                   4 oldpence
 5487 tanner                  6 oldpence
 5488 brpenny                 0.01 britainpound
 5489 pence                   brpenny
 5490 tuppence                2 pence
 5491 tuppenny                tuppence
 5492 ha'penny                halfbrpenny
 5493 hapenny                 ha'penny
 5494 oldpenny                oldpence
 5495 oldtuppence             2 oldpence
 5496 oldtuppenny             oldtuppence
 5497 threepence              3 oldpence    # threepence never refers to new money
 5498 threepenny              threepence
 5499 oldthreepence           threepence
 5500 oldthreepenny           threepence
 5501 oldhalfpenny            halfoldpenny
 5502 oldha'penny             oldhalfpenny
 5503 oldhapenny              oldha'penny
 5504 brpony                  25 britainpound
 5505 
 5506 # Canadian currency
 5507 
 5508 loony                   1 canadadollar    # This coin depicts a loon
 5509 toony                   2 canadadollar
 5510 
 5511 # Cryptocurrency
 5512 
 5513 satoshi                 1e-8 bitcoin
 5514 XBT                     bitcoin           # nonstandard code
 5515 
 5516 #
 5517 # Units used for measuring volume of wood
 5518 #
 5519 
 5520 cord                    4*4*8 ft^3   # 4 ft by 4 ft by 8 ft bundle of wood
 5521 facecord                1|2 cord
 5522 cordfoot                1|8 cord     # One foot long section of a cord
 5523 cordfeet                cordfoot
 5524 housecord               1|3 cord     # Used to sell firewood for residences,
 5525                                      #   often confusingly called a "cord"
 5526 boardfoot               ft^2 inch    # Usually 1 inch thick wood
 5527 boardfeet               boardfoot
 5528 fbm                     boardfoot    # feet board measure
 5529 stack                   4 yard^3     # British, used for firewood and coal [18]
 5530 rick                    4 ft 8 ft 16 inches # Stack of firewood, supposedly
 5531                                      #   sometimes called a face cord, but this
 5532                                      #   value is equal to 1|3 cord.  Name
 5533                                      #   comes from an old Norse word for a
 5534                                      #   stack of wood.
 5535 stere                   m^3
 5536 timberfoot              ft^3         # Used for measuring solid blocks of wood
 5537 standard                120 12 ft 11 in 1.5 in  # This is the St Petersburg or
 5538                                      #   Pittsburg standard.  Apparently the
 5539                                      #   term is short for "standard hundred"
 5540                                      #   which was meant to refer to 100 pieces
 5541                                      #   of wood (deals).  However, this
 5542                                      #   particular standard is equal to 120
 5543                                      #   deals which are 12 ft by 11 in by 1.5
 5544                                      #   inches (not the standard deal).
 5545 hoppusfoot               (4/pi) ft^3 # Volume calculation suggested in 1736
 5546 hoppusboardfoot      1|12 hoppusfoot #   forestry manual by Edward Hoppus, for
 5547 hoppuston              50 hoppusfoot #   estimating the usable volume of a log.
 5548                                      #   It results from computing the volume
 5549                                      #   of a cylindrical log of length, L, and
 5550                                      #   girth (circumference), G, by V=L(G/4)^2.
 5551                                      #   The hoppus ton is apparently still in
 5552                                      #   use for shipments from Southeast Asia.
 5553 
 5554 # In Britain, the deal is apparently any piece of wood over 6 feet long, over
 5555 # 7 wide and 2.5 inches thick.  The OED doesn't give a standard size.  A piece
 5556 # of wood less than 7 inches wide is called a "batten".  This unit is now used
 5557 # exclusively for fir and pine.
 5558 
 5559 deal              12 ft 11 in 2.5 in # The standard North American deal [OED]
 5560 wholedeal        12 ft 11 in 1.25 in # If it's half as thick as the standard
 5561                                      #   deal it's called a "whole deal"!
 5562 splitdeal         12 ft 11 in 5|8 in # And half again as thick is a split deal.
 5563 
 5564 
 5565 # Used for shellac mixing rate
 5566 
 5567 poundcut            pound / gallon
 5568 lbcut               poundcut
 5569 
 5570 #
 5571 # Gas and Liquid flow units
 5572 #
 5573 
 5574 FLUID_FLOW              VOLUME / TIME
 5575 
 5576 # Some obvious volumetric gas flow units (cu is short for cubic)
 5577 
 5578 cumec                   m^3/s
 5579 cusec                   ft^3/s
 5580 
 5581 # Conventional abbreviations for fluid flow units
 5582 
 5583 gph                     gal/hr
 5584 gpm                     gal/min
 5585 mgd                     megagal/day
 5586 cfs                     ft^3/s
 5587 cfh                     ft^3/hour
 5588 cfm                     ft^3/min
 5589 lpm                     liter/min
 5590 lfm                     ft/min     # Used to report air flow produced by fans.
 5591                                    # Multiply by cross sectional area to get a
 5592                                    # flow in cfm.
 5593 
 5594 pru                     mmHg / (ml/min)  # peripheral resistance unit, used in
 5595                                          # medicine to assess blood flow in
 5596                                          # the capillaries.
 5597 
 5598 # Miner's inch:  This is an old historic unit used in the Western  United
 5599 # States.  It is generally defined as the rate of flow through a one square
 5600 # inch hole at a specified depth such as 4 inches.  In the late 19th century,
 5601 # volume of water was sometimes measured in the "24 hour inch".  Values for the
 5602 # miner's inch were fixed by state statues.  (This information is from a web
 5603 # site operated by the Nevada Division of Water Planning:  The Water Words
 5604 # Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.)
 5605 
 5606 minersinchAZ            1.5 ft^3/min
 5607 minersinchCA            1.5 ft^3/min
 5608 minersinchMT            1.5 ft^3/min
 5609 minersinchNV            1.5 ft^3/min
 5610 minersinchOR            1.5 ft^3/min
 5611 minersinchID            1.2 ft^3/min
 5612 minersinchKS            1.2 ft^3/min
 5613 minersinchNE            1.2 ft^3/min
 5614 minersinchNM            1.2 ft^3/min
 5615 minersinchND            1.2 ft^3/min
 5616 minersinchSD            1.2 ft^3/min
 5617 minersinchUT            1.2 ft^3/min
 5618 minersinchCO            1 ft^3/sec / 38.4  # 38.4 miner's inches = 1 ft^3/sec
 5619 minersinchBC            1.68 ft^3/min      # British Columbia
 5620 
 5621 # Oceanographic flow
 5622 
 5623 sverdrup                1e6 m^3 / sec   # Used to express flow of ocean
 5624                                         # currents.  Named after Norwegian
 5625                                         # oceanographer H. Sverdrup.
 5626 
 5627 # In vacuum science and some other applications, gas flow is measured
 5628 # as the product of volumetric flow and pressure.  This is useful
 5629 # because it makes it easy to compare with the flow at standard
 5630 # pressure (one atmosphere).  It also directly relates to the number
 5631 # of gas molecules per unit time, and hence to the mass flow if the
 5632 # molecular mass is known.
 5633 
 5634 GAS_FLOW                PRESSURE FLUID_FLOW
 5635 
 5636 sccm                    atm cc/min     # 's' is for "standard" to indicate
 5637 sccs                    atm cc/sec     # flow at standard pressure
 5638 scfh                    atm ft^3/hour  #
 5639 scfm                    atm ft^3/min
 5640 slpm                    atm liter/min
 5641 slph                    atm liter/hour
 5642 lusec                   liter micron Hg / s  # Used in vacuum science
 5643 
 5644 # US Standard Atmosphere (1976)
 5645 # Atmospheric temperature and pressure vs. geometric height above sea level
 5646 # This definition covers only the troposphere (the lowest atmospheric
 5647 # layer, up to 11 km), and assumes the layer is polytropic.
 5648 # A polytropic process is one for which PV^k = const, where P is the
 5649 # pressure, V is the volume, and k is the polytropic exponent.  The
 5650 # polytropic index is n = 1 / (k - 1).  As noted in the Wikipedia article
 5651 # https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
 5652 # the definitions of "exponent" and "index."  The functions below assume
 5653 # the following parameters:
 5654 
 5655 # temperature lapse rate, -dT/dz, in troposphere
 5656 
 5657 lapserate       6.5 K/km        # US Std Atm (1976)
 5658 
 5659 # air molecular weight, including constituent mol wt, given
 5660 # in Table 3, p. 3
 5661 
 5662 air_1976        78.084   %    28.0134 \
 5663               + 20.9476  %    31.9988 \
 5664               + 9340     ppm  39.948 \
 5665               +  314     ppm  44.00995 \
 5666               +   18.18  ppm  20.183 \
 5667               +    5.24  ppm   4.0026 \
 5668               +    2     ppm  16.04303 \
 5669               +    1.14  ppm  83.80 \
 5670               +    0.55  ppm   2.01594 \
 5671               +    0.087 ppm 131.30
 5672 
 5673 # universal gas constant
 5674 R_1976          8.31432e3 N m/(kmol K)
 5675 
 5676 # polytropic index n
 5677 polyndx_1976    air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
 5678 
 5679 # If desired, redefine using current values for air mol wt and R
 5680 
 5681 polyndx         polyndx_1976
 5682 # polyndx       air (kg/kmol) gravity/(R lapserate) - 1
 5683 
 5684 # for comparison with various references
 5685 
 5686 polyexpnt       (polyndx + 1) / polyndx
 5687 
 5688 # The model assumes the following reference values:
 5689 # sea-level temperature and pressure
 5690 
 5691 stdatmT0        288.15 K
 5692 stdatmP0        atm
 5693 
 5694 # "effective radius" for relation of geometric to geopotential height,
 5695 # at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
 5696 # relation to actual radius
 5697 
 5698 earthradUSAtm   6356766 m
 5699 
 5700 # Temperature vs. geopotential height h
 5701 # Assumes 15 degC at sea level
 5702 # Based on approx 45 deg latitude
 5703 # Lower limits of domain and upper limits of range are those of the
 5704 # tables in US Standard Atmosphere (NASA 1976)
 5705 
 5706 stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
 5707     stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
 5708 
 5709 # Temperature vs. geometric height z; based on approx 45 deg latitude
 5710 stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
 5711     stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
 5712 
 5713 # Pressure vs. geopotential height h
 5714 # Assumes 15 degC and 101325 Pa at sea level
 5715 # Based on approx 45 deg latitude
 5716 # Lower limits of domain and upper limits of range are those of the
 5717 # tables in US Standard Atmosphere (NASA 1976)
 5718 
 5719 stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
 5720     atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
 5721     (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
 5722 
 5723 # Pressure vs. geometric height z; based on approx 45 deg latitude
 5724 stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
 5725    stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
 5726 
 5727 # Geopotential height from geometric height
 5728 # Based on approx 45 deg latitude
 5729 # Lower limits of domain and range are somewhat arbitrary; they
 5730 # correspond to the limits in the US Std Atm tables
 5731 
 5732 geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
 5733     (earthradUSAtm z) / (earthradUSAtm + z) ; \
 5734     (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
 5735 
 5736 # The standard value for the sea-level acceleration due to gravity is
 5737 # 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
 5738 # R_eff = 2 g_phi / denom
 5739 # g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
 5740 #   or
 5741 # g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
 5742 # denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
 5743 # There is no inverse function; the standard value applies at a latitude
 5744 # of about 45.543 deg
 5745 
 5746 g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror  \
 5747     980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
 5748 
 5749 # effective Earth radius for relation of geometric height to
 5750 # geopotential height, as function of latitude (Harrison 1949)
 5751 
 5752 earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
 5753     m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
 5754     (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
 5755 
 5756 # References
 5757 # Harrison, L.P. 1949.  Relation Between Geopotential and Geometric
 5758 #   Height.  In Smithsonian Meteorological Tables. List, Robert J., ed.
 5759 #   6th ed., 4th reprint, 1968.  Washington, DC: Smithsonian Institution.
 5760 # NASA.  US National Aeronautics and Space Administration. 1976.
 5761 #   US Standard Atmosphere 1976.  Washington, DC: US Government Printing Office.
 5762 
 5763 # Gauge pressure functions
 5764 #
 5765 # Gauge pressure is measured relative to atmospheric pressure.  In the English
 5766 # system, where pressure is often given in pounds per square inch, gauge
 5767 # pressure is often indicated by 'psig' to distinguish it from absolute
 5768 # pressure, often indicated by 'psia'.  At the standard atmospheric pressure
 5769 # of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
 5770 # psia; an automobile tire inflated to 31 psig has an absolute pressure of
 5771 # 45.696 psia.
 5772 #
 5773 # With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
 5774 # bar)); with psig(), the units are taken as psi, so the example above of tire
 5775 # pressure could be given as psig(31).
 5776 #
 5777 # If the normal elevation is significantly different from sea level, change
 5778 # Patm appropriately, and adjust the lower domain limit on the gaugepressure
 5779 # definition.
