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+#
+# This file is the units database for use with GNU units, a units conversion
+# program by Adrian Mariano adrianm@gnu.org
+#
+# Febuary 2024 Version 3.19
+# last updated 16 February 2024
+#
+# Copyright (C) 1996-2002, 2004-2020, 2022, 2024
+# Free Software Foundation, Inc
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 51 Franklin Street, Fifth Floor,
+# Boston, MA  02110-1301  USA
+#
+############################################################################
+#
+# Improvements and corrections are welcome.
+#
+# See the end of this file for a list of items we have chosen to exclude
+# or have decided are out of scope for GNU units.  
+#
+# Fundamental constants in this file are the 2018 CODATA recommended values.
+#
+# Most units data was drawn from
+#            1. NIST Special Publication 811, Guide for the
+#                 Use of the International System of Units (SI).
+#                 Barry N. Taylor. 2008
+#                 https://www.nist.gov/pml/special-publication-811
+#            2. CRC Handbook of Chemistry and Physics 70th edition
+#            3. Oxford English Dictionary
+#            4. Webster's New Universal Unabridged Dictionary
+#            5. Units of Measure by Stephen Dresner
+#            6. A Dictionary of English Weights and Measures by Ronald Zupko
+#            7. British Weights and Measures by Ronald Zupko
+#            8. Realm of Measure by Isaac Asimov
+#            9. United States standards of weights and measures, their
+#                   creation and creators by Arthur H. Frazier.
+#           10. French weights and measures before the Revolution: a
+#                   dictionary of provincial and local units by Ronald Zupko
+#           11. Weights and Measures: their ancient origins and their
+#                   development in Great Britain up to AD 1855 by FG Skinner
+#           12. The World of Measurements by H. Arthur Klein
+#           13. For Good Measure by William Johnstone
+#           14. NTC's Encyclopedia of International Weights and Measures
+#                   by William Johnstone
+#           15. Sizes by John Lord
+#           16. Sizesaurus by Stephen Strauss
+#           17. CODATA Recommended Values of Physical Constants available at
+#                   http://physics.nist.gov/cuu/Constants/index.html
+#           18. How Many?  A Dictionary of Units of Measurement.  Available at
+#                   http://www.ibiblio.org/units/
+#           19. Numericana.  http://www.numericana.com
+#           20. UK history of measurement
+#                   https://metrication.uk/more/timeline/
+#           21. NIST Handbook 44, Specifications, Tolerances, and
+#                 Other Technical Requirements for Weighing and Measuring
+#                 Devices. 2011
+#           22. NIST Special Publication 447, Weights and Measures Standards
+#                 of the United States: a brief history. Lewis V. Judson.
+#                 1963; rev. 1976
+#           23. CRC Handbook of Chemistry and Physics, 96th edition
+#           24. Dictionary of Scientific Units, 6th ed.  H.G.  Jerrard and D.B.
+#                 McNeill. 1992
+#           25. NIST Special Publication 330, The International System of
+#                 Units (SI). ed. Barry N. Taylor and Ambler Thompson. 2008
+#                 https://www.nist.gov/pml/special-publication-330
+#           26. BIPM Brochure, The International System of Units (SI).
+#                 9th ed., 2019
+#                 https://www.bipm.org/en/publications/si-brochure/
+#
+###########################################################################
+#
+# If units you use are missing or defined incorrectly, please contact me.
+# If your country's local units are missing and you are willing to supply
+# them, please send me a list.
+#
+###########################################################################
+
+###########################################################################
+#
+# Brief Philosophy of this file
+#
+# Most unit definitions are made in terms of integers or simple fractions of
+# other definitions.  The typical exceptions are when converting between two
+# different unit systems, or the values of measured physical constants.  In
+# this file definitions are given in the most natural and revealing way in
+# terms of integer factors.
+#
+# If you make changes be sure to run 'units --check' to check your work.
+#
+# The file is USA-centric, but there is some modest effort to support other
+# countries.  This file is now coded in UTF-8.  To support environments where
+# UTF-8 is not available, definitions that require this character set are
+# wrapped in !utf8 directives.
+#
+# When a unit name is used in different countries with the different meanings
+# the system should be as follows:
+#
+# Suppose countries ABC and XYZ both use the "foo".  Then globally define
+#
+#   ABCfoo  <some value>
+#   XYZfoo  <different value>
+#
+# Then, using the !locale directive, define the "foo" appropriately for each of
+# the two countries with a definition like
+#
+# !locale ABC
+#    foo  ABCfoo
+# !endlocale
+#
+###########################################################################
+
+!locale en_US
+!  set UNITS_ENGLISH US
+!endlocale
+
+!locale en_GB
+!  set UNITS_ENGLISH GB
+!endlocale
+
+!set UNITS_ENGLISH US   # Default setting for English units
+
+!set UNITS_SYSTEM default   # Set a default value
+
+!varnot UNITS_SYSTEM si emu esu gaussian gauss hlu natural natural-gauss hartree planck planck-red default 
+!message Unknown unit system given with -u or UNITS_SYSTEM environment variable
+!message Valid systems: si, emu, esu, gauss[ian], hlu, natural, natural-gauss
+!message                planck, planck-red, hartree
+!message Using SI
+!prompt (SI)
+!endvar
+
+!var UNITS_SYSTEM si
+!message SI units selected
+!prompt (SI)
+!endvar
+
+###########################################################################
+#                                                                         #
+# Primitive units.  Any unit defined to contain a '!' character is a      #
+# primitive unit which will not be reduced any further.  All units should #
+# reduce to primitive units.                                              #
+#                                                                         #
+###########################################################################
+
+#
+# SI units
+#
+# On 20 May 2019, the SI was revised to define the units by fixing the
+# values of physical constants that depend on those units.
+#
+# https://www.nist.gov/si-redefinition/
+#
+# The BIPM--the International Bureau of Weights and Measures--provides a
+# succinct description of the new SI in its Concise Summary:
+#
+# https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN.pdf
+#
+#     The SI is the system of units in which:
+#
+#       *  the unperturbed ground state hyperfine transition frequency of the
+#          caesium 133 atom is delta nu_Cs = 9 192 631 770 Hz,
+#       *  the speed of light in vacuum, c, is 299 792 458 m/s,
+#       *  the Planck constant, h, is 6.626 070 15 * 10^-34 J s,
+#       *  the elementary charge, e, is 1.602 176 634 * 10^-19 C,
+#       *  the Boltzmann constant, k, is 1.380 649 * 10^-23 J/K,
+#       *  the Avogadro constant, N_A, is 6.022 140 76 * 10^23 mol^-1,
+#       *  the luminous efficacy of monochromatic radiation of frequency
+#          540 * 10^12 Hz, K_cd, is 683 lm/W,
+#
+#     where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz,
+#     J, C, lm, and W, respectively, are related to the units second, metre,
+#     kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg,
+#     A, K, mol, and cd, respectively, according to Hz = s^-1, J = kg m^2 s^-2,
+#     C = A s, lm = cd m^2 m^-2 = cd sr, and W = kg m^2 s^-3.
+# 
+#     These definitions specify the exact numerical value of each constant when
+#     its value is expressed in the corresponding SI unit.  By fixing the exact
+#     numerical value the unit becomes defined, since the product of the
+#     numerical value and the unit has to equal the value of the constant,
+#     which is invariant.
+# 
+#     The defining constants have been chosen such that, when taken together,
+#     their units cover all of the units of the SI.  In general, there is no
+#     one-to-one correspondence between the defining constants and the SI base
+#     units.  Any SI unit is a product of powers of these seven constants and a
+#     dimensionless factor.
+# 
+# Until 2018, the SI was defined in terms of base units and derived units.
+# These categories are no longer essential in the SI, but they are maintained
+# in view of their convenience and widespread use.  They are arguably more
+# intuitive than the new definitions.  (They are also essential to the
+# operation of GNU units.)  The definitions of the base units, which follow
+# from the definition of the SI in terms of the seven defining constants, are
+# given below.
+#
+
+s         !      # The second, symbol s, is the SI unit of time.  It is defined
+second    s      # by taking the fixed numerical value of the unperturbed
+                 # ground-state hyperfine transition frequency of the
+                 # cesium-133 atom to be 9 192 631 770 when expressed in the
+                 # unit Hz, which is equal to 1/s.  
+                 #
+                 # This definition is a restatement of the previous one, the
+                 # duration of 9192631770 periods of the radiation corresponding
+                 # to the cesium-133 transition.
+
+nu_133Cs  9192631770 Hz   # Cesium-133 transition frequency (exact)
+
+c_SI      299792458
+c         299792458 m/s   # speed of light in vacuum (exact)
+
+m         !      # The metre, symbol m, is the SI unit of length.  It is
+meter     m      # defined by taking the fixed numerical value of the speed
+metre     m      # of light in vacuum, c, to be 299 792 458 when expressed in
+                 # units of m/s.
+                 #
+                 # This definition is a rewording of the previous one and is
+                 # equivalent to defining the meter as the distance light
+                 # travels in 1|299792458 seconds.  The meter was originally
+                 # intended to be 1e-7 of the length along a meridian from the
+                 # equator to a pole.
+
+h_SI      6.62607015e-34
+h         6.62607015e-34 J s # Planck constant (exact)
+
+kg        !      # The kilogram, symbol kg, is the SI unit of mass.  It is
+kilogram  kg     # defined by taking the fixed numerical value of the Planck
+                 # constant, h, to be 6.626 070 15 * 10^-34 when expressed in
+                 # the unit J s which is equal to kg m^2 / s.
+                 # 
+                 # One advantage of fixing h to define the kilogram is that this
+                 # affects constants used to define the ampere.  If the kg were
+                 # defined by directly fixing the mass of something, then h
+                 # would be subject to error.
+                 #
+                 # The previous definition of the kilogram was the mass of the
+                 # international prototype kilogram.  The kilogram was the last
+                 # unit whose definition relied on reference to an artifact.
+                 #
+                 # It is not obvious what this new definition means, or
+                 # intuitively how fixing Planck's constant defines the
+                 # kilogram.  To define the kilogram we need to give the mass
+                 # of some reference in kilograms.  Previously the prototype in
+                 # France served as this reference, and it weighed exactly 1
+                 # kg.  But the reference can have any weight as long as you
+                 # know the weight of the reference.  The new definition uses
+                 # the "mass" of a photon, or more accurately, the mass
+                 # equivalent of the energy of a photon.  The energy of a
+                 # photon depends on its frequency.  If you pick a frequency,
+                 # f, then the energy of the photon is hf, and hence the mass
+                 # equivalent is hf/c^2.  If we reduce this expression using
+                 # the constant defined values for h and c the result is a
+                 # value in kilograms for the mass-equivalent of a photon of
+                 # frequency f, which can therefore define the size of the
+                 # kilogram.
+                 #
+                 # For more on the relationship between mass an Planck's
+                 # constant:
+                 #
+                 # https://www.nist.gov/si-redefinition/kilogram-mass-and-plancks-constant
+                 # This definition may still seem rather abstract: you can't
+                 # place a "kilogram of radiation" on one side of a balance.
+                 # Metrologists realize the kilogram using a Kibble Balance, a
+                 # device which relates mechanical energy to electrical energy
+                 # and can measure mass with extreme accuracy if h is known.
+                 #
+                 # For more on the Kibble Balance see
+                 #
+                 # https://www.nist.gov/si-redefinition/kilogram-kibble-balance
+                 # https://en.wikipedia.org/wiki/Kibble_balance
+
+k_SI      1.380649e-23
+boltzmann 1.380649e-23 J/K   # Boltzmann constant (exact)
+k         boltzmann
+
+K         !      # The kelvin, symbol K, is the SI unit of thermodynamic
+kelvin    K      # temperature.  It is defined by taking the fixed numerical
+                 # value of the Boltzmann constant, k, to be 1.380 649 * 10^-23
+                 # when expressed in the unit J/K, which is equal to 
+                 # kg m^2/s^2 K.
+                 #
+                 # The boltzmann constant establishes the relationship between
+                 # energy and temperature.  The average thermal energy carried
+                 # by each degree of freedom is kT/2.  A monatomic ideal gas
+                 # has three degrees of freedom corresponding to the three
+                 # spatial directions, which means its thermal energy is
+                 # (3/2) k T.
+                 #
+                 # The previous definition of the kelvin was based on the
+                 # triple point of water.  The change in the definition of the
+                 # kelvin will not have much effect on measurement practice.
+                 # Practical temperature calibration makes use of two scales,
+                 # the International Temperature Scale of 1990 (ITS-90), which
+                 # covers the range of 0.65 K to 1357.77K and the Provisional
+                 # Low Temperature Scale of 2000 (PLTS-2000), which covers the
+                 # range of 0.9 mK to 1 K.
+                 # https://www.bipm.org/en/committees/cc/cct/publications-cc.html
+                 #
+                 # The ITS-90 contains 17 reference points including things
+                 # like the triple point of hydrogen (13.8033 K) or the
+                 # freezing point of gold (1337.33 K), and of course the triple
+                 # point of water.  The PLTS-2000 specifies four reference
+                 # points, all based on properties of helium-3.
+                 #
+                 # The redefinition of the kelvin will not affect the values of
+                 # these reference points, which have been determined by
+                 # primary thermometry, using thermometers that rely only on
+                 # relationships that allow temperature to be calculated
+                 # directly without using any unknown quantities. Examples
+                 # include acoustic thermometers, which measure the speed of
+                 # sound in a gas, or electronic thermometers, which measure
+                 # tiny voltage fluctuations in resistors. Both variables
+                 # depend directly on temperature.
+
+e_SI      1.602176634e-19
+e         1.602176634e-19 C  # electron charge (exact)
+
+A         !      # The ampere, symbol A, is the SI unit of electric current.
+ampere    A      # It is defined by taking the fixed numerical value of the
+amp       ampere # elementary charge, e, to be 1.602 176 634 * 10^-19 when
+                 # expressed in the unit C, which is equal to A*s.
+                 #
+                 # The previous definition was the current which produces a
+                 # force of 2e-7 N/m between two infinitely long wires a meter
+                 # apart.  This definition was difficult to realize accurately.
+                 #
+                 # The ampere is actually realized by establishing the volt and
+                 # the ohm, since A = V / ohm.  These measurements can be done
+                 # using the Josephson effect and the quantum Hall effect,
+                 # which accurately measure voltage and resistance, respectively,
+                 # with reference to two fixed constants, the Josephson
+                 # constant, K_J=2e/h and the von Klitzing constant, R_K=h/e^2.
+                 # Under the previous SI system, these constants had official
+                 # fixed values, defined in 1990.  This created a situation
+                 # where the standard values for the volt and ohm were in some
+                 # sense outside of SI because they depended primarily on
+                 # constants different from the ones used to define SI. After
+                 # the revision, since e and h have exact definitions, the
+                 # Josephson and von Klitzing constants will also have exact
+                 # definitions that derive from SI instead of the conventional
+                 # 1990 values.
+                 #
+                 # In fact we know that there is a small offset between the
+                 # conventional values of the electrical units based on the
+                 # conventional 1990 values and the SI values.  The new
+                 # definition, which brings the practical electrical units back
+                 # into SI, will lead to a one time change of +0.1ppm for
+                 # voltage values and +0.02ppm for resistance values.
+                 #
+                 # The previous definition resulted in fixed exact values for
+                 # the vacuum permeability (mu0), the impedance of free space
+                 # (Z0), the vacuum permittivity (epsilon0), and the Coulomb
+                 # constant. With the new definition, these four values are
+                 # subject to experimental error.
+
+avogadro  6.02214076e23 / mol # Size of a mole (exact)
+N_A       avogadro
+
+mol       !      # The mole, symbol mol, is the SI unit of amount of
+mole      mol    # substance.  One mole contains exactly 6.022 140 76 * 10^23
+                 # elementary entities.  This number is the fixed numerical
+                 # value of the Avogadro constant, N_A, when expressed in the
+                 # unit 1/mol and is called the Avogadro number.  The amount of
+                 # substance, symbol n, of a system is a measure of the number
+                 # of specified elementary entities.  An elementary entity may
+                 # be an atom, a molecule, an ion, an electron, any other
+                 # particle or specified group of particles.
+                 #
+                 # The atomic mass unit (u) is defined as 1/12 the mass of
+                 # carbon-12.  Previously the mole was defined so that a mole
+                 # of carbon-12 weighed exactly 12g, or N_A u = 1 g/mol
+                 # exactly. This relationship is now an experimental, 
+                 # approximate relationship.
+                 #
+                 # To determine the size of the mole, researchers used spheres
+                 # of very pure silicon-28 that weighed a kilogram.  They
+                 # measured the molar mass of Si-28 using mass spectrometry and
+                 # used X-ray diffraction interferometry to determine the
+                 # spacing of the silicon atoms in the sphere.  Using the
+                 # sphere's volume it was then possible to determine the number
+                 # of silicon atoms in the sphere, and hence determine the
+                 # Avogadro constant.  The results of this experiment were used 
+                 # to define N_A, which is henceforth a fixed, unchanging
+                 # quantity.  
+
+cd        !      # The candela, symbol cd, is the SI unit of luminous intensity
+candela   cd     # in a given direction.  It is defined by taking the fixed
+                 # numerical value of the luminous efficacy of monochromatic
+                 # radiation of the frequency 540e12 Hz to be 683 when
+                 # expressed in the unit lumen/watt, which is equal to
+                 # cd sr/W, or cd sr s^3/kg m^2
+                 #
+                 # This definition is a rewording of the previous definition.
+                 # Luminous intensity differs from radiant intensity (W/sr) in
+                 # that it is adjusted for human perceptual dependence on
+                 # wavelength.  The frequency of 540e12 Hz (yellow;
+                 # wavelength approximately 555 nm in vacuum) is where human
+                 # perception is most efficient.
+                 
+K_cd 683 lumen/W # Luminous efficiency at 540e12 Hz (exact)
+
+# Angular Measure
+#
+# The radian and steradian are defined as dimensionless primitive units.
+# The radian is equal to m/m and the steradian to m^2/m^2 so these units are
+# dimensionless.  Retaining them as named units is useful because it allows
+# clarity in expressions and makes the meaning of unit definitions more clear.
+# These units will reduce to 1 in conversions but not for sums of units or for
+# arguments to functions.
+#
+
+radian    !dimensionless   # Plane angle subtended at the center of a circle by
+                           #   an arc equal in length to the radius of the
+                           #   circle.  
+                           #   Dimension: LENGTH (of arc) / DISTANCE (radius)
+
+sr        !dimensionless   # Solid angle which cuts off an area of the surface
+steradian sr               #   of the sphere equal to that of a square with
+                           #   sides of length equal to the radius of the
+                           #   sphere.
+                           #   Dimension: AREA (of surface) / DISTANCE^2
+                           #                                         (radius^2)
+#
+# A primitive non-SI unit
+#
+
+bit       !      # Basic unit of information (entropy).  The entropy in bits
+                 #   of a random variable over a finite alphabet is defined
+                 #   to be the sum of -p(i)*log2(p(i)) over the alphabet where
+                 #   p(i) is the probability that the random variable takes
+                 #   on the value i.
+
+#
+# Currency: the primitive unit of currency is defined in currency.units. 
+# It is usually the US$ or the euro, but it is user selectable.  
+#
+
+#
+# Absolute value
+#
+
+abs(x)                  noerror sqrt(x^2)  
+
+###########################################################################
+#                                                                         #
+# Prefixes (longer names must come first)                                 #
+#                                                                         #
+###########################################################################
+
+quetta-                 1e30     # Allegedly from "q" plus Greek "deka" (ten)
+ronna-                  1e27     # Allegedly from "r" plus Greek "ennea" (nine)
+yotta-                  1e24     # Greek or Latin "octo" (eight)
+zetta-                  1e21     # Latin "septem" (seven)
+exa-                    1e18     # Greek "hex" (six)
+peta-                   1e15     # Greek "pente" (five)
+tera-                   1e12     # Greek "teras" (monster)
+giga-                   1e9      # Greek "gigas" (giant)
+mega-                   1e6      # Greek "megas" (large)
+myria-                  1e4      # Not an official SI prefix
+kilo-                   1e3      # Greek "chilioi" (thousand)
+hecto-                  1e2      # Greek "hekaton" (hundred)
+deca-                   1e1      # Greek "deka" (ten)
+deka-                   deca
+deci-                   1e-1     # Latin "decimus" (tenth)
+centi-                  1e-2     # Latin "centum" (hundred)
+milli-                  1e-3     # Latin "mille" (thousand)
+micro-                  1e-6     # Latin "micro" or Greek "mikros" (small)
+nano-                   1e-9     # Latin "nanus" or Greek "nanos" (dwarf)
+pico-                   1e-12    # Spanish "pico" (a bit)
+femto-                  1e-15    # Danish-Norwegian "femten" (fifteen)
+atto-                   1e-18    # Danish-Norwegian "atten" (eighteen)
+zepto-                  1e-21    # Latin "septem" (seven)
+yocto-                  1e-24    # Greek or Latin "octo" (eight)
+ronto-                  1e-27    # Allegedly "r" plus Latin "novum" (nine)
+quecto-                 1e-30    # Allegedly "q" plus Latin "decim" (ten)
+
+quarter-                1|4
+semi-                   0.5
+demi-                   0.5
+hemi-                   0.5
+half-                   0.5
+double-                 2
+triple-                 3
+treble-                 3
+
+kibi-                   2^10     # In response to the improper and confusing
+mebi-                   2^20     # use of SI prefixes for powers of two,
+gibi-                   2^30     # the International Electrotechnical
+tebi-                   2^40     # Commission aproved these binary prefixes
+pebi-                   2^50     # in IEC 60027-2 Amendment 2 (1999).
+exbi-                   2^60
+zebi-                   2^70     # Zebi- and yobi- were added in the 2005 ed.,
+yobi-                   2^80     # later superseded by ISO/IEC 80000-13:2008.
+robi-                   2^90
+quebi-                  2^100
+Ki-                     kibi
+Mi-                     mebi
+Gi-                     gibi
+Ti-                     tebi
+Pi-                     pebi
+Ei-                     exbi
+Zi-                     zebi
+Yi-                     yobi
+Ri-                     robi
+Qi-                     quebi
+
+Q-                      quetta
+R-                      ronna
+Y-                      yotta
+Z-                      zetta
+E-                      exa
+P-                      peta
+T-                      tera
+G-                      giga
+M-                      mega
+k-                      kilo
+h-                      hecto
+da-                     deka
+d-                      deci
+c-                      centi
+m-                      milli
+u-                      micro   # it should be a mu but u is easy to type
+n-                      nano
+p-                      pico
+f-                      femto
+a-                      atto
+z-                      zepto
+y-                      yocto
+r-                      ronto
+q-                      quecto
+
+#
+# Names of some numbers
+#
+
+one                     1
+two                     2
+double                  2
+couple                  2
+three                   3
+triple                  3
+four                    4
+quadruple               4
+five                    5
+quintuple               5
+six                     6
+seven                   7
+eight                   8
+nine                    9
+ten                     10
+eleven                  11
+twelve                  12
+thirteen                13
+fourteen                14
+fifteen                 15
+sixteen                 16
+seventeen               17
+eighteen                18
+nineteen                19
+twenty                  20
+thirty                  30
+forty                   40
+fifty                   50
+sixty                   60
+seventy                 70
+eighty                  80
+ninety                  90
+hundred                 100
+thousand                1000
+million                 1e6
+
+twoscore                two score
+threescore              three score
+fourscore               four score
+fivescore               five score
+sixscore                six score
+sevenscore              seven score
+eightscore              eight score
+ninescore               nine score
+tenscore                ten score
+twelvescore             twelve score
+
+# These number terms were described by N. Chuquet and De la Roche in the 16th
+# century as being successive powers of a million.  These definitions are still
+# used in most European countries.  The current US definitions for these
+# numbers arose in the 17th century and don't make nearly as much sense.  These
+# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
+# W. Weisstein.
+
+shortbillion               1e9
+shorttrillion              1e12
+shortquadrillion           1e15
+shortquintillion           1e18
+shortsextillion            1e21
+shortseptillion            1e24
+shortoctillion             1e27
+shortnonillion             1e30
+shortnoventillion          shortnonillion
+shortdecillion             1e33
+shortundecillion           1e36
+shortduodecillion          1e39
+shorttredecillion          1e42
+shortquattuordecillion     1e45
+shortquindecillion         1e48
+shortsexdecillion          1e51
+shortseptendecillion       1e54
+shortoctodecillion         1e57
+shortnovemdecillion        1e60
+shortvigintillion          1e63
+
+centillion              1e303
+googol                  1e100
+
+longbillion               million^2
+longtrillion              million^3
+longquadrillion           million^4
+longquintillion           million^5
+longsextillion            million^6
+longseptillion            million^7
+longoctillion             million^8
+longnonillion             million^9
+longnoventillion          longnonillion
+longdecillion             million^10
+longundecillion           million^11
+longduodecillion          million^12
+longtredecillion          million^13
+longquattuordecillion     million^14
+longquindecillion         million^15
+longsexdecillion          million^16
+longseptdecillion         million^17
+longoctodecillion         million^18
+longnovemdecillion        million^19
+longvigintillion          million^20
+
+# These numbers fill the gaps left by the long system above.
+
+milliard                1000 million
+billiard                1000 million^2
+trilliard               1000 million^3
+quadrilliard            1000 million^4
+quintilliard            1000 million^5
+sextilliard             1000 million^6
+septilliard             1000 million^7
+octilliard              1000 million^8
+nonilliard              1000 million^9
+noventilliard           nonilliard
+decilliard              1000 million^10
+
+# For consistency
+
+longmilliard              milliard
+longbilliard              billiard
+longtrilliard             trilliard
+longquadrilliard          quadrilliard
+longquintilliard          quintilliard
+longsextilliard           sextilliard
+longseptilliard           septilliard
+longoctilliard            octilliard
+longnonilliard            nonilliard
+longnoventilliard         noventilliard
+longdecilliard            decilliard
+
+# The long centillion would be 1e600.  The googolplex is another
+# familiar large number equal to 10^googol.  These numbers give overflows.