 5780 
 5781 Patm    atm
 5782 
 5783 gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
 5784                 x + Patm ; gaugepressure+(-Patm)
 5785 
 5786 psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
 5787     gaugepressure(x psi) ; ~gaugepressure(psig) / psi
 5788 
 5789 
 5790 # Pressure for underwater diving
 5791 
 5792 seawater             0.1 bar / meter
 5793 msw                  meter seawater
 5794 fsw                  foot seawater
 5795 
 5796 #
 5797 # Wire Gauge
 5798 #
 5799 # This area is a nightmare with huge charts of wire gauge diameters
 5800 # that usually have no clear origin.  There are at least 5 competing wire gauge
 5801 # systems to add to the confusion.  The use of wire gauge is related to the
 5802 # manufacturing method: a metal rod is heated and drawn through a hole.  The
 5803 # size change can't be too big.  To get smaller wires, the process is repeated
 5804 # with a series of smaller holes.  Generally larger gauges mean smaller wires.
 5805 # The gauges often have values such as "00" and "000" which are larger sizes
 5806 # than simply "0" gauge.  In the tables that appear below, these gauges must be
 5807 # specified as negative numbers (e.g. "00" is -1, "000" is -2, etc).
 5808 # Alternatively, you can use the following units:
 5809 #
 5810 
 5811 g00                      (-1)
 5812 g000                     (-2)
 5813 g0000                    (-3)
 5814 g00000                   (-4)
 5815 g000000                  (-5)
 5816 g0000000                 (-6)
 5817 
 5818 # American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
 5819 # important gauge. ASTM B-258 specifies that this gauge is based on geometric
 5820 # interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
 5821 # which is 0.005 inches exactly.  Therefore, the diameter in inches of a wire
 5822 # is given by the formula 1|200 92^((36-g)/39).  Note that 92^(1/39) is close
 5823 # to 2^(1/6), so diameter is approximately halved for every 6 gauges.  For the
 5824 # repeated zero values, use negative numbers in the formula.  The same document
 5825 # also specifies rounding rules which seem to be ignored by makers of tables.
 5826 # Gauges up to 44 are to be specified with up to 4 significant figures, but no
 5827 # closer than 0.0001 inch.  Gauges from 44 to 56 are to be rounded to the
 5828 # nearest 0.00001 inch.
 5829 #
 5830 # In addition to being used to measure wire thickness, this gauge is used to
 5831 # measure the thickness of sheets of aluminum, copper, and most metals other
 5832 # than steel, iron and zinc.
 5833 
 5834 wiregauge(g) units=[1;m] range=(0,) \
 5835              1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
 5836 awg()        wiregauge
 5837 
 5838 # Next we have the SWG, the Imperial or British Standard Wire Gauge.  This one
 5839 # is piecewise linear.  It was used for aluminum sheets.
 5840 
 5841 brwiregauge[in]  \
 5842        -6 0.5    \
 5843        -5 0.464  \
 5844        -3 0.4    \
 5845        -2 0.372  \
 5846         3 0.252  \
 5847         6 0.192  \
 5848        10 0.128  \
 5849        14 0.08   \
 5850        19 0.04   \
 5851        23 0.024  \
 5852        26 0.018  \
 5853        28 0.0148 \
 5854        30 0.0124 \
 5855        39 0.0052 \
 5856        49 0.0012 \
 5857        50 0.001
 5858 
 5859 # The following is from the Appendix to ASTM B 258
 5860 #
 5861 #    For example, in U.S. gage, the standard for sheet metal is based on the
 5862 #    weight of the metal, not on the thickness. 16-gage is listed as
 5863 #    approximately .0625 inch thick and 40 ounces per square foot (the original
 5864 #    standard was based on wrought iron at .2778 pounds per cubic inch; steel
 5865 #    has almost entirely superseded wrought iron for sheet use, at .2833 pounds
 5866 #    per cubic inch). Smaller numbers refer to greater thickness. There is no
 5867 #    formula for converting gage to thickness or weight.
 5868 #
 5869 # It's rather unclear from the passage above whether the plate gauge values are
 5870 # therefore wrong if steel is being used.  Reference [15] states that steel is
 5871 # in fact measured using this gauge (under the name Manufacturers' Standard
 5872 # Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
 5873 # But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
 5874 # closer).
 5875 #
 5876 # This gauge was established in 1893 for purposes of taxation.
 5877 
 5878 # Old plate gauge for iron
 5879 
 5880 plategauge[(oz/ft^2)/(480*lb/ft^3)] \
 5881       -5 300   \
 5882        1 180   \
 5883       14  50   \
 5884       16  40   \
 5885       17  36   \
 5886       20  24   \
 5887       26  12   \
 5888       31   7   \
 5889       36   4.5 \
 5890       38   4
 5891 
 5892 # Manufacturers Standard Gage
 5893 
 5894 stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \
 5895       -5 300   \
 5896        1 180   \
 5897       14  50   \
 5898       16  40   \
 5899       17  36   \
 5900       20  24   \
 5901       26  12   \
 5902       31   7   \
 5903       36   4.5 \
 5904       38   4
 5905 
 5906 # A special gauge is used for zinc sheet metal.  Notice that larger gauges
 5907 # indicate thicker sheets.
 5908 
 5909 zincgauge[in]    \
 5910         1 0.002  \
 5911        10 0.02   \
 5912        15 0.04   \
 5913        19 0.06   \
 5914        23 0.1    \
 5915        24 0.125  \
 5916        27 0.5    \
 5917        28 1
 5918 
 5919 #
 5920 # Imperial drill bit sizes are reported in inches or in a numerical or
 5921 # letter gauge.
 5922 #
 5923 
 5924 drillgauge[in] \
 5925        1  0.2280 \
 5926        2  0.2210 \
 5927        3  0.2130 \
 5928        4  0.2090 \
 5929        5  0.2055 \
 5930        6  0.2040 \
 5931        7  0.2010 \
 5932        8  0.1990 \
 5933        9  0.1960 \
 5934       10  0.1935 \
 5935       11  0.1910 \
 5936       12  0.1890 \
 5937       13  0.1850 \
 5938       14  0.1820 \
 5939       15  0.1800 \
 5940       16  0.1770 \
 5941       17  0.1730 \
 5942       18  0.1695 \
 5943       19  0.1660 \
 5944       20  0.1610 \
 5945       22  0.1570 \
 5946       23  0.1540 \
 5947       24  0.1520 \
 5948       25  0.1495 \
 5949       26  0.1470 \
 5950       27  0.1440 \
 5951       28  0.1405 \
 5952       29  0.1360 \
 5953       30  0.1285 \
 5954       31  0.1200 \
 5955       32  0.1160 \
 5956       33  0.1130 \
 5957       34  0.1110 \
 5958       35  0.1100 \
 5959       36  0.1065 \
 5960       38  0.1015 \
 5961       39  0.0995 \
 5962       40  0.0980 \
 5963       41  0.0960 \
 5964       42  0.0935 \
 5965       43  0.0890 \
 5966       44  0.0860 \
 5967       45  0.0820 \
 5968       46  0.0810 \
 5969       48  0.0760 \
 5970       51  0.0670 \
 5971       52  0.0635 \
 5972       53  0.0595 \
 5973       54  0.0550 \
 5974       55  0.0520 \
 5975       56  0.0465 \
 5976       57  0.0430 \
 5977       65  0.0350 \
 5978       66  0.0330 \
 5979       68  0.0310 \
 5980       69  0.0292 \
 5981       70  0.0280 \
 5982       71  0.0260 \
 5983       73  0.0240 \
 5984       74  0.0225 \
 5985       75  0.0210 \
 5986       76  0.0200 \
 5987       78  0.0160 \
 5988       79  0.0145 \
 5989       80  0.0135 \
 5990       88  0.0095 \
 5991       104 0.0031 
 5992 
 5993 drillA    0.234 in
 5994 drillB    0.238 in
 5995 drillC    0.242 in
 5996 drillD    0.246 in
 5997 drillE    0.250 in
 5998 drillF    0.257 in
 5999 drillG    0.261 in
 6000 drillH    0.266 in
 6001 drillI    0.272 in
 6002 drillJ    0.277 in
 6003 drillK    0.281 in
 6004 drillL    0.290 in
 6005 drillM    0.295 in
 6006 drillN    0.302 in
 6007 drillO    0.316 in
 6008 drillP    0.323 in
 6009 drillQ    0.332 in
 6010 drillR    0.339 in
 6011 drillS    0.348 in
 6012 drillT    0.358 in
 6013 drillU    0.368 in
 6014 drillV    0.377 in
 6015 drillW    0.386 in
 6016 drillX    0.397 in
 6017 drillY    0.404 in
 6018 drillZ    0.413 in
 6019 
 6020 #
 6021 # Screw sizes
 6022 #
 6023 # In the USA, screw diameters for both wood screws and machine screws
 6024 # are reported using a gauge number.  Metric machine screws are
 6025 # reported as Mxx where xx is the diameter in mm.
 6026 #
 6027 
 6028 screwgauge(g) units=[1;m] range=[0,) \
 6029               (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
 6030 
 6031 #
 6032 # Abrasive grit size
 6033 #
 6034 # Standards governing abrasive grit sizes are complicated, specifying
 6035 # fractions of particles that are passed or retained by different mesh
 6036 # sizes.  As a result, it is not possible to make precise comparisons
 6037 # of different grit standards.  The tables below allow the
 6038 # determination of rough equivlants by using median particle size.
 6039 #
 6040 # Standards in the USA are determined by the Unified Abrasives
 6041 # Manufacturers' Association (UAMA), which resulted from the merger of
 6042 # several previous organizations.  One of the old organizations was
 6043 # CAMI (Coated Abrasives Manufacturers' Institute).
 6044 #
 6045 # UAMA has a web page with plots showing abrasive particle ranges for
 6046 # various different grits and comparisons between standards.
 6047 #
 6048 # http://www.uama.org/Abrasives101/101Standards.html
 6049 #
 6050 # Abrasives are grouped into "bonded" abrasives for use with grinding
 6051 # wheels and "coated" abrasives for sandpapers and abrasive films.
 6052 # The industry uses different grit standards for these two
 6053 # categories.
 6054 #
 6055 # Another division is between "macrogrits", grits below 240 and
 6056 # "microgrits", which are above 240.  Standards differ, as do methods
 6057 # for determining particle size.  In the USA, ANSI B74.12 is the
 6058 # standard governing macrogrits.  ANSI B74.10 covers bonded microgrit
 6059 # abrasives, and ANSI B74.18 covers coated microgrit abrasives.  It
 6060 # appears that the coated standard is identical to the bonded standard
 6061 # for grits up through 600 but then diverges significantly.
 6062 #
 6063 # European grit sizes are determined by the Federation of European
 6064 # Producers of Abrasives.  http://www.fepa-abrasives.org
 6065 #
 6066 # They give two standards, the "F" grit for bonded abrasives and the
 6067 # "P" grit for coated abrasives.  This data is taken directly from
 6068 # their web page.
 6069 
 6070 # FEPA P grit for coated abrasives is commonly seen on sandpaper in
 6071 # the USA where the paper will be marked P600, for example.  FEPA P
 6072 # grits are said to be more tightly constrained than comparable ANSI
 6073 # grits so that the particles are more uniform in size and hence give
 6074 # a better finish.
 6075 
 6076 grit_P[micron] \
 6077         12 1815 \
 6078         16 1324 \
 6079         20 1000 \
 6080         24 764 \
 6081         30 642 \
 6082         36 538 \
 6083         40 425 \
 6084         50 336 \
 6085         60 269 \
 6086         80 201 \
 6087         100 162 \
 6088         120 125 \
 6089         150 100 \
 6090         180 82 \
 6091         220 68 \
 6092         240 58.5 \
 6093         280 52.2 \
 6094         320 46.2 \
 6095         360 40.5 \
 6096         400 35 \
 6097         500 30.2 \
 6098         600 25.8 \
 6099         800 21.8 \
 6100         1000 18.3 \
 6101         1200 15.3 \
 6102         1500 12.6 \
 6103         2000 10.3 \
 6104         2500 8.4
 6105 
 6106 # The F grit is the European standard for bonded abrasives such as
 6107 # grinding wheels
 6108 
 6109 grit_F[micron] \
 6110         4 4890 \
 6111         5 4125 \
 6112         6 3460 \
 6113         7 2900 \
 6114         8 2460 \
 6115         10 2085 \
 6116         12 1765 \
 6117         14 1470 \
 6118         16 1230 \
 6119         20 1040 \
 6120         22 885 \
 6121         24 745 \
 6122         30 625 \
 6123         36 525 \
 6124         40 438 \
 6125         46 370 \
 6126         54 310 \
 6127         60 260 \
 6128         70 218 \
 6129         80 185 \
 6130         90 154 \
 6131         100 129 \
 6132         120 109 \
 6133         150 82 \
 6134         180 69 \
 6135         220 58 \
 6136         230 53 \
 6137         240 44.5 \
 6138         280 36.5 \
 6139         320 29.2 \
 6140         360 22.8 \
 6141         400 17.3 \
 6142         500 12.8 \
 6143         600 9.3 \
 6144         800 6.5 \
 6145         1000 4.5 \
 6146         1200 3 \
 6147         1500 2.0 \
 6148         2000 1.2
 6149 
 6150 # According to the UAMA web page, the ANSI bonded and ANSI coated standards
 6151 # are identical to FEPA F in the macrogrit range (under 240 grit), so these
 6152 # values are taken from the FEPA F table.  The values for 240 and above are
 6153 # from the UAMA web site and represent the average of the "d50" range
 6154 # endpoints listed there.