+
+#
+# The short system prevails in English speaking countries
+#
+
+billion                 shortbillion
+trillion                shorttrillion
+quadrillion             shortquadrillion
+quintillion             shortquintillion
+sextillion              shortsextillion
+septillion              shortseptillion
+octillion               shortoctillion
+nonillion               shortnonillion
+noventillion            shortnoventillion
+decillion               shortdecillion
+undecillion             shortundecillion
+duodecillion            shortduodecillion
+tredecillion            shorttredecillion
+quattuordecillion       shortquattuordecillion
+quindecillion           shortquindecillion
+sexdecillion            shortsexdecillion
+septendecillion         shortseptendecillion
+octodecillion           shortoctodecillion
+novemdecillion          shortnovemdecillion
+vigintillion            shortvigintillion
+
+#
+# Numbers used in India 
+#
+
+lakh                    1e5
+crore                   1e7
+arab                    1e9
+kharab                  1e11
+neel                    1e13
+padm                    1e15
+shankh                  1e17
+
+#############################################################################
+#                                                                           #
+# Derived units which can be reduced to the primitive units                 #
+#                                                                           #
+#############################################################################
+
+
+
+#
+# Named SI derived units (officially accepted)
+#
+
+newton                  kg m / s^2   # force
+N                       newton
+pascal                  N/m^2        # pressure or stress
+Pa                      pascal
+joule                   N m          # energy
+J                       joule
+watt                    J/s          # power
+W                       watt
+coulomb                 A s          # charge
+C                       coulomb
+volt                    W/A          # potential difference
+V                       volt
+ohm                     V/A          # electrical resistance
+siemens                 A/V          # electrical conductance
+S                       siemens
+farad                   C/V          # capacitance
+F                       farad
+weber                   V s          # magnetic flux
+Wb                      weber
+henry                   V s / A      # inductance, also Wb/A, but needs to be
+H                       henry        #   defined this way for CGS units
+tesla                   Wb/m^2       # magnetic flux density
+T                       tesla
+hertz                   /s           # frequency
+Hz                      hertz
+
+#
+# Dimensions.  These are here to help with dimensional analysis and
+# because they will appear in the list produced by hitting '?' at the
+# "You want:" prompt to tell the user the dimension of the unit.
+#
+
+LENGTH                  meter
+AREA                    LENGTH^2
+VOLUME                  LENGTH^3
+MASS                    kilogram
+AMOUNT                  mole
+ANGLE                   radian
+SOLID_ANGLE             steradian
+MONEY                   US$
+FORCE                   newton
+PRESSURE                FORCE / AREA
+STRESS                  FORCE / AREA
+FREQUENCY               hertz
+WAVELENGTH              LENGTH
+WAVENUMBER              1/WAVELENGTH          # number of waves per distance
+VELOCITY                DISPLACEMENT / TIME   # a vector (includes direction)
+SPEED                   DISTANCE / TIME       # a scalar 
+ACCELERATION            VELOCITY / TIME
+MOMENTUM                MASS VELOCITY    # Also ENERGY / VELOCITY or IMPULSE
+IMPULSE                 FORCE TIME
+DISPLACEMENT            LENGTH
+DISTANCE                LENGTH
+ELONGATION              LENGTH
+STRAIN                  ELONGATION / LENGTH
+ENERGY                  joule
+POWER                   watt
+WORK                    FORCE DISTANCE
+DENSITY                 MASS / VOLUME
+LINEAR_DENSITY          MASS / LENGTH
+SPECIFIC_ENERGY         ENERGY / MASS
+VISCOSITY               FORCE TIME / AREA
+KINEMATIC_VISCOSITY     VISCOSITY / DENSITY
+CURRENT                 ampere
+CHARGE                  coulomb
+CAPACITANCE             farad
+RESISTANCE              ohm
+CONDUCTANCE             siemens
+# It may be easier to understand the relationship by considering
+# an object with specified dimensions and resistivity, whose
+# resistance is given by the resistivity * length / area. 
+RESISTIVITY             RESISTANCE AREA / LENGTH
+CONDUCTIVITY            CONDUCTANCE LENGTH / AREA
+INDUCTANCE              henry
+E_FIELD                 ELECTRIC_POTENTIAL / LENGTH
+B_FIELD                 tesla
+# The D and H fields are related to the E and B fields by factors of
+# epsilon and mu respectively, so their units can be found by
+# multiplying/dividing by the epsilon0 and mu0.  The more complex
+# definitions below make it possible to use D_FIELD and E_FIELD to
+# convert between SI and CGS units for these dimensions.
+D_FIELD                 E_FIELD epsilon0 / epsilon0_SI  #   mu0_SI c^2 F / m
+H_FIELD                 B_FIELD / (mu0/mu0_SI)
+ELECTRIC_DIPOLE_MOMENT  C m
+MAGNETIC_DIPOLE_MOMENT  J / T
+POLARIZATION            ELECTRIC_DIPOLE_MOMENT / VOLUME
+MAGNETIZATION           MAGNETIC_DIPOLE_MOMENT / VOLUME
+ELECTRIC_POTENTIAL      ENERGY / CHARGE #volt
+VOLTAGE                 ELECTRIC_POTENTIAL
+E_FLUX                  E_FIELD AREA    
+D_FLUX                  D_FIELD AREA
+B_FLUX                  B_FIELD AREA    
+H_FLUX                  H_FIELD AREA
+
+#
+# units derived easily from SI units
+#
+
+gram                    millikg
+gm                      gram
+g                       gram
+tonne                   1000 kg
+t                       tonne
+metricton               tonne
+sthene                  tonne m / s^2
+funal                   sthene
+pieze                   sthene / m^2
+quintal                 100 kg
+bar                     1e5 Pa     # About 1 atm
+b                       bar
+vac                     millibar
+micron                  micrometer # One millionth of a meter
+bicron                  picometer  # One brbillionth of a meter
+cc                      cm^3
+are                     100 m^2
+a                       are
+liter                   1000 cc       # The liter was defined in 1901 as the
+oldliter                1.000028 dm^3 # space occupied by 1 kg of pure water at
+L                       liter         # the temperature of its maximum density
+l                       liter         # under a pressure of 1 atm.  This was
+                                      # supposed to be 1000 cubic cm, but it
+                                      # was discovered that the original
+                                      # measurement was off.  In 1964, the
+                                      # liter was redefined to be exactly 1000
+                                      # cubic centimeters.
+Ah                      amp hour   # Unit of charge                                      
+mho                     siemens    # Inverse of ohm, hence ohm spelled backward
+galvat                  ampere     # Named after Luigi Galvani
+angstrom                1e-10 m    # Convenient for describing molecular sizes
+xunit                   xunit_cu      # Used for measuring x-ray wavelengths.
+siegbahn                xunit         # Originally defined to be 1|3029.45 of
+xunit_cu             1.00207697e-13 m # the spacing of calcite planes at 18
+xunit_mo             1.00209952e-13 m # degC.  It was intended to be exactly
+                                      # 1e-13 m, but was later found to be
+                                      # slightly off.  Current usage is with
+                                      # reference to common x-ray lines, either
+                                      # the K-alpha 1 line of copper or the
+                                      # same line of molybdenum.
+angstromstar   1.00001495 angstrom # Defined by JA Bearden in 1965 to replace 
+                                   #   the X unit.  The wavelength of the
+                                   #   tungsten K alpha1 line was defined as
+                                   #   exactly 0.20901 angstrom star, with the
+                                   #   value chosen to try to make the new
+                                   #   unit close to the angstrom.  
+silicon_d220     1.920155716e-10 m # Silicon lattice spacing
+siliconlattice sqrt(8) silicon_d220# Silicon lattice parameter, (a), the side
+                                   #   length of the unit cell for the diamond
+                                   #   centered cubic structure of silicon.
+fermi                   1e-15 m    # Convenient for describing nuclear sizes
+                                   #   Nuclear radius is from 1 to 10 fermis
+barn                    1e-28 m^2  # Used to measure cross section for
+                                   #   particle physics collision, said to
+                                   #   have originated in the phrase "big as
+                                   #   a barn".
+shed                    1e-24 barn # Defined to be a smaller companion to the
+                                   #   barn, but it's too small to be of
+                                   #   much use.
+brewster                micron^2/N # measures stress-optical coef
+diopter                 /m         # measures reciprocal of lens focal length
+fresnel                 1e12 Hz    # occasionally used in spectroscopy
+shake                   1e-8 sec
+svedberg                1e-13 s    # Used for measuring the sedimentation
+                                   # coefficient for centrifuging.
+gamma                   microgram  # Also used for 1e-9 tesla
+lambda                  microliter
+spat                    1e12 m     # Rarely used for astronomical measurements
+preece                  1e13 ohm m # resistivity
+planck                  J s        # action of one joule over one second
+sturgeon                /henry     # magnetic reluctance
+daraf                   1/farad    # elastance (farad spelled backwards)
+leo                     10 m/s^2
+poiseuille              N s / m^2  # viscosity
+mayer                   J/g K      # specific heat
+mired                   / microK   # reciprocal color temperature.  The name
+                                   #   abbreviates micro reciprocal degree.
+crocodile               megavolt   # used informally in UK physics labs
+metricounce             25 g
+mounce                  metricounce
+finsenunit              1e5 W/m^2  # Measures intensity of ultraviolet light
+                                   # with wavelength 296.7 nm.
+fluxunit                1e-26 W/m^2 Hz # Used in radio astronomy to measure
+                                       #   the energy incident on the receiving
+                                       #   body across a specified frequency
+                                       #   bandwidth.  [12]
+jansky                  fluxunit   # K. G. Jansky identified radio waves coming
+Jy                      jansky     # from outer space in 1931.
+flick       W / cm^2 sr micrometer # Spectral radiance or irradiance
+pfu                    / cm^2 sr s # particle flux unit -- Used to measure
+                                   #   rate at which particles are received by
+                                   #   a spacecraft as particles per solid
+                                   #   angle per detector area per second. [18]
+pyron            cal_IT / cm^2 min # Measures heat flow from solar radiation,
+                                   #   from Greek work "pyr" for fire.
+katal                   mol/sec    # Measure of the amount of a catalyst.  One
+kat                     katal      #   katal of catalyst enables the reaction
+                                   #   to consume or produce one mol/sec.
+solarluminosity         382.8e24 W # A common yardstick for comparing the
+                                   #   output of different stars.
+                # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
+# at mean Earth-Sun distance
+solarirradiance         solarluminosity / (4 pi sundist^2)
+solarconstant           solarirradiance
+TSI                     solarirradiance         # total solar irradiance
+
+#
+# time
+#
+
+sec                     s
+minute                  60 s
+min                     minute
+hour                    60 min
+hr                      hour
+day                     24 hr
+d                       day
+da                      day
+week                    7 day
+wk                      week
+sennight                7 day
+fortnight               14 day
+blink                   1e-5 day   # Actual human blink takes 1|3 second
+ce                      1e-2 day
+cron                    1e6 years
+watch                   4 hours    # time a sentry stands watch or a ship's
+                                   # crew is on duty.
+bell                    1|8 watch  # Bell would be sounded every 30 minutes.
+
+# French Revolutionary Time or Decimal Time.  It was Proposed during
+# the French Revolution.  A few clocks were made, but it never caught
+# on.  In 1998 Swatch defined a time measurement called ".beat" and
+# sold some watches that displayed time in this unit.
+
+decimalhour             1|10 day            
+decimalminute           1|100 decimalhour   
+decimalsecond           1|100 decimalminute 
+beat                    decimalminute          # Swatch Internet Time
+
+#
+# angular measure
+#
+
+circle                  2 pi radian
+degree                  1|360 circle
+deg                     degree
+arcdeg                  degree
+arcmin                  1|60 degree
+arcminute               arcmin
+'                       arcmin
+arcsec                  1|60 arcmin
+arcsecond               arcsec
+"                       arcsec
+''                      "
+rightangle              90 degrees
+quadrant                1|4 circle
+quintant                1|5 circle
+sextant                 1|6 circle
+
+sign                    1|12 circle # Angular extent of one sign of the zodiac
+turn                    circle
+revolution              turn
+rev                     turn
+pulsatance              radian / sec
+gon                     1|100 rightangle  # measure of grade
+grade                   gon
+centesimalminute        1|100 grade
+centesimalsecond        1|100 centesimalminute
+milangle                1|6400 circle     # Official NIST definition.
+                                          # Another choice is 1e-3 radian.
+pointangle              1|32 circle  # Used for reporting compass readings
+centrad                 0.01 radian  # Used for angular deviation of light
+                                     # through a prism.
+mas                     milli arcsec # Used by astronomers
+seclongitude            circle (seconds/day) # Astronomers measure longitude
+                                     # (which they call right ascension) in
+                                     # time units by dividing the equator into
+                                     # 24 hours instead of 360 degrees.
+#
+# Some geometric formulas
+#
+
+circlearea(r)   units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
+spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
+                                         cuberoot(spherevolume/4|3 pi)
+spherevol()     spherevolume
+square(x)       range=[0,)          x^2 ; sqrt(square)
+
+#
+# Solid angle measure
+#
+
+sphere                  4 pi sr
+squaredegree            1|180^2 pi^2 sr
+squareminute            1|60^2 squaredegree
+squaresecond            1|60^2 squareminute
+squarearcmin            squareminute
+squarearcsec            squaresecond
+sphericalrightangle     1|8 sphere
+octant                  1|8 sphere
+
+#
+# Concentration measures
+#
+
+percent                 0.01
+%                       percent
+mill                    0.001     # Originally established by Congress in 1791
+                                  # as a unit of money equal to 0.001 dollars,
+                                  # it has come to refer to 0.001 in general.
+                                  # Used by some towns to set their property
+                                  # tax rate, and written with a symbol similar
+                                  # to the % symbol but with two 0's in the
+                                  # denominator.  [18]
+proof                   1|200     # Alcohol content measured by volume at
+                                  # 60 degrees Fahrenheit.  This is a USA
+                                  # measure.  In Europe proof=percent.
+ppm                     1e-6
+partspermillion         ppm
+ppb                     1e-9
+partsperbillion         ppb       # USA billion
+ppt                     1e-12
+partspertrillion        ppt       # USA trillion
+karat                   1|24      # measure of gold purity
+caratgold               karat
+gammil                  mg/l
+basispoint              0.01 %    # Used in finance
+fine                    1|1000    # Measure of gold purity
+
+# The pH scale is used to measure the concentration of hydronium (H3O+) ions in
+# a solution.  A neutral solution has a pH of 7 as a result of dissociated
+# water molecules.
+
+pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
+
+
+#
+# Temperature
+#
+# Two types of units are defined: units for converting temperature differences
+# and functions for converting absolute temperatures.  Conversions for
+# differences start with "deg" and conversions for absolute temperature start
+# with "temp".
+#
+# If the temperature inside is 72 degrees Fahrenheit and you want to
+# convert this to degrees Celsius then you need absolute temperature:
+#
+# You have: tempF(72)
+# You want: tempC
+#         22.222222
+#
+# If the temperature rose 72 degrees Fahrenheit during the chemical reaction
+# then this is a temperature difference:
+#
+# You have: 72 degF
+# You want: degC
+#        * 40
+#        / 0.025
+#
+
+TEMPERATURE             kelvin
+TEMPERATURE_DIFFERENCE  kelvin
+
+# In 1741 Anders Celsius introduced a temperature scale with water boiling at
+# 0 degrees and freezing at 100 degrees at standard pressure. After his death
+# the fixed points were reversed and the scale was called the centigrade
+# scale.  Due to the difficulty of accurately measuring the temperature of
+# melting ice at standard pressure, the centigrade scale was replaced in 1954
+# by the Celsius scale which is defined by subtracting 273.15 from the
+# temperature in Kelvins.  This definition differed slightly from the old
+# centigrade definition, but the Kelvin scale depends on the triple point of
+# water rather than a melting point, so it can be measured accurately.
+
+tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
+                             x K + stdtemp ; (tempC +(-stdtemp))/K
+tempcelsius() tempC
+degcelsius              K
+degC                    K
+
+# Fahrenheit defined his temperature scale by setting 0 to the coldest
+# temperature he could produce in his lab with a salt water solution and by
+# setting 96 degrees to body heat.  In Fahrenheit's words:
+#
+#    Placing the thermometer in a mixture of sal ammoniac or sea
+#    salt, ice, and water a point on the scale will be found which
+#    is denoted as zero. A second point is obtained if the same
+#    mixture is used without salt. Denote this position as 30. A
+#    third point, designated as 96, is obtained if the thermometer
+#    is placed in the mouth so as to acquire the heat of a healthy
+#    man."  (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
+
+tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
+                (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
+tempfahrenheit() tempF
+degfahrenheit           5|9 degC
+degF                    5|9 degC
+
+
+degreesrankine          degF              # The Rankine scale has the
+degrankine              degreesrankine    # Fahrenheit degree, but its zero
+degreerankine           degF              # is at absolute zero.
+degR                    degrankine
+tempR                   degrankine
+temprankine             degrankine
+
+tempreaumur(x)    units=[1;K] domain=[-218.52,) range=[0,) \
+                  x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
+degreaumur              10|8 degC # The Reaumur scale was used in Europe and
+                                  # particularly in France.  It is defined
+                                  # to be 0 at the freezing point of water
+                                  # and 80 at the boiling point.  Reaumur
+                                  # apparently selected 80 because it is
+                                  # divisible by many numbers.
+
+degK                    K         # "Degrees Kelvin" is forbidden usage.
+tempK                   K         # For consistency
+
+# Gas mark is implemented below but in a terribly ugly way.  There is
+# a simple formula, but it requires a conditional which is not
+# presently supported.
+#
+# The formula to convert to degrees Fahrenheit is:
+#
+# 25 log2(gasmark) + k_f   gasmark<=1
+# 25 (gasmark-1) + k_f     gasmark>=1
+#
+# k_f = 275
+#
+gasmark[degR] \
+  .0625    634.67 \
+  .125     659.67 \
+  .25      684.67 \
+  .5       709.67 \
+  1        734.67 \
+  2        759.67 \
+  3        784.67 \
+  4        809.67 \
+  5        834.67 \
+  6        859.67 \
+  7        884.67 \
+  8        909.67 \
+  9        934.67 \
+  10       959.67
+
+
+# The Beaufort wind force scale was developed from 1805-1807 by Sir Francis
+# Beaufort to categorize wind conditions at sea. It is normally defined from
+# Beaufort 0, also called "Force 0," through Beaufort 12. Beaufort numbers
+# 13-17 were later defined for tropical cyclones but are rarely used. The
+# original Beaufort scale was qualitative and did not relate directly to wind
+# speed. In 1906, George Simpson of the British Met Office fit wind-speed
+# measurements to visual Beaufort estimates made from five coastal and inland
+# stations in Britain. Simpson's formula was adopted by the World Meterological
+# Organization in 1946 to produce a table, known as WMO Code 1100, giving mean
+# (and min/max) wind speed equivalents at a height of 10 meters for each
+# Beaufort number. This is the "operational" Beaufort scale that mariners
+# use. Meterological and climatic researchers typically use a "scientific"
+# Beaufort scale based on more recent and comprehensive fits. See Wallbrink and
+# Cook, Historical Wind Speed Equivalents Of The Beaufort Scale, 1850-1950, at
+# https://icoads.noaa.gov/reclaim/pdf/Hisklim13.pdf
+#
+beaufort_WMO1100(B) units=[1;m/s] domain=[0,17] range=[0,) \
+                    0.836 B^3|2 m/s; (beaufort_WMO1100 s / 0.836 m)^2|3
+
+beaufort(B) units=[1;m/s] domain=[0,17] range=[0,) \
+            beaufort_WMO1100(B); ~beaufort_WMO1100(beaufort)
+
+# Units cannot handle wind chill or heat index because they are two-variable
+# functions, but they are included here for your edification.  Clearly these
+# equations are the result of a model fitting operation.
+#
+# wind chill index (WCI) a measurement of the combined cooling effect of low
+#      air temperature and wind on the human body. The index was first defined
+#      by the American Antarctic explorer Paul Siple in 1939. As currently used
+#      by U.S. meteorologists, the wind chill index is computed from the
+#      temperature T (in  deg F) and wind speed V (in mi/hr) using the formula:
+#          WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
+#      For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
+#      the air temperature, but for higher wind speeds it is lower than the air
+#      temperature.
+#
+# heat index (HI or HX) a measure of the combined effect of heat and
+#      humidity on the human body. U.S. meteorologists compute the index
+#      from the temperature T (in  deg F) and the relative humidity H (as a
+#      value from 0 to 1).
+#        HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
+#             - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
+#             - 0.0199 T^2 H^2.
+
+#
+# Physical constants
+#
+
+# Basic constants
+
+pi                      3.14159265358979323846
+tau                     2 pi
+phi                     (sqrt(5)+1)/2
+light                   c
+coulombconst          alpha hbar c / e^2 # Coulomb constant          
+k_C                     coulombconst     #   Gets overridden in CGS modes
+k_C_SI       alpha hbar_SI c_SI / e_SI^2 
+epsilon0_SI             1 / 4 pi k_C_SI  # Vacuum electric permittivity
+epsilon0                1 / 4 pi k_C     #   Also overridden in CGS modes
+mu0_SI            1 / epsilon0_SI c_SI^2 # Vacuum magnetic permeability
+mu0                     1 / epsilon0 c^2 #   Also overridden in CGS modes
+Z0                      4 pi k_C / c     # Free space impedance
+energy                  c^2              # Convert mass to energy
+hbar                    h / 2 pi
+hbar_SI                 h_SI / 2 pi
+spin                    hbar
+G_SI            6.67430e-11
+G               6.67430e-11 N m^2 / kg^2 # Newtonian gravitational constant
+
+# Physico-chemical constants
+
+atomicmassunit_SI   1.66053906660e-27    # Unified atomic mass unit, defined as
+atomicmassunit      1.66053906660e-27 kg # Unified atomic mass unit, defined as
+u                       atomicmassunit   #   1|12 of the mass of carbon 12.
+amu                     atomicmassunit   #   The relationship N_A u = 1 g/mol
+dalton                  u                #   is approximately, but not exactly 
+Da                      dalton           #   true (with the 2019 SI).
+                                         #   Previously the mole was defined to
+                                         #   make this relationship exact.
+amu_chem                1.66026e-27 kg   # 1|16 of the weighted average mass of
+                                         #   the 3 naturally occuring neutral
+                                         #   isotopes of oxygen
+amu_phys                1.65981e-27 kg   # 1|16 of the mass of a neutral
+                                         #   oxygen 16 atom
+gasconstant             k N_A            # Molar gas constant (exact)
+R                       gasconstant
+kboltzmann              boltzmann
+molarvolume             R stdtemp / atm  # Volume occupied by one mole of an
+V_m                     molarvolume      #   ideal gas at STP. (exact)
+loschmidt         avogadro / molarvolume # Molecules per cubic meter of an
+n0                      loschmidt        #   ideal gas at STP.  Loschmidt did
+                                         #   work similar to Avogadro.
+molarvolume_si  N_A siliconlattice^3 / 8 # Volume of a mole of crystalline
+                                         #   silicon. The unit cell contains 8
+                                         #   silicon atoms and has a side
+                                         #   length of siliconlattice.
+stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
+sigma                   stefanboltzmann  #   blackbody at temperature T is
+                                         #   given by sigma T^4. (exact)
+wiendisplacement     (h c/k)/4.9651142317442763  # Wien's Displacement Law gives
+                                         #   the frequency at which the
+                                         #   Planck spectrum has maximum
+                                         #   intensity.  The relation is lambda
+                                         #   T = b where lambda is wavelength,
+                                         #   T is temperature and b is the Wien
+                                         #   displacement.  This relation is
+                                         #   used to determine the temperature
+                                         #   of stars.  The constant is the
+                                         #   solution to x=5(1-exp(-x)).
+                                         #   This expression has no experimental
+                                         #   error, and x is defined exactly
+                                         #   by the equation above, so it is
+                                         #   an exact definition.  
+K_J90 483597.9 GHz/V    # Direct measurement of the volt is difficult.  Until
+K_J   2e/h              #   recently, laboratories kept Weston cadmium cells as
+                        #   a reference, but they could drift.  In 1987 the
+                        #   CGPM officially recommended the use of the
+                        #   Josephson effect as a laboratory representation of
+                        #   the volt.  The Josephson effect occurs when two
+                        #   superconductors are separated by a thin insulating
+                        #   layer.  A "supercurrent" flows across the insulator
+                        #   with a frequency that depends on the potential
+                        #   applied across the superconductors.  This frequency
+                        #   can be very accurately measured.  The Josephson
+                        #   constant K_J relates the measured frequency to the
+                        #   potential.  Two values given, the conventional
+                        #   (exact) value from 1990, which was used until the
+                        #   2019 SI revision, and the current exact value.
+R_K90 25812.807 ohm     # Measurement of the ohm also presents difficulties.
+R_K   h/e^2             #   The old approach involved maintaining resistances
+                        #   that were subject to drift.  The new standard is
+                        #   based on the Hall effect.  When a current carrying
+                        #   ribbon is placed in a magnetic field, a potential
+                        #   difference develops across the ribbon.  The ratio
+                        #   of the potential difference to the current is
+                        #   called the Hall resistance.  Klaus von Klitzing
+                        #   discovered in 1980 that the Hall resistance varies
+                        #   in discrete jumps when the magnetic field is very
+                        #   large and the temperature very low.  This enables
+                        #   accurate realization of the resistance h/e^2 in the
+                        #   lab.  The 1990 value was an exact conventional 
+                        #   value used until the SI revision in 2019. This value
+                        #   did not agree with measurements.  The new value
+                        #   is exact.
+
+# The 2019 update to SI gives exact definitions for R_K and K_J.  Previously
+# the electromagnetic units were realized using the 1990 conventional values
+# for these constants, and as a result, the standard definitions were in some
+# sense outside of SI.  The revision corrects this problem.  The definitions
+# below give the 1990 conventional values for the electromagnetic units in
+# terms of 2019 SI.  
+
+ampere90 (K_J90 R_K90 / K_J R_K) A
+coulomb90 (K_J90 R_K90 / K_J R_K) C
+farad90 (R_K90/R_K) F
+henry90 (R_K/R_K90) H
+ohm90 (R_K/R_K90) ohm
+volt90 (K_J90/K_J) V
+watt90 (K_J90^2 R_K90 / K_J^2 R_K) W
+
+# Various conventional values
+
+gravity                 9.80665 m/s^2    # std acceleration of gravity (exact)
+                                         #   Established by the 3rd CGPM in
+                                         #   1901.  This is a nominal midrange
+                                         #   value, originally based on the
+                                         #   acceleration of a body at sea
+                                         #   level at 45 degrees latitude.
+                                         #   The value was actually determined
+                                         #   by measuring at the International
+                                         #   Bureau and correcting the
+                                         #   measurement by a theoretical
+                                         #   cofficient to get the 45 deg
+                                         #   latitude sea level value.
+                                         #   (Wikipedia: Standard gravity)
+force                   gravity          # use to turn masses into forces
+atm                     101325 Pa        # Standard atmospheric pressure
+atmosphere              atm
+Hg             13.5951 gram force / cm^3 # Standard weight of mercury (exact)
+water                   gram force/cm^3  # Standard weight of water (exact)
+waterdensity            gram / cm^3      # Density of water
+H2O                     water
+wc                      water            # water column
+mach                    331.46 m/s       # speed of sound in dry air at STP
+standardtemp            273.15 K         # standard temperature
+stdtemp                 standardtemp
+normaltemp              tempF(70)        # for gas density, from NIST
+normtemp                normaltemp       # Handbook 44
+
+# Weight of mercury and water at different temperatures using the standard
+# force of gravity.
+
+Hg10C         13.5708 force gram / cm^3  # These units, when used to form
+Hg20C         13.5462 force gram / cm^3  # pressure measures, are not accurate
+Hg23C         13.5386 force gram / cm^3  # because of considerations of the
+Hg30C         13.5217 force gram / cm^3  # revised practical temperature scale.
+Hg40C         13.4973 force gram / cm^3
+Hg60F         13.5574 force gram / cm^3
+H2O0C         0.99987 force gram / cm^3
+H2O5C         0.99999 force gram / cm^3
+H2O10C        0.99973 force gram / cm^3
+H2O15C        0.99913 force gram / cm^3
+H2O18C        0.99862 force gram / cm^3
+H2O20C        0.99823 force gram / cm^3
+H2O25C        0.99707 force gram / cm^3
+H2O50C        0.98807 force gram / cm^3
+H2O100C       0.95838 force gram / cm^3
+
+# Atomic constants
+
+hartree            4.3597447222071e-18 J # Approximate electric potential energy
+E_h                     hartree          #   of the hydrogen atom in its ground
+                                         #   state, and approximately twice its
+                                         #   ionization energy.  The hartree
+                                         #   energy is traditionally defined as
+                                         #      coulombconst^2 m_e e^4 / hbar^2,
+                                         #   but it can be measured to greater
+                                         #   precision using the relationship
+                                         #      hartree = 2 h c Rinfinity
+                                         #   because Rinfinity is one of the
+                                         #   most accurately measured physical
+                                         #   constants.  Because h and c are
+                                         #   exact we can choose either hartree
+                                         #   or Rinfinity from CODATA to use as
+                                         #   the primary value without
+                                         #   affecting the precision.  
+Rinfinity               hartree / 2 h c  # The wavelengths of a spectral series
+R_H          Rinfinity m_p / (m_e + m_p) #   can be expressed as
+                                         #     1/lambda = R (1/m^2 - 1/n^2).
+                                         #   where R is a number that various
+                                         #   slightly from element to element.
+                                         #   For hydrogen, R_H is the value,
+                                         #   and for heavy elements, the value
+                                         #   approaches Rinfinity, which can be
+                                         #   computed from
+                                         #      Rinfinity = m_e c alpha^2 / 2 h
+                                         #   with loss of precision. Rinfinity
+                                         #   is one of the most accurately
+                                         #   measured physical constants and is
+                                         #   known to higher precision than m_e
+                                         #   or alpha.
+alpha                    7.2973525693e-3 # The fine structure constant was
+                                         #   introduced to explain fine
+                                         #   structure visible in spectral
+                                         #   lines.  
+bohrradius              hbar / alpha m_e c
+a0                      bohrradius
+prout                   185.5 keV        # nuclear binding energy equal to 1|12
+                                         #   binding energy of the deuteron
+conductancequantum      e^2 / pi hbar
+G0                      conductancequantum
+magneticfluxquantum     pi hbar / e
+Phi0                    magneticfluxquantum
+
+# Particle radius
+
+electronradius    coulombconst e^2 / electronmass c^2   # Classical
+deuteronchargeradius    2.12799e-15 m
+protonchargeradius      0.8751e-15 m
+
+# Masses of elementary particles
+
+electronmass_SI         electronmass_u atomicmassunit_SI
+electronmass_u          5.48579909065e-4
+electronmass            5.48579909065e-4 u
+m_e                     electronmass
+muonmass                0.1134289259 u
+m_mu                    muonmass
+taumass                 1.90754 u
+m_tau                   taumass
+protonmass              1.007276466621 u
+m_p                     protonmass
+neutronmass             1.00866491595 u
+m_n                     neutronmass
+deuteronmass            2.013553212745 u    # Nucleus of deuterium, one
+m_d                     deuteronmass        #   proton and one neutron
+alphaparticlemass       4.001506179127 u    # Nucleus of He, two protons
+m_alpha                 alphaparticlemass   #   and two neutrons
+tritonmass              3.01550071621 u     # Nucleus of H3, one proton
+m_t                     tritonmass          #   and two neutrons
+helionmass              3.014932247175 u    # Nucleus of He3, two protons
+m_h                     helionmass          #   and one neutron
+
+# particle wavelengths: the compton wavelength of a particle is
+# defined as h / m c where m is the mass of the particle.
+
+electronwavelength      h / m_e c
+lambda_C                electronwavelength
+protonwavelength        h / m_p c
+lambda_C,p              protonwavelength
+neutronwavelength       h / m_n c
+lambda_C,n              neutronwavelength
+muonwavelength          h / m_mu c
+lambda_C,mu             muonwavelength
+
+# The g-factor or dimensionless magnetic moment is a quantity that
+# characterizes the magnetic moment of a particle.  The electron g-factor is
+# one of the most precisely measured values in physics, with a relative
+# uncertainty of 1.7e-13.  
+
+g_d                     0.8574382338       # Deuteron g-factor
+g_e                    -2.00231930436256   # Electron g-factor
+g_h                    -4.255250615        # Helion g-factor
+g_mu                   -2.0023318418       # Muon g-factor
+g_n                    -3.82608545         # Neutron g-factor
+g_p                     5.5856946893       # Proton g-factor
+g_t                     5.957924931        # Triton g-factor
+
+fermicoupling           1.1663787e-5 / GeV^2
+
+# Magnetic moments (derived from the more accurate g-factors)
+#
+# The magnetic moment is g * mu_ref * spin where in most cases
+# the reference is the nuclear magneton, and all of the particles
+# except the deuteron have spin 1/2.  
+
+bohrmagneton            e hbar / 2 electronmass  # Reference magnetic moment for
+mu_B                    bohrmagneton             #   the electron
+mu_e                    g_e mu_B / 2             # Electron spin magnet moment
+mu_mu                 g_mu mu_B m_e / 2 muonmass # Muon spin magnetic moment
+nuclearmagneton         mu_B m_e / protonmass    # Convenient reference magnetic
+mu_N                    nuclearmagneton          #   moment for heavy particles
+mu_p                    g_p mu_N / 2             # Proton magnetic moment
+mu_n                    g_n mu_N / 2             # Neutron magnetic moment
+mu_d                    g_d mu_N            # Deuteron magnetic moment, spin 1
+mu_t                    g_t mu_N / 2             # Triton magnetic moment
+mu_h                    g_h mu_N / 2             # Helion magnetic moment
+
+#
+# Units derived from physical constants
+#
+
+kgf                     kg force
+technicalatmosphere     kgf / cm^2
+at                      technicalatmosphere
+hyl                     kgf s^2 / m   # Also gram-force s^2/m according to [15]
+mmHg                    mm Hg
+torr                    atm / 760  # The torr, named after Evangelista
+                                   # Torricelli, and is very close to the mm Hg
+tor                     Pa         # Suggested in 1913 but seldom used [24].
+                                   # Eventually renamed the Pascal.  Don't 
+                                   # confuse the tor with the torr.  
+inHg                    inch Hg    
+inH2O                   inch water
+mmH2O                   mm water
+eV                      e V      # Energy acquired by a particle with charge e
+electronvolt            eV       #   when it is accelerated through 1 V
+lightyear               c julianyear # The 365.25 day year is specified in
+ly                      lightyear    # NIST publication 811
+lightsecond             c s
+lightminute             c min
+parsec                  au / tan(arcsec)    # Unit of length equal to distance
+pc                      parsec              #   from the Sun to a point having
+                                            #   heliocentric parallax of 1
+                                            #   arcsec (derived from parallax
+                                            #   second).  A distant object with
+                                            #   parallax theta will be about
+                                            #   (arcsec/theta) parsecs from the
+                                            #   Sun (using the approximation
+                                            #   that tan(theta) = theta).
+rydberg                 1|2 hartree         # Rydberg energy
+crith                   0.089885 gram       # The crith is the mass of one
+                                            #   liter of hydrogen at standard
+                                            #   temperature and pressure.
+amagat                  N_A / molarvolume   # Used to measure gas as a number
+amagatvolume            mol molarvolume     #   density
+lorentz                 bohrmagneton / h c  # Used to measure the extent
+                                            #   that the frequency of light
+                                            #   is shifted by a magnetic field.
+cminv                   h c / cm            # Unit of energy used in infrared
+invcm                   cminv               #   spectroscopy.
+wavenumber              1/cm                # 
+kcal_mol                kcal_th / mol N_A   # kcal/mol is used as a unit of
+                                            #   energy by physical chemists.
+#
+# CGS system based on centimeter, gram and second
+#
+
+dyne                    cm gram / s^2   # force
+dyn                     dyne
+erg                     cm dyne         # energy
+poise                   gram / cm s     # viscosity, honors Jean Poiseuille
+P                       poise
+rhe                     /poise          # reciprocal viscosity
+stokes                  cm^2 / s        # kinematic viscosity
+St                      stokes
+stoke                   stokes
+lentor                  stokes          # old name
+Gal                     cm / s^2        # acceleration, used in geophysics
+galileo                 Gal             # for Earth's gravitational field
+                                        # (note that "gal" is for gallon
+                                        # but "Gal" is the standard symbol
+                                        # for the gal which is evidently a
+                                        # shortened form of "galileo".)
+barye                   dyne/cm^2       # pressure
+barad                   barye           # old name
+kayser                  1/cm            # Proposed as a unit for wavenumber
+balmer                  kayser          # Even less common name than "kayser"
+kine                    cm/s            # velocity
+bole                    g cm / s        # momentum
+pond                    gram force
+glug                gram force s^2 / cm # Mass which is accelerated at
+                                        #   1 cm/s^2 by 1 gram force
+darcy           centipoise cm^2 / s atm # Measures permeability to fluid flow.
+                                        #   One darcy is the permeability of a
+                                        #   medium that allows a flow of cc/s
+                                        #   of a liquid of centipoise viscosity
+                                        #   under a pressure gradient of
+                                        #   atm/cm.  Named for H. Darcy.
+mobileohm               cm / dyn s      # mobile ohm, measure of mechanical
+                                        #   mobility
+mechanicalohm           dyn s / cm      # mechanical resistance
+acousticalohm           dyn s / cm^5    # ratio of the sound pressure of
+                                        #   1 dyn/cm^2 to a source of strength
+                                        #   1 cm^3/s
+ray                     acousticalohm
+rayl                    dyn s / cm^3    # Specific acoustical resistance
+eotvos                  1e-9 Gal/cm     # Change in gravitational acceleration
+                                        #   over horizontal distance
+#
+# Electromagnetic CGS Units
+# 
+# For measuring electromagnetic quantities in SI, we introduce the new base
+# dimension of current, define the ampere to measure current, and derive the
+# other electromagnetic units from the ampere.  With the CGS units one approach
+# is to use the basic equations of electromagnetism to define units that
+# eliminate constants from those equations.  Coulomb's law has the form
+#
+#          F = k_C q1 q2 / r^2
+#
+# where k_C is the Coulomb constant equal to 1|4 pi epsilon0 in SI units.
+# Ampere's force law takes the form
+#
+#          dF/dl = 2 k_A I1 I2 / r
+#
+# where k_A is the ampere constant.  In the CGS system we force either k_C or
+# k_A to 1 which then defines either a unit for charge or a unit for current.
+# The other unit then becomes a derived unit.  When k_C is 1 the ESU system
+# results.  When k_A is 1 the EMU system results.  Note that these parameters
+# are not independent of each other: Maxwell's equations indicate that
+#         
+#           k_C / k_A = c^2
+#
+# where c is the speed of light. 
+#
+# One more choice is needed to define a complete system.  Using Coulomb's law
+# we define the electric field as the force per unit charge
+#
+#           E = k_C 1 / r^2.
+#
+# But what about the magnetic field?  It is derived from Ampere's law but we
+# have the option of adding a proportionality constant, k_B, that may have
+# dimensions:
+#
+#           B = 2 k_A k_B I / r
+#
+# We can choose k_B = 1, which is done in the SI, ESU and EMU systems.  But if
+# instead we give k_B units of length/time then the magnetic field has
+# the same units as the electric field.  This choice leads to the Gaussian
+# and Heaviside-Lorentz systems.
+#
+# The relations above are used to determine the dimensions, but the units are
+# derived from the base units of CGS, not directly from those formulas.  We
+# will use the notation [unit] to refer to the dimension of the unit in
+# brackets.  This same process gives rise to the SI units such as the tesla, 
+# which is defined by
+#
+#         [tesla] = [2 (1/4 pi c^2 epsilon0) amp / m] = [(mu0 / 2) amp / m]
+#
+# which gives kg / A s^2 as expected.  
+#
+# References:
+#
+# Classical Electrodynamics by John David Jackson, 3rd edition. 
+# Cardarelli, Francois. 1999.  Scientific Unit Conversion. 2nd ed.  Trans.
+#     M.J.  Shields.  London: Springer-Verlag. ISBN 1-85233-043-0
+#
+#
+# All of the CGS systems result in electromagnetic units that involve the square
+# roots of the centimeter and gram.  This requires a change in the primitive
+# units.
+# 
+
+!var UNITS_SYSTEM esu emu gaussian gauss hlu
+sqrt_cm                 ! 
+sqrt_centimeter         sqrt_cm
++m                      100 sqrt_cm^2
+sqrt_g                  !
+sqrt_gram               sqrt_g
++kg                     kilo sqrt_g^2
+!endvar
+
+# Electrostatic CGS (ESU)
+#
+# This system uses the statcoulomb as the fundamental unit of charge, with
+# derived units that parallel the conventional terminology but use the stat-
+# prefix.  The statcoulomb is derived from Coulomb's law based on the dyne
+#
+#                      dyne = statcoulomb^2 / k_C cm^2.
+#
+# and in the EUS system, k_C=1.  The statcoulomb is also called the
+# franklin or esu.
+#
+# The ESU system was specified by a committee report in 1873 and rarely used.
+
+statcoulomb             sqrt(dyne cm^2/k_C)   # Charge such that two charges
+esu                     statcoulomb           # of 1 statC separated by 1 cm
+statcoul                statcoulomb           # exert a force of 1 dyne
+statC                   statcoulomb
+stC                     statcoulomb
+franklin                statcoulomb
+Fr                      franklin
+
+!var UNITS_SYSTEM esu
+!message CGS-ESU units selected
+!prompt (ESU)
++coulombconst           1
++epsilon0               1 / k_C               # SI relation: 1 / 4 pi k_C
++A                      10 c_SI statamp
+!endvar
+
+statampere              statcoulomb / s
+statamp                 statampere
+statA                   statampere
+stA                     statampere
+statvolt                dyne cm / statamp sec
+statV                   statvolt
+stV                     statvolt
+statfarad               statamp sec / statvolt
+statF                   statfarad
+stF                     statfarad
+cmcapacitance           statfarad
+stathenry               statvolt sec / statamp
+statH                   stathenry
+stH                     stathenry
+statohm                 statvolt / statamp
+stohm                   statohm
+statmho                 /statohm
+stmho                   statmho
+statweber               statvolt sec
+statWb                  statweber
+stWb                    statweber
+stattesla               statWb/cm^2   # Defined by analogy with SI; rarely
+statT                   stattesla     #   if ever used
+stT                     stattesla
+debye                   1e-10 statC angstrom # unit of electrical dipole moment
+helmholtz               debye/angstrom^2     # Dipole moment per area
+jar                     1000 statfarad       # approx capacitance of Leyden jar
+
+# Electromagnetic CGS (EMU)
+#
+# The abampere is the fundamental unit of this system, with the derived units
+# using the ab- prefix.  The dimensions of the abampere are defined by assuming
+# that k_A=1, which 
+#
+#            [dyne / cm]  = [2 abampere^2 / cm]
+#
+# where the brackets indicate taking the dimension of the unit in base units
+# and discarding any constant factors.  This results in the definition from
+# base CGS units of:
+#
+#            abampere = sqrt(dyne). 
+#
+# The abampere is also called the biot.  The magnetic field unit (the gauss)
+# follows from the assumption that k_B=1, which means
+#
+#            B = 2 I / r,
+#
+# and hence the dimensions of the gauss are given by
+#
+#            [gauss] = [2 abampere / cm]
+#
+# or rewriting in terms of the base units
+#
+#            gauss = abampere / cm.
+#
+# The definition given below is different because it is in a form that
+# gives a valid reduction for SI and ESU and still gives the correct 
+# result in EMU.  (It can be derived from Faraday's law.)  
+#
+# The EMU system was developed by Gauss and Weber and formalized as a system in
+# a committee report by the British Association for the Advancement of Science
+# in 1873.  
+
+abampere                10 A            # Current which produces a force of
+abamp                   abampere        #   2 dyne/cm between two infinitely
+aA                      abampere        #   long wires that are 1 cm apart
+abA                     abampere
+biot                    abampere
+Bi                      biot
+
+!var UNITS_SYSTEM emu
+!message CGS-EMU units selected
+!prompt (EMU)
++coulombconst           c^2
++epsilon0               1 / k_C        # SI relation: 1 / 4 pi k_C
++abampere               sqrt(dyne)
++A                      0.1 abamp
+!endvar
+
+abcoulomb               abamp sec
+abcoul                  abcoulomb
+abC                     abcoulomb
+abfarad                 abampere sec / abvolt
+abF                     abfarad
+abhenry                 abvolt sec / abamp
+abH                     abhenry
+abvolt                  dyne cm  / abamp sec
+abV                     abvolt
+abohm                   abvolt / abamp
+abmho                   /abohm
+maxwell                 erg / abamp       # Also called the "line"
+Mx                      maxwell
+gauss                   maxwell / cm^2    # The magnetic field 2 cm from a wire
+Gs                      gauss             # carrying a current of 1 abampere
+oersted                 gauss / mu0   # From the relation H = B / mu
+Oe                      oersted      
+gilbert                 gauss cm / mu0
+Gb                      gilbert
+Gi                      gilbert
+unitpole                4 pi maxwell    # unit magnetic pole
+emu                     erg/gauss  # "electro-magnetic unit", a measure of
+                                   # magnetic moment, often used as emu/cm^3
+                                   # to specify magnetic moment density.
+
+# Electromagnetic CGS (Gaussian)
+#
+# The Gaussian system uses the statcoulomb and statamp from the ESU system
+# derived by setting k_C=1, but it defines the magnetic field unit differently
+# by taking k_B=c instead of k_B=1.  As noted above, k_C and k_A are not
+# independent.  With k_C=1 we must have k_A=c^-2.  This results in the magnetic
+# field unit, the gauss, having dimensions give by:
+#
+#         [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm]
+#
+# We then define the gauss using base CGS units to obtain
+#
+#         gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2.
+#
+# Note that this definition happens to give the same result as the definition
+# for the EMU system, so the definitions of the gauss are consistent.
+#
+# This definition gives the same dimensions for the E and B fields and was also
+# known as the "symmetric system".  This system was proposed by Hertz in 1888.
+
+!var UNITS_SYSTEM gaussian gauss
+!message CGS-Gaussian units selected
+!prompt (Gaussian)
+!endvar
+!var UNITS_SYSTEM gaussian gauss natural-gauss 
++coulombconst           1
++A                      10 c_SI statamp
+      # Some SI-based definitions need re-scaling
+      # by factors of "c" and/or "4 pi":
++epsilon0               1 / k_C        # SI relation: 1 / 4 pi k_C
++mu0                    1 / epsilon0   # SI relation: 1 / epsilon0 c^2
++bohrmagneton           (e hbar / 2 electronmass) / c
++magneticfluxquantum    c (pi hbar / e)
++maxwell                c (erg / abamp)
++weber                  c (J / A)
+!endvar
+
+# Electromagnetic CGS (Heaviside-Lorentz)
+
+# The Heaviside-Lorentz system is similar to the Gaussian system, but it is
+# "rationalized" so that factors of 4 pi do not appear in Maxwell's equations.
+# The SI system is similarly rationalized, but the other CGS systems are not.
+#
+# The factor of 4 pi appears instead in Coulomb's law, so in this system
+# k_C = 1 / 4 pi, which means the charge unit is defined by
+#
+#                      dyne = (1 / 4 pi) hlu_charge^2 / cm^2.
+# 
+# Since we have the leading constant of (1 / 4pi) the numerical value of the
+# charge number is larger by sqrt(4pi), which in turns means that the HLU
+# charge unit is smaller by this multiple.  But note that the dimensions of the
+# charge unit are the same as the Gaussian system, so both systems measure
+# charge with cm^(3/2) g^(1/2) / s, but the amount of charge for this dimension
+# differs by a factor of sqrt(4pi) between the two systems.
+#
+# Ampere's law for the Heaviside-Lorentz system has the form
+#
+#                B = 1/(2 pi c) * I/r
+
+# The Heaviside-Lorentz system does not appear to have any named units, so we
+# use "hlu" for "Heaviside-Lorentz unit" so we can define values for the basic
+# units in this system.
+
+hlu_charge    statcoulomb / sqrt(4 pi) 
+hlu_current   hlu_charge / sec
+hlu_volt      erg / hlu_charge
+hlu_efield    hlu_volt / cm
+hlu_bfield    sqrt(4 pi) gauss
+
+!var UNITS_SYSTEM hlu
+!message CGS-Heaviside-Lorentz Units selected
+!prompt (HLU)
+!endvar
+!var UNITS_SYSTEM hlu natural planck planck-red
++coulombconst           1 / 4 pi
++A                      10 c_SI statamp 
+        # Some SI-based magnetism definitions
+        # need re-scaling by factors of "c":
++mu0                    1 / epsilon0   # SI relation: 1 / epsilon0 c^2
++bohrmagneton           (e hbar / 2 electronmass) / c
++magneticfluxquantum    c (pi hbar / e)
++weber                  c (J / A)
++maxwell                c (erg / abamp)
+!endvar
+
+# "Natural units" (high energy physics and cosmology)
+#
+# In particle physics "natural units" (which don't seem to have a more specific
+# name) are defined by setting hbar = c = boltzmann = 1.  In this system the
+# electron volt is the only base unit.  The electromagnetic units can be 
+# derived from the rationalized Heaviside-Lorentz units or from Gaussian units.
+# The default form is the rationalized HLU derived version.
+#
+# The basic mechanical and thermodynamic definitions for the natural
+# units are identical in both systems.  These appear below.  The
+# natural-gauss system has additional electromagnetic redefinitions
+# that appear above in the "Electromagnetic CGS (Gaussian)" Section.
+
+# These are the Heaviside-Lorentz natural units
+
+natural_energy          eV
+natural_charge          e / sqrt(4 pi alpha)
+natural_time            hbar / natural_energy
+natural_length          natural_time c
+natural_mass            natural_energy / c^2
+natural_temp            natural_energy / boltzmann
+natural_force           natural_energy / natural_length
+natural_power           natural_energy / natural_time
+natural_volt            natural_energy / natural_charge
+natural_Efield          natural_volt   / natural_length
+natural_Bfield          natural_Efield / c
+natural_current         natural_charge / natural_time
+
+!var UNITS_SYSTEM natural
+!message Natural units selected (Heavyside-Lorentz based)
+!prompt (natural)
+!endvar
+
+!var UNITS_SYSTEM natural-gauss
+!message Natural units selected (Gaussian based)
+!prompt (natgauss)
+!endvar
+
+# These definitions are the same in both natural unit systems
+
+!var UNITS_SYSTEM natural natural-gauss
++eV                     !
++h                      2 pi
++c                      1
++boltzmann              1
++m                      e_SI / hbar_SI c_SI eV
++kg                     (c_SI^2 / e_SI) eV
++s                      e_SI / hbar_SI eV
++K                      (k_SI / e_SI) eV
+!endvar
+
+#
+# Planck units
+#
+# Planck units are a set of "natural" units based on physical constants c, G,
+# hbar, boltzmann's constant, and epsilon0, often used when working with
+# gravitational theory.  In planck units, all quantities are dimensionless.
+# Some variations are possible for exactly how the units are defined.  We
+# provide two variations, the rationalized planck units and the
+# rationalized-reduced planck units.
+#
+# In both forms the units are defined by c = hbar = boltzmann = 1. 
+# But the choice of rationalized and reduced affects how epsilon0 and G
+# are treated.  
+#
+# In the "rationalized" units, factors of 4 pi do not appear in Maxwell's 
+# equation, and Coulomb's law bears a factor of 1/4 pi.  See the section on
+# the Heaviside-Lorentz units for more about this.  The choice of rationalized 
+# units means that epsilon0 = 1.  (In the unrationalized case, which is not
+# supported, 1/(4 pi epsilon0) = 1.)  
+#
+# The "reduced" units similarly are defined to eliminate factors of 8 pi
+# from the Einstein field equations for gravitation.  With reduced units
+# we set 8 pi G = 1 and with the unreduced units, simply G = 1.
+
+# Rationalized, unreduced planck units
+
+planckmass              sqrt(hbar c / G)
+m_P                     planckmass
+planckenergy            planckmass c^2
+E_P                     planckenergy
+plancktime              hbar / planckenergy
+t_P                     plancktime
+plancklength            plancktime c
+l_P                     plancklength
+plancktemperature       planckenergy / k
+T_P                     plancktemperature
+planckforce             planckenergy / plancklength
+planckcharge            sqrt(epsilon0 hbar c)
+planckcurrent           planckcharge / plancktime
+planckvolt              planckenergy / planckcharge
+planckEfield            planckvolt / plancklength
+planckBfield            planckEfield / c
+
+# Rationalized, reduced planck units
+
+planckmass_red          sqrt(hbar c / 8 pi G)
+planckenergy_red        planckmass_red c^2
+plancktime_red          hbar / planckenergy_red
+plancklength_red        plancktime_red c
+plancktemperature_red   planckenergy_red / k
+planckforce_red         planckenergy_red / plancklength_red
+planckcharge_red        sqrt(epsilon0 hbar c)
+planckcurrent_red       planckcharge_red / plancktime_red
+planckvolt_red          planckenergy_red / planckcharge_red
+planckEfield_red        planckvolt_red / plancklength_red
+planckBfield_red        planckEfield_red /c
+
+
+!var UNITS_SYSTEM planck
+!message Planck units selected
+!prompt (planck)
++c 1
++h 2 pi
++G 1
++boltzmann 1
++kg sqrt(G_SI / hbar_SI c_SI)
++s  c_SI^2 / hbar_SI kg 
++m  s / c_SI            
++K  k_SI / hbar_SI s    
+!endvar
+
+
+!var UNITS_SYSTEM planck-red
+!message Reduced planck units selected
+!prompt (planck reduced)
++c 1
++h 2 pi
++G 1/8 pi
++boltzmann 1
++kg sqrt(8 pi G_SI / hbar_SI c_SI)
++s  c_SI^2 / hbar_SI kg
++m  s / c_SI           
++K  k_SI / hbar_SI s   
+!endvar
+
+#
+# Some historical electromagnetic units
+#
+
+intampere               0.999835 A    # Defined as the current which in one
+intamp                  intampere     #   second deposits .001118 gram of
+                                      #   silver from an aqueous solution of
+                                      #   silver nitrate.
+intfarad                0.999505 F
+intvolt                 1.00033 V
+intohm                  1.000495 ohm  # Defined as the resistance of a
+                                      #   uniform column of mercury containing
+                                      #   14.4521 gram in a column 1.063 m
+                                      #   long and maintained at 0 degC.