 6155 
 6156 ansibonded[micron] \
 6157     4 4890 \
 6158     5 4125 \
 6159     6 3460 \
 6160     7 2900 \
 6161     8 2460 \
 6162     10 2085 \
 6163     12 1765 \
 6164     14 1470 \
 6165     16 1230 \
 6166     20 1040 \
 6167     22 885 \
 6168     24 745 \
 6169     30 625 \
 6170     36 525 \
 6171     40 438 \
 6172     46 370 \
 6173     54 310 \
 6174     60 260 \
 6175     70 218 \
 6176     80 185 \
 6177     90 154 \
 6178     100 129 \
 6179     120 109 \
 6180     150 82 \
 6181     180 69 \
 6182     220 58 \
 6183     240 50 \
 6184     280 39.5 \
 6185     320 29.5 \
 6186     360 23 \
 6187     400 18.25 \
 6188     500 13.9 \
 6189     600 10.55 \
 6190     800 7.65 \
 6191     1000 5.8 \
 6192     1200 3.8
 6193 
 6194 grit_ansibonded() ansibonded
 6195 
 6196 # Like the bonded grit, the coated macrogrits below 240 are taken from the
 6197 # FEPA F table.  Data above this is from the UAMA site.  Note that the coated
 6198 # and bonded standards are evidently the same from 240 up to 600 grit, but
 6199 # starting at 800 grit, the coated standard diverges.  The data from UAMA show
 6200 # that 800 grit coated has an average size slightly larger than the average
 6201 # size of 600 grit coated/bonded.  However, the 800 grit has a significantly
 6202 # smaller particle size variation.
 6203 #
 6204 # Because of this non-monotonicity from 600 grit to 800 grit this definition
 6205 # produces a warning about the lack of a unique inverse.
 6206 
 6207 ansicoated[micron] noerror \
 6208     4 4890 \
 6209     5 4125 \
 6210     6 3460 \
 6211     7 2900 \
 6212     8 2460 \
 6213     10 2085 \
 6214     12 1765 \
 6215     14 1470 \
 6216     16 1230 \
 6217     20 1040 \
 6218     22 885 \
 6219     24 745 \
 6220     30 625 \
 6221     36 525 \
 6222     40 438 \
 6223     46 370 \
 6224     54 310 \
 6225     60 260 \
 6226     70 218 \
 6227     80 185 \
 6228     90 154 \
 6229     100 129 \
 6230     120 109 \
 6231     150 82 \
 6232     180 69 \
 6233     220 58 \
 6234     240 50 \
 6235     280 39.5 \
 6236     320 29.5 \
 6237     360 23 \
 6238     400 18.25 \
 6239     500 13.9 \
 6240     600 10.55 \
 6241     800 11.5 \
 6242     1000 9.5 \
 6243     2000 7.2 \
 6244     2500 5.5 \
 6245     3000 4 \
 6246     4000 3 \
 6247     6000 2 \
 6248     8000 1.2
 6249 
 6250 grit_ansicoated()  ansicoated
 6251 
 6252 
 6253 #
 6254 # Is this correct?  This is the JIS Japanese standard used on waterstones
 6255 #
 6256 jisgrit[micron] \
 6257      150 75 \
 6258      180 63 \
 6259      220 53 \
 6260      280 48 \
 6261      320 40 \
 6262      360 35 \
 6263      400 30 \
 6264      600 20 \
 6265      700 17 \
 6266      800 14 \
 6267      1000 11.5 \
 6268      1200 9.5 \
 6269      1500 8 \
 6270      2000 6.7 \
 6271      2500 5.5 \
 6272      3000 4 \
 6273      4000 3 \
 6274      6000 2 \
 6275      8000 1.2
 6276 
 6277 # The "Finishing Scale" marked with an A (e.g. A75).  This information
 6278 # is from the web page of the sand paper manufacturer Klingspor
 6279 # http://www.klingspor.com/gritgradingsystems.htm
 6280 #
 6281 # I have no information about what this scale is used for.
 6282 
 6283 grit_A[micron]\
 6284      16 15.3 \
 6285      25 21.8 \
 6286      30 23.6 \
 6287      35 25.75 \
 6288      45 35 \
 6289      60 46.2 \
 6290      65 53.5 \
 6291      75 58.5 \
 6292      90 65 \
 6293      110 78 \
 6294      130 93 \
 6295      160 127 \
 6296      200 156
 6297 #
 6298 # Grits for DMT brand diamond sharpening stones from
 6299 # http://dmtsharp.com/products/colorcode.htm
 6300 #
 6301 
 6302 dmtxxcoarse  120 micron    # 120 mesh
 6303 dmtsilver    dmtxxcoarse
 6304 dmtxx        dmtxxcoarse
 6305 dmtxcoarse   60 micron     # 220 mesh
 6306 dmtx         dmtxcoarse
 6307 dmtblack     dmtxcoarse
 6308 dmtcoarse    45 micron     # 325 mesh
 6309 dmtc         dmtcoarse
 6310 dmtblue      dmtcoarse
 6311 dmtfine      25 micron     # 600 mesh
 6312 dmtred       dmtfine
 6313 dmtf         dmtfine
 6314 dmtefine     9 micron      # 1200 mesh
 6315 dmte         dmtefine
 6316 dmtgreen     dmtefine
 6317 dmtceramic   7 micron      # 2200 mesh
 6318 dmtcer       dmtceramic
 6319 dmtwhite     dmtceramic
 6320 dmteefine    3 micron      # 8000 mesh
 6321 dmttan       dmteefine
 6322 dmtee        dmteefine
 6323 
 6324 #
 6325 # The following values come from a page in the Norton Stones catalog,
 6326 # available at their web page, http://www.nortonstones.com.
 6327 #
 6328 
 6329 hardtranslucentarkansas  6 micron     # Natural novaculite (silicon quartz)
 6330 softarkansas             22 micron    #   stones
 6331 
 6332 extrafineindia           22 micron    # India stones are Norton's manufactured
 6333 fineindia                35 micron    #   aluminum oxide product
 6334 mediumindia              53.5 micron
 6335 coarseindia              97 micron
 6336 
 6337 finecrystolon            45 micron    # Crystolon stones are Norton's
 6338 mediumcrystalon          78 micron    #   manufactured silicon carbide product
 6339 coarsecrystalon          127 micron
 6340 
 6341 # The following are not from the Norton catalog
 6342 hardblackarkansas        6 micron
 6343 hardwhitearkansas        11 micron
 6344 washita                  35 micron
 6345 
 6346 #
 6347 # Mesh systems for measuring particle sizes by sifting through a wire
 6348 # mesh or sieve
 6349 #
 6350 
 6351 # The Tyler system and US Sieve system are based on four steps for
 6352 # each factor of 2 change in the size, so each size is 2^1|4 different
 6353 # from the adjacent sizes.  Unfortunately, the mesh numbers are
 6354 # arbitrary, so the sizes cannot be expressed with a functional form.
 6355 # Various references round the values differently.  The mesh numbers
 6356 # are supposed to correspond to the number of holes per inch, but this
 6357 # correspondence is only approximate because it doesn't include the
 6358 # wire size of the mesh.
 6359 
 6360 # The Tyler Mesh system was apparently introduced by the WS Tyler
 6361 # company, but it appears that they no longer use it.  They follow the
 6362 # ASTM E11 standard.
 6363 
 6364 meshtyler[micron] \
 6365           2.5 8000 \
 6366           3   6727 \
 6367           3.5 5657 \
 6368           4   4757 \
 6369           5   4000 \
 6370           6   3364 \
 6371           7   2828 \
 6372           8   2378 \
 6373           9   2000 \
 6374          10   1682 \
 6375          12   1414 \
 6376          14   1189 \
 6377          16   1000 \
 6378          20    841 \
 6379          24    707 \
 6380          28    595 \
 6381          32    500 \
 6382          35    420 \
 6383          42    354 \
 6384          48    297 \
 6385          60    250 \
 6386          65    210 \
 6387          80    177 \
 6388         100    149 \
 6389         115    125 \
 6390         150    105 \
 6391         170     88 \
 6392         200     74 \
 6393         250     63 \
 6394         270     53 \
 6395         325     44 \
 6396         400     37 
 6397 
 6398 # US Sieve size, ASTM E11
 6399 #
 6400 # The WS Tyler company prints the list from ASTM E11 in their catalog, 
 6401 # http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf
 6402 
 6403 sieve[micron] \
 6404           3.5   5600 \
 6405           4     4750 \
 6406           5     4000 \
 6407           6     3350 \
 6408           7     2800 \
 6409           8     2360 \
 6410          10     2000 \
 6411          12     1700 \
 6412          14     1400 \
 6413          16     1180 \
 6414          18     1000 \
 6415          20      850 \
 6416          25      710 \
 6417          30      600 \
 6418          35      500 \
 6419          40      425 \
 6420          45      355 \
 6421          50      300 \
 6422          60      250 \
 6423          70      212 \
 6424          80      180 \
 6425         100      150 \
 6426         120      125 \
 6427         140      106 \
 6428         170       90 \
 6429         200       75 \
 6430         230       63 \
 6431         270       53 \
 6432         325       45 \
 6433         400       38 \
 6434         450       32 \
 6435         500       25 \
 6436         625       20   # These last two values are not in the standard series
 6437                        # but were included in the ASTM standard because they
 6438 meshUS()  sieve        # were in common usage.                               
 6439 
 6440 # British Mesh size, BS 410: 1986
 6441 # This system appears to correspond to the Tyler and US system, but
 6442 # with different mesh numbers.
 6443 #
 6444 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
 6445 # 
 6446 
 6447 meshbritish[micron] \
 6448           3    5657 \
 6449           3.5  4757 \
 6450           4    4000 \
 6451           5    3364 \
 6452           6    2828 \
 6453           7    2378 \
 6454           8    2000 \
 6455          10    1682 \
 6456          12    1414 \
 6457          14    1189 \
 6458          16    1000 \
 6459          18     841 \
 6460          22     707 \
 6461          25     595 \
 6462          30     500 \
 6463          36     420 \
 6464          44     354 \
 6465          52     297 \
 6466          60     250 \
 6467          72     210 \
 6468          85     177 \
 6469         100     149 \
 6470         120     125 \
 6471         150     105 \
 6472         170      88 \
 6473         200      74 \
 6474         240      63 \
 6475         300      53 \
 6476         350      44 \
 6477         400      37  
 6478 
 6479 # French system, AFNOR NFX11-501: 1970
 6480 # The system appears to be based on size doubling every 3 mesh
 6481 # numbers, though the values have been agressively rounded.
 6482 # It's not clear if the unrounded values would be considered
 6483 # incorrect, so this is given as a table rather than a function.
 6484 # Functional form:
 6485 #    meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron
 6486 #
 6487 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
 6488 
 6489 meshtamis[micron] \
 6490         17   40 \
 6491         18   50 \
 6492         19   63 \
 6493         20   80 \
 6494         21  100 \
 6495         22  125 \
 6496         23  160 \
 6497         24  200 \
 6498         25  250 \
 6499         26  315 \
 6500         27  400 \
 6501         28  500 \
 6502         29  630 \
 6503         30  800 \
 6504         31 1000 \
 6505         32 1250 \
 6506         33 1600 \
 6507         34 2000 \
 6508         35 2500 \
 6509         36 3150 \
 6510         37 4000 \
 6511         38 5000 
 6512 
 6513 #
 6514 # Ring size. All ring sizes are given as the circumference of the ring.
 6515 #
 6516 
 6517 # USA ring sizes.  Several slightly different definitions seem to be in
 6518 # circulation.  According to [15], the interior diameter of size n ring in
 6519 # inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5.  The
 6520 # size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
 6521 #
 6522 # However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
 6523 # diameter and list no special case for size 2.  (Or alternatively they are
 6524 # 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.)  One
 6525 # reference claimed that the original system was that each size was 1|10 inch
 6526 # circumference, but that source doesn't have an explanation for the modern
 6527 # system which is somewhat different.
 6528 
 6529 ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
 6530             (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
 6531 
 6532 # Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
 6533 # specified alphabetically and based on the ring inside diameter in steps of
 6534 # 1|64 inch.  This system was replaced in 1987 by British Standard 6820 which
 6535 # specifies sizes based on circumference.  Each size is 1.25 mm different from
 6536 # the preceding size.  The baseline is size C which is 40 mm circumference.