+daniell                 1.042 V       # Meant to be electromotive force of a
+                                      #   Daniell cell, but in error by .04 V
+faraday                 N_A e mol     # Charge that must flow to deposit or
+faraday_phys            96521.9 C     #   liberate one gram equivalent of any
+faraday_chem            96495.7 C     #   element.  (The chemical and physical
+faradayconst            N_A e         #   values are off slightly from what is
+                                      #   obtained by multiplying by amu_chem
+                                      #   or amu_phys.  These values are from
+                                      #   a 1991 NIST publication.)  Note that
+                                      #   there is also a Faraday constant,
+                                      #   which has units of C/mol.  
+kappline                6000 maxwell  # Named by and for Gisbert Kapp
+siemensunit             0.9534 ohm    # Resistance of a meter long column of
+                                      #   mercury with a 1 mm cross section.
+#
+# Printed circuit board units.  
+#
+# Iowa State University Center for Nondestructive Evaluation
+# Electrical Conductivity and Resistivity
+# https://www.nde-ed.org/Physics/Materials/Physical_Chemical/Electrical.xhtml
+#
+# Conductivity is often expressed as a percentage of IACS.  A copper wire a
+# meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at 
+# 20 deg C.  Copper density also has a standard IACS value at that temperature.
+#
+
+copperconductivity      58 siemens m / mm^2     # A wire a meter long with
+IACS                    copperconductivity      #   a 1 mm^2 cross section
+copperdensity           8.89 g/cm^3             # The "ounce" measures the     
+ouncecopper             oz / ft^2 copperdensity #   thickness of copper used   
+ozcu                    ouncecopper             #   in circuitboard fabrication
+                                                
+#
+# Photometric units
+#
+
+LUMINOUS_INTENSITY      candela
+LUMINOUS_FLUX           lumen
+LUMINOUS_ENERGY         talbot
+ILLUMINANCE             lux
+EXITANCE                lux
+
+candle                  1.02 candela  # Standard unit for luminous intensity
+hefnerunit              0.9 candle    #   in use before candela
+hefnercandle            hefnerunit    #
+violle                  20.17 cd      # luminous intensity of 1 cm^2 of
+                                      #   platinum at its temperature of
+                                      #   solidification (2045 K)
+
+lumen                   cd sr         # Luminous flux (luminous energy per
+lm                      lumen         #    time unit)
+
+talbot                  lumen s       # Luminous energy
+lumberg                 talbot        # References give these values for
+lumerg                  talbot        #    lumerg and lumberg both.  Note that
+                                      #    a paper from 1948 suggests that
+                                      #    lumerg should be 1e-7 talbots so
+                                      #    that lumergs/erg = talbots/joule.
+                                      #    lumerg = luminous erg
+lux                     lm/m^2        # Illuminance or exitance (luminous
+lx                      lux           #   flux incident on or coming from
+phot                    lumen / cm^2  #   a surface)
+ph                      phot          #
+footcandle              lumen/ft^2    # Illuminance from a 1 candela source
+                                      #    at a distance of one foot
+metercandle             lumen/m^2     # Illuminance from a 1 candela source
+                                      #    at a distance of one meter
+
+mcs                     metercandle s # luminous energy per area, used to
+                                      #    measure photographic exposure
+
+nox                     1e-3 lux      # These two units were proposed for
+skot                    1e-3 apostilb # measurements relating to dark adapted
+                                      # eyes.
+# Luminance measures
+
+LUMINANCE               nit
+
+nit                     cd/m^2        # Luminance: the intensity per projected
+stilb                   cd / cm^2     # area of an extended luminous source.
+sb                      stilb         # (nit is from latin nitere = to shine.)
+
+apostilb                cd/pi m^2
+asb                     apostilb
+blondel                 apostilb      # Named after a French scientist.
+
+# Equivalent luminance measures.  These units are units which measure
+# the luminance of a surface with a specified exitance which obeys
+# Lambert's law.  (Lambert's law specifies that luminous intensity of
+# a perfectly diffuse luminous surface is proportional to the cosine
+# of the angle at which you view the luminous surface.)
+
+equivalentlux           cd / pi m^2   # luminance of a 1 lux surface
+equivalentphot          cd / pi cm^2  # luminance of a 1 phot surface
+lambert                 cd / pi cm^2
+footlambert             cd / pi ft^2
+
+# The bril is used to express "brilliance" of a source of light on a
+# logarithmic scale to correspond to subjective perception.  An increase of 1
+# bril means doubling the luminance.  A luminance of 1 lambert is defined to
+# have a brilliance of 1 bril.
+
+bril(x) units=[1;lambert]  2^(x+-100) lamberts ;log2(bril/lambert)+100
+
+# Some luminance data from the IES Lighting Handbook, 8th ed, 1993
+
+sunlum                  1.6e9 cd/m^2  # at zenith
+sunillum                100e3 lux     # clear sky
+sunillum_o              10e3 lux      # overcast sky
+sunlum_h                6e6 cd/m^2    # value at horizon
+skylum                  8000 cd/m^2   # average, clear sky
+skylum_o                2000 cd/m^2   # average, overcast sky
+moonlum                 2500 cd/m^2
+
+#
+# Photographic Exposure Value
+# This section by Jeff Conrad (jeff_conrad@msn.com)
+#
+# The Additive system of Photographic EXposure (APEX) proposed in ASA
+# PH2.5-1960 was an attempt to simplify exposure determination for people who
+# relied on exposure tables rather than exposure meters.  Shortly thereafter,
+# nearly all cameras incorporated exposure meters, so the APEX system never
+# caught on, but the concept of exposure value remains in use.  Though given as
+# 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'.  EV is
+# related to exposure parameters by
+#
+#            A^2   LS   ES
+#     2^EV = --- = -- = --
+#             t    K    C
+#
+# Where
+#     A = Relative aperture (f-number)
+#     t = Exposure time in seconds
+#     L = Scene luminance in cd/m2
+#     E = Scene illuminance in lux
+#     S = Arithmetic ISO speed
+#     K = Reflected-light meter calibration constant
+#     C = Incident-light meter calibration constant
+#
+# Strictly, an exposure value is a combination of aperture and exposure time,
+# but it's also commonly used to indicate luminance (or illuminance).
+# Conversion to luminance or illuminance units depends on the ISO speed and the
+# meter calibration constant.  Common practice is to use an ISO speed of 100.
+# Calibration constants vary among camera and meter manufacturers: Canon,
+# Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
+# Kenko (formerly Minolta) and Pentax use a value of 14.  Kenko and Sekonic use
+# a value of 250 for incident-light meters with flat receptors.
+#
+# The values for in-camera meters apply only averaging, weighted-averaging, or
+# spot metering--the multi-segment metering incorporated in most current
+# cameras uses proprietary algorithms that evaluate many factors related to the
+# luminance distribution of what is being metered; they are not amenable to
+# simple conversions, and are usually not disclosed by the manufacturers.
+
+s100                    100 / lx s            # ISO 100 speed
+iso100                  s100
+
+# Reflected-light meter calibration constant with ISO 100 speed
+
+k1250                   12.5 (cd/m2) / lx s   # For Canon, Nikon, and Sekonic
+k1400                   14   (cd/m2) / lx s   # For Kenko (Minolta) and Pentax
+
+# Incident-light meter calibration constant with ISO 100 film
+
+c250                    250 lx / lx s         # flat-disc receptor
+
+# Exposure value to scene luminance with ISO 100 imaging media
+
+# For Kenko (Minolta) or Pentax
+#ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
+# For Canon, Nikon, or Sekonic
+ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
+EV100()  ev100
+
+# Exposure value to scene illuminance with ISO 100 imaging media
+
+iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
+
+# Other Photographic Exposure Conversions
+# 
+# As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
+# related by
+#
+#    Ev = Av + Tv = Bv + Sv
+#
+# where
+#  Av = log2(A^2)       Aperture value
+#  Tv = log2(1/t)       Time value
+#  Sv = log2(N Sx)      Speed value
+#  Bv = log2(B S / K)   Luminance ("brightness") value
+#  Iv = log2(I S / C)   Illuminance value
+#
+# and
+#  A  = Relative aperture (f-number)
+#  t  = Exposure time in seconds
+#  Sx = Arithmetic ISO speed in 1/lux s
+#  B  = luminance in cd/m2
+#  I  = luminance in lux
+
+# The constant N derives from the arcane relationship between arithmetic
+# and logarithmic speed given in ASA PH2.5-1960.  That relationship
+# apparently was not obvious--so much so that it was thought necessary
+# to explain it in PH2.12-1961.  The constant has had several values
+# over the years, usually without explanation for the changes.  Although
+# APEX had little impact on consumer cameras, it has seen a partial
+# resurrection in the Exif standards published by the Camera & Imaging
+# Products Association of Japan.
+
+#N_apex         2^-1.75 lx s    # precise value implied in ASA PH2.12-1961,
+                                # derived from ASA PH2.5-1960.
+#N_apex         0.30 lx s       # rounded value in ASA PH2.5-1960, 
+                                # ASA PH2.12-1961, and ANSI PH2.7-1986
+#N_apex         0.3162 lx s     # value in ANSI PH2.7-1973
+N_exif          1|3.125 lx s    # value in Exif 2.3 (2010), making Sv(5) = 100
+K_apex1961      11.4 (cd/m2) / lx s    # value in ASA PH2.12-1961
+K_apex1971      12.5 (cd/m2) / lx s    # value in ANSI PH3.49-1971; more common
+C_apex1961      224 lx / lx s   # value in PH2.12-1961 (20.83 for I in 
+                                #   footcandles; flat sensor?)
+C_apex1971      322 lx / lx s   # mean value in PH3.49-1971 (30 +/- 5 for I in
+                                # footcandles; hemispherical sensor?)
+N_speed         N_exif
+K_lum           K_apex1971
+C_illum         C_apex1961
+
+# Units for Photographic Exposure Variables
+#
+# Practical photography sometimes pays scant attention to units for exposure
+# variables.  In particular, the "speed" of the imaging medium is treated as if
+# it were dimensionless when it should have units of reciprocal lux seconds;
+# this practice works only because "speed" is almost invariably given in
+# accordance with international standards (or similar ones used by camera
+# manufacturers)--so the assumed units are invariant.  In calculating
+# logarithmic quantities--especially the time value Tv and the exposure value
+# EV--the units for exposure time ("shutter speed") are often ignored; this
+# practice works only because the units of exposure time are assumed to be in
+# seconds, and the missing units that make the argument to the logarithmic
+# function dimensionless are silently provided.
+#
+# In keeping with common practice, the definitions that follow treat "speeds"
+# as dimensionless, so ISO 100 speed is given simply as '100'.  When
+# calculating the logarithmic APEX quantities Av and Tv, the definitions
+# provide the missing units, so the times can be given with any appropriate
+# units.  For example, giving an exposure time of 1 minute as either '1 min' or
+# '60 s' will result in Tv of -5.9068906.
+#
+# Exposure Value from f-number and Exposure Time
+# 
+# Because nonlinear unit conversions only accept a single quantity,
+# there is no direct conversion from f-number and exposure time to
+# exposure value EV.  But the EV can be obtained from a combination of
+# Av and Tv.  For example, the "sunny 16" rule states that correct
+# exposure for a sunlit scene can achieved by using f/16 and an exposure
+# time equal to the reciprocal of the ISO speed in seconds; this can be
+# calculated as
+#
+#    ~Av(16) + ~Tv(1|100 s),
+#
+# which gives 14.643856.  These conversions may be combined with the
+# ev100 conversion:
+#
+#    ev100(~Av(16) + ~Tv(1|100 s))
+#
+# to yield the assumed average scene luminance of 3200 cd/m^2.
+
+# convert relative aperture (f-number) to aperture value
+Av(A)           units=[1;1] domain=[-2,) range=[0.5,)  2^(A/2); 2 log2(Av)
+# convert exposure time to time value
+Tv(t)           units=[1;s] range=(0,)  2^(-t) s; log2(s / Tv)
+# convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
+# make arithmetic speed dimensionless
+# 'Sv' conflicts with the symbol for sievert; you can uncomment this function
+# definition if you don't need that symbol
+#Sv(S)    units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
+Sval(S)   units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
+
+# convert luminance value Bv in ASA PH2.12-1961 to luminance
+Bv(x)           units=[1;cd/m^2] range=(0,) \
+                2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
+
+# convert illuminance value Iv in ASA PH2.12-1961 to illuminance
+Iv(x)           units=[1;lx] range=(0,) \
+                2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
+
+# convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in 
+# ASA PH2.5-1960; make arithmetic speed dimensionless
+Sx(S)           units=[1;1] domain=(0,) \
+                log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
+
+# convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
+# for convenience, speed is treated here as if it were dimensionless
+Sdeg(S)         units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
+Sdin()          Sdeg
+
+# Numerical Aperture and f-Number of a Lens
+#
+# The numerical aperture (NA) is given by
+#
+#   NA = n sin(theta)
+#
+# where n is the index of refraction of the medium and theta is half
+# of the angle subtended by the aperture stop from a point in the image
+# or object plane. For a lens in air, n = 1, and
+#
+#   NA = 0.5 / f-number
+#
+# convert NA to f-number
+numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
+                     0.5 / x ; 0.5 / numericalaperture
+NA()            numericalaperture
+#
+# convert f-number to itself; restrict values to those possible
+fnumber(x)      units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
+
+# Referenced Photographic Standards
+#
+# ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
+#    Continuous-Tone) Speed of Photographic Negative Materials.
+# ASA PH2.12-1961. American Standard, General-Purpose Photographic
+#    Exposure Meters (photoelectric type).
+# ANSI PH3.49-1971. American National Standard for general-purpose
+#    photographic exposure meters (photoelectric type).
+# ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
+# ANSI PH2.7-1986. American National Standard for Photography --
+#    Photographic Exposure Guide.
+# CIPA DC-008-2010. Exchangeable image file format for digital still
+#    cameras: Exif Version 2.3
+# ISO 6:1993.  International Standard, Photography -- Black-and-white
+#    pictorial still camera negative film/process systems --
+#    Determination of ISO Speed.
+
+
+#
+# Astronomical time measurements
+#
+# Astronomical time measurement is a complicated matter.  The length of the
+# true day at a given place can be 21 seconds less than 24 hours or 30 seconds
+# over 24 hours.  The two main reasons for this are the varying speed of
+# Earth in its elliptical orbit and the fact that the Sun moves on the ecliptic
+# instead of along the celestial equator.  To devise a workable system for time
+# measurement, Simon Newcomb (1835-1909) used a fictitious "mean Sun".
+# Consider a first fictitious Sun traveling along the ecliptic at a constant
+# speed and coinciding with the true Sun at perigee and apogee.  Then
+# considering a second fictitious Sun traveling along the celestial equator at
+# a constant speed and coinciding with the first fictitious Sun at the
+# equinoxes.  The second fictitious Sun is the "mean Sun".  From this equations
+# can be written out to determine the length of the mean day, and the tropical
+# year.  The length of the second was determined based on the tropical year
+# from such a calculation and was officially used from 1960-1967 until atomic
+# clocks replaced astronomical measurements for a standard of time.  All of the
+# values below give the mean time for the specified interval.
+#
+# See "Mathematical Astronomy Morsels" by Jean Meeus for more details
+# and a description of how to compute the correction to mean time.
+#
+
+TIME                    second
+
+anomalisticyear         365.2596 days       # The time between successive
+                                            #   perihelion passages of 
+                                            #   Earth.
+siderealyear            365.256360417 day   # The time for Earth to make
+                                            #   one revolution around the Sun
+                                            #   relative to the stars.
+tropicalyear            365.242198781 day   # The time needed for the mean Sun
+                                            #   as defined above to increase
+                                            #   its longitude by 360 degrees.
+                                            #   Most references defined the
+                                            #   tropical year as the interval
+                                            #   between vernal equinoxes, but
+                                            #   this is misleading.  The length
+                                            #   of the season changes over time
+                                            #   because of the eccentricity of
+                                            #   Earth's orbit.  The time
+                                            #   between vernal equinoxes is
+                                            #   approximately 365.24237 days
+                                            #   around the year 2000.  See
+                                            #   "Mathematical Astronomy
+                                            #   Morsels" for more details.
+eclipseyear             346.62 days         # The line of nodes is the
+                                            #   intersection of the plane of
+                                            #   Earth's orbit around the Sun
+                                            #   with the plane of the Moon's
+                                            #   orbit around Earth.  Eclipses
+                                            #   can only occur when the Moon
+                                            #   and Sun are close to this
+                                            #   line.  The line rotates and
+                                            #   appearances of the Sun on the
+                                            #   line of nodes occur every
+                                            #   eclipse year.
+saros                   223 synodicmonth    # The Earth, Moon and Sun appear in
+                                            #   the same arrangement every
+                                            #   saros, so if an eclipse occurs,
+                                            #   then one saros later, a similar
+                                            #   eclipse will occur.  (The saros
+                                            #   is close to 19 eclipse years.)
+                                            #   The eclipse will occur about
+                                            #   120 degrees west of the
+                                            #   preceding one because the
+                                            #   saros is not an even number of
+                                            #   days.  After 3 saros, an
+                                            #   eclipse will occur at
+                                            #   approximately the same place.
+solarday                day                 # Time from noon to noon
+siderealday             86164.09054 s       # The sidereal day is the interval
+siderealhour            1|24 siderealday    #   between two successive transits
+siderealminute          1|60 siderealhour   #   of a star over the meridian,
+siderealsecond          1|60 siderealminute #   or the time required  for
+                                            #   Earth to make one rotation
+                                            #   relative to the stars.  Another
+                                            #   way to think about it is to
+                                            #   imagine looking down at the
+                                            #   solar system and noting when
+                                            #   Earth has made a rotation.
+                                            #   The more usual solar day is the
+                                            #   time required to make a
+                                            #   rotation relative to the Sun,
+                                            #   which means the same point on
+                                            #   Earth faces the Sun again.
+                                            #   Because Earth moves in its
+                                            #   orbit, it has to rotate a bit
+                                            #   more to face the Sun again,
+                                            #   hence the solar day is slightly
+                                            #   longer than the sidereal day.
+                                            #   The value given here is the
+                                            #   mean day length taken from
+                                            #   ssd.jpl.nasa.gov/astro_par.html
+                                            #   which in turn cites the
+                                            #   "Explanatory Supplement to the
+                                            #   Astronomical Almanac", 1992.
+anomalisticmonth        27.55454977 day     # Time for the Moon to travel from
+                                            #   perigee to perigee
+nodicalmonth            27.2122199 day      # The nodes are the points where
+draconicmonth           nodicalmonth        #   an orbit crosses the ecliptic.
+draconiticmonth         nodicalmonth        #   This is the time required to
+                                            #   travel from the ascending node
+                                            #   to the next ascending node.
+siderealmonth           27.321661 day       # Time required for the Moon to
+                                            #   orbit the Earth
+lunarmonth              29 days + 12 hours + 44 minutes + 2.8 seconds
+                                            # Mean time between full moons.
+synodicmonth            lunarmonth          #   Full moons occur when the Sun
+lunation                synodicmonth        #   and Moon are on opposite sides
+lune                    1|30 lunation       #   of the Earth.  Since the Earth
+lunour                  1|24 lune           #   moves around the Sun, the Moon
+                                            #   has to move a bit further in its
+                                            #   orbit to return to the full moon
+                                            #   configuration.
+year                    tropicalyear
+yr                      year
+month                   1|12 year
+mo                      month
+lustrum                 5 years             # The Lustrum was a Roman
+                                            #   purification ceremony that took
+                                            #   place every five years.
+                                            #   Classically educated Englishmen
+                                            #   used this term.
+decade                  10 years
+century                 100 years
+millennium              1000 years
+millennia               millennium
+solaryear               year
+lunaryear               12 lunarmonth
+calendaryear            365 day
+commonyear              365 day
+leapyear                366 day
+ 
+# The Julian year is The length of an average year over a 4-year cycle in the
+# Julian calendar.  The calendar was proposed by Julius Caesar in 46 BCE and
+# took effect the following year. It has a normal year of 365 days and a leap
+# year of 366 days every four years.  Though this calendar was used in
+# Europe for more than 1600 years, it drifts from the topical year by
+# about 1 day every 128 years, which became noticeable over its period
+# of use.
+
+# This growing discrepancy between the seasons and the calendar was perhaps
+# confusing but was also of concern to the Catholic Church because it led to a
+# shift in the date of Easter.  To correct this discrepancy, Pope Gregory XIII
+# introduced the more accurate Gregorian calendar in 1582.  The Gregorian year
+# is the length of an average year over a 400-year cycle in the Gregorian
+# calendar.  Every year that is exactly divisible by four is a
+# leap year, except for years that are exactly divisible by 100, unless these
+# centurial years are exactly divisible by 400.  This calendar was adopted by
+# many Catholic countries when it was proclaimed, but was not adopted by many
+# other countries until much later; Britain and the British Empire, including
+# what is now the eastern part of the United States, adopted it in 1752.  See
+# https://en.wikipedia.org/wiki/List_of_adoption_dates_of_the_Gregorian_calendar_by_country
+# for additional details.
+
+julianyear              365.25 days
+gregorianyear           365.2425 days
+                                            
+islamicyear             354 day          # A year of 12 lunar months. They
+islamicleapyear         355 day          # began counting on July 16, AD 622
+                                         # when Muhammad emigrated to Medina
+                                         # (the year of the Hegira).  They need
+                                         # 11 leap days in 30 years to stay in
+                                         # sync with the lunar year which is a
+                                         # bit longer than the 29.5 days of the
+                                         # average month.  The months do not
+                                         # keep to the same seasons, but
+                                         # regress through the seasons every
+                                         # 32.5 years.
+islamicmonth            1|12 islamicyear # They have 29 day and 30 day months.
+
+# The Hebrew year is also based on lunar months, but synchronized to the solar
+# calendar.  The months vary irregularly between 29 and 30 days in length, and
+# the years likewise vary.  The regular year is 353, 354, or 355 days long.  To
+# keep up with the solar calendar, a leap month of 30 days is inserted every
+# 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle.  This
+# gives leap years that last 383, 384, or 385 days.
+
+#
+# Planetary data from JPL's planet fact sheets.  Each planet has its
+# own sheet at https://nssdc.gsfc.nasa.gov/planetary/factsheet/<name>fact.html
+# The source for data on the fact sheets is described at
+# https://nssdc.gsfc.nasa.gov/planetary/factsheet/fact_notes.html
+# and they also indicate that the values listed are not "official" values:
+# there is no single set of agreed upon values.  
+
+# Sidereal days.  The sidereal day is the time required for a planet to make a
+# revolution relative to the stars.  This is the default day value.  
+
+mercuryday              mercuryday_sidereal
+venusday                venusday_sidereal
+earthday                earthday_sidereal
+marsday                 marsday_sidereal
+jupiterday              jupiterday_sidereal
+saturnday               saturnday_sidereal
+uranusday               uranusday_sidereal
+neptuneday              neptuneday_sidereal
+plutoday                plutoday_sidereal
+
+mercuryday_sidereal     1407.6 hr   # Mercury is in a 3:2 resonance lock
+                                    # where it makes 3 rotations per 2 orbits
+                                    # so 3 sidereal days = 2 years
+venusday_sidereal       5832.6 hr   # Retrograde
+earthday_sidereal       siderealday
+marsday_sidereal        24.6229 hr
+jupiterday_sidereal     9.9250 hr
+saturnday_sidereal      10.656 hr
+uranusday_sidereal      17.24 hr    # Retrograde
+neptuneday_sidereal     16.11 hr
+plutoday_sidereal       153.2928 hr # Retrograde
+
+# In astronomy, an object's rotation is "prograde" if it rotates in
+# the same direction as the primary object it orbits.  Prograde
+# rotation is the more common case: in Earth's solar system, Mercury,
+# Earth, Mars, Jupiter, Saturn, and Neptune have prograde rotation.
+# When an object rotates opposite the direction of its primary object,
+# the object's rotation is "retrograde".  Venus, Uranus, and Pluto have
+# retrograde rotation.
+#
+# The solar (or synodic) day is the time from noon to noon on a planet.  This
+# is different from the sidereal day because the planet has moved in its orbit,
+# so (if its rotation is prograde) it needs additional rotation to return to
+# the same orientation relative to the Sun.  In one orbital period (a year),
+# this amounts to one additional complete rotation, so the number of sidereal
+# days in a year is one greater than the number of solar days.
+#
+# If the planet's rotation is retrograde, less rotation is needed to return to
+# the same orientation relative to the Sun, and the number of sidereal days in
+# a year is one fewer than the number of solar days.
+#
+# The solar day can be computed from the sidereal day in the typical prograde
+# case by:
+#       solar_day = sidereal_day year / (year - sidereal_day)
+# If the planet's rotation is retrograde like Venus then the formula is
+#       solar_day = sidereal_day year / (year + sidereal_day)
+# If the sidereal day and year are the same length then the same face of the
+# planet faces the Sun and there is no solar day.
+
+mercuryday_solar        4222.6 hr 
+venusday_solar          2802.0 hr
+earthday_solar          24 hr
+marsday_solar           24.6597 hr
+jupiterday_solar        9.9259 hr
+saturnday_solar         10.656 hr
+uranusday_solar         17.24 hr
+neptuneday_solar        16.11 hr
+plutoday_solar          153.2820 hr
+
+# Sidereal years 
+
+mercuryyear             87.969 day
+venusyear               224.701 day
+earthyear               siderealyear
+marsyear                686.980 day
+jupiteryear             4332.589 day
+saturnyear              10759.22 day
+uranusyear              30685.4 day
+neptuneyear             60189 day
+plutoyear               90560 day
+
+# Equatorial radii for the planets from JPL fact sheets
+
+mercuryradius           2440.5 km
+venusradius             6051.8 km
+earthradius             6378.137 km
+marsradius              3396.2 km
+jupiterradius           71492 km   # 1 bar level
+saturnradius            60268 km   # 1 bar level
+uranusradius            25559 km   # 1 bar level
+neptuneradius           24764 km   # 1 bar level
+plutoradius             1188 km
+
+# Volumetric mean radii
+
+mercuryradius_mean      2440.5 km
+venusradius_mean        6051.8 km
+earthradius_mean        6371 km
+marsradius_mean         3389.5 km
+jupiterradius_mean      69911 km
+saturnradius_mean       58232 km
+uranusradius_mean       25362 km
+neptuneradius_mean      24622 km
+plutoradius_mean        1188 km
+
+# Polar radii
+
+mercuryradius_polar      2438.3 km
+venusradius_polar        6051.8 km
+marsradius_polar         3376.2 km
+jupiterradius_polar      66854 km
+saturnradius_polar       54364 km
+uranusradius_polar       24973 km
+neptuneradius_polar      24341 km
+plutoradius_polar        1188 km
+
+mercurysundist_min      46.000 Gm
+mercurysundist_max      69.818 Gm
+venussundist_min        107.480 Gm
+venussundist_max        108.941 Gm
+earthsundist_min        sundist_min
+earthsundist_max        sundist_max
+marssundist_min         206.650 Gm
+marssundist_max         249.261 Gm
+jupitersundist_min      740.595 Gm
+jupitersundist_max      816.363 Gm
+saturnsundist_min       1357.554 Gm
+saturnsundist_max       1506.527 Gm
+uranussundist_min       2732.696 Gm
+uranussundist_max       3001.390 Gm
+neptunesundist_min      4471.050 Gm
+neptunesundist_max      4558.857 Gm
+plutosundist_min        4434.987 Gm
+plutosundist_max        7304.326 Gm
+
+sundist                 1.0000010178 au # mean Earth-Sun distance
+moondist                384400 km       # mean Earth-Moon distance
+sundist_near            147.095 Gm      # Earth-Sun distance at perihelion
+sundist_min             sundist_near
+sundist_far             152.100 Gm      # Earth-Sun distance at aphelion
+sundist_max             sundist_far
+
+# The Earth-Moon distances at perigee and apogee are different for every
+# lunation.  The values here are the extremes for 1500-2500 according to
+# Jean Meeus's Astronomical Algorithms (1991, 332).