 6537 # The new sizes are close to the old ones.  Sometimes it's necessary to go
 6538 # beyond size Z to Z+1, Z+2, etc.
 6539 
 6540 sizeAring               37.50 mm
 6541 sizeBring               38.75 mm
 6542 sizeCring               40.00 mm
 6543 sizeDring               41.25 mm
 6544 sizeEring               42.50 mm
 6545 sizeFring               43.75 mm
 6546 sizeGring               45.00 mm
 6547 sizeHring               46.25 mm
 6548 sizeIring               47.50 mm
 6549 sizeJring               48.75 mm
 6550 sizeKring               50.00 mm
 6551 sizeLring               51.25 mm
 6552 sizeMring               52.50 mm
 6553 sizeNring               53.75 mm
 6554 sizeOring               55.00 mm
 6555 sizePring               56.25 mm
 6556 sizeQring               57.50 mm
 6557 sizeRring               58.75 mm
 6558 sizeSring               60.00 mm
 6559 sizeTring               61.25 mm
 6560 sizeUring               62.50 mm
 6561 sizeVring               63.75 mm
 6562 sizeWring               65.00 mm
 6563 sizeXring               66.25 mm
 6564 sizeYring               67.50 mm
 6565 sizeZring               68.75 mm
 6566 
 6567 # Japanese sizes start with size 1 at a 13mm inside diameter and each size is
 6568 # 1|3 mm larger in diameter than the previous one.  They are multiplied by pi
 6569 # to give circumference.
 6570 
 6571 jpringsize(n)  units=[1;mm] domain=[1,) range=[0.040840704,) \
 6572                (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
 6573 
 6574 # The European ring sizes are the length of the circumference in mm minus 40.
 6575 
 6576 euringsize(n)  units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
 6577 
 6578 #
 6579 # Abbreviations
 6580 #
 6581 
 6582 mph                     mile/hr
 6583 mpg                     mile/gal
 6584 kph                     km/hr
 6585 fL                      footlambert
 6586 fpm                     ft/min
 6587 fps                     ft/s
 6588 rpm                     rev/min
 6589 rps                     rev/sec
 6590 mi                      mile
 6591 smi                     mile
 6592 nmi                     nauticalmile
 6593 mbh                     1e3 btu/hour
 6594 mcm                     1e3 circularmil
 6595 ipy                     inch/year    # used for corrosion rates
 6596 ccf                     100 ft^3     # used for selling water [18]
 6597 Mcf                     1000 ft^3    # not million cubic feet [18]
 6598 kp                      kilopond
 6599 kpm                     kp meter
 6600 Wh                      W hour
 6601 hph                     hp hour
 6602 plf                     lb / foot    # pounds per linear foot
 6603 
 6604 #
 6605 # Compatibility units with Unix version
 6606 #
 6607 
 6608 pa                      Pa
 6609 ev                      eV
 6610 hg                      Hg
 6611 oe                      Oe
 6612 mh                      mH
 6613 rd                      rod
 6614 pf                      pF
 6615 gr                      grain
 6616 nt                      N
 6617 hz                      Hz
 6618 hd                      hogshead
 6619 dry                     drygallon/gallon
 6620 nmile                   nauticalmile
 6621 beV                     GeV
 6622 bev                     beV
 6623 coul                    C
 6624 
 6625 #
 6626 # Radioactivity units
 6627 #
 6628 
 6629 becquerel               /s           # Activity of radioactive source
 6630 Bq                      becquerel    #
 6631 curie                   3.7e10 Bq    # Defined in 1910 as the radioactivity
 6632 Ci                      curie        # emitted by the amount of radon that is
 6633                                      # in equilibrium with 1 gram of radium.
 6634 rutherford              1e6 Bq       #
 6635 
 6636 RADIATION_DOSE          gray
 6637 gray                    J/kg         # Absorbed dose of radiation
 6638 Gy                      gray         #
 6639 rad                     1e-2 Gy      # From Radiation Absorbed Dose
 6640 rep                     8.38 mGy     # Roentgen Equivalent Physical, the amount
 6641                                      #   of radiation which , absorbed in the
 6642                                      #   body, would liberate the same amount
 6643                                      #   of energy as 1 roentgen of X rays
 6644                                      #   would, or 97 ergs.
 6645 
 6646 sievert                 J/kg         # Dose equivalent:  dosage that has the
 6647 Sv                      sievert      #   same effect on human tissues as 200
 6648 rem                     1e-2 Sv      #   keV X-rays.  Different types of
 6649                                      #   radiation are weighted by the
 6650                                      #   Relative Biological Effectiveness
 6651                                      #   (RBE).
 6652                                      #
 6653                                      #      Radiation type       RBE
 6654                                      #       X-ray, gamma ray     1
 6655                                      #       beta rays, > 1 MeV   1
 6656                                      #       beta rays, < 1 MeV  1.08
 6657                                      #       neutrons, < 1 MeV   4-5
 6658                                      #       neutrons, 1-10 MeV   10
 6659                                      #       protons, 1 MeV      8.5
 6660                                      #       protons, .1 MeV      10
 6661                                      #       alpha, 5 MeV         15
 6662                                      #       alpha, 1 MeV         20
 6663                                      #
 6664                                      #   The energies are the kinetic energy
 6665                                      #   of the particles.  Slower particles
 6666                                      #   interact more, so they are more
 6667                                      #   effective ionizers, and hence have
 6668                                      #   higher RBE values.
 6669                                      #
 6670                                      # rem stands for Roentgen Equivalent
 6671                                      # Mammal
 6672 banana_dose           0.1e-6 sievert # Informal measure of the dose due to 
 6673                                      #   eating one average sized banana
 6674 roentgen              2.58e-4 C / kg # Ionizing radiation that produces
 6675                                      #   1 statcoulomb of charge in 1 cc of
 6676                                      #   dry air at stp.
 6677 rontgen                 roentgen     # Sometimes it appears spelled this way
 6678 sievertunit             8.38 rontgen # Unit of gamma ray dose delivered in one
 6679                                      #   hour at a distance of 1 cm from a
 6680                                      #   point source of 1 mg of radium
 6681                                      #   enclosed in platinum .5 mm thick.
 6682 
 6683 eman                    1e-7 Ci/m^3  # radioactive concentration
 6684 mache                   3.7e-7 Ci/m^3
 6685 
 6686 #
 6687 # Atomic weights.  The atomic weight of an element is the ratio of the mass of
 6688 # a mole of the element to 1|12 of a mole of Carbon 12.  The Standard Atomic
 6689 # Weights apply to the elements as they occur naturally on earth.  Elements
 6690 # which do not occur naturally or which occur with wide isotopic variability do
 6691 # not have Standard Atomic Weights.  For these elements, the atomic weight is
 6692 # based on the longest lived isotope, as marked in the comments.  In some
 6693 # cases, the comment for these entries also gives a number which is an atomic
 6694 # weight for a different isotope that may be of more interest than the longest
 6695 # lived isotope.
 6696 #
 6697 
 6698 actinium                227.0278
 6699 aluminum                26.981539
 6700 americium               243.0614     # Longest lived. 241.06
 6701 antimony                121.760
 6702 argon                   39.948
 6703 arsenic                 74.92159
 6704 astatine                209.9871     # Longest lived
 6705 barium                  137.327
 6706 berkelium               247.0703     # Longest lived. 249.08
 6707 beryllium               9.012182
 6708 bismuth                 208.98037
 6709 boron                   10.811
 6710 bromine                 79.904
 6711 cadmium                 112.411
 6712 calcium                 40.078
 6713 californium             251.0796     # Longest lived.  252.08
 6714 carbon                  12.011
 6715 cerium                  140.115
 6716 cesium                  132.90543
 6717 chlorine                35.4527
 6718 chromium                51.9961
 6719 cobalt                  58.93320
 6720 copper                  63.546
 6721 curium                  247.0703
 6722 deuterium               2.0141017778
 6723 dysprosium              162.50
 6724 einsteinium             252.083      # Longest lived
 6725 erbium                  167.26
 6726 europium                151.965
 6727 fermium                 257.0951     # Longest lived
 6728 fluorine                18.9984032
 6729 francium                223.0197     # Longest lived
 6730 gadolinium              157.25
 6731 gallium                 69.723
 6732 germanium               72.61
 6733 gold                    196.96654
 6734 hafnium                 178.49
 6735 helium                  4.002602
 6736 holmium                 164.93032
 6737 hydrogen                1.00794
 6738 indium                  114.818
 6739 iodine                  126.90447
 6740 iridium                 192.217
 6741 iron                    55.845
 6742 krypton                 83.80
 6743 lanthanum               138.9055
 6744 lawrencium              262.11       # Longest lived
 6745 lead                    207.2
 6746 lithium                 6.941
 6747 lutetium                174.967
 6748 magnesium               24.3050
 6749 manganese               54.93805
 6750 mendelevium             258.10       # Longest lived
 6751 mercury                 200.59
 6752 molybdenum              95.94
 6753 neodymium               144.24
 6754 neon                    20.1797
 6755 neptunium               237.0482
 6756 nickel                  58.6934
 6757 niobium                 92.90638
 6758 nitrogen                14.00674
 6759 nobelium                259.1009     # Longest lived
 6760 osmium                  190.23
 6761 oxygen                  15.9994
 6762 palladium               106.42
 6763 phosphorus              30.973762
 6764 platinum                195.08
 6765 plutonium               244.0642     # Longest lived.  239.05
 6766 polonium                208.9824     # Longest lived.  209.98
 6767 potassium               39.0983
 6768 praseodymium            140.90765
 6769 promethium              144.9127     # Longest lived.  146.92
 6770 protactinium            231.03588
 6771 radium                  226.0254
 6772 radon                   222.0176     # Longest lived
 6773 rhenium                 186.207
 6774 rhodium                 102.90550
 6775 rubidium                85.4678
 6776 ruthenium               101.07
 6777 samarium                150.36
 6778 scandium                44.955910
 6779 selenium                78.96
 6780 silicon                 28.0855
 6781 silver                  107.8682
 6782 sodium                  22.989768
 6783 strontium               87.62
 6784 sulfur                  32.066
 6785 tantalum                180.9479
 6786 technetium              97.9072      # Longest lived.  98.906
 6787 tellurium               127.60
 6788 terbium                 158.92534
 6789 thallium                204.3833
 6790 thorium                 232.0381
 6791 thullium                168.93421
 6792 tin                     118.710
 6793 titanium                47.867
 6794 tungsten                183.84
 6795 uranium                 238.0289
 6796 vanadium                50.9415
 6797 xenon                   131.29
 6798 ytterbium               173.04
 6799 yttrium                 88.90585
 6800 zinc                    65.39
 6801 zirconium               91.224
 6802 
 6803 # Average molecular weight of air
 6804 #
 6805 # The atmospheric composition listed is from NASA Earth Fact Sheet (accessed
 6806 # 28 August 2015)
 6807 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
 6808 # Numbers do not add up to exactly 100% due to roundoff and uncertainty Water
 6809 # is highly variable, typically makes up about 1%
 6810 
 6811 air            78.08% nitrogen 2 \
 6812               + 20.95% oxygen 2 \
 6813               + 9340 ppm argon \
 6814               +  400 ppm (carbon + oxygen 2) \
 6815               +   18.18 ppm neon \
 6816               +    5.24 ppm helium \
 6817               +    1.7  ppm (carbon + 4 hydrogen) \
 6818               +    1.14 ppm krypton \
 6819               +    0.55 ppm hydrogen 2
 6820 
 6821 
 6822 # Density of the elements
 6823 #
 6824 # Note some elements occur in multiple forms (allotropes) with different
 6825 # densities, and they are accordingly listed multiple times.  