+
+moondist_min            356371 km      # minimum distance at perigee 1500-2500
+moondist_max            406720 km      # maximum distance at apogee 1500-2500
+
+# Objects on Earth are charted relative to a perfect ellipsoid whose
+# dimensions are specified by different organizations.  The ellipsoid is
+# specified by an equatorial radius and a flattening value which defines the
+# polar radius.
+
+earthflattening         IERS_earthflattening
+earthradius_equatorial  IERS_earthradius_equatorial
+earthradius_polar       (1-earthflattening) earthradius_equatorial
+
+# The World Geodetic System maintains a standard, WGS84, which is used by the
+# the GPS system.  This system uses a conventional ellipsoid that was fixed in
+# 1984 and has remained constant so that data collected at different times is
+# referenced to the same ellipsoid.   https://epsg.io/4326
+
+WGS84_earthflattening         1|298.257223563
+WGS84_earthradius_equatorial  6378137 m
+WGS84_earthradius_polar   (1-WGS84_earthflattening) WGS84_earthradius_equatorial
+
+# The International Earth Rotation Service (IERS) attempts to
+# maintain an accurate model of Earth, with updates to maintain the highest
+# possible accuracy, even though this makes it more difficult to relate geodetic
+# measurements made at different times.
+# IERS Conventions, Chapter 1, General definitions and numerical standards (16 November 2017)
+# https://iers-conventions.obspm.fr/content/chapter1/icc1.pdf
+
+IERS_earthflattening        1|298.25642
+IERS_earthradius_equatorial 6378136.6 m
+IERS_earthradius_polar      (1-IERS_earthflattening) IERS_earthradius_equatorial
+
+
+landarea                148.847e6 km^2
+oceanarea               361.254e6 km^2
+
+moonradius              1738 km         # mean value
+sunradius               6.96e8 m
+
+# Many astronomical values can be measured most accurately in a system of units
+# using the astronomical unit and the mass of the Sun as base units.  The
+# uncertainty in the gravitational constant makes conversion to SI units
+# significantly less accurate.
+
+# The astronomical unit was defined to be the length of the of the semimajor
+# axis of a massless object with the same year as Earth.  With such a
+# definition in force, and with the mass of the Sun set equal to one, Kepler's
+# third law can be used to solve for the value of the gravitational constant.
+
+# Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital
+# period, a is the size of the semimajor axis, G is the gravitational constant
+# and M is the mass.  With M = 1 and T and a chosen for Earth's orbit, we
+# find sqrt(G) = (2 pi / T) sqrt(AU^3).  This constant is called the Gaussian
+# gravitational constant, apparently because Gauss originally did the
+# calculations.  However, when the original calculation was done, the value
+# for the length of Earth's year was inaccurate.  The value used is called
+# the Gaussian year.  Changing the astronomical unit to bring it into
+# agreement with more accurate values for the year would have invalidated a
+# lot of previous work, so instead the astronomical unit has been kept equal
+# to this original value.  This is accomplished by using a standard value for
+# the Gaussian gravitational constant.  This constant is called k.
+
+gauss_k                 0.01720209895   # This beast has dimensions of
+                                        # au^(3|2) / day and is exact.
+gaussianyear      (2 pi / gauss_k) days # Year that corresponds to the Gaussian
+                                        # gravitational constant. This is a
+                                        # fictional year, and doesn't
+                                        # correspond to any celestial event.
+astronomicalunit         149597870700 m # IAU definition from 2012, exact
+au                     astronomicalunit # ephemeris for the above described
+                                        # astronomical unit.  (See the NASA
+                                        # site listed above.)
+GMsun    132712440041.279419 km^3 / s^2 # heliocentric gravitational constant
+solarmass                       GMsun/G # is known more accurately than G.
+sunmass                       solarmass # Estimated from DE440
+
+
+# The following are masses for planetary systems, not just the planet itself,
+# except for the case of Earth, where the Moon is excluded.  Masses are
+# relative to G because they are known much more accurately than G.
+#
+# See https://ssd.jpl.nasa.gov/astro_par.html.  Values are from
+# the DE440 Ephemeris: https://ssd.jpl.nasa.gov/doc/Park.2021.AJ.DE440.pdf
+
+mercurymass             22031.868551 km^3 / s^2 G
+venusmass               324858.592000 km^3 / s^2 G
+marsmass                42828.375816 km^3 / s^2 G
+jupitermass             126712764.100000 km^3 / s^2 G
+saturnmass              37940584.841800 km^3 / s^2 G
+uranusmass              5794556.400000 km^3 / s^2 G
+neptunemass             6836527.100580 km^3 / s^2 G
+plutomass               975.500000 km^3 / s^2 G
+ceresmass               62.62890 km^3 / s^2 G
+vestamass               17.288245 km^3 / s^2 G
+
+earthmass               398600.435507 km^3 / s^2 G    # Earth alone
+moonmass                4902.800118 km^3 / s^2 G
+moonearthmassratio      moonmass/earthmass
+earthmoonmass           earthmass+moonmass
+
+moongravity             1.62 m/s^2
+
+# Earth gravity values at the equator and poles.  These values are
+# obtained from the WGS84 model.
+
+gravity_equatorial      9.7803263359 m / s^2
+gravity_polar           9.8321849378 m / s^2
+
+# The Hubble constant gives the speed at which distance galaxies are moving
+# away from Earth according to v = H0*d, where H0 is the hubble constant
+# and d is the distance to the galaxy.
+
+hubble                  70 km/s/Mpc        # approximate
+H0                      hubble
+
+# Parallax is the angular difference between the topocentric (on Earth's
+# surface) and geocentric (at Earth's center) direction toward a celestial body
+# when the body is at a given altitude.  When the body is on the horizon, the
+# parallax is the horizontal parallax; when the body is on the horizon and the
+# observer is on the equator, the parallax is the equatorial horizontal
+# parallax.  When the body is at zenith, the parallax is zero.
+
+lunarparallax  asin(earthradius_equatorial / moondist) # Moon equatorial 
+moonhp         lunarparallax                           # horizontal parallax
+                                                       # at mean distance
+
+# Light from celestial objects is attenuated by passage through Earth's
+# atmosphere.  A body near the horizon passes through much more air than an
+# object at zenith, and is consequently less bright.  Air mass is the ratio of
+# the length of the optical path at a given altitude (angle above the horizon)
+# to the length at zenith.  Air mass at zenith is by definition unity; at the
+# horizon, air mass is approximately 38, though the latter value can vary
+# considerably with atmospheric conditions.  The general formula is # E = E0
+# exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value
+# seen by an observer, X is the air mass and c is the extinction coefficient.
+# A common value for c in reasonably clear air is 0.21, but values can be
+# considerably greater in urban areas.  Apparent altitude is that perceived by
+# an observer; it includes the effect of atmospheric refraction.  There is no
+# shortage of formulas for air mass
+# (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to
+# variations in local atmospheric conditions.  The formula used here is simple
+# and is in good agreement with rigorously calculated values under standard
+# conditions.
+#
+# Extraterrestrial illuminance or luminance of an object at a given altitude
+# determined with vmag() or SB_xxx() below can be multiplied by
+# atm_transmission() or atm_transmissionz() to estimate the terrestrial value.
+#
+# Kasten and Young (1989) air mass formula. alt is apparent altitude
+# Reference:
+# Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables
+#     and Approximation Formula."  Applied Optics.  Vol. 28, 4735-4738.
+#     Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735.
+
+airmass(alt) units=[degree;1] domain=[0,90] noerror \
+    1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364)
+
+# zenith is apparent zenith angle (zenith = 90 deg - alt)
+airmassz(zenith) units=[degree;1] domain=[0,90] noerror \
+    1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364)
+
+# For reasonably clear air at sea level; values may need adjustment for
+# elevation and local atmospheric conditions
+# for scotopic vision (510 nm), appropriate for the dark-adapted eye
+# extinction_coeff           0.26
+# for photopic vision, appropriate for observing brighter objects such
+# as the full moon
+extinction_coeff        0.21
+
+atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \
+                        exp(-extinction_coeff airmass(alt))
+
+# in terms of zenith angle (zenith = 90 deg - alt)
+atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \
+                        exp(-extinction_coeff airmassz(zenith))
+
+# Moon and Sun data at mean distances
+moonvmag               -12.74  # Moon apparent visual magnitude at mean distance
+sunvmag                -26.74  # Sun apparent visual magnitude at mean distance
+moonsd  asin(moonradius / moondist) # Moon angular semidiameter at mean distance
+sunsd     asin(sunradius / sundist) # Sun angular semidiameter at mean distance
+
+# Visual magnitude of star or other celestial object.  The system of stellar
+# magnitudes, developed in ancient Greece, assigned magnitudes from 1
+# (brightest) to 6 (faintest visible to the naked eye).  In 1856, British
+# astronomer Norman Pogson made the system precise, with a magnitude 1 object
+# 100 times as bright as a magnitude 6 object, and each magnitude differing
+# from the next by a constant ratio; the ratio, sometimes known as Pogson's
+# ratio, is thus 100^0.2, or approximately 2.5119.  The logarithm of 100^0.2 is
+# 0.4, hence the common use of powers of 10 and base-10 logarithms.
+#
+# Reference:
+# Allen, C.W. 1976.  Astrophysical Quantities, 3rd ed. 1973, reprinted
+#     with corrections, 1976.  London: Athlone.
+#
+# The function argument is the (dimensionless) visual magnitude; reference
+# illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside
+# Earth's atmosphere.  Illuminance values can be adjusted to terrestrial values
+# by multiplying by one of the atm_transmission functions above.
+
+# Illuminance from apparent visual magnitude
+vmag(mag) units=[1;lx] domain=[,]  range=(0,] \
+                       2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx))
+
+# Surface brightness of a celestial object of a given visual magnitude
+# is a logarithmic measure of the luminance the object would have if its
+# light were emitted by an object of specified solid angle; it is
+# expressed in magnitudes per solid angle.  Surface brightness can be
+# obtained from the visual magnitude by
+#    S = m + 2.5 log(pi pi k a b),
+# where k is the phase (fraction illuminated), a is the equatorial
+# radius, and b is the polar radius.  For 100% illumination (e.g., full
+# moon), this is often simplified to
+#    S = m + 2.5 log(pi k s^2),
+# where s is the object's angular semidiameter; the units of s determine
+# the units of solid angle.  The visual magnitude and semidiameter must
+# be appropriate for the object's distance; for other than 100%
+# illumination, the visual magnitude must be appropriate for the phase.
+# Luminance values are for outside Earth's atmosphere; they can be
+# adjusted to terrestrial values by multiplying by one of the atm_transmission
+# functions above.
+
+# luminance from surface brightness in magnitudes per square degree
+SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
+    vmag(sb) / squaredegree ; \
+    ~vmag(SB_degree squaredegree)
+
+# luminance from surface brightness in magnitudes per square minute
+SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
+    vmag(sb) / squareminute ; \
+    ~vmag(SB_minute squareminute)
+
+# luminance from surface brightness in magnitudes per square second
+SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
+    vmag(sb) / squaresecond ; \
+    ~vmag(SB_second squaresecond)
+
+# luminance from surface brightness in magnitudes per steradian
+SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
+    vmag(sb) / sr ; \
+    ~vmag(SB_sr sr)
+
+SB()            SB_second
+SB_sec()        SB_second
+SB_min()        SB_minute
+SB_deg()        SB_degree
+
+# The brightness of one tenth-magnitude star per square degree outside
+# Earth's atmosphere; often used for night sky brightness.
+S10     SB_degree(10)
+
+# Examples for magnitude and surface brightness functions
+# Sun illuminance from visual magnitude
+#     You have: sunvmag
+#     You want:
+#           Definition: -26.74 = -26.74
+#     You have: vmag(sunvmag)
+#     You want: lx
+#           * 126134.45
+#           / 7.9280482e-06
+#
+# Moon surface brightness from visual magnitude and semidiameter at 100%
+# illumination (full moon):
+#     You have: moonvmag
+#     You want:
+#           Definition: -12.74 = -12.74
+#     You have: moonsd
+#     You want: arcsec
+#           * 932.59484
+#           / 0.001072277
+#     You have: moonvmag + 2.5 log(pi 932.59484^2)
+#     You want:
+#           Definition: 3.3513397
+#
+# Similar example with specific data obtained from another source (JPL
+# Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in
+# arcseconds
+#
+#     You have: -12.9 + 2.5 log(pi 2023.201|2^2)
+#     You want:
+#           Definition: 3.3679199
+#     You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2))
+#     You want:
+#           Definition: 4858.6547 cd / m^2
+#
+# If surface brightness is provided by another source (e.g., Horizons),
+# it can simply be used directly:
+# You have: SB_second(3.3679199)
+# You want: cd/m^2
+#         * 4858.6546
+#         / 0.0002058183
+# The illuminance and luminance values are extraterrestrial (outside
+# Earth's atmosphere).  The values at Earth's surface are less than these
+# because of atmospheric extinction.  For example, in the last example
+# above, if the Moon were at an altitude of 55 degrees, the terrestrial
+# luminance could be calculated with
+#     You have: SB_second(3.3679199)
+#     You want: cd/m^2
+#           * 4858.6546
+#           / 0.0002058183
+#     You have: _ atm_transmission(55 deg)
+#     You want: cd/m^2
+#           * 3760.6356
+#           / 0.0002659125
+# If desired, photographic exposure can be determined with EV100(),
+# leading to acceptable combinations of aperture and exposure time.
+# For the example above, but with the Moon at 10 degrees,
+#     You have: SB_second(3.3679199) atm_transmission(10 deg)
+#     You want: EV100
+#           13.553962
+
+#
+# The Hartree system of atomic units, derived from fundamental units
+# of mass (of the electron), action (Planck's constant), charge, and
+# the Coulomb constant.  This system is used in the fields of physical
+# chemistry and condensed matter physics.  
+#
+
+# Fundamental units
+
+atomicmass              electronmass
+atomiccharge            e
+atomicaction            hbar
+atomicenergy            hartree
+
+# Derived units
+
+atomicvelocity          sqrt(atomicenergy / atomicmass)
+atomictime              atomicaction / atomicenergy
+atomiclength            atomicvelocity atomictime
+atomicforce             atomicenergy / atomiclength
+atomicmomentum          atomicenergy / atomicvelocity
+atomiccurrent           atomiccharge / atomictime
+atomicpotential         atomicenergy / atomiccharge   # electrical potential
+atomicvolt              atomicpotential
+atomicEfield            atomicpotential / atomiclength
+atomicBfield            atomicEfield / atomicvelocity
+atomictemperature       atomicenergy / boltzmann
+
+#
+# In Hartree units, m_e = hbar = e = coulombconst = bohrradius = alpha*c = 1
+#
+
+!var UNITS_SYSTEM hartree
+!message Hartree units selected
+!prompt (hartree)
++hartree      1
++kg           1/electronmass_SI
++K            k_SI / hbar_SI s 
++m            alpha c_SI electronmass_SI / hbar_SI
++s            alpha c_SI m
++A            1 / s e_SI
+!endvar
+
+#
+# These thermal units treat entropy as charge, from [5]
+#
+
+thermalcoulomb          J/K        # entropy
+thermalampere           W/K        # entropy flow
+thermalfarad            J/K^2
+thermalohm              K^2/W      # thermal resistance
+fourier                 thermalohm
+thermalhenry            J K^2/W^2  # thermal inductance
+thermalvolt             K          # thermal potential difference
+
+
+#
+# United States units
+#
+
+# linear measure
+
+# The US Metric Law of 1866 legalized the metric system in the USA and
+# defined the meter in terms of the British system with the exact
+# 1 meter = 39.37 inches.  On April 5, 1893 Thomas Corwin Mendenhall,
+# Superintendent of Weights and Measures, decided, in what has become
+# known as the "Mendenhall Order" that the meter and kilogram would be the
+# fundamental standards in the USA.  The definition from 1866 was turned
+# around to give an exact definition of the yard as 3600|3937 meters This
+# definition was used until July of 1959 when the definition was changed
+# to bring the US and other English-speaking countries into agreement; the
+# Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it
+# was approximately halfway between the British and US values; it had the
+# added advantage of making 1 inch = 25.4 mm (exactly).  Since 1959, the
+# "international" foot has been exactly 0.3048 meters.  At the same time,
+# it was decided that any data expressed in feet derived from geodetic
+# surveys within the US would continue to use the old definition and call
+# the old unit the "survey foot."
+#
+# Until 1 January 2023, the US continued to define the statute
+# mile, furlong, chain, rod, link, and fathom in terms of the US survey
+# foot.  Since then, use of the US survey foot has been officially
+# deprecated, with its use limited to historical and legacy applications.
+# These units are now defined in terms of the international foot.
+#
+# Sources:
+# NIST Special Publication 447, Sects. 5, 7, and 8.
+# NIST Handbook 44, 2024 ed., Appendix C.
+# Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014.
+
+inch                    2.54 cm          # Exact, international inch (1959)
+in                      inch
+foot                    12 inch
+feet                    foot
+ft                      foot
+yard                    3 ft
+yd                      yard
+mile                    5280 ft          # The mile was enlarged from 5000 ft
+                                         # to this number in order to make
+                                         # it an even number of furlongs.
+                                         # (The Roman mile is 5000 romanfeet.)
+line                    1|12 inch  # Also defined as '.1 in' or as '1e-8 Wb'
+rod                     16.5 ft
+pole                    rod
+perch                   rod
+furlong                 40 rod           # From "furrow long"
+statutemile             mile
+league                  3 mile           # Intended to be an hour's walk
+
+# surveyor's measure
+# The US survey foot is officially deprecated as of 1 January 2023
+US                      1200|3937 m/ft   # These four values will convert
+US-                     US               #   international measures to
+survey-                 US               #   US Survey measures
+geodetic-               US
+int                     3937|1200 ft/m   # Convert US Survey measures to
+int-                    int              #   international measures
+
+# values based on the US survey foot are deprecated as of 1 January 2023
+surveyorschain          66 surveyft
+surveychain             surveyorschain
+surveyorspole           1|4 surveyorschain
+surveyorslink           1|100 surveyorschain
+USacre                  10 surveychain^2
+USacrefoot              USacre surveyfoot
+
+chain                   66 ft
+link                    1|100 chain
+ch                      chain
+intacre                 10 chain^2       # Acre based on international ft
+intacrefoot             acre foot
+acrefoot                intacrefoot
+acre                    intacre
+ac                      acre
+section                 mile^2
+township                36 section
+homestead               160 acre # Area of land granted by the 1862 Homestead
+                                 # Act of the United States Congress
+gunterschain            surveyorschain
+
+engineerschain          100 ft
+engineerslink           1|100 engineerschain
+ramsdenschain           engineerschain
+ramsdenslink            engineerslink
+
+gurleychain             33 feet           # Andrew Ellicott chain is the
+gurleylink              1|50 gurleychain  # same length
+
+wingchain               66 feet           # Chain from 1664, introduced by
+winglink                1|80 wingchain    # Vincent Wing, also found in a
+                                          # 33 foot length with 40 links.
+# early US length standards
+
+# The US has had four standards for the yard: one by Troughton of London
+# (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent
+# with the definition of the meter in the metric joint resolution of
+# Congress in 1866, but defining the yard in terms of the meter; and the
+# international yard (1959), which standardized definitions for Australia,
+# Canada, New Zealand, South Africa, the UK, and the US.
+# Sources: Pat Naughtin (2009), Which Inch?:
+# https://metricationmatters.org/docs/WhichInch.pdf, 
+# Lewis E.  Barbrow and Lewis V.  Judson (1976).  NBS Special
+# Publication 447, Weights and Measures Standards of the United States: A
+# Brief History.
+
+troughtonyard           914.42190 mm
+bronzeyard11            914.39980 mm
+mendenhallyard          surveyyard
+internationalyard       yard
+
+# nautical measure
+
+fathom                  6 ft     # Originally defined as the distance from
+                                 #   fingertip to fingertip with arms fully
+                                 #   extended.
+nauticalmile            1852 m   # Supposed to be one minute of latitude at
+                                 # the equator.  That value is about 1855 m.
+                                 # Early estimates of Earth's circumference
+                                 # were a bit off.  The value of 1852 m was
+                                 # made the international standard in 1929.
+                                 # The US did not accept this value until
+                                 # 1954.  The UK switched in 1970.
+                                 
+# The cable is used for depth in water and has a wide range of definitions
+
+intcable                1|10 nauticalmile # international cable
+uscable                 120 fathom	  # value after 1 January 2023
+surveycable             120 USfathom	  # value before 1 January 2023
+UScable                 surveycable
+cableslength            cable
+cablelength             cable
+navycablelength         cable
+brcable                 1|10 brnauticalmile   
+admiraltycable          brcable
+
+marineleague            3 nauticalmile
+geographicalmile        brnauticalmile
+knot                    nauticalmile / hr
+click                   km       # US military slang
+klick                   click
+
+# Avoirdupois weight
+
+pound                   0.45359237 kg   # Exact, International Pound (1959)
+lb                      pound           # From the Latin libra
+grain                   1|7000 pound    # The grain is the same in all three
+                                        # weight systems.  It was originally
+                                        # defined as the weight of a barley
+                                        # corn taken from the middle of the
+                                        # ear.
+ounce                   1|16 pound
+oz                      ounce
+dram                    1|16 ounce
+dr                      dram
+ushundredweight         100 pounds
+cwt                     hundredweight
+shorthundredweight      ushundredweight
+uston                   shortton
+shortton                2000 lb
+quarterweight           1|4 uston
+shortquarterweight      1|4 shortton
+shortquarter            shortquarterweight
+
+# Troy Weight.  In 1828 the troy pound was made the first United States
+# standard weight.  It was to be used to regulate coinage.
+
+troypound               5760 grain
+troyounce               1|12 troypound
+ozt                     troyounce
+pennyweight             1|20 troyounce  # Abbreviated "d" in reference to a
+dwt                     pennyweight     #   Frankish coin called the "denier"
+                                        #   minted in the late 700's.  There
+                                        #   were 240 deniers to the pound.
+assayton                mg ton / troyounce  # mg / assayton = troyounce / ton
+usassayton              mg uston / troyounce
+brassayton              mg brton / troyounce
+fineounce               troyounce       # A troy ounce of 99.5% pure gold
+
+# Some other jewelers units
+
+metriccarat             0.2 gram        # Defined in 1907
+metricgrain             50 mg
+carat                   metriccarat
+ct                      carat
+jewelerspoint           1|100 carat
+silversmithpoint        1|4000 inch
+momme                   3.75 grams      # Traditional Japanese unit based
+                                        # on the chinese mace.  It is used for
+                                        # pearls in modern times and also for
+                                        # silk density.  The definition here
+                                        # was adopted in 1891.
+# Apothecaries' weight
+
+appound                 troypound
+apounce                 troyounce
+apdram                  1|8 apounce
+apscruple               1|3 apdram
+
+# Liquid measure
+
+usgallon                231 in^3        # US liquid measure is derived from
+gal                     gallon          # the British wine gallon of 1707.
+quart                   1|4 gallon      # See the "winegallon" entry below
+pint                    1|2 quart       # more historical information.
+gill                    1|4 pint
+usquart                 1|4 usgallon
+uspint                  1|2 usquart
+usgill                  1|4 uspint
+usfluidounce            1|16 uspint
+fluiddram               1|8 usfloz
+minimvolume             1|60 fluiddram
+qt                      quart
+pt                      pint
+floz                    fluidounce
+usfloz                  usfluidounce
+fldr                    fluiddram
+liquidbarrel            31.5 usgallon
+usbeerbarrel            2 beerkegs
+beerkeg                 15.5 usgallon   # Various among brewers
+ponykeg                 1|2 beerkeg
+winekeg                 12 usgallon
+petroleumbarrel         42 usgallon     # Originated in Pennsylvania oil
+barrel                  petroleumbarrel # fields, from the winetierce
+bbl                     barrel
+ushogshead              2 liquidbarrel
+usfirkin                9 usgallon
+
+# Dry measures: The Winchester Bushel was defined by William III in 1702 and
+# legally adopted in the US in 1836.
+
+usbushel                2150.42 in^3  # Volume of 8 inch cylinder with 18.5
+bu                      bushel        # inch diameter (rounded)
+peck                    1|4 bushel
+uspeck                  1|4 usbushel
+brpeck                  1|4 brbushel
+pk                      peck
+drygallon               1|2 uspeck
+dryquart                1|4 drygallon
+drypint                 1|2 dryquart
+drybarrel               7056 in^3     # Used in US for fruits, vegetables,
+                                      #   and other dry commodities except for
+                                      #   cranberries.
+cranberrybarrel         5826 in^3     # US cranberry barrel
+heapedbushel            1.278 usbushel# The following explanation for this
+                                      #   value was provided by Wendy Krieger
+                                      #   <os2fan2@yahoo.com> based on
+                                      #   guesswork.  The cylindrical vessel is
+                                      #   18.5 inches in diameter and 1|2 inch
+                                      #   thick.  A heaped bushel includes the
+                                      #   contents of this cylinder plus a heap
+                                      #   on top.  The heap is a cone 19.5
+                                      #   inches in diameter and 6 inches
+                                      #   high.  With these values, the volume
+                                      #   of the bushel is 684.5 pi in^3 and
+                                      #   the heap occupies 190.125 pi in^3.
+                                      #   Therefore, the heaped bushel is
+                                      #   874.625|684.5 bushels.  This value is
+                                      #   approximately 1.2777575 and it rounds
+                                      #   to the value listed for the size of
+                                      #   the heaped bushel.  Sometimes the
+                                      #   heaped bushel is reported as 1.25
+                                      #   bushels.  This same explanation gives
+                                      #   that value if the heap is taken to
+                                      #   have an 18.5 inch diameter.
+
+# Grain measures.  The bushel as it is used by farmers in the USA is actually
+# a measure of mass which varies for different commodities.  Canada uses the
+# same bushel masses for most commodities, but not for oats.