 6826 
 6827 # Density of gas phase elements at STP
 6828 
 6829 hydrogendensity            0.08988 g/l    
 6830 heliumdensity              0.1786 g/l     
 6831 neondensity                0.9002 g/l     
 6832 nitrogendensity            1.2506 g/l     
 6833 oxygendensity              1.429 g/l      
 6834 fluorinedensity            1.696 g/l      
 6835 argondensity               1.784 g/l      
 6836 chlorinedensity            3.2 g/l        
 6837 kryptondensity             3.749 g/l      
 6838 xenondensity               5.894 g/l      
 6839 radondensity               9.73 g/l       
 6840 
 6841 # Density of liquid phase elements near room temperature
 6842 
 6843 brominedensity             3.1028 g/cm^3  
 6844 mercurydensity            13.534 g/cm^3  
 6845 
 6846 # Density of solid elements near room temperature
 6847 
 6848 lithiumdensity             0.534 g/cm^3  
 6849 potassiumdensity           0.862 g/cm^3  
 6850 sodiumdensity              0.968 g/cm^3  
 6851 rubidiumdensity            1.532 g/cm^3  
 6852 calciumdensity             1.55 g/cm^3   
 6853 magnesiumdensity           1.738 g/cm^3  
 6854 phosphorus_white_density   1.823 g/cm^3  
 6855 berylliumdensity           1.85 g/cm^3   
 6856 sulfur_gamma_density       1.92 g/cm^3   
 6857 cesiumdensity              1.93 g/cm^3
 6858 carbon_amorphous_density   1.95 g/cm^3   # average value
 6859 sulfur_betadensity         1.96 g/cm^3   
 6860 sulfur_alpha_density       2.07 g/cm^3   
 6861 carbon_graphite_density    2.267 g/cm^3  
 6862 phosphorus_red_density     2.27 g/cm^3   # average value
 6863 silicondensity             2.3290 g/cm^3 
 6864 phosphorus_violet_density  2.36 g/cm^3   
 6865 borondensity               2.37 g/cm^3   
 6866 strontiumdensity           2.64 g/cm^3   
 6867 phosphorus_black_density   2.69 g/cm^3   
 6868 aluminumdensity            2.7 g/cm^3    
 6869 bariumdensity              3.51 g/cm^3   
 6870 carbon_diamond_density     3.515 g/cm^3  
 6871 scandiumdensity            3.985 g/cm^3  
 6872 selenium_vitreous_density  4.28 g/cm^3   
 6873 selenium_alpha_density     4.39 g/cm^3   
 6874 titaniumdensity            4.406 g/cm^3  
 6875 yttriumdensity             4.472 g/cm^3  
 6876 selenium_gray_density      4.81 g/cm^3   
 6877 iodinedensity              4.933 g/cm^3  
 6878 europiumdensity            5.264 g/cm^3  
 6879 germaniumdensity           5.323 g/cm^3  
 6880 radiumdensity              5.5 g/cm^3    
 6881 arsenicdensity             5.727 g/cm^3  
 6882 tin_alpha_density          5.769 g/cm^3  
 6883 galliumdensity             5.91 g/cm^3   
 6884 vanadiumdensity            6.11 g/cm^3   
 6885 lanthanumdensity           6.162 g/cm^3  
 6886 telluriumdensity           6.24 g/cm^3   
 6887 zirconiumdensity           6.52 g/cm^3   
 6888 antimonydensity            6.697 g/cm^3  
 6889 ceriumdensity              6.77 g/cm^3   
 6890 praseodymiumdensity        6.77 g/cm^3   
 6891 ytterbiumdensity           6.9 g/cm^3    
 6892 neodymiumdensity           7.01 g/cm^3   
 6893 zincdensity                7.14 g/cm^3   
 6894 chromiumdensity            7.19 g/cm^3   
 6895 manganesedensity           7.21 g/cm^3   
 6896 promethiumdensity          7.26 g/cm^3   
 6897 tin_beta_density           7.265 g/cm^3  
 6898 indiumdensity              7.31 g/cm^3   
 6899 samariumdensity            7.52 g/cm^3   
 6900 irondensity                7.874 g/cm^3  
 6901 gadoliniumdensity          7.9 g/cm^3    
 6902 terbiumdensity             8.23 g/cm^3   
 6903 dysprosiumdensity          8.54 g/cm^3   
 6904 niobiumdensity             8.57 g/cm^3   
 6905 cadmiumdensity             8.65 g/cm^3   
 6906 holmiumdensity             8.79 g/cm^3   
 6907 cobaltdensity              8.9 g/cm^3    
 6908 nickeldensity              8.908 g/cm^3  
 6909 erbiumdensity              9.066 g/cm^3  
 6910 polonium_alpha_density     9.196 g/cm^3  
 6911 thuliumdensity             9.32 g/cm^3   
 6912 polonium_beta_density      9.398 g/cm^3  
 6913 bismuthdensity             9.78 g/cm^3   
 6914 lutetiumdensity            9.841 g/cm^3  
 6915 actiniumdensity           10 g/cm^3      
 6916 molybdenumdensity         10.28 g/cm^3   
 6917 silverdensity             10.49 g/cm^3   
 6918 technetiumdensity         11 g/cm^3      
 6919 leaddensity               11.34 g/cm^3   
 6920 thoriumdensity            11.7 g/cm^3    
 6921 thalliumdensity           11.85 g/cm^3   
 6922 americiumdensity          12 g/cm^3      
 6923 palladiumdensity          12.023 g/cm^3  
 6924 rhodiumdensity            12.41 g/cm^3   
 6925 rutheniumdensity          12.45 g/cm^3   
 6926 berkelium_beta_density    13.25 g/cm^3   
 6927 hafniumdensity            13.31 g/cm^3   
 6928 curiumdensity             13.51 g/cm^3   
 6929 berkelium_alphadensity    14.78 g/cm^3   
 6930 californiumdensity        15.1 g/cm^3    
 6931 protactiniumdensity       15.37 g/cm^3   
 6932 tantalumdensity           16.69 g/cm^3   
 6933 uraniumdensity            19.1 g/cm^3    
 6934 tungstendensity           19.3 g/cm^3    
 6935 golddensity               19.30 g/cm^3   
 6936 plutoniumdensity          19.816 g/cm^3  
 6937 neptuniumdensity          20.45 g/cm^3 # alpha form, only one at room temp
 6938 rheniumdensity            21.02 g/cm^3   
 6939 platinumdensity           21.45 g/cm^3   
 6940 iridiumdensity            22.56 g/cm^3   
 6941 osmiumdensity             22.59 g/cm^3
 6942 
 6943 # A few alternate names
 6944 
 6945 tin_gray tin_alpha_density
 6946 tin_white tin_beta_density
 6947 graphitedensity carbon_graphite_density
 6948 diamonddensity carbon_diamond_density
 6949 
 6950 # Predicted density of elements that have not been made in sufficient
 6951 # quantities for measurement.  
 6952 
 6953 franciumdensity            2.48 g/cm^3 # liquid, predicted melting point 8 degC
 6954 astatinedensity            6.35 g/cm^3    
 6955 einsteiniumdensity         8.84 g/cm^3    
 6956 fermiumdensity             9.7 g/cm^3     
 6957 nobeliumdensity            9.9 g/cm^3     
 6958 mendeleviumdensity        10.3 g/cm^3    
 6959 lawrenciumdensity         16 g/cm^3      
 6960 rutherfordiumdensity      23.2 g/cm^3
 6961 roentgeniumdensity        28.7 g/cm^3    
 6962 dubniumdensity            29.3 g/cm^3    
 6963 darmstadtiumdensity       34.8 g/cm^3    
 6964 seaborgiumdensity         35 g/cm^3      
 6965 bohriumdensity            37.1 g/cm^3    
 6966 meitneriumdensity         37.4 g/cm^3    
 6967 hassiumdensity            41 g/cm^3      
 6968 
 6969 #
 6970 # population units
 6971 #
 6972 
 6973 people                  1
 6974 person                  people
 6975 death                   people
 6976 capita                  people
 6977 percapita               per capita
 6978 
 6979 # TGM dozen based unit system listed on the "dozenal" forum
 6980 # http://www.dozenalsociety.org.uk/apps/tgm.htm.  These units are
 6981 # proposed as an allegedly more rational alternative to the SI system.
 6982 
 6983 Tim                     12^-4 hour         # Time 
 6984 Grafut                  gravity Tim^2      # Length based on gravity
 6985 Surf                    Grafut^2           # area
 6986 Volm                    Grafut^3           # volume
 6987 Vlos                    Grafut/Tim         # speed
 6988 Denz                    Maz/Volm           # density
 6989 Mag                     Maz gravity        # force
 6990 Maz                     Volm kg / oldliter # mass based on water
 6991 
 6992 Tm                      Tim                # Abbreviations
 6993 Gf                      Grafut
 6994 Sf                      Surf
 6995 Vm                      Volm
 6996 Vl                      Vlos
 6997 Mz                      Maz
 6998 Dz                      Denz
 6999 
 7000 # Dozen based unit prefixes
 7001 
 7002 Zena-                   12
 7003 Duna-                   12^2
 7004 Trina-                  12^3
 7005 Quedra-                 12^4
 7006 Quena-                  12^5
 7007 Hesa-                   12^6
 7008 Seva-                   12^7
 7009 Aka-                    12^8
 7010 Neena-                  12^9
 7011 Dexa-                   12^10
 7012 Lefa-                   12^11
 7013 Zennila-                12^12
 7014 
 7015 Zeni-                   12^-1
 7016 Duni-                   12^-2
 7017 Trini-                  12^-3
 7018 Quedri-                 12^-4
 7019 Queni-                  12^-5
 7020 Hesi-                   12^-6
 7021 Sevi-                   12^-7
 7022 Aki-                    12^-8
 7023 Neeni-                  12^-9
 7024 Dexi-                   12^-10
 7025 Lefi-                   12^-11
 7026 Zennili-                12^-12
 7027 
 7028 #
 7029 # Traditional Japanese units (shakkanhou)
 7030 #
 7031 # The traditional system of weights and measures is called shakkanhou from the
 7032 # shaku and the ken.  Japan accepted SI units in 1891 and legalized conversions
 7033 # to the traditional system.  In 1909 the inch-pound system was also legalized,
 7034 # so Japan had three legally approved systems.  A change to the metric system
 7035 # started in 1921 but there was a lot of resistance.  The Measurement Law of
 7036 # October 1999 prohibits sales in anything but SI units.  However, the old
 7037 # units still live on in construction and as the basis for paper sizes of books
 7038 # and tools used for handicrafts.
 7039 #
 7040 # Note that units below use the Hepburn romanization system.  Some other
 7041 # systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho".
 7042 #
 7043 #
 7044 # http://hiramatu-hifuka.com/onyak/onyindx.html
 7045 
 7046 # Japanese Proportions.  These are still in everyday use.  They also
 7047 # get used as units to represent the proportion of the standard unit.
 7048 
 7049 wari_proportion      1|10
 7050 wari                 wari_proportion
 7051 bu_proportion        1|100    # The character bu can also be read fun or bun
 7052                               # but usually "bu" is used for units.
 7053 rin_proportion       1|1000
 7054 mou_proportion       1|10000
 7055 
 7056 
 7057 # Japanese Length Measures
 7058 #
 7059 # The length system is called kanejaku or
 7060 # square and originated in China.  It was
 7061 # adopted as Japan's official measure in 701
 7062 # by the Taiho Code.  This system is still in
 7063 # common use in architecture and clothing.
 7064 
 7065 shaku              1|3.3 m
 7066 mou                1|10000 shaku
 7067 rin                1|1000 shaku
 7068 bu_distance        1|100 shaku
 7069 sun                1|10 shaku
 7070 jou_distance       10 shaku
 7071 jou                jou_distance
 7072 
 7073 kanejakusun        sun      # Alias to emphasize architectural name
 7074 kanejaku           shaku
 7075 kanejakujou        jou
 7076 
 7077 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
 7078 taichi             shaku   # http://zh.wikipedia.org/wiki/台尺
 7079 taicun             sun     # http://zh.wikipedia.org/wiki/台制
 7080 !utf8
 7081 台尺               taichi  # via Hanyu Pinyin romanizations
 7082 台寸               taicun
 7083 !endutf8
 7084 
 7085 # In context of clothing, shaku is different from architecture
 7086 # http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html
 7087 
 7088 kujirajaku         10|8 shaku
 7089 kujirajakusun      1|10 kujirajaku
 7090 kujirajakubu       1|100 kujirajaku
 7091 kujirajakujou      10 kujirajaku
 7092 tan_distance       3 kujirajakujou
 7093 
 7094 ken                6 shaku  # Also sometimes 6.3, 6.5, or 6.6
 7095                             # http://www.homarewood.co.jp/syakusun.htm
 7096 
 7097 # mostly unused
 7098 chou_distance      60 ken
 7099 chou               chou_distance
 7100 ri                 36 chou
 7101 
 7102 # Japanese Area Measures
 7103 
 7104 # Tsubo is still used for land size, though the others are more
 7105 # recognized by their homonyms in the other measurements.
 7106 
 7107 gou_area             1|10 tsubo
 7108 tsubo                36 shaku^2    # Size of two tatami = ken^2 ??
 7109 se                   30 tsubo
 7110 tan_area             10 se
 7111 chou_area            10 tan_area
 7112 
 7113 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
 7114 ping                 tsubo     # http://zh.wikipedia.org/wiki/坪
 7115 jia                  2934 ping # http://zh.wikipedia.org/wiki/甲_(单位)
 7116 fen                  1|10 jia  # http://zh.wikipedia.org/wiki/分
 7117 fen_area             1|10 jia  # Protection against future collisions
 7118 !utf8
 7119 坪                   ping      # via Hanyu Pinyin romanizations
 7120 甲                   jia
 7121 分                   fen
 7122 分地                 fen_area  # Protection against future collisions
 7123 !endutf8
 7124 
 7125 # Japanese architecture is based on a "standard" size of tatami mat.
 7126 # Room sizes today are given in number of tatami, and this number
 7127 # determines the spacing between colums and hence sizes of sliding
 7128 # doors and paper screens.  However, every region has its own slightly
 7129 # different tatami size.  Edoma, used in and around Tokyo and
 7130 # Hokkaido, is becoming a nationwide standard.  Kyouma is used around
 7131 # Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.
 7132 # Note that the tatami all have the aspect ratio 2:1 so that the mats
 7133 # can tile the room with some of them turned 90 degrees.
 7134 #
 7135 # http://www.moon2.net/tatami/infotatami/structure.html
 7136 
 7137 edoma                (5.8*2.9) shaku^2
 7138 kyouma               (6.3*3.15) shaku^2
 7139 chuukyouma           (6*3) shaku^2
 7140 jou_area             edoma
 7141 tatami               jou_area
 7142 
 7143 # Japanese Volume Measures
 7144 
 7145 # The "shou" is still used for such things as alcohol and seasonings.
 7146 # Large quantities of paint are still purchased in terms of "to".
 7147 
 7148 shaku_volume         1|10 gou_volume
 7149 gou_volume           1|10 shou
 7150 gou                  gou_volume
 7151 shou                 (4.9*4.9*2.7) sun^3   # The character shou which is
 7152                                            # the same as masu refers to a
 7153                                            # rectangular wooden cup used to
 7154                                            # measure liquids and cereal.
 7155                                            # Sake is sometimes served in a masu
 7156                                            # Note that it happens to be
 7157                                            # EXACTLY 7^4/11^3 liters.
 7158 to                   10 shou
 7159 koku                 10 to  # No longer used; historically a measure of rice
 7160 
 7161 # Japanese Weight Measures
 7162 #
 7163 # http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html
 7164 
 7165 # Not really used anymore.
 7166 
 7167 rin_weight           1|10 bu_weight
 7168 bu_weight            1|10 monme
 7169 fun                  1|10 monme
 7170 monme                momme
 7171 kin                  160 monme
 7172 kan                  1000 monme
 7173 kwan                 kan         # This was the old pronounciation of the unit.
 7174                                  # The old spelling persisted a few centuries
 7175                                  # longer and was not changed until around
 7176                                  # 1950.
 7177 
 7178 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
 7179 # says: "Volume measure in Taiwan is largely metric".
 7180 taijin               kin      # http://zh.wikipedia.org/wiki/台斤
 7181 tailiang             10 monme # http://zh.wikipedia.org/wiki/台斤
 7182 taiqian              monme    # http://zh.wikipedia.org/wiki/台制
 7183 !utf8
 7184 台斤                 taijin # via Hanyu Pinyin romanizations
 7185 台兩                 tailiang
 7186 台錢                 taiqian
 7187 !endutf8
 7188 
 7189 #
 7190 # Australian unit
 7191 #
 7192 
 7193 australiasquare         (10 ft)^2   # Used for house area
 7194 
 7195 
 7196 #
 7197 # A few German units as currently in use.
 7198 #
 7199 
 7200 zentner                 50 kg
 7201 doppelzentner           2 zentner
 7202 pfund                   500 g
 7203 
 7204 # The klafter, which was used in central Europe, was derived from the span of
 7205 # outstretched arms.
 7206 #
 7207 # https://en.wikipedia.org/wiki/Obsolete_Austrian_units_of_measurement
 7208 # https://www.llv.li/files/abi/klafter-m2-en.pdf
 7209 
 7210 austriaklafter          1.89648384 m    # Exact definition, 23 July 1871 
 7211 austriafoot             1|6 austriaklafter
 7212 prussiaklafter          1.88 m
 7213 prussiafoot             1|6 prussiaklafter
 7214 bavariaklafter          1.751155 m
 7215 bavariafoot             1|6 bavariaklafter
 7216 hesseklafter            2.5 m
 7217 hessefoot               1|6 hesseklafter
 7218 switzerlandklafter      metricklafter
 7219 switzerlandfoot         1|6 switzerlandklafter
 7220 swissklafter            switzerlandklafter
 7221 swissfoot               1|6 swissklafter
 7222 metricklafter           1.8 m
 7223 
 7224 austriayoke             8 austriaklafter * 200 austriaklafter
 7225 
 7226 liechtensteinsquareklafter 3.596652 m^2 # Used until 2017 to measure land area 
 7227 liechtensteinklafter  sqrt(liechtensteinsquareklafter)
 7228 
 7229 # The klafter was also used to measure volume of wood, generally being a stack
 7230 # of wood one klafter wide, one klafter long, with logs 3 feet (half a klafter)
 7231 # in length
 7232 
 7233 prussiawoodklafter      0.5 prussiaklafter^3
 7234 austriawoodklafter      0.5 austriaklafter^3
 7235 festmeter               m^3             # modern measure of wood, solid cube
 7236 raummeter               0.7 festmeter   # Air space between the logs, stacked
 7237 schuettraummeter        0.65 raummeter  # A cubic meter volume of split and cut
 7238 schüttraummeter         schuettraummeter#   firewood in a loose, unordered
 7239                                         #   pile, not stacked.  This is called
 7240                                         #   "tipped".
 7241 
 7242 
 7243 #
 7244 # Swedish (Sweden) pre-metric units of 1739.
 7245 # The metric system was adopted in 1878.
 7246 # https://sv.wikipedia.org/wiki/Verkm%C3%A5tt
 7247 #
 7248 
 7249 verklinje               2.0618125 mm
 7250 verktum                 12 verklinje
 7251 kvarter                 6 verktum
 7252 fot                     2 kvarter
 7253 aln                     2 fot
 7254 famn                    3 aln
 7255 
 7256 #
 7257 # Some traditional Russian measures
 7258 #
 7259 # If you would like to help expand this section and understand
 7260 # cyrillic transliteration, let me know.  These measures are meant to
 7261 # reflect common usage, e.g. in translated literature.  
 7262 #
 7263 
 7264 dessiatine              2400 sazhen^2    # Land measure
 7265 dessjatine              dessiatine
 7266 
 7267 funt                    409.51718 grams  # similar to pound
 7268 zolotnik                1|96 funt        # used for precious metal measure
 7269 pood                    40 funt          # common in agricultural measure
 7270 
 7271 arshin                  (2 + 1|3) feet
 7272 sazhen                  3 arshin         # analogous to fathom
 7273 verst                   500 sazhen       # of similar use to mile
 7274 versta                  verst
 7275 borderverst             1000 sazhen
 7276 russianmile             7 verst
 7277 
 7278 
 7279 
 7280 
 7281 #
 7282 # Old French distance measures, from French Weights and Measures
 7283 # Before the Revolution by Zupko
 7284 #
 7285 
 7286 frenchfoot              144|443.296 m     # pied de roi, the standard of Paris.
 7287 pied                    frenchfoot        #   Half of the hashimicubit,
 7288 frenchfeet              frenchfoot        #   instituted by Charlemagne.
 7289 frenchinch              1|12 frenchfoot   #   This exact definition comes from
 7290 frenchthumb             frenchinch        #   a law passed on 10 Dec 1799 which
 7291 pouce                   frenchthumb       #   fixed the meter at
 7292                                           #   3 frenchfeet + 11.296 lignes.
 7293 frenchline              1|12 frenchinch   # This is supposed to be the size
 7294 ligne                   frenchline        #   of the average barleycorn
 7295 frenchpoint             1|12 frenchline
 7296 toise                   6 frenchfeet
 7297 arpent                  180^2 pied^2      # The arpent is 100 square perches,
 7298                                           # but the perche seems to vary a lot
 7299                                           # and can be 18 feet, 20 feet, or 22
 7300                                           # feet.  This measure was described
 7301                                           # as being in common use in Canada in
 7302                                           # 1934 (Websters 2nd).  The value
 7303                                           # given here is the Paris standard
 7304                                           # arpent.
 7305 frenchgrain             1|18827.15 kg     # Weight of a wheat grain, hence
 7306                                           # smaller than the British grain.
 7307 frenchpound             9216 frenchgrain
 7308 
 7309 #
 7310 # Before the Imperial Weights and Measures Act of 1824, various different
 7311 # weights and measures were in use in different places.
 7312 #
 7313 
 7314 # Scots linear measure
 7315 
 7316 scotsinch        1.00540054 UKinch
 7317 scotslink        1|100 scotschain
 7318 scotsfoot        12 scotsinch
 7319 scotsfeet        scotsfoot
 7320 scotsell         37 scotsinch
 7321 scotsfall        6 scotsell
 7322 scotschain       4 scotsfall
 7323 scotsfurlong     10 scotschain
 7324 scotsmile        8 scotsfurlong
 7325 
 7326 # Scots area measure
 7327 
 7328 scotsrood        40 scotsfall^2
 7329 scotsacre        4 scotsrood
 7330 
 7331 # Irish linear measure
 7332 
 7333 irishinch       UKinch
 7334 irishpalm       3 irishinch
 7335 irishspan       3 irishpalm
 7336 irishfoot       12 irishinch
 7337 irishfeet       irishfoot
 7338 irishcubit      18 irishinch
 7339 irishyard       3 irishfeet
 7340 irishpace       5 irishfeet
 7341 irishfathom     6 irishfeet
 7342 irishpole       7 irishyard      # Only these values
 7343 irishperch      irishpole        # are different from
 7344 irishchain      4 irishperch     # the British Imperial
 7345 irishlink       1|100 irishchain # or English values for
 7346 irishfurlong    10 irishchain    # these lengths.
 7347 irishmile       8 irishfurlong   #
 7348 
 7349 #  Irish area measure
 7350 
 7351 irishrood       40 irishpole^2
 7352 irishacre       4 irishrood
 7353 
 7354 # English wine capacity measures (Winchester measures)
 7355 
 7356 winepint       1|2 winequart
 7357 winequart      1|4 winegallon
 7358 winegallon     231 UKinch^3   # Sometimes called the Winchester Wine Gallon,
 7359                               # it was legalized in 1707 by Queen Anne, and
 7360                               # given the definition of 231 cubic inches.  It
 7361                               # had been in use for a while as 8 pounds of wine
 7362                               # using a merchant's pound, but the definition of
 7363                               # the merchant's pound had become uncertain.  A
 7364                               # pound of 15 tower ounces (6750 grains) had been
 7365                               # common, but then a pound of 15 troy ounces
 7366                               # (7200 grains) gained popularity.  Because of
 7367                               # the switch in the value of the merchants pound,
 7368                               # the size of the wine gallon was uncertain in
 7369                               # the market, hence the official act in 1707.
 7370                               # The act allowed that a six inch tall cylinder
 7371                               # with a 7 inch diameter was a lawful wine
 7372                               # gallon.  (This comes out to 230.9 in^3.)
 7373                               # Note also that in Britain a legal conversion
 7374                               # was established to the 1824 Imperial gallon
 7375                               # then taken as 277.274 in^3 so that the wine
 7376                               # gallon was 0.8331 imperial gallons.  This is
 7377                               # 231.1 cubic inches (using the international
 7378                               # inch).