+
+wheatbushel             60 lb
+soybeanbushel           60 lb
+cornbushel              56 lb
+ryebushel               56 lb
+barleybushel            48 lb
+oatbushel               32 lb
+ricebushel              45 lb
+canada_oatbushel        34 lb
+
+# Wine and Spirits measure
+
+ponyvolume              1 usfloz
+jigger                  1.5 usfloz   # Can vary between 1 and 2 usfloz
+shot                    jigger     # Sometimes 1 usfloz
+eushot                  25 ml      # EU standard spirits measure
+fifth                   1|5 usgallon
+winebottle              750 ml     # US industry standard, 1979
+winesplit               1|4 winebottle
+magnum                  1.5 liter  # Standardized in 1979, but given
+                                   # as 2 qt in some references
+metrictenth             375 ml
+metricfifth             750 ml
+metricquart             1 liter
+
+# Old British bottle size
+
+reputedquart            1|6 brgallon
+reputedpint             1|2 reputedquart
+brwinebottle            reputedquart       # Very close to 1|5 winegallon
+
+# French champagne bottle sizes
+
+split                   200 ml
+jeroboam                2 magnum
+rehoboam                3 magnum
+methuselah              4 magnum
+imperialbottle          4 magnum
+salmanazar              6 magnum
+balthazar               8 magnum
+nebuchadnezzar          10 magnum
+solomon                 12 magnum
+melchior                12 magnum
+sovereign               17.5 magnum
+primat                  18 magnum
+goliath                 18 magnum
+melchizedek             20 magnum
+midas                   20 magnum
+
+# The wine glass doesn't seem to have an official standard, but the same value
+# is suggested by several sources in the US. 
+
+wineglass               150 mL 
+
+# In the UK, serving size offerings legally mandated by The Weights and
+# Measures (Specified Quantities) (Unwrapped Bread and Intoxicating
+# Liquor) Order 2011, effective 1st October 2011.  The quantities--not
+# the names--are mandated.  Lawful size offerings are these or multiples
+# thereof, but other sizes can be provided at the express request of a
+# buyer.
+
+smallwineglass          125 mL
+mediumwineglass         175 mL
+
+# Values vary considerably among countries and even more so in practice.  The
+# "standard" US value gives 5 glasses per standard 750 ml bottle.  Old practice
+# in the UK was 125 ml per glass, or 6 glasses per bottle. Some sources suggest
+# a more recent common value of 250 ml per glass, or 3 glasses per
+# bottle; as a multiple of 125 ml, this would be a lawful serving size offering.
+#
+# The value refers to the size of the serving, not the total volume of the
+# glass, which is typically not filled above the height of its greatest
+# diameter.
+#
+# A unit of alcohol is a specified amount of pure ethyl alcohol, expressed as a
+# mass or volumetric equivalent.  Many countries use the same concept but use
+# different terms. "Alcohol unit" is used officially in the UK; the US, Canada,
+# and Australia use "standard drink."  Values vary considerably among
+# countries.  The UK value of 8 g is nominally the amount of alcohol that a
+# typical adult can metabolize in one hour.
+
+alcoholunitus           14 g   / ethanoldensity
+alcoholunitca           13.6 g / ethanoldensity
+alcoholunituk            8 g   / ethanoldensity
+alcoholunitau           10 g   / ethanoldensity
+
+# Common serving sizes have roughly equivalent amounts of alcohol, as
+# illustrated by US examples for wine (12% Alcohol By Volume), beer (5% ABV),
+# and spirits (80 proof).
+#
+# alcoholunitus / 12% = 147.8 mL, close to the "standard" serving of 150 mL.
+# alcoholunitus / 5% = 11.995346 floz, close to a standard 12 floz bottle or can
+# alcoholunitus / 80 proof = 1.4994182 floz, close to a standard "shot" or jigger
+
+# https://www.rethinkingdrinking.niaaa.nih.gov/
+# https://www.cdc.gov/alcohol/faqs.htm
+# https://www.canada.ca/en/health-canada/services/substance-use/alcohol/low-risk-alcohol-drinking-guidelines
+# https://www.drinkaware.co.uk/
+# https://www.drinkaware.co.uk/facts/alcoholic-drinks-and-units
+# https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf
+# https://adf.org.au/reducing-risk/alcohol/alcohol-guidelines/
+# https://www.health.gov.au/topics/alcohol/about-alcohol/standard-drinks-guide
+# https://en.wikipedia.org/wiki/Unit_of_alcohol
+# https://en.wikipedia.org/wiki/Standard_drink
+
+# Coffee 
+#
+# The recommended ratio of coffee to water. Values vary considerably;
+# one is from the  Specialty Coffee Association of America: Brewing Best Practices
+# https://sca.coffee/research/protocols-best-practices
+
+coffeeratio             55 g/L  # +/- 10%
+
+# other recommendations are more loose, e.g.,
+# http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee
+
+
+#
+# Water is "hard" if it contains various minerals, especially calcium
+# carbonate.
+#
+
+clarkdegree     grains/brgallon # Content by weigh of calcium carbonate
+gpg             grains/usgallon # Divide by water's density to convert to
+                                #   a dimensionless concentration measure
+#
+# Shoe measures
+#
+
+shoeiron                1|48 inch    # Used to measure leather in soles
+shoeounce               1|64 inch    # Used to measure non-sole shoe leather
+
+# USA shoe sizes.  These express the length of the shoe or the length
+# of the "last", the form that the shoe is made on.  But note that
+# this only captures the length.  It appears that widths change 1/4
+# inch for each letter within the same size, and if you change the
+# length by half a size then the width changes between 1/8 inch and
+# 1/4 inch.  But this may not be standard.  If you know better, please
+# contact me.
+
+shoesize_delta          1|3 inch     # USA shoe sizes differ by this amount
+shoe_men0               8.25 inch
+shoe_women0             (7+11|12) inch
+shoe_boys0              (3+11|12) inch
+shoe_girls0             (3+7|12) inch
+
+shoesize_men(n) units=[1;inch]   shoe_men0 + n shoesize_delta ; \
+                                (shoesize_men+(-shoe_men0))/shoesize_delta
+shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
+                                (shoesize_women+(-shoe_women0))/shoesize_delta
+shoesize_boys(n) units=[1;inch]  shoe_boys0 + n shoesize_delta ; \
+                                (shoesize_boys+(-shoe_boys0))/shoesize_delta
+shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
+                                (shoesize_girls+(-shoe_girls0))/shoesize_delta
+
+# European shoe size.  According to
+#      http://www.shoeline.com/footnotes/shoeterm.shtml
+# shoe sizes in Europe are measured with Paris points which simply measure
+# the length of the shoe.
+
+europeshoesize          2|3 cm
+
+#
+# USA slang units
+#
+
+buck                    US$
+fin                     5 US$
+sawbuck                 10 US$
+usgrand                 1000 US$
+greenback               US$
+key                     kg           # usually of marijuana, 60's
+lid                     1 oz         # Another 60's weed unit
+footballfield           usfootballfield
+usfootballfield         100 yards
+canadafootballfield     110 yards    # And 65 yards wide
+marathon                26 miles + 385 yards
+
+#
+# British
+#
+
+# The length measure in the UK was defined by a bronze bar manufactured in
+# 1844.  Various conversions were sanctioned for convenience at different
+# times, which makes conversions before 1963 a confusing matter.  Apparently
+# previous conversions were never explicitly revoked.  Four different
+# conversion factors appear below.  Multiply them times an imperial length
+# units as desired.  The Weights and Measures Act of 1963 switched the UK away
+# from their bronze standard and onto a definition of the yard in terms of the
+# meter.  This happened after an international agreement in 1959 to align the
+# world's measurement systems.
+
+UK                      UKlength_SJJ
+UK-                     UK
+british-                UK
+
+UKlength_B            0.9143992 meter / yard  # Benoit found the yard to be
+                                              #   0.9143992 m at a weights and
+                                              #   measures conference around
+                                              #   1896.   Legally sanctioned
+                                              #   in 1898.
+UKlength_SJJ          0.91439841 meter / yard # In 1922, Seers, Jolly and
+                                              #   Johnson found the yard to be
+                                              #   0.91439841 meters.
+                                              #   Used starting in the 1930's.
+UKlength_K              meter / 39.37079 inch # In 1816 Kater found this ratio
+                                              #   for the meter and inch.  This
+                                              #   value was used as the legal
+                                              #   conversion ratio when the
+                                              #   metric system was legalized
+                                              #   for contract in 1864.
+UKlength_C            meter / 1.09362311 yard # In 1866 Clarke found the meter
+                                              #   to be 1.09362311 yards.  This
+                                              #   conversion was legalized
+                                              #   around 1878.
+brnauticalmile          6080 ft               # Used until 1970 when the UK
+brknot                  brnauticalmile / hr   #   switched to the international
+admiraltymile           brnauticalmile        #   nautical mile.
+admiraltyknot           brknot
+seamile                 6000 ft
+shackle                 15 fathoms            # Adopted 1949 by British navy
+
+# British Imperial weight is mostly the same as US weight.  A few extra
+# units are added here.
+
+clove                   7 lb
+stone                   14 lb
+tod                     28 lb
+brquarterweight         1|4 brhundredweight
+brhundredweight         8 stone
+longhundredweight       brhundredweight
+longton                 20 brhundredweight
+brton                   longton
+
+# British Imperial volume measures
+
+brminim                 1|60 brdram
+brscruple               1|3 brdram
+fluidscruple            brscruple
+brdram                  1|8 brfloz
+brfluidounce            1|20 brpint
+brfloz                  brfluidounce
+brgill                  1|4 brpint
+brpint                  1|2 brquart
+brquart                 1|4 brgallon
+brgallon                4.54609 l      # The British Imperial gallon was
+                                       # defined in 1824 to be the volume of
+                                       # water which weighed 10 pounds at 62
+                                       # deg F with a pressure of 30 inHg.
+                                       # It was also defined as 277.274 in^3,
+                                       # Which is slightly in error.  In
+                                       # 1963 it was defined to be the volume
+                                       # occupied by 10 pounds of distilled
+                                       # water of density 0.998859 g/ml weighed
+                                       # in air of density 0.001217 g/ml
+                                       # against weights of density 8.136 g/ml.
+                                       # This gives a value of approximately
+                                       # 4.5459645 liters, but the old liter
+                                       # was in force at this time.  In 1976
+                                       # the definition was changed to exactly
+                                       # 4.54609 liters using the new
+                                       # definition of the liter (1 dm^3).
+brbarrel                36 brgallon    # Used for beer
+brbushel                8 brgallon
+brheapedbushel          1.278 brbushel
+brquarter               8 brbushel
+brchaldron              36 brbushel
+
+# Obscure British volume measures.  These units are generally traditional
+# measures whose definitions have fluctuated over the years.  Often they
+# depended on the quantity being measured.  They are given here in terms of
+# British Imperial measures.  For example, the puncheon may have historically
+# been defined relative to the wine gallon or beer gallon or ale gallon
+# rather than the British Imperial gallon.
+
+bag                     4 brbushel
+bucket                  4 brgallon
+kilderkin               2 brfirkin
+last                    40 brbushel
+noggin                  brgill
+pottle                  0.5 brgallon
+pin                     4.5 brgallon
+puncheon                72 brgallon
+seam                    8 brbushel
+coomb                   4 brbushel
+boll                    6 brbushel
+firlot                  1|4 boll
+brfirkin                9 brgallon     # Used for ale and beer
+cran                    37.5 brgallon  # measures herring, about 750 fish
+brwinehogshead          52.5 brgallon  # This value is approximately equal
+brhogshead              brwinehogshead #   to the old wine hogshead of 63
+                                       #   wine gallons.  This adjustment
+                                       #   is listed in the OED and in
+                                       #   "The Weights and Measures of
+                                       #   England" by R. D. Connor
+brbeerhogshead          54 brgallon
+brbeerbutt              2 brbeerhogshead
+registerton             100 ft^3  # Used for internal capacity of ships
+shippington             40 ft^3   # Used for ship's cargo freight or timber
+brshippington           42 ft^3   #
+freightton            shippington # Both register ton and shipping ton derive
+                                  # from the "tun cask" of wine.
+displacementton         35 ft^3   # Approximate volume of a longton weight of
+                                  # sea water.  Measures water displaced by
+                                  # ships.
+waterton                224 brgallon
+strike                  70.5 l    # 16th century unit, sometimes
+                                  #   defined as .5, 2, or 4 bushels
+                                  #   depending on the location.  It
+                                  #   probably doesn't make a lot of
+                                  #   sense to define in terms of imperial
+                                  #   bushels.  Zupko gives a value of
+                                  #   2 Winchester grain bushels or about
+                                  #   70.5 liters.
+amber                   4 brbushel# Used for dry and liquid capacity [18]
+
+# British volume measures with "imperial"
+
+imperialminim           brminim
+imperialscruple         brscruple
+imperialdram            brdram
+imperialfluidounce      brfluidounce
+imperialfloz            brfloz
+imperialgill            brgill
+imperialpint            brpint
+imperialquart           brquart
+imperialgallon          brgallon
+imperialbarrel          brbarrel
+imperialbushel          brbushel
+imperialheapedbushel    brheapedbushel
+imperialquarter         brquarter
+imperialchaldron        brchaldron
+imperialwinehogshead    brwinehogshead
+imperialhogshead        brhogshead
+imperialbeerhogshead    brbeerhogshead
+imperialbeerbutt        brbeerbutt
+imperialfirkin          brfirkin
+
+# obscure British lengths
+
+barleycorn              1|3 UKinch   # Given in Realm of Measure as the
+                                     # difference between successive shoe sizes
+nail                    1|16 UKyard  # Originally the width of the thumbnail,
+                                     #   or 1|16 ft.  This took on the general
+                                     #   meaning of 1|16 and settled on the
+                                     #   nail of a yard or 1|16 yards as its
+                                     #   final value.  [12]
+UKpole                  16.5 UKft    # This was 15 Saxon feet, the Saxon
+rope                    20 UKft      #   foot (aka northern foot) being longer
+englishell              45 UKinch
+flemishell              27 UKinch
+ell                     englishell   # supposed to be measure from elbow to
+                                     #   fingertips
+span                    9 UKinch     # supposed to be distance from thumb
+                                     #   to pinky with full hand extension
+goad                    4.5 UKft     # used for cloth, possibly named after the
+                                     #   stick used for prodding animals.
+
+# misc obscure British units
+
+hide                    120 acre  # English unit of land area dating to the 7th
+                                  #   century, originally the amount of land
+                                  #   that a single plowman could cultivate,
+                                  #   which varied from 60-180 acres regionally.
+                                  #   Standardized at Normon conquest.
+virgate                 1|4 hide
+nook                    1|2 virgate
+rood                    furlong rod  # Area of a strip a rod by a furlong
+englishcarat            troyounce/151.5 # Originally intended to be 4 grain
+                                        #   but this value ended up being
+                                        #   used in the London diamond market
+mancus                  2 oz
+mast                    2.5 lb
+nailkeg                 100 lbs
+basebox                 31360 in^2      # Used in metal plating
+
+# alternate spellings
+
+gramme                  gram
+litre                   liter
+dioptre                 diopter
+sulphur                 sulfur
+
+#
+# Units derived the human body (may not be very accurate)
+#
+
+geometricpace           5 ft   # distance between points where the same
+                               # foot hits the ground
+pace                    2.5 ft # distance between points where alternate
+                               # feet touch the ground
+USmilitarypace          30 in  # United States official military pace
+USdoubletimepace        36 in  # United States official doubletime pace
+fingerbreadth           7|8 in # The finger is defined as either the width
+fingerlength            4.5 in #   or length of the finger
+finger                  fingerbreadth
+palmwidth               hand   # The palm is a unit defined as either the width
+palmlength              8 in   #   or the length of the hand
+hand                    4 inch # width of hand
+shaftment               6 inch # Distance from tip of outstretched thumb to the
+                               #   opposite side of the palm of the hand.  The
+                               #   ending -ment is from the old English word
+                               #   for hand. [18]
+smoot              5 ft + 7 in # Created as part of an MIT fraternity prank.
+                               #   In 1958 Oliver Smoot was used to measure
+                               #   the length of the Harvard Bridge, which was
+                               #   marked off in Smoot lengths.  These
+                               #   markings have been maintained on the bridge
+                               #   since then and repainted by subsequent
+                               #   incoming fraternity members.  During a
+                               #   bridge renovation the new sidewalk was
+                               #   scored every Smoot rather than at the
+                               #   customary 6 ft spacing.
+tomcruise       5 ft + 7.75 in # Height of Tom Cruise
+
+#
+# Cooking measures
+#
+
+# Common abbreviations
+
+tbl                     tablespoon
+tbsp                    tablespoon
+tblsp                   tablespoon
+Tb                      tablespoon
+tsp                     teaspoon
+saltspoon               1|4 tsp
+
+# US measures
+
+uscup                   8 usfloz
+ustablespoon            1|16 uscup
+usteaspoon              1|3 ustablespoon
+ustbl                   ustablespoon
+ustbsp                  ustablespoon
+ustblsp                 ustablespoon
+ustsp                   usteaspoon
+metriccup               250 ml
+stickbutter             1|4 lb            # Butter in the USA is sold in one
+                                          # pound packages that contain four
+                                          # individually wrapped pieces.  The
+                                          # pieces are marked into tablespoons,
+                                          # making it possible to measure out
+                                          # butter by volume by slicing the
+                                          # butter.
+
+legalcup                240 ml            # The cup used on nutrition labeling
+legaltablespoon         1|16 legalcup
+legaltbsp               legaltablespoon
+
+# Scoop size.  Ice cream scoops in the US are marked with numbers
+# indicating the number of scoops required to fill a US quart.
+
+scoop(n)  units=[1;cup] domain=[4,100] range=[0.04,1] \
+           32 usfloz / n ; 32 usfloz / scoop
+
+
+# US can sizes.
+
+number1can              10 usfloz
+number2can              19 usfloz
+number2.5can            3.5 uscups
+number3can              4 uscups
+number5can              7 uscups
+number10can             105 usfloz
+
+# British measures
+
+brcup                   1|2 brpint
+brteacup                1|3 brpint
+brtablespoon            15 ml             # Also 5|8 brfloz, approx 17.7 ml
+brteaspoon              1|3 brtablespoon  # Also 1|4 brtablespoon
+brdessertspoon          2 brteaspoon
+dessertspoon            brdessertspoon
+dsp                     dessertspoon
+brtsp                   brteaspoon
+brtbl                   brtablespoon
+brtbsp                  brtablespoon
+brtblsp                 brtablespoon
+
+# Australian
+
+australiatablespoon     20 ml
+austbl                  australiatablespoon
+austbsp                 australiatablespoon
+austblsp                australiatablespoon
+australiateaspoon       1|4 australiatablespoon
+austsp                  australiateaspoon
+
+# Italian
+
+etto                    100 g          # Used for buying items like meat and
+etti                    etto           #   cheese.
+
+# Chinese
+
+catty                   0.5 kg
+oldcatty                4|3 lbs        # Before metric conversion.
+tael                    1|16 oldcatty  # Should the tael be defined both ways?
+mace                    0.1 tael
+oldpicul                100 oldcatty
+picul                   100 catty      # Chinese usage
+
+# Indian
+
+seer                    14400 grain    # British Colonial standard
+ser                     seer
+maund                   40 seer
+pakistanseer            1 kg
+pakistanmaund           40 pakistanseer
+chittak                 1|16 seer
+tola                    1|5 chittak
+ollock                  1|4 liter      # Is this right?
+
+# Japanese
+
+japancup                200 ml
+
+# densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
+# so you can convert '2 cups sugar' to grams, for example, or in the other
+# direction grams could be converted to 'cup flour_scooped'.
+
+butter                  8 oz/uscup
+butter_clarified        6.8 oz/uscup
+cocoa_butter            9 oz/uscup
+shortening              6.75 oz/uscup   # vegetable shortening
+oil                     7.5 oz/uscup
+cakeflour_sifted        3.5 oz/uscup    # The density of flour depends on the
+cakeflour_spooned       4 oz/uscup      # measuring method.  "Scooped",  or
+cakeflour_scooped       4.5 oz/uscup    # "dip and sweep" refers to dipping a
+flour_sifted            4 oz/uscup      # measure into a bin, and then sweeping
+flour_spooned           4.25 oz/uscup   # the excess off the top.  "Spooned"
+flour_scooped           5 oz/uscup      # means to lightly spoon into a measure
+breadflour_sifted       4.25 oz/uscup   # and then sweep the top.  Sifted means
+breadflour_spooned      4.5 oz/uscup    # sifting the flour directly into a
+breadflour_scooped      5.5 oz/uscup    # measure and then sweeping the top.
+cornstarch              120 grams/uscup
+dutchcocoa_sifted       75 g/uscup      # These are for Dutch processed cocoa
+dutchcocoa_spooned      92 g/uscup
+dutchcocoa_scooped      95 g/uscup
+cocoa_sifted            75 g/uscup      # These are for nonalkalized cocoa
+cocoa_spooned           82 g/uscup
+cocoa_scooped           95 g/uscup
+heavycream              232 g/uscup
+milk                    242 g/uscup
+sourcream               242 g/uscup
+molasses                11.25 oz/uscup
+cornsyrup               11.5 oz/uscup
+honey                   11.75 oz/uscup
+sugar                   200 g/uscup
+powdered_sugar          4 oz/uscup
+brownsugar_light        217 g/uscup     # packed
+brownsugar_dark         239 g/uscup
+
+baking_powder           4.6 grams / ustsp
+salt                    6 g / ustsp
+koshersalt              2.8 g / ustsp   # Diamond Crystal kosher salt
+koshersalt_morton       4.8 g / ustsp   # Morton kosher salt
+                                        # Values are from the nutrition info
+                                        # on the packages
+
+
+# Egg weights and volumes for a USA large egg
+
+egg                     50 grams        # without shell
+eggwhite                30 grams
+eggyolk                 18.6 grams
+eggvolume               3 ustablespoons + 1|2 ustsp
+eggwhitevolume          2 ustablespoons
+eggyolkvolume           3.5 ustsp
+
+# Alcohol density
+
+ethanoldensity          0.7893 g/cm^3   # From CRC Handbook, 91st Edition
+alcoholdensity          ethanoldensity
+
+#
+# Density measures.  Density has traditionally been measured on a variety of
+# bizarre nonlinear scales.
+#
+
+# Density of a sugar syrup is frequently measured in candy making procedures.
+# In the USA the boiling point of the syrup is measured.  Some recipes instead
+# specify the density using degrees Baume.  Conversion between degrees Baume
+# and the boiling point measure has proved elusive.  This table appeared in one
+# text, and provides a fragmentary relationship to the concentration.
+#
+# temp(C)  conc (%)
+#   100      30
+#   101      40
+#   102      50
+#   103      60
+#   106      70
+#   112      80
+#   123      90
+#   140      95
+#   151      97
+#   160      98.2
+#   166      99.5
+#   171      99.6
+#
+# The best source identified to date came from "Boiling point elevation of
+# technical sugarcane solutions and its use in automatic pan boiling" by
+# Michael Saska.  International Sugar Journal, 2002, 104, 1247, pp 500-507.
+#
+# But I'm using equation (3) which is credited to Starzak and Peacock,
+# "Water activity coefficient in aqueous solutions of sucrose--A comprehensive
+# data analysis.  Zuckerindustrie, 122, 380-387.  (I couldn't find this
+# document.)
+#
+# Note that the range of validity is uncertain, but answers are in agreement
+# with the above table all the way to 99.6.
+#
+# The original equation has a parameter for the boiling point of water, which
+# of course varies with altitude.  It also includes various other model
+# parameters.  The input is the molar concentration of sucrose in the solution,
+# (moles sucrose) / (total moles).
+#
+# Bsp 3797.06 degC
+# Csp 226.28 degC
+# QQ -17638 J/mol
+# asp -1.0038
+# bsp -0.24653
+# tbw 100 degC     # boiling point of water
+# sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \
+#           /(tbw+stdtemp)) /  (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp)
+#
+# To convert mass concentration (brix) to molar concentration
+#
+# sc(x)  (x / 342.3) / (( x/342.3) + (100-x)/18.02); \
+#        100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1)
+#
+# Here is a simplified version of this equation where the temperature of boiling
+# water has been fixed at 100 degrees Celsius and the argument is now the
+# concentration (brix).
+#
+# sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \
+#                   / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K
+#
+#
+# The formula is not invertible, so to implement it in units we unfortunately
+# must turn it into a table.
+
+# This table gives the boiling point elevation as a function of the sugar syrup
+# concentration expressed as a percentage.
+
+sugar_conc_bpe[K] \
+ 0 0.0000   5 0.0788  10 0.1690  15 0.2729  20 0.3936  25 0.5351  \
+30 0.7027  35 0.9036  40 1.1475  42 1.2599  44 1.3825  46 1.5165  \
+48 1.6634  50 1.8249  52 2.0031  54 2.2005  56 2.4200  58 2.6651  \
+60 2.9400  61 3.0902  62 3.2499  63 3.4198  64 3.6010  65 3.7944  \
+66 4.0012  67 4.2227  68 4.4603  69 4.7156  70 4.9905  71 5.2870  \
+72 5.6075  73 5.9546  74 6.3316  75 6.7417  76 7.1892  77 7.6786  \
+78.0  8.2155  79.0  8.8061  80.0  9.4578  80.5  9.8092  81.0 10.1793  \
+81.5 10.5693  82.0 10.9807  82.5 11.4152  83.0 11.8743  83.5 12.3601  \
+84.0 12.8744  84.5 13.4197  85.0 13.9982  85.5 14.6128  86.0 15.2663  \
+86.5 15.9620  87.0 16.7033  87.5 17.4943  88.0 18.3391  88.5 19.2424  \
+89.0 20.2092  89.5 21.2452  90.0 22.3564  90.5 23.5493  91.0 24.8309  \
+91.5 26.2086  92.0 27.6903  92.5 29.2839  93.0 30.9972  93.5 32.8374  \
+94.0 34.8104  94.5 36.9195  95.0 39.1636  95.5 41.5348  96.0 44.0142  \
+96.5 46.5668  97.0 49.1350  97.5 51.6347  98.0 53.9681  98.1 54.4091  \
+98.2 54.8423  98.3 55.2692  98.4 55.6928  98.5 56.1174  98.6 56.5497  \
+98.7 56.9999  98.8 57.4828  98.9 58.0206  99.0 58.6455  99.1 59.4062  \
+99.2 60.3763  99.3 61.6706  99.4 63.4751  99.5 66.1062  99.6 70.1448  \
+99.7 76.7867
+
+# Using the brix table we can use this to produce a mapping from boiling point
+# to density which makes all of the units interconvertible.  Because the brix
+# table stops at 95 this approach works up to a boiling point elevation of 39 K
+# or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy
+# making.  The "hard crack" stage continues up to 310 F.