 7379 winerundlet    18 winegallon
 7380 winebarrel     31.5 winegallon
 7381 winetierce     42 winegallon
 7382 winehogshead   2 winebarrel
 7383 winepuncheon   2 winetierce
 7384 winebutt       2 winehogshead
 7385 winepipe       winebutt
 7386 winetun        2 winebutt
 7387 
 7388 # English beer and ale measures used 1803-1824 and used for beer before 1688
 7389 
 7390 beerpint       1|2 beerquart
 7391 beerquart      1|4 beergallon
 7392 beergallon     282 UKinch^3
 7393 beerbarrel     36 beergallon
 7394 beerhogshead   1.5 beerbarrel
 7395 
 7396 # English ale measures used from 1688-1803 for both ale and beer
 7397 
 7398 alepint        1|2 alequart
 7399 alequart       1|4 alegallon
 7400 alegallon      beergallon
 7401 alebarrel      34 alegallon
 7402 alehogshead    1.5 alebarrel
 7403 
 7404 # Scots capacity measure
 7405 
 7406 scotsgill      1|4 mutchkin
 7407 mutchkin       1|2 choppin
 7408 choppin        1|2 scotspint
 7409 scotspint      1|2 scotsquart
 7410 scotsquart     1|4 scotsgallon
 7411 scotsgallon    827.232 UKinch^3
 7412 scotsbarrel    8 scotsgallon
 7413 jug            scotspint
 7414 
 7415 # Scots dry capacity measure
 7416 
 7417 scotswheatlippy   137.333 UKinch^3    # Also used for peas, beans, rye, salt
 7418 scotswheatlippies scotswheatlippy
 7419 scotswheatpeck    4 scotswheatlippy
 7420 scotswheatfirlot  4 scotswheatpeck
 7421 scotswheatboll    4 scotswheatfirlot
 7422 scotswheatchalder 16 scotswheatboll
 7423 
 7424 scotsoatlippy     200.345 UKinch^3    # Also used for barley and malt
 7425 scotsoatlippies   scotsoatlippy
 7426 scotsoatpeck      4 scotsoatlippy
 7427 scotsoatfirlot    4 scotsoatpeck
 7428 scotsoatboll      4 scotsoatfirlot
 7429 scotsoatchalder   16 scotsoatboll
 7430 
 7431 # Scots Tron weight
 7432 
 7433 trondrop       1|16 tronounce
 7434 tronounce      1|20 tronpound
 7435 tronpound      9520 grain
 7436 tronstone      16 tronpound
 7437 
 7438 # Irish liquid capacity measure
 7439 
 7440 irishnoggin    1|4 irishpint
 7441 irishpint      1|2 irishquart
 7442 irishquart     1|2 irishpottle
 7443 irishpottle    1|2 irishgallon
 7444 irishgallon    217.6 UKinch^3
 7445 irishrundlet   18 irishgallon
 7446 irishbarrel    31.5 irishgallon
 7447 irishtierce    42 irishgallon
 7448 irishhogshead  2 irishbarrel
 7449 irishpuncheon  2 irishtierce
 7450 irishpipe      2 irishhogshead
 7451 irishtun       2 irishpipe
 7452 
 7453 # Irish dry capacity measure
 7454 
 7455 irishpeck      2 irishgallon
 7456 irishbushel    4 irishpeck
 7457 irishstrike    2 irishbushel
 7458 irishdrybarrel 2 irishstrike
 7459 irishquarter   2 irishbarrel
 7460 
 7461 # English Tower weights, abolished in 1528
 7462 
 7463 towerpound       5400 grain
 7464 towerounce       1|12 towerpound
 7465 towerpennyweight 1|20 towerounce
 7466 towergrain       1|32 towerpennyweight
 7467 
 7468 # English Mercantile weights, used since the late 12th century
 7469 
 7470 mercpound      6750 grain
 7471 mercounce      1|15 mercpound
 7472 mercpennyweight 1|20 mercounce
 7473 
 7474 # English weights for lead
 7475 
 7476 leadstone     12.5 lb
 7477 fotmal        70 lb
 7478 leadwey       14 leadstone
 7479 fothers       12 leadwey
 7480 
 7481 # English Hay measure
 7482 
 7483 newhaytruss 60 lb             # New and old here seem to refer to "new"
 7484 newhayload  36 newhaytruss    # hay and "old" hay rather than a new unit
 7485 oldhaytruss 56 lb             # and an old unit.
 7486 oldhayload  36 oldhaytruss
 7487 
 7488 # English wool measure
 7489 
 7490 woolclove   7 lb
 7491 woolstone   2 woolclove
 7492 wooltod     2 woolstone
 7493 woolwey     13 woolstone
 7494 woolsack    2 woolwey
 7495 woolsarpler 2 woolsack
 7496 woollast    6 woolsarpler
 7497 
 7498 #
 7499 # Ancient history units:  There tends to be uncertainty in the definitions
 7500 #                         of the units in this section
 7501 # These units are from [11]
 7502 
 7503 # Roman measure.  The Romans had a well defined distance measure, but their
 7504 # measures of weight were poor.  They adopted local weights in different
 7505 # regions without distinguishing among them so that there are half a dozen
 7506 # different Roman "standard" weight systems.
 7507 
 7508 romanfoot    296 mm          # There is some uncertainty in this definition
 7509 romanfeet    romanfoot       # from which all the other units are derived.
 7510 pes          romanfoot       # This value appears in numerous sources. In "The
 7511 pedes        romanfoot       # Roman Land Surveyors", Dilke gives 295.7 mm.
 7512 romaninch    1|12 romanfoot  # The subdivisions of the Roman foot have the
 7513 romandigit   1|16 romanfoot  #   same names as the subdivisions of the pound,
 7514 romanpalm    1|4 romanfoot   #   but we can't have the names for different
 7515 romancubit   18 romaninch    #   units.
 7516 romanpace    5 romanfeet     # Roman double pace (basic military unit)
 7517 passus       romanpace
 7518 romanperch   10 romanfeet
 7519 stade        125 romanpaces
 7520 stadia       stade
 7521 stadium      stade
 7522 romanmile    8 stadia        # 1000 paces
 7523 romanleague  1.5 romanmile
 7524 schoenus     4 romanmile
 7525 
 7526 # Other values for the Roman foot (from Dilke)
 7527 
 7528 earlyromanfoot    29.73 cm
 7529 pesdrusianus      33.3 cm    # or 33.35 cm, used in Gaul & Germany in 1st c BC
 7530 lateromanfoot     29.42 cm
 7531 
 7532 # Roman areas
 7533 
 7534 actuslength  120 romanfeet     # length of a Roman furrow
 7535 actus        120*4 romanfeet^2 # area of the furrow
 7536 squareactus  120^2 romanfeet^2 # actus quadratus
 7537 acnua        squareactus
 7538 iugerum      2 squareactus
 7539 iugera       iugerum
 7540 jugerum      iugerum
 7541 jugera       iugerum
 7542 heredium     2 iugera          # heritable plot
 7543 heredia      heredium
 7544 centuria     100 heredia
 7545 centurium    centuria
 7546 
 7547 # Roman volumes
 7548 
 7549 sextarius       35.4 in^3      # Basic unit of Roman volume.  As always,
 7550 sextarii        sextarius      # there is uncertainty.  Six large Roman
 7551                                # measures survive with volumes ranging from
 7552                                # 34.4 in^3 to 39.55 in^3.  Three of them
 7553                                # cluster around the size given here.
 7554                                #
 7555                                # But the values for this unit vary wildly
 7556                                # in other sources.  One reference  gives 0.547
 7557                                # liters, but then says the amphora is a
 7558                                # cubic Roman foot.  This gives a value for the
 7559                                # sextarius of 0.540 liters.  And the
 7560                                # encyclopedia Britannica lists 0.53 liters for
 7561                                # this unit.  Both [7] and [11], which were
 7562                                # written by scholars of weights and measures,
 7563                                # give the value of 35.4 cubic inches.
 7564 cochlearia      1|48 sextarius
 7565 cyathi          1|12 sextarius
 7566 acetabula       1|8 sextarius
 7567 quartaria       1|4 sextarius
 7568 quartarius      quartaria
 7569 heminae         1|2 sextarius
 7570 hemina          heminae
 7571 cheonix         1.5 sextarii
 7572 
 7573 # Dry volume measures (usually)
 7574 
 7575 semodius        8 sextarius
 7576 semodii         semodius
 7577 modius          16 sextarius
 7578 modii           modius
 7579 
 7580 # Liquid volume measures (usually)
 7581 
 7582 congius         12 heminae
 7583 congii          congius
 7584 amphora         8 congii
 7585 amphorae        amphora      # Also a dry volume measure
 7586 culleus         20 amphorae
 7587 quadrantal      amphora
 7588 
 7589 # Roman weights
 7590 
 7591 libra           5052 grain   # The Roman pound varied significantly
 7592 librae          libra        # from 4210 grains to 5232 grains.  Most of
 7593 romanpound      libra        # the standards were obtained from the weight
 7594 uncia           1|12 libra   # of particular coins.  The one given here is
 7595 unciae          uncia        # based on the Gold Aureus of Augustus which
 7596 romanounce      uncia        # was in use from BC 27 to AD 296.
 7597 deunx           11 uncia
 7598 dextans         10 uncia
 7599 dodrans         9 uncia
 7600 bes             8 uncia
 7601 seprunx         7 uncia
 7602 semis           6 uncia
 7603 quincunx        5 uncia
 7604 triens          4 uncia
 7605 quadrans        3 uncia
 7606 sextans         2 uncia
 7607 sescuncia       1.5 uncia
 7608 semuncia        1|2 uncia
 7609 siscilius       1|4 uncia
 7610 sextula         1|6 uncia
 7611 semisextula     1|12 uncia
 7612 scriptulum      1|24 uncia
 7613 scrupula        scriptulum
 7614 romanobol       1|2 scrupula
 7615 
 7616 romanaspound    4210 grain    # Old pound based on bronze coinage, the
 7617                               # earliest money of Rome BC 338 to BC 268.
 7618 
 7619 # Egyptian length measure
 7620 
 7621 egyptianroyalcubit      20.63 in    # plus or minus .2 in
 7622 egyptianpalm            1|7 egyptianroyalcubit
 7623 egyptiandigit           1|4 egyptianpalm
 7624 egyptianshortcubit      6 egyptianpalm
 7625 
 7626 doubleremen             29.16 in  # Length of the diagonal of a square with
 7627 remendigit       1|40 doubleremen # side length of 1 royal egyptian cubit.
 7628                                   # This is divided into 40 digits which are
 7629                                   # not the same size as the digits based on
 7630                                   # the royal cubit.
 7631 
 7632 # Greek length measures
 7633 
 7634 greekfoot               12.45 in      # Listed as being derived from the
 7635 greekfeet               greekfoot     # Egyptian Royal cubit in [11].  It is
 7636 greekcubit              1.5 greekfoot # said to be 3|5 of a 20.75 in cubit.
 7637 pous                    greekfoot
 7638 podes                   greekfoot
 7639 orguia                  6 greekfoot
 7640 greekfathom             orguia
 7641 stadion                 100 orguia
 7642 akaina                  10 greekfeet
 7643 plethron                10 akaina
 7644 greekfinger             1|16 greekfoot
 7645 homericcubit            20 greekfingers  # Elbow to end of knuckles.
 7646 shortgreekcubit         18 greekfingers  # Elbow to start of fingers.
 7647 
 7648 ionicfoot               296 mm
 7649 doricfoot               326 mm
 7650 
 7651 olympiccubit            25 remendigit    # These olympic measures were not as
 7652 olympicfoot             2|3 olympiccubit # common as the other greek measures.
 7653 olympicfinger           1|16 olympicfoot # They were used in agriculture.
 7654 olympicfeet             olympicfoot
 7655 olympicdakylos          olympicfinger
 7656 olympicpalm             1|4 olympicfoot
 7657 olympicpalestra         olympicpalm
 7658 olympicspithame         3|4 foot
 7659 olympicspan             olympicspithame
 7660 olympicbema             2.5 olympicfeet
 7661 olympicpace             olympicbema
 7662 olympicorguia           6 olympicfeet
 7663 olympicfathom           olympicorguia
 7664 olympiccord             60 olympicfeet
 7665 olympicamma             olympiccord
 7666 olympicplethron         100 olympicfeet
 7667 olympicstadion          600 olympicfeet
 7668 
 7669 # Greek capacity measure
 7670 
 7671 greekkotyle             270 ml           # This approximate value is obtained
 7672 xestes                  2 greekkotyle    # from two earthenware vessels that
 7673 khous                   12 greekkotyle   # were reconstructed from fragments.
 7674 metretes                12 khous         # The kotyle is a day's corn ration
 7675 choinix                 4 greekkotyle    # for one man.
 7676 hekteos                 8 choinix
 7677 medimnos                6 hekteos
 7678 
 7679 # Greek weight.  Two weight standards were used, an Aegina standard based
 7680 # on the Beqa shekel and an Athens (attic) standard.
 7681 
 7682 aeginastater            192 grain        # Varies up to 199 grain
 7683 aeginadrachmae          1|2 aeginastater
 7684 aeginaobol              1|6 aeginadrachmae
 7685 aeginamina              50 aeginastaters
 7686 aeginatalent            60 aeginamina    # Supposedly the mass of a cubic foot
 7687                                          # of water (whichever foot was in use)
 7688 
 7689 atticstater             135 grain        # Varies 134-138 grain
 7690 atticdrachmae           1|2 atticstater
 7691 atticobol               1|6 atticdrachmae
 7692 atticmina               50 atticstaters
 7693 attictalent             60 atticmina     # Supposedly the mass of a cubic foot
 7694                                          # of water (whichever foot was in use)
 7695 
 7696 # "Northern" cubit and foot.  This was used by the pre-Aryan civilization in
 7697 # the Indus valley.  It was used in Mesopotamia, Egypt, North Africa, China,
 7698 # central and Western Europe until modern times when it was displaced by
 7699 # the metric system.
 7700 
 7701 northerncubit           26.6 in           # plus/minus .2 in
 7702 northernfoot            1|2 northerncubit
 7703 
 7704 sumeriancubit           495 mm
 7705 kus                     sumeriancubit
 7706 sumerianfoot            2|3 sumeriancubit
 7707 
 7708 assyriancubit           21.6 in
 7709 assyrianfoot            1|2 assyriancubit
 7710 assyrianpalm            1|3 assyrianfoot
 7711 assyriansusi            1|20 assyrianpalm
 7712 susi                    assyriansusi
 7713 persianroyalcubit       7 assyrianpalm
 7714 
 7715 
 7716 # Arabic measures.  The arabic standards were meticulously kept.  Glass weights
 7717 # accurate to .2 grains were made during AD 714-900.