+
+# Boiling point elevation
+sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \
+               brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe))
+# Absolute boiling point (produces an absolute temperature)
+sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \
+                                         range=[0.99717,1.5144619] \
+                        brix(~sugar_conc_bpe(T-tempC(100))) ;\
+                        sugar_conc_bpe(~brix(sugar_bp))+tempC(100)
+
+# In practice dealing with the absolute temperature is annoying because it is
+# not possible to convert to a nested function, so you're stuck retyping the
+# absolute temperature in Kelvins to convert to celsius or Fahrenheit.  To
+# prevent this we supply definitions that build in the temperature conversion
+# and produce results in the Fahrenheit and Celsius scales.  So using these
+# measures, to convert 46 degrees Baume to a Fahrenheit boiling point:
+#
+#      You have: baume(45)
+#      You want: sugar_bpF
+#              239.05647
+#
+sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\
+                        brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\
+                        ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100))
+sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\
+                        brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\
+                        ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100))
+
+# Degrees Baume is used in European recipes to specify the density of a sugar
+# syrup.  An entirely different definition is used for densities below
+# 1 g/cm^3.  An arbitrary constant appears in the definition.  This value is
+# equal to 145 in the US, but was according to [], the old scale used in
+# Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
+
+baumeconst 145      # US value
+baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
+                          (baumeconst/(baumeconst+-d)) g/cm^3 ; \
+                          (baume+((-g)/cm^3)) baumeconst / baume
+
+# It's not clear if this value was ever used with negative degrees.
+twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
+                             (1 + 0.005 x) g / cm^3 ; \
+                             200 (twaddell / (g/cm^3) +- 1)
+
+# The degree quevenne is a unit for measuring the density of milk.
+# Similarly it's unclear if negative values were allowed here.
+quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
+                             (1 + 0.001 x) g / cm^3 ; \
+                             1000 (quevenne / (g/cm^3) +- 1)
+
+# Degrees brix measures sugar concentration by weigh as a percentage, so a
+# solution that is 3 degrees brix is 3% sugar by weight.  This unit was named
+# after Adolf Brix who invented a hydrometer that read this percentage
+# directly.  This data is from Table 114 of NIST Circular 440, "Polarimetry,
+# Saccharimetry and the Sugars".  It gives apparent specific gravity at 20
+# degrees Celsius of various sugar concentrations.  As rendered below this
+# data is converted to apparent density at 20 degrees Celsius using the
+# density figure for water given in the same NIST reference.  They use the
+# word "apparent" to refer to measurements being made in air with brass
+# weights rather than vacuum.
+
+brix[0.99717g/cm^3]\
+    0 1.00000  1 1.00390  2 1.00780  3 1.01173  4 1.01569  5 1.01968 \
+    6 1.02369  7 1.02773  8 1.03180  9 1.03590 10 1.04003 11 1.04418 \
+   12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \
+   18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \
+   24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \
+   30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \
+   36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \
+   42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \
+   48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \
+   54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \
+   60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \
+   66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \
+   72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \
+   78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \
+   84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \
+   90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876
+
+# Density measure invented by the American Petroleum Institute.  Lighter
+# petroleum products are more valuable, and they get a higher API degree.
+#
+# The intervals of range and domain should be open rather than closed.
+#
+apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
+                              141.5 g/cm^3 / (x+131.5) ; \
+                              141.5 (g/cm^3) / apidegree + (-131.5)
+#
+# Average densities of various woods (dried)
+# Data from The Wood Database https://www.wood-database.com
+#
+
+# North American Hardwoods
+
+wood_cherry             35 lb/ft^3
+wood_redoak             44 lb/ft^3
+wood_whiteoak           47 lb/ft^3
+wood_blackwalnut        38 lb/ft^3
+wood_walnut             wood_blackwalnut
+wood_birch              43 lb/ft^3
+wood_hardmaple          44 lb/ft^3
+
+wood_bigleafmaple       34 lb/ft^3
+wood_boxeldermaple      30 lb/ft^3
+wood_redmaple           38 lb/ft^3
+wood_silvermaple        33 lb/ft^3
+wood_stripedmaple       32 lb/ft^3
+wood_softmaple         (wood_bigleafmaple \
+                      + wood_boxeldermaple \
+                      + wood_redmaple \
+                      + wood_silvermaple \
+                      + wood_stripedmaple) / 5
+wood_poplar             29 lb/ft^3
+wood_beech              45 lb/ft^3
+
+# North American Softwoods
+
+wood_jeffreypine        28 lb/ft^3
+wood_ocotepine          44 lb/ft^3
+wood_ponderosapine      28 lb/ft^3
+
+wood_loblollypine       35 lb/ft^3
+wood_longleafpine       41 lb/ft^3
+wood_shortleafpine      35 lb/ft^3
+wood_slashpine          41 lb/ft^3
+wood_yellowpine        (wood_loblollypine \
+                      + wood_longleafpine \
+                      + wood_shortleafpine \
+                      + wood_slashpine) / 4
+wood_redpine            34 lb/ft^3
+
+wood_easternwhitepine   25 lb/ft^3
+wood_westernwhitepine   27 lb/ft^3
+wood_whitepine         (wood_easternwhitepine + wood_westernwhitepine) / 2
+
+wood_douglasfir         32 lb/ft^3
+
+wood_blackspruce        28 lb/ft^3
+wood_engelmannspruce    24 lb/ft^3
+wood_redspruce          27 lb/ft^3
+wood_sitkaspruce        27 lb/ft^3
+wood_whitespruce        27 lb/ft^3
+wood_spruce            (wood_blackspruce \
+                      + wood_engelmannspruce \
+                      + wood_redspruce \
+                      + wood_sitkaspruce \
+                      + wood_whitespruce) / 5
+
+# Other woods 
+
+wood_basswood           26 lb/ft^3
+wood_balsa               9 lb/ft^3
+wood_ebony_gaboon       60 lb/ft^3
+wood_ebony_macassar     70 lb/ft^3
+wood_mahogany           37 lb/ft^3   # True (Honduran) mahogany,
+                                     # Swietenia macrophylla
+wood_teak               41 lb/ft^3   
+wood_rosewood_brazilian 52 lb/ft^3
+wood_rosewood_honduran  64 lb/ft^3
+wood_rosewood_indian    52 lb/ft^3
+wood_cocobolo           69 lb/ft^3          
+wood_bubinga            56 lb/ft^3
+wood_zebrawood          50 lb/ft^3
+wood_koa                38 lb/ft^3
+wood_snakewood          75.7 lb/ft^3
+wood_lignumvitae        78.5 lb/ft^3
+wood_blackwood          79.3 lb/ft^3
+wood_blackironwood      84.5 lb/ft^3 # Krugiodendron ferreum, listed
+                                     #   in database as the heaviest wood
+
+#
+# Modulus of elasticity of selected woods.
+# Data from The Wood Database https://www.wood-database.com
+#
+
+# North American Hardwoods
+
+wood_mod_beech              1.720e6 lbf/in^2
+wood_mod_birchyellow        2.010e6 lbf/in^2
+wood_mod_birch              wood_mod_birchyellow
+wood_mod_cherry             1.490e6 lbf/in^2
+wood_mod_hardmaple          1.830e6 lbf/in^2
+
+wood_mod_bigleafmaple       1.450e6 lbf/in^2
+wood_mod_boxeldermaple      1.050e6 lbf/in^2
+wood_mod_redmaple           1.640e6 lbf/in^2
+wood_mod_silvermaple        1.140e6 lbf/in^2
+wood_mod_softmaple         (wood_mod_bigleafmaple \
+                          + wood_mod_boxeldermaple \
+                          + wood_mod_redmaple \
+                          + wood_mod_silvermaple) / 4
+
+wood_mod_redoak             1.761e6 lbf/in^2
+wood_mod_whiteoak           1.762e6 lbf/in^2
+wood_mod_poplar             1.580e6 lbf/in^2
+wood_mod_blackwalnut        1.680e6 lbf/in^2
+wood_mod_walnut             wood_mod_blackwalnut
+
+# North American Softwoods
+
+wood_mod_jeffreypine        1.240e6 lbf/in^2
+wood_mod_ocotepine          2.209e6 lbf/in^2
+wood_mod_ponderosapine      1.290e6 lbf/in^2
+
+wood_mod_loblollypine       1.790e6 lbf/in^2
+wood_mod_longleafpine       1.980e6 lbf/in^2
+wood_mod_shortleafpine      1.750e6 lbf/in^2
+wood_mod_slashpine          1.980e6 lbf/in^2
+wood_mod_yellowpine        (wood_mod_loblollypine \
+                          + wood_mod_longleafpine \
+                          + wood_mod_shortleafpine \
+                          + wood_mod_slashpine) / 4
+
+wood_mod_redpine            1.630e6 lbf/in^2
+
+wood_mod_easternwhitepine   1.240e6 lbf/in^2
+wood_mod_westernwhitepine   1.460e6 lbf/in^2
+wood_mod_whitepine         (wood_mod_easternwhitepine + \
+                            wood_mod_westernwhitepine) / 2
+
+wood_mod_douglasfir         1.765e6  lbf/in^2
+
+wood_mod_blackspruce        1.523e6 lbf/in^2
+wood_mod_englemannspruce    1.369e6 lbf/in^2
+wood_mod_redspruce          1.560e6 lbf/in^2
+wood_mod_sitkaspruce        1.600e6 lbf/in^2
+wood_mod_whitespruce        1.315e6 lbf/in^2
+wood_mod_spruce            (wood_mod_blackspruce \
+                          + wood_mod_englemannspruce \
+                          + wood_mod_redspruce + wood_mod_sitkaspruce \
+                          + wood_mod_whitespruce) / 5
+
+# Other woods 
+
+wood_mod_balsa              0.538e6 lbf/in^2
+wood_mod_basswood           1.460e6 lbf/in^2
+wood_mod_blackwood          2.603e6 lbf/in^2  # African, Dalbergia melanoxylon
+wood_mod_bubinga            2.670e6 lbf/in^2
+wood_mod_cocobolo           2.712e6 lbf/in^2
+wood_mod_ebony_gaboon       2.449e6 lbf/in^2
+wood_mod_ebony_macassar     2.515e6 lbf/in^2
+wood_mod_blackironwood      2.966e6 lbf/in^2  # Krugiodendron ferreum
+wood_mod_koa                1.503e6 lbf/in^2
+wood_mod_lignumvitae        2.043e6 lbf/in^2
+wood_mod_mahogany           1.458e6 lbf/in^2  # True (Honduran) mahogany,
+                                              # Swietenia macrophylla
+wood_mod_rosewood_brazilian 2.020e6 lbf/in^2
+wood_mod_rosewood_honduran  3.190e6 lbf/in^2
+wood_mod_rosewood_indian    1.668e6 lbf/in^2
+wood_mod_snakewood          3.364e6 lbf/in^2
+wood_mod_teak               1.781e6 lbf/in^2
+wood_mod_zebrawood          2.374e6 lbf/in^2
+
+#
+# Area of countries and other regions.  This is the "total area" which
+# includes land and water areas within international boundaries and
+# coastlines.  Data from January, 2019.  
+#
+# except as noted, sources are
+# https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area
+# US Central Intelligence Agency: The World Factbook
+# https://www.cia.gov/the-world-factbook/
+
+area_russia              17098246 km^2
+area_antarctica          14000000 km^2
+# area_canada is covered below as sum of province and territory areas
+area_china                9596961 km^2
+# area_unitedstates is covered below as sum of state areas
+# includes only the 50 states and District of Columbia
+area_us                   area_unitedstates
+area_brazil               8515767 km^2
+area_australia            7692024 km^2
+# area_europeanunion is covered below as sum of member areas
+area_india                3287263 km^2
+area_argentina            2780400 km^2
+area_kazakhstan           2724900 km^2
+area_algeria              2381741 km^2
+area_drcongo              2344858 km^2
+area_greenland            2166086 km^2
+area_saudiarabia          2149690 km^2
+area_mexico               1964375 km^2
+area_indonesia            1910931 km^2
+area_sudan                1861484 km^2
+area_libya                1759540 km^2
+area_iran                 1648195 km^2
+area_mongolia             1564110 km^2
+area_peru                 1285216 km^2
+area_chad                 1284000 km^2
+area_niger                1267000 km^2
+area_angola               1246700 km^2
+area_mali                 1240192 km^2
+area_southafrica          1221037 km^2
+area_colombia             1141748 km^2
+area_ethiopia             1104300 km^2
+area_bolivia              1098581 km^2
+area_mauritania           1030700 km^2
+area_egypt                1002450 km^2
+area_tanzania              945087 km^2
+area_nigeria               923768 km^2
+area_venezuela             916445 km^2
+area_pakistan              881912 km^2
+area_namibia               825615 km^2
+area_mozambique            801590 km^2
+area_turkey                783562 km^2
+area_chile                 756102 km^2
+area_zambia                752612 km^2
+area_myanmar               676578 km^2
+area_burma                area_myanmar
+area_afghanistan           652230 km^2
+area_southsudan            644329 km^2
+area_france                640679 km^2
+area_somalia               637657 km^2
+area_centralafrica         622984 km^2
+area_ukraine               603500 km^2
+area_crimea                 27000 km^2  # occupied by Russia; included in
+                                        # (Encyclopedia Britannica)
+area_madagascar            587041 km^2
+area_botswana              581730 km^2
+area_kenya                 580367 km^2
+area_yemen                 527968 km^2
+area_thailand              513120 km^2
+area_spain                 505992 km^2
+area_turkmenistan          488100 km^2
+area_cameroon              475422 km^2
+area_papuanewguinea        462840 km^2
+area_sweden                450295 km^2
+area_uzbekistan            447400 km^2
+area_morocco               446550 km^2
+area_iraq                  438317 km^2
+area_paraguay              406752 km^2
+area_zimbabwe              390757 km^2
+area_japan                 377973 km^2
+area_germany               357114 km^2
+area_congorepublic         342000 km^2
+area_finland               338424 km^2
+area_vietnam               331212 km^2
+area_malaysia              330803 km^2
+area_norway                323802 km^2
+area_ivorycoast            322463 km^2
+area_poland                312696 km^2
+area_oman                  309500 km^2
+area_italy                 301339 km^2
+area_philippines           300000 km^2
+area_ecuador               276841 km^2
+area_burkinafaso           274222 km^2
+area_newzealand            270467 km^2
+area_gabon                 267668 km^2
+area_westernsahara         266000 km^2
+area_guinea                245857 km^2
+# area_unitedkingdom is covered below
+area_uganda                241550 km^2
+area_ghana                 238533 km^2
+area_romania               238397 km^2
+area_laos                  236800 km^2
+area_guyana                214969 km^2
+area_belarus               207600 km^2
+area_kyrgyzstan            199951 km^2
+area_senegal               196722 km^2
+area_syria                 185180 km^2
+area_golanheights            1150 km^2  # occupied by Israel; included in 
+                                        # Syria (Encyclopedia Britannica)
+area_cambodia              181035 km^2
+area_uruguay               176215 km^2
+area_somaliland            176120 km^2
+area_suriname              163820 km^2
+area_tunisia               163610 km^2
+area_bangladesh            147570 km^2
+area_nepal                 147181 km^2
+area_tajikistan            143100 km^2
+area_greece                131990 km^2
+area_nicaragua             130373 km^2
+area_northkorea            120540 km^2
+area_malawi                118484 km^2
+area_eritrea               117600 km^2
+area_benin                 114763 km^2
+area_honduras              112492 km^2
+area_liberia               111369 km^2
+area_bulgaria              110879 km^2
+area_cuba                  109884 km^2
+area_guatemala             108889 km^2
+area_iceland               103000 km^2
+area_southkorea            100210 km^2
+area_hungary                93028 km^2
+area_portugal               92090 km^2
+area_jordan                 89342 km^2
+area_serbia                 88361 km^2
+area_azerbaijan             86600 km^2
+area_austria                83871 km^2
+area_uae                    83600 km^2
+area_czechia                78865 km^2
+area_czechrepublic         area_czechia
+area_panama                 75417 km^2
+area_sierraleone            71740 km^2
+area_ireland                70273 km^2
+area_georgia                69700 km^2
+area_srilanka               65610 km^2
+area_lithuania              65300 km^2
+area_latvia                 64559 km^2
+area_togo                   56785 km^2
+area_croatia                56594 km^2
+area_bosnia                 51209 km^2
+area_costarica              51100 km^2
+area_slovakia               49037 km^2
+area_dominicanrepublic      48671 km^2
+area_estonia                45227 km^2
+area_denmark                43094 km^2
+area_netherlands            41850 km^2
+area_switzerland            41284 km^2
+area_bhutan                 38394 km^2
+area_taiwan                 36193 km^2
+area_guineabissau           36125 km^2
+area_moldova                33846 km^2
+area_belgium                30528 km^2
+area_lesotho                30355 km^2
+area_armenia                29743 km^2
+area_solomonislands         28896 km^2
+area_albania                28748 km^2
+area_equitorialguinea       28051 km^2
+area_burundi                27834 km^2
+area_haiti                  27750 km^2
+area_rwanda                 26338 km^2
+area_northmacedonia         25713 km^2
+area_djibouti               23200 km^2
+area_belize                 22966 km^2
+area_elsalvador             21041 km^2
+area_israel                 20770 km^2
+area_slovenia               20273 km^2
+area_fiji                   18272 km^2
+area_kuwait                 17818 km^2
+area_eswatini               17364 km^2
+area_easttimor              14919 km^2
+area_bahamas                13943 km^2
+area_montenegro             13812 km^2
+area_vanatu                 12189 km^2
+area_qatar                  11586 km^2
+area_gambia                 11295 km^2
+area_jamaica                10991 km^2
+area_kosovo                 10887 km^2
+area_lebanon                10452 km^2
+area_cyprus                  9251 km^2
+area_puertorico              9104 km^2  # United States territory; not included
+                                        #   in United States area
+area_westbank                5860 km^2  # (CIA World Factbook)
+area_hongkong                2755 km^2
+area_luxembourg              2586 km^2
+area_singapore                716 km^2
+area_gazastrip                360 km^2  # (CIA World Factbook)
+area_malta                    316 km^2  # smallest EU country
+area_liechtenstein            160 km^2
+area_monaco                     2.02 km^2
+area_vaticancity                0.44 km^2
+
+# Members as of 1 Feb 2020
+area_europeanunion        area_austria + area_belgium + area_bulgaria \
+                        + area_croatia + area_cyprus + area_czechia + area_denmark \
+                        + area_estonia + area_finland + area_france + area_germany \
+                        + area_greece + area_hungary + area_ireland + area_italy \
+                        + area_latvia + area_lithuania + area_luxembourg \
+                        + area_malta + area_netherlands + area_poland \
+                        + area_portugal + area_romania + area_slovakia \
+                        + area_slovenia + area_spain + area_sweden
+area_eu                   area_europeanunion
+
+#
+# Areas of the individual US states
+#
+# https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area
+#
+# United States Summary: 2010, Population and Housing Unit Counts, Table 18, p. 41
+# Issued September 2012
+
+area_alaska               1723336.8 km^2
+area_texas                 695661.6 km^2
+area_california            423967.4 km^2
+area_montana               380831.1 km^2
+area_newmexico             314917.4 km^2
+area_arizona               295233.5 km^2
+area_nevada                286379.7 km^2
+area_colorado              269601.4 km^2
+area_oregon                254799.2 km^2
+area_wyoming               253334.5 km^2
+area_michigan              250486.8 km^2
+area_minnesota             225162.8 km^2
+area_utah                  219881.9 km^2
+area_idaho                 216442.6 km^2
+area_kansas                213100.0 km^2
+area_nebraska              200329.9 km^2
+area_southdakota           199728.7 km^2
+area_washington            184660.8 km^2
+area_northdakota           183107.8 km^2
+area_oklahoma              181037.2 km^2
+area_missouri              180540.3 km^2
+area_florida               170311.7 km^2
+area_wisconsin             169634.8 km^2
+area_georgia_us            153910.4 km^2
+area_illinois              149995.4 km^2
+area_iowa                  145745.9 km^2
+area_newyork               141296.7 km^2
+area_northcarolina         139391.0 km^2
+area_arkansas              137731.8 km^2
+area_alabama               135767.4 km^2
+area_louisiana             135658.7 km^2
+area_mississippi           125437.7 km^2
+area_pennsylvania          119280.2 km^2
+area_ohio                  116097.7 km^2
+area_virginia              110786.6 km^2
+area_tennessee             109153.1 km^2
+area_kentucky              104655.7 km^2
+area_indiana                94326.2 km^2
+area_maine                  91633.1 km^2
+area_southcarolina          82932.7 km^2
+area_westvirginia           62755.5 km^2
+area_maryland               32131.2 km^2
+area_hawaii                 28313.0 km^2
+area_massachusetts          27335.7 km^2
+area_vermont                24906.3 km^2
+area_newhampshire           24214.2 km^2
+area_newjersey              22591.4 km^2
+area_connecticut            14357.4 km^2
+area_delaware                6445.8 km^2
+area_rhodeisland             4001.2 km^2
+area_districtofcolumbia       177.0 km^2
+
+area_unitedstates          area_alabama + area_alaska + area_arizona \
+                         + area_arkansas + area_california + area_colorado \
+                         + area_connecticut + area_delaware \
+                         + area_districtofcolumbia + area_florida \
+                         + area_georgia_us + area_hawaii + area_idaho \
+                         + area_illinois + area_indiana + area_iowa \
+                         + area_kansas + area_kentucky + area_louisiana \
+                         + area_maine + area_maryland + area_massachusetts \
+                         + area_michigan + area_minnesota + area_mississippi \
+                         + area_missouri + area_montana + area_nebraska \
+                         + area_nevada + area_newhampshire + area_newjersey \
+                         + area_newmexico + area_newyork + area_northcarolina \
+                         + area_northdakota + area_ohio + area_oklahoma \
+                         + area_oregon + area_pennsylvania + area_rhodeisland \
+                         + area_southcarolina + area_southdakota \
+                         + area_tennessee + area_texas + area_utah \
+                         + area_vermont + area_virginia + area_washington \
+                         + area_westvirginia + area_wisconsin + area_wyoming
+
+# Total area of Canadian province and territories
+#
+# Statistics Canada, "Land and freshwater area, by province and territory",
+# 2016-10-07:
+#
+# https://www150.statcan.gc.ca/n1/pub/11-402-x/2012000/chap/geo/tbl/tbl06-eng.htm
+
+area_ontario                    1076395 km^2    # confederated 1867-Jul-01
+area_quebec                     1542056 km^2    # confederated 1867-Jul-01
+area_novascotia                 55284 km^2      # confederated 1867-Jul-01
+area_newbrunswick               72908 km^2      # confederated 1867-Jul-01
+area_canada_original            area_ontario + area_quebec + area_novascotia \
+                                             + area_newbrunswick
+area_manitoba                   647797 km^2     # confederated 1870-Jul-15
+area_britishcolumbia            944735 km^2     # confederated 1871-Jul-20
+area_princeedwardisland         5660 km^2       # confederated 1873-Jul-01
+area_canada_additional          area_manitoba + area_britishcolumbia \
+                                              + area_princeedwardisland
+area_alberta                    661848 km^2     # confederated 1905-Sep-01
+area_saskatchewan               651036 km^2     # confederated 1905-Sep-01
+area_newfoundlandandlabrador    405212 km^2     # confederated 1949-Mar-31
+area_canada_recent              area_alberta + area_saskatchewan \
+                                             + area_newfoundlandandlabrador
+area_canada_provinces           area_canada_original + area_canada_additional \
+                                                     + area_canada_recent
+area_northwestterritories       1346106 km^2    # NT confederated 1870-Jul-15
+area_yukon                      482443 km^2     # YT confederated 1898-Jun-13
+area_nunavut                    2093190 km^2    # NU confederated 1999-Apr-01
+area_canada_territories         area_northwestterritories + area_yukon \
+                                              + area_nunavut
+area_canada                     area_canada_provinces + area_canada_territories
+
+# area-uk-countries.units - UK country (/province) total areas
+# https://en.wikipedia.org/wiki/Countries_of_the_United_Kingdom#Statistics
+# GB is official UK country code for some purposes but internally is a Kingdom
+#
+# areas from A Beginners Guide to UK Geography 2019 v1.0, Office for National Statistics
+# England: country; 0927-Jul-12 united; 1603-Mar-24 union of crowns
+area_england            132947.76 km^2
+#
+# Wales: 1282 conquered; 1535 union; principality until 2011
+area_wales              21224.48 km^2
+#
+# England and Wales: nation; 1535 union
+area_englandwales       area_england + area_wales
+#
+# Scotland: country; ~900 united; 1603-Mar-24 union of crowns
+area_scotland           80226.36 km^2
+#
+# Great Britain: kingdom; excludes NI;
+# 1707 Treaty and Acts of Union: union of parliaments
+area_greatbritain       area_england + area_wales + area_scotland
+area_gb                 area_greatbritain
+#
+# Northern Ireland: province; Ireland: 1177 Henry II lordship;
+# 1542 Henry VIII kingdom; 1652 Cromwell commonwealth;
+# 1691 William III kingdom; 1800 Acts of Union: UK of GB & Ireland;
+# 1921 Irish Free State independent of UK
+area_northernireland    14133.38 km^2
+#
+# United Kingdom of GB & NI: 1800 Acts of Union: UK of GB & Ireland;
+# 1921 Irish Free State independent of UK
+area_unitedkingdom      area_greatbritain + area_northernireland
+area_uk                 area_unitedkingdom
+
+#
+# Units derived from imperial system
+#
+
+ouncedal                oz ft / s^2     # force which accelerates an ounce
+                                        #    at 1 ft/s^2
+poundal                 lb ft / s^2     # same thing for a pound
+tondal                  longton ft / s^2    # and for a ton
+pdl                     poundal
+osi                     ounce force / inch^2   # used in aviation
+psi                     pound force / inch^2
+psia                    psi             # absolute pressure
+                                        #   Note that gauge pressure can be given
+                                        #   using the gaugepressure() and
+                                        #   psig() nonlinear unit definitions
+tsi                     ton force / inch^2
+reyn                    psi sec
+slug                    lbf s^2 / ft
+slugf                   slug force
+slinch                  lbf s^2 / inch  # Mass unit derived from inch second
+slinchf                 slinch force    #   pound-force system.  Used in space
+                                        #   applications where in/sec^2 was a
+                                        #   natural acceleration measure.
+geepound                slug
+lbf                     lb force
+tonf                    ton force
+lbm                     lb
+kip                     1000 lbf     # from kilopound
+ksi                     kip / in^2
+mil                     0.001 inch
+thou                    0.001 inch
+tenth                   0.0001 inch  # one tenth of one thousandth of an inch
+millionth               1e-6 inch    # one millionth of an inch
+circularinch            1|4 pi in^2  # area of a one-inch diameter circle
+circleinch              circularinch #    A circle with diameter d inches has
+                                     #    an area of d^2 circularinches
+cylinderinch         circleinch inch # Cylinder h inch tall, d inches diameter
+                                     #    has volume d^2 h cylinder inches
+circularmil             1|4 pi mil^2 # area of one-mil diameter circle
+cmil                    circularmil
+cental                  100 pound
+centner                 cental
+
+# Shotgun gauge measures the inside diameter of the barrel by counting
+# the number of spherical lead balls you can make to fit that barrel
+# using a pound of lead.  Equivalently, this means that an n gauge gun
+# has a bore diameter that fits a ball of lead that weighs 1|n pounds
+ 
+shotgungauge(ga)        units=[1;m] domain=(0,] range=(0,] \
+                        2 ~spherevol(1 pound / ga leaddensity) ; \
+                        1 pound / leaddensity spherevol(shotgungauge/2)
+shotgunga()             shotgungauge
+caliber                 0.01 inch    # for measuring bullets
+
+duty                    ft lbf
+celo                    ft / s^2
+jerk                    ft / s^3
+australiapoint          0.01 inch    # The "point" is used to measure rainfall
+                                     #   in Australia
+sabin                   ft^2         # Measure of sound absorption equal to the
+                                     #   absorbing power of one square foot of
+                                     #   a perfectly absorbing material.  The
+                                     #   sound absorptivity of an object is the
+                                     #   area times a dimensionless
+                                     #   absorptivity coefficient.