 7718 
 7719 hashimicubit            25.56 in          # Standard of linear measure used
 7720                                           # in Persian dominions of the Arabic
 7721                                           # empire 7-8th cent.  Is equal to two
 7722                                           # French feet.
 7723 
 7724 blackcubit              21.28 in
 7725 arabicfeet              1|2 blackcubit
 7726 arabicfoot              arabicfeet
 7727 arabicinch              1|12 arabicfoot
 7728 arabicmile              4000 blackcubit
 7729 
 7730 silverdirhem            45 grain  # The weights were derived from these two
 7731 tradedirhem             48 grain  # units with two identically named systems
 7732                                   # used for silver and used for trade purposes
 7733 
 7734 silverkirat             1|16 silverdirhem
 7735 silverwukiyeh           10 silverdirhem
 7736 silverrotl              12 silverwukiyeh
 7737 arabicsilverpound       silverrotl
 7738 
 7739 tradekirat              1|16 tradedirhem
 7740 tradewukiyeh            10 tradedirhem
 7741 traderotl               12 tradewukiyeh
 7742 arabictradepound        traderotl
 7743 
 7744 # Miscellaneous ancient units
 7745 
 7746 parasang                3.5 mile # Persian unit of length usually thought
 7747                                  # to be between 3 and 3.5 miles
 7748 biblicalcubit           21.8 in
 7749 hebrewcubit             17.58 in
 7750 li                      10|27.8 mile  # Chinese unit of length
 7751                                       #   100 li is considered a day's march
 7752 liang                   11|3 oz       # Chinese weight unit
 7753 
 7754 
 7755 # Medieval time units.  According to the OED, these appear in Du Cange
 7756 # by Papias.
 7757 
 7758 timepoint               1|5 hour  # also given as 1|4
 7759 timeminute              1|10 hour
 7760 timeostent              1|60 hour
 7761 timeounce               1|8 timeostent
 7762 timeatom                1|47 timeounce
 7763 
 7764 # Given in [15], these subdivisions of the grain were supposedly used
 7765 # by jewelers.  The mite may have been used but the blanc could not
 7766 # have been accurately measured.
 7767 
 7768 mite                    1|20 grain
 7769 droit                   1|24 mite
 7770 periot                  1|20 droit
 7771 blanc                   1|24 periot
 7772 
 7773 #
 7774 # Localization
 7775 #
 7776 
 7777 !var UNITS_ENGLISH US
 7778 hundredweight           ushundredweight
 7779 ton                     uston
 7780 scruple                 apscruple
 7781 fluidounce              usfluidounce
 7782 gallon                  usgallon
 7783 bushel                  usbushel
 7784 quarter                 quarterweight
 7785 cup                     uscup
 7786 tablespoon              ustablespoon
 7787 teaspoon                usteaspoon
 7788 dollar                  US$
 7789 cent                    $ 0.01
 7790 penny                   cent
 7791 minim                   minimvolume
 7792 pony                    ponyvolume
 7793 grand                   usgrand
 7794 firkin                  usfirkin
 7795 hogshead                ushogshead
 7796 !endvar
 7797 
 7798 !var UNITS_ENGLISH GB
 7799 hundredweight           brhundredweight
 7800 ton                     brton
 7801 scruple                 brscruple
 7802 fluidounce              brfluidounce
 7803 gallon                  brgallon
 7804 bushel                  brbushel
 7805 quarter                 brquarter
 7806 chaldron                brchaldron
 7807 cup                     brcup
 7808 teacup                  brteacup
 7809 tablespoon              brtablespoon
 7810 teaspoon                brteaspoon
 7811 dollar                  US$
 7812 cent                    $ 0.01
 7813 penny                   brpenny
 7814 minim                   minimnote
 7815 pony                    brpony
 7816 grand                   brgrand
 7817 firkin                  brfirkin
 7818 hogshead                brhogshead
 7819 !endvar
 7820 
 7821 !varnot UNITS_ENGLISH GB US
 7822 !message Unknown value for environment variable UNITS_ENGLISH.  Should be GB or US.
 7823 !endvar
 7824 
 7825 
 7826 !utf8
 7827 ⅛-                      1|8
 7828 ¼-                      1|4
 7829 ⅜-                      3|8
 7830 ½-                      1|2
 7831 ⅝-                      5|8
 7832 ¾-                      3|4
 7833 ⅞-                      7|8
 7834 ⅙-                      1|6
 7835 ⅓-                      1|3
 7836 ⅔-                      2|3
 7837 ⅚-                      5|6
 7838 ⅕-                      1|5
 7839 ⅖-                      2|5
 7840 ⅗-                      3|5
 7841 ⅘-                      4|5
 7842 # U+2150-               1|7  For some reason these characters are getting
 7843 # U+2151-               1|9  flagged as invalid UTF8.
 7844 # U+2152-               1|10
 7845 #⅐-               1|7   # fails under MacOS
 7846 #⅑-               1|9   # fails under MacOS
 7847 #⅒-               1|10  # fails under MacOS
 7848 ℯ                       exp(1)      # U+212F, base of natural log
 7849 µ-                      micro       # micro sign U+00B5
 7850 μ-                      micro       # small mu U+03BC
 7851 ångström                angstrom
 7852 Å                       angstrom    # angstrom symbol U+212B
 7853 Å                       angstrom    # A with ring U+00C5
 7854 röntgen                 roentgen
 7855 °C                      degC
 7856 °F                      degF
 7857 °K                      K           # °K is incorrect notation
 7858 °R                      degR
 7859 °                       degree
 7860 ℃                       degC
 7861 ℉                       degF
 7862 K                       K          # Kelvin symbol, U+212A
 7863 ℓ                       liter      # unofficial abbreviation used in some places
 7864 Ω                       ohm       # Ohm symbol U+2126
 7865 Ω                       ohm       # Greek capital omega U+03A9
 7866 ℧                       mho
 7867 ʒ                        dram     # U+0292
 7868 ℈                       scruple
 7869 ℥                       ounce
 7870 ℔                       lb
 7871 ℎ                       h
 7872 ℏ                       hbar
 7873 ‰                       1|1000
 7874 ‱                       1|10000
 7875 ′                       '        # U+2032
 7876 ″                       "        # U+2033
 7877 
 7878 #
 7879 # Unicode currency symbols
 7880 #
 7881 
 7882 ¢                       cent
 7883 £                       britainpound
 7884 ¥                       japanyen
 7885 €                       euro
 7886 ₩                       southkoreawon
 7887 ₪                       israelnewshekel
 7888 ₤                       lira
 7889 # ₺                       turkeylira  # fails under MacOS
 7890 ₨                       rupee           # unofficial legacy rupee sign
 7891 # ₹                       indiarupee      # official rupee sign # MacOS fail
 7892 #؋                       afghanafghani    # fails under MacOS
 7893 ฿                       thailandbaht
 7894 ₡                       elsalvadorcolon # Also costaricacolon
 7895 ₣                       francefranc
 7896 ₦                       nigerianaira
 7897 ₧                       spainpeseta
 7898 ₫                       vietnamdong
 7899 ₭                       laokip 
 7900 ₮                       mongoliatugrik
 7901 ₯                       greecedrachma
 7902 ₱                       philippinepeso
 7903 # ₲                       paraguayguarani # fails under MacOS
 7904 #₴                       ukrainehryvnia   # fails under MacOS
 7905 #₵                       ghanacedi        # fails under MacOS
 7906 #₸                       kazakhstantenge  # fails under MacOS
 7907 #₼                       azerbaijanmanat # fails under MacOS
 7908 #₽                       russiaruble     # fails under MacOS
 7909 #₾                       georgialari     # fails under MacOS
 7910 ﷼                       iranrial
 7911 ﹩                      $
 7912 ¢                      ¢
 7913 £                      £
 7914 ¥                      ¥
 7915 ₩                      ₩
 7916 
 7917 #
 7918 # Square Unicode symbols starting at U+3371
 7919 #
 7920 
 7921 ㍱                      hPa
 7922 ㍲                      da
 7923 ㍳                      au
 7924 ㍴                      bar
 7925 # ㍵                          oV???
 7926 ㍶                      pc
 7927 #㍷                      dm      invalid on Mac
 7928 #㍸                      dm^2    invalid on Mac
 7929 #㍹                      dm^3    invalid on Mac
 7930 ㎀                      pA
 7931 ㎁                      nA
 7932 ㎂                      µA
 7933 ㎃                      mA
 7934 ㎄                      kA
 7935 ㎅                      kB
 7936 ㎆                      MB
 7937 ㎇                      GB
 7938 ㎈                      cal
 7939 ㎉                      kcal
 7940 ㎊                      pF
 7941 ㎋                      nF
 7942 ㎌                      µF
 7943 ㎍                      µg
 7944 ㎎                      mg
 7945 ㎏                      kg
 7946 ㎐                      Hz
 7947 ㎑                      kHz
 7948 ㎒                      MHz
 7949 ㎓                      GHz
 7950 ㎔                      THz
 7951 ㎕                      µL
 7952 ㎖                      mL
 7953 ㎗                      dL
 7954 ㎘                      kL
 7955 ㎙                      fm
 7956 ㎚                      nm
 7957 ㎛                      µm
 7958 ㎜                      mm
 7959 ㎝                      cm
 7960 ㎞                      km
 7961 ㎟                      mm^2
 7962 ㎠                      cm^2
 7963 ㎡                      m^2
 7964 ㎢                      km^2
 7965 ㎣                      mm^3
 7966 ㎤                      cm^3
 7967 ㎥                      m^3
 7968 ㎦                      km^3
 7969 ㎧                      m/s
 7970 ㎨                      m/s^2
 7971 ㎩                      Pa
 7972 ㎪                      kPa
 7973 ㎫                      MPa
 7974 ㎬                      GPa
 7975 ㎭                      rad
 7976 ㎮                      rad/s
 7977 ㎯                      rad/s^2
 7978 ㎰                      ps
 7979 ㎱                      ns
 7980 ㎲                      µs
 7981 ㎳                      ms
 7982 ㎴                      pV
 7983 ㎵                      nV
 7984 ㎶                      µV
 7985 ㎷                      mV
 7986 ㎸                      kV
 7987 ㎹                      MV
 7988 ㎺                      pW
 7989 ㎻                      nW
 7990 ㎼                      µW
 7991 ㎽                      mW
 7992 ㎾                      kW
 7993 ㎿                      MW
 7994 ㏀                      kΩ
 7995 ㏁                      MΩ
 7996 ㏃                      Bq
 7997 ㏄                      cc
 7998 ㏅                      cd
 7999 ㏆                      C/kg
 8000 ㏈()                    dB
 8001 ㏉                      Gy
 8002 ㏊                      ha
 8003 # ㏋  HP??
 8004 ㏌                      in
 8005 # ㏍                      KK??
 8006 # ㏎                      KM???
 8007 ㏏                      kt
 8008 ㏐                      lm
 8009 # ㏑                      ln
 8010 # ㏒                      log
 8011 ㏓                      lx
 8012 ㏔                      mb
 8013 ㏕                      mil
 8014 ㏖                      mol
 8015 ㏗()                    pH
 8016 ㏙                      ppm
 8017 #   ㏚     PR???
 8018 ㏛                      sr
 8019 ㏜                      Sv
 8020 ㏝                      Wb
 8021 #㏞                      V/m     Invalid on Mac
 8022 #㏟                      A/m     Invalid on Mac
 8023 #㏿                      gal     Invalid on Mac
 8024 
 8025 !endutf8
 8026 
 8027 ############################################################################
 8028 #
 8029 # Unit list aliases
 8030 #
 8031 # These provide a shorthand for conversions to unit lists.
 8032 #
 8033 ############################################################################
 8034 
 8035 !unitlist hms hr;min;sec
 8036 !unitlist time year;day;hr;min;sec
 8037 !unitlist dms deg;arcmin;arcsec
 8038 !unitlist ftin ft;in;1|8 in
 8039 !unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
 8040 !unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
 8041                 tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
 8042 
 8043 ############################################################################
 8044 #
 8045 # The following units were in the Unix units database but do not appear in
 8046 # this file:
 8047 #
 8048 #      wey        used for cheese, salt and other goods.  Measured mass or
 8049 #      waymass    volume depending on what was measured and where the measuring
 8050 #                 took place.  A wey of cheese ranged from 200 to 324 pounds.
 8051 #
 8052 #      sack       No precise definition
 8053 #
 8054 #      spindle    The length depends on the type of yarn
 8055 #
 8056 #      block      Defined variously on different computer systems
 8057 #
 8058 #      erlang     A unit of telephone traffic defined variously.
 8059 #                 Omitted because there are no other units for this
 8060 #                 dimension.  Is this true?  What about CCS = 1/36 erlang?
 8061 #                 Erlang is supposed to be dimensionless.  One erlang means
 8062 #                 a single channel occupied for one hour.
 8063 #
 8064 ############################################################################
 8065