+standardgauge          4 ft + 8.5 in # Standard width between railroad track
+flag                   5 ft^2        # Construction term referring to sidewalk.
+rollwallpaper          30 ft^2       # Area of roll of wall paper
+fillpower              in^3 / ounce  # Density of down at standard pressure.
+                                     #   The best down has 750-800 fillpower.
+pinlength              1|16 inch     # A #17 pin is 17/16 in long in the USA.
+buttonline             1|40 inch     # The line was used in 19th century USA
+                                     #   to measure width of buttons.
+beespace               1|4 inch      # Bees will fill any space that is smaller
+                                     #   than the bee space and leave open
+                                     #   spaces that are larger.  The size of
+                                     #   the space varies with species.
+diamond                8|5 ft        # Marking on US tape measures that is
+                                     #   useful to carpenters who wish to place
+                                     #   five studs in an 8 ft distance.  Note
+                                     #   that the numbers appear in red every
+                                     #   16 inches as well, giving six
+                                     #   divisions in 8 feet.
+retmaunit              1.75 in       # Height of rack mountable equipment.
+U                      retmaunit     #   Equipment should be 1|32 inch narrower
+RU                     U             #   than its U measurement indicates to
+                                     #   allow for clearance, so 4U=(6+31|32)in
+                                     #   RETMA stands for the former name of
+                                     #   the standardizing organization, Radio
+                                     #   Electronics Television Manufacturers
+                                     #   Association.  This organization is now
+                                     #   called the Electronic Industries
+                                     #   Alliance (EIA) and the rack standard
+                                     #   is specified in EIA RS-310-D.
+count                  per pound     # For measuring the size of shrimp
+flightlevel            100 ft        # Flight levels are used to ensure safe
+FL                     flightlevel   #   vertical separation between aircraft
+                                     #   despite variations in local air
+                                     #   pressure.  Flight levels define
+                                     #   altitudes based on a standard air
+                                     #   pressure so that altimeter calibration
+                                     #   is not needed.  This means that
+                                     #   aircraft at separated flight levels
+                                     #   are guaranteed to be separated.
+                                     #   Hence the definition of 100 feet is
+                                     #   a nominal, not true, measure.
+                                     #   Customarily written with no space in
+                                     #   the form FL290, which will not work in
+                                     #   units.  But note "FL 290" will work.  
+
+#
+# Other units of work, energy, power, etc
+#
+
+# Calorie: approximate energy to raise a gram of water one degree celsius
+
+calorie                 cal_th       # Default is the thermochemical calorie
+cal                     calorie
+calorie_th              4.184 J      # Thermochemical calorie, defined in 1930
+thermcalorie            calorie_th   #   by Frederick Rossini as 4.1833 J to 
+cal_th                  calorie_th   #   avoid difficulties associated with the 
+                                     #   uncertainty in the heat capacity of 
+                                     #   water.  In 1948 the value of the joule 
+                                     #   was changed, so the thermochemical
+                                     #   calorie was redefined to 4.184 J.
+                                     #   This kept the energy measured by this
+                                     #   unit the same. 
+calorie_IT              4.1868 J     # International (Steam) Table calorie,
+cal_IT                  calorie_IT   #   defined in 1929 as watt-hour/860 or
+                                     #   equivalently 180|43 joules.  At this
+                                     #   time the international joule had a
+                                     #   different value than the modern joule,
+                                     #   and the values were different in the
+                                     #   USA and in Europe.  In 1956 at the
+                                     #   Fifth International Conference on
+                                     #   Properties of Steam the exact
+                                     #   definition given here was adopted. 
+calorie_15              4.18580 J    # Energy to go from 14.5 to 15.5 degC
+cal_15                  calorie_15
+calorie_fifteen         cal_15
+calorie_20              4.18190 J    # Energy to go from 19.5 to 20.5 degC
+cal_20                  calorie_20
+calorie_twenty          calorie_20
+calorie_4               4.204 J      # Energy to go from 3.5 to 4.5 degC
+cal_4                   calorie_4
+calorie_four            calorie_4
+cal_mean                4.19002 J    # 1|100 energy to go from 0 to 100 degC
+Calorie                 kilocalorie  # the food Calorie
+thermie              1e6 cal_15      # Heat required to raise the
+                                     # temperature of a tonne of
+                                     # water from 14.5 to 15.5 degC.
+
+# btu definitions: energy to raise a pound of water 1 degF
+
+btu                     btu_IT       # International Table BTU is the default
+britishthermalunit      btu
+btu_IT                  cal_IT lb degF / gram K
+btu_th                  cal_th lb degF / gram K
+btu_mean                cal_mean lb degF / gram K
+btu_15                  cal_15 lb degF / gram K
+btu_ISO                 1055.06 J    # Exact, rounded ISO definition based
+                                     #    on the IT calorie
+quad                    quadrillion btu
+
+ECtherm                 1e5 btu_ISO    # Exact definition
+UStherm                 1.054804e8 J   # Exact definition
+therm                   UStherm
+
+# Water latent heat from [23]
+
+water_fusion_heat       6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
+water_vaporization_heat 2256.4 J/g  # At saturation, 100 deg C, 101.42 kPa
+
+# Specific heat capacities of various substances
+#
+# SPECFIC_HEAT          ENERGY / MASS / TEMPERATURE_DIFFERENCE
+# SPECFIC_HEAT_CAPACITY ENERGY / MASS / TEMPERATURE_DIFFERENCE
+
+specificheat_water      calorie / g K
+water_specificheat      specificheat_water
+     # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+specificheat_aluminum   0.91 J/g K
+specificheat_antimony   0.21 J/g K
+specificheat_barium     0.20 J/g K
+specificheat_beryllium  1.83 J/g K
+specificheat_bismuth    0.13 J/g K
+specificheat_cadmium    0.23 J/g K
+specificheat_cesium     0.24 J/g K
+specificheat_chromium   0.46 J/g K
+specificheat_cobalt     0.42 J/g K
+specificheat_copper     0.39 J/g K
+specificheat_gallium    0.37 J/g K
+specificheat_germanium  0.32 J/g K
+specificheat_gold       0.13 J/g K
+specificheat_hafnium    0.14 J/g K
+specificheat_indium     0.24 J/g K
+specificheat_iridium    0.13 J/g K
+specificheat_iron       0.45 J/g K
+specificheat_lanthanum  0.195 J/g K
+specificheat_lead       0.13 J/g K
+specificheat_lithium    3.57 J/g K
+specificheat_lutetium   0.15 J/g K
+specificheat_magnesium  1.05 J/g K
+specificheat_manganese  0.48 J/g K
+specificheat_mercury    0.14 J/g K
+specificheat_molybdenum 0.25 J/g K
+specificheat_nickel     0.44 J/g K
+specificheat_osmium     0.13 J/g K
+specificheat_palladium  0.24 J/g K
+specificheat_platinum   0.13 J/g K
+specificheat_plutonum   0.13 J/g K
+specificheat_potassium  0.75 J/g K
+specificheat_rhenium    0.14 J/g K
+specificheat_rhodium    0.24 J/g K
+specificheat_rubidium   0.36 J/g K
+specificheat_ruthenium  0.24 J/g K
+specificheat_scandium   0.57  J/g K
+specificheat_selenium   0.32 J/g K
+specificheat_silicon    0.71 J/g K
+specificheat_silver     0.23 J/g K
+specificheat_sodium     1.21 J/g K
+specificheat_strontium  0.30 J/g K
+specificheat_tantalum   0.14 J/g K
+specificheat_thallium   0.13 J/g K
+specificheat_thorium    0.13 J/g K
+specificheat_tin        0.21 J/g K
+specificheat_titanium   0.54 J/g K
+specificheat_tungsten   0.13 J/g K
+specificheat_uranium    0.12 J/g K
+specificheat_vanadium   0.39 J/g K
+specificheat_yttrium    0.30 J/g K
+specificheat_zinc       0.39 J/g K
+specificheat_zirconium  0.27 J/g K
+specificheat_ethanol    2.3  J/g K
+specificheat_ammonia    4.6 J/g K
+specificheat_freon      0.91 J/g K   # R-12 at 0 degrees Fahrenheit
+specificheat_gasoline   2.22 J/g K
+specificheat_iodine     2.15 J/g K
+specificheat_oliveoil   1.97 J/g K
+
+#  en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
+specificheat_hydrogen   14.3 J/g K
+specificheat_helium     5.1932 J/g K
+specificheat_argon      0.5203 J/g K
+specificheat_tissue     3.5 J/g K
+specificheat_diamond    0.5091 J/g K
+specificheat_granite    0.79 J/g K
+specificheat_graphite   0.71 J/g K
+specificheat_ice        2.11 J/g K
+specificheat_asphalt    0.92 J/g K
+specificheat_brick      0.84 J/g K
+specificheat_concrete   0.88 J/g K
+specificheat_glass_silica 0.84 J/g K
+specificheat_glass_flint  0.503 J/g K
+specificheat_glass_pyrex  0.753 J/g K
+specificheat_gypsum     1.09 J/g K
+specificheat_marble     0.88 J/g K
+specificheat_sand       0.835 J/g K
+specificheat_soil       0.835 J/g K
+specificheat_wood       1.7 J/g K
+
+specificheat_sucrose    1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
+
+
+# Energy densities of various fuels
+#
+# Most of these fuels have varying compositions or qualities and hence their
+# actual energy densities vary.  These numbers are hence only approximate.
+#
+# E1. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm
+# E2. https://web.archive.org/web/20100825042309/http://www.ior.com.au/ecflist.html
+
+tonoil                  1e10 cal_IT    # Ton oil equivalent.  A conventional
+                                       # value for the energy released by
+toe                     tonoil         # burning one metric ton of oil. [18,E1]
+                                       # Note that energy per mass of petroleum
+                                       # products is fairly constant.
+                                       # Variations in volumetric energy
+                                       # density result from variations in the
+                                       # density (kg/m^3) of different fuels.
+                                       # This definition is given by the
+                                       # IEA/OECD.
+toncoal                 7e9 cal_IT     # Energy in metric ton coal from [18].
+                                       # This is a nominal value which
+                                       # is close to the heat content
+                                       # of coal used in the 1950's
+barreloil               5.8 Mbtu       # Conventional value for barrel of crude
+                                       # oil [E1].  Actual range is 5.6 - 6.3.
+naturalgas_HHV          1027 btu/ft3   # Energy content of natural gas.  HHV
+naturalgas_LHV          930 btu/ft3    # is for Higher Heating Value and
+naturalgas              naturalgas_HHV # includes energy from condensation
+                                       # combustion products.  LHV is for Lower
+                                       # Heating Value and excludes these.
+                                       # American publications typically report
+                                       # HHV whereas European ones report LHV.
+charcoal                30 GJ/tonne
+woodenergy_dry          20 GJ/tonne    # HHV, a cord weights about a tonne
+woodenergy_airdry       15 GJ/tonne    # 20% moisture content
+coal_bituminous         27 GJ / tonne
+coal_lignite            15 GJ / tonne
+coal_US                 22 GJ / uston  # Average for US coal (short ton), 1995
+ethanol_HHV         84000 btu/usgallon
+ethanol_LHV         75700 btu/usgallon
+diesel             130500 btu/usgallon
+gasoline_LHV       115000 btu/usgallon
+gasoline_HHV       125000 btu/usgallon
+gasoline                gasoline_HHV
+heating                 37.3 MJ/liter
+fueloil                 39.7 MJ/liter  # low sulphur
+propane                 93.3 MJ/m^3
+butane                  124 MJ/m^3
+
+# The US EPA defines a "miles per gallon equivalent" for alternative
+# energy vehicles:
+
+mpg_e          miles / gallon gasoline_LHV
+MPGe           mpg_e
+
+# These values give total energy from uranium fission.  Actual efficiency
+# of nuclear power plants is around 30%-40%.  Note also that some reactors
+# use enriched uranium around 3% U-235.  Uranium during processing or use
+# may be in a compound of uranium oxide or uranium hexafluoride, in which
+# case the energy density would be lower depending on how much uranium is
+# in the compound.
+
+uranium_pure     200 MeV avogadro / (235.0439299 g/mol)  # Pure U-235
+uranium_natural         0.7% uranium_pure        # Natural uranium: 0.7% U-235
+
+# Celsius heat unit: energy to raise a pound of water 1 degC
+
+celsiusheatunit         cal lb degC / gram K
+chu                     celsiusheatunit
+
+# "Apparent" average power in an AC circuit, the product of rms voltage
+# and rms current, equal to the true power in watts when voltage and
+# current are in phase.  In a DC circuit, always equal to the true power.
+
+VA                      volt ampere
+
+kWh                     kilowatt hour
+
+# The horsepower is supposedly the power of one horse pulling.   Obviously
+# different people had different horses.
+
+horsepower              550 foot pound force / sec    # Invented by James Watt
+mechanicalhorsepower    horsepower
+hp                      horsepower
+metrichorsepower        75 kilogram force meter / sec # PS=Pferdestaerke in
+electrichorsepower      746 W                         # Germany
+boilerhorsepower        9809.50 W
+waterhorsepower         746.043 W
+brhorsepower            horsepower   # Value corrected Dec, 2019.  Was 745.7 W.
+donkeypower             250 W
+chevalvapeur            metrichorsepower
+
+#
+# Heat Transfer
+#
+# Thermal conductivity, K, measures the rate of heat transfer across
+# a material.  The heat transferred is
+#     Q = K dT A t / L
+# where dT is the temperature difference across the material, A is the
+# cross sectional area, t is the time, and L is the length (thickness).
+# Thermal conductivity is a material property.
+
+THERMAL_CONDUCTIVITY    POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH)
+THERMAL_RESISTIVITY     1/THERMAL_CONDUCTIVITY
+
+# Thermal conductance is the rate at which heat flows across a given
+# object, so the area and thickness have been fixed.  It depends on
+# the size of the object and is hence not a material property.
+
+THERMAL_CONDUCTANCE     POWER / TEMPERATURE_DIFFERENCE
+THERMAL_RESISTANCE      1/THERMAL_CONDUCTANCE
+
+# Thermal admittance is the rate of heat flow per area across an
+# object whose thickness has been fixed.  Its reciprocal, thermal
+# insulation, is used to for measuring the heat transfer per area
+# of sheets of insulation or cloth that are of specified thickness.
+
+THERMAL_ADMITTANCE      THERMAL_CONDUCTIVITY / LENGTH
+THERMAL_INSULANCE       THERMAL_RESISTIVITY LENGTH
+THERMAL_INSULATION      THERMAL_RESISTIVITY LENGTH
+
+Rvalue                  degF ft^2 hr / btu
+Uvalue                  1/Rvalue
+europeanUvalue          watt / m^2 K
+RSI                     degC m^2 / W
+clo                     0.155 degC m^2 / W # Supposed to be the insulance
+                                           # required to keep a resting person
+                                           # comfortable indoors.  The value
+                                           # given is from NIST and the CRC,
+                                           # but [5] gives a slightly different
+                                           # value of 0.875 ft^2 degF hr / btu.
+tog                     0.1 degC m^2 / W   # Also used for clothing.
+
+
+# Thermal Conductivity of a few materials
+
+diamond_natural_thermal_conductivity    2200 W / m K
+diamond_synthetic_thermal_conductivity  3320 W / m K  # 99% pure C12
+silver_thermal_conductivity             406 W / m K
+aluminum_thermal_conductivity           205 W / m K
+copper_thermal_conductivity             385 W / m K
+gold_thermal_conductivity               314 W / m K
+iron_thermal_conductivity               79.5 W / m K
+stainless_304_thermal_conductivity      15.5 W / m K  # average value
+
+# The bel was defined by engineers of Bell Laboratories to describe the
+# reduction in audio level over a length of one mile. It was originally
+# called the transmission unit (TU) but was renamed around 1923 to honor
+# Alexander Graham Bell. The bel proved inconveniently large so the decibel
+# has become more common.  The decibel is dimensionless since it reports a
+# ratio, but it is used in various contexts to report a signal's power
+# relative to some reference level.
+
+bel(x)     units=[1;1] range=(0,) 10^(x);    log(bel)    # Basic bel definition
+decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
+dB()       decibel                                           # Abbreviation
+dBW(x)     units=[1;W] range=(0,) dB(x) W ;  ~dB(dBW/W)      # Reference = 1 W
+dBk(x)     units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW)     # Reference = 1 kW
+dBf(x)     units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW)     # Reference = 1 fW
+dBm(x)     units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW)     # Reference = 1 mW
+dBmW(x)    units=[1;W] range=(0,) dBm(x) ;   ~dBm(dBmW)      # Reference = 1 mW
+dBJ(x)     units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J)        # Energy relative
+                                     # to 1 joule.  Used for power spectral
+                                     # density since W/Hz = J
+
+
+# When used to measure amplitude, voltage, or current the signal is squared
+# because power is proportional to the square of these measures.  The root
+# mean square (RMS) voltage is typically used with these units.
+
+dB_amplitude(x) units=[1;1]  dB(0.5 x) ; ~dB(dB_amplitude^2) 
+dBV(x)  units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
+dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
+dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
+                                   # Reference = 1 microvolt
+
+# Here are dB measurements for current.  Be aware that dbA is also 
+# a unit for frequency weighted sound pressure.  
+dBA(x)  units=[1;A] range=(0,) dB(0.5 x) A;~dB(dBA^2 / A^2) # Reference = 1 A
+dBmA(x) units=[1;A] range=(0,) dB(0.5 x) mA;~dB(dBmA^2/mA^2)# Reference = 1 mA
+dBuA(x) units=[1;A] range=(0,) dB(0.5 x) microA ; ~dB(dBuA^2 / microA^2)
+                                                    # Reference = 1 microamp
+
+# Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
+# Originally defined as dBv but changed to prevent confusion with dBV.
+# The "u" is for unloaded.
+dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
+                              ~dB(dBu^2 / mW 600 ohm)
+dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv)  # Synonym for dBu
+
+# Measurements for sound in air, referenced to the threshold of human hearing
+# Note that sound in other media typically uses 1 micropascal as a reference
+# for sound pressure.  Units dBA, dBB, dBC, refer to different frequency
+# weightings meant to approximate the human ear's response.
+
+# sound pressure level
+dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ;  \
+                                 ~dB(dBSPL^2 / (20 microPa)^2)
+# sound intensity level
+dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
+                                    ~dB(dBSIL / (1e-12 W/m^2))
+# sound power level (The W in SWL is for the reference power, 1 W.)
+dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
+
+# The neper is another similar logarithmic unit.  Note that the neper
+# is defined based on the ratio of amplitudes rather than the power
+# ratio like the decibel.  This means that if the data is power, and
+# you convert to nepers you should take the square root of the data
+# to convert to amplitude.  If you want to convert nepers to a power
+# measurement you need to square the resulting output.  
+
+neper(x)       units=[1;1]  range=(0,)  exp(x);      ln(neper)
+centineper(x)  units=[1;1]  range=(0,)  exp(x/100);  100 ln(centineper)
+Np()           neper
+cNp()          centineper
+Np_power(x)    units=[1;1]  Np(2 x) ; ~Np(Np_power)/2
+
+# Misc other measures
+
+ENTROPY                 ENERGY / TEMPERATURE
+clausius                1e3 cal/K       # A unit of physical entropy
+langley                 thermcalorie/cm^2    # Used in radiation theory
+poncelet                100 kg force m / s
+tonrefrigeration        uston 144 btu / lb day # One ton refrigeration is
+                                        # the rate of heat extraction required
+                                        # turn one ton of water to ice in
+                                        # a day.  Ice is defined to have a
+                                        # latent heat of 144 btu/lb.
+tonref                  tonrefrigeration
+refrigeration           tonref / ton
+frigorie                1000 cal_15     # Used in refrigeration engineering.
+airwatt                 8.5 (ft^3/min) inH2O # Measure of vacuum power as
+                                             # pressure times air flow.
+
+# The unit "tnt" is defined so that you can write "tons tnt".  The
+# question of which ton, exactly, is intended.  The answer is that
+# nobody knows: 
+#
+# Quoting the footnote from page 13 of
+# The Effects of Nuclear Weapons, 3rd ed.
+# https://www.fourmilab.ch/etexts/www/effects/eonw_1.pdf
+# 
+#     The majority of the experimental and theoretical values of the
+#     explosive energy released by TNT range from 900 to 1,100 calories per
+#     gram. At one time, there was some uncertainty as to whether the term
+#     "kiloton" of TNT referred to a short kiloton (2*10^6 pounds), a metric
+#     kiloton (2.205*10^6 pounds), or a long kiloton (2.24*10^6 pounds). In
+#     order to avoid ambiguity, it was agreed that the term "kiloton" would
+#     refer to the release of 10^12 calories of explosive energy. This is
+#     equivalent to 1 short kiloton of TNT if the energy release is 1,102
+#     calories per gram or to 1 long kiloton if the energy is 984 calories
+#     per gram of TNT.
+#
+# It is therefore not well-defined how much energy a "gram of tnt" is,
+# though this term does appear in some references.
+
+tnt                     1e9 cal_th / ton   # Defined exact value
+
+# Nuclear weapon yields 
+
+davycrocket             10 ton tnt         # lightest US tactical nuclear weapon
+hiroshima               15.5 kiloton tnt   # Uranium-235 fission bomb
+nagasaki                21 kiloton tnt     # Plutonium-239 fission bomb
+fatman                  nagasaki
+littleboy               hiroshima
+ivyking                 500 kiloton tnt    # most powerful fission bomb
+castlebravo             15 megaton tnt     # most powerful US test
+tsarbomba               50 megaton tnt     # most powerful test ever: USSR,
+                                           # 30 October 1961
+b53bomb                 9 megaton tnt
+                 # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/
+trinity                 18 kiloton tnt     # July 16, 1945
+gadget                  trinity
+
+#
+# Permeability: The permeability or permeance, n, of a substance determines
+# how fast vapor flows through the substance.  The formula W = n A dP
+# holds where W is the rate of flow (in mass/time), n is the permeability,
+# A is the area of the flow path, and dP is the vapor pressure difference.
+#
+
+perm_0C                 grain / hr ft^2 inHg
+perm_zero               perm_0C
+perm_0                  perm_0C
+perm                    perm_0C
+perm_23C                grain / hr ft^2 in Hg23C
+perm_twentythree        perm_23C
+
+#
+# Counting measures
+#
+
+pair                    2
+brace                   2
+nest                    3     # often used for items like bowls that
+                              #   nest together
+hattrick                3     # Used in sports, especially cricket and ice
+                              #   hockey to report the number of goals.
+dicker                  10
+dozen                   12
+bakersdozen             13
+score                   20
+flock                   40
+timer                   40
+shock                   60
+toncount                100   # Used in sports in the UK
+longhundred             120   # From a germanic counting system
+gross                   144
+greatgross              12 gross
+tithe                   1|10  # From Anglo-Saxon word for tenth
+
+# Paper counting measure
+
+shortquire              24
+quire                   25
+shortream               480
+ream                    500
+perfectream             516
+bundle                  2 reams
+bale                    5 bundles
+
+#
+# Paper measures
+#
+
+# USA paper sizes
+
+lettersize              8.5 inch 11 inch
+legalsize               8.5 inch 14 inch
+ledgersize              11 inch 17 inch
+executivesize           7.25 inch 10.5 inch
+Apaper                  8.5 inch 11 inch
+Bpaper                  11 inch 17 inch
+Cpaper                  17 inch 22 inch
+Dpaper                  22 inch 34 inch
+Epaper                  34 inch 44 inch
+
+# Correspondence envelope sizes.  #10 is the standard business
+# envelope in the USA. 
+
+envelope6_25size        3.5 inch 6 inch
+envelope6_75size        3.625 inch 6.5 inch
+envelope7size           3.75 inch 6.75 inch
+envelope7_75size        3.875 inch 7.5 inch
+envelope8_625size       3.625 inch 8.625 inch
+envelope9size           3.875 inch 8.875 inch
+envelope10size          4.125 inch 9.5 inch
+envelope11size          4.5 inch 10.375 inch
+envelope12size          4.75 inch 11 inch
+envelope14size          5 inch 11.5 inch
+envelope16size          6 inch 12 inch
+
+# Announcement envelope sizes (no relation to metric paper sizes like A4)
+
+envelopeA1size          3.625 inch 5.125 inch  # same as 4bar
+envelopeA2size          4.375 inch 5.75 inch
+envelopeA6size          4.75 inch 6.5 inch
+envelopeA7size          5.25 inch 7.25 inch
+envelopeA8size          5.5 inch 8.125 inch   
+envelopeA9size          5.75 inch 8.75 inch
+envelopeA10size         6 inch 9.5 inch
+
+# Baronial envelopes
+
+envelope4bar            3.625 inch 5.125 inch  # same as A1
+envelope5_5bar          4.375 inch 5.75 inch
+envelope6bar            4.75 inch 6.5 inch
+
+# Coin envelopes
+
+envelope1baby           2.25 inch 3.5 inch     # same as #1 coin
+envelope00coin          1.6875 inch 2.75 inch
+envelope1coin           2.25 inch 3.5 inch
+envelope3coin           2.5 inch 4.25 inch
+envelope4coin           3 inch 4.5 inch
+envelope4_5coin         3 inch 4.875 inch
+envelope5coin           2.875 inch 5.25 inch
+envelope5_5coin         3.125 inch 5.5 inch
+envelope6coin           3.375 inch 6 inch
+envelope7coin           3.5 inch 6.5 inch
+
+# The metric paper sizes are defined so that if a sheet is cut in half
+# along the short direction, the result is two sheets which are
+# similar to the original sheet.  This means that for any metric size,
+# the long side is close to sqrt(2) times the length of the short
+# side.  Each series of sizes is generated by repeated cuts in half,
+# with the values rounded down to the nearest millimeter.
+
+A0paper                 841 mm 1189 mm   # The basic size in the A series
+A1paper                 594 mm  841 mm   # is defined to have an area of
+A2paper                 420 mm  594 mm   # one square meter.
+A3paper                 297 mm  420 mm
+A4paper                 210 mm  297 mm
+A5paper                 148 mm  210 mm
+A6paper                 105 mm  148 mm
+A7paper                  74 mm  105 mm
+A8paper                  52 mm   74 mm
+A9paper                  37 mm   52 mm
+A10paper                 26 mm   37 mm
+
+B0paper                1000 mm 1414 mm   # The basic B size has an area
+B1paper                 707 mm 1000 mm   # of sqrt(2) square meters.
+B2paper                 500 mm  707 mm
+B3paper                 353 mm  500 mm
+B4paper                 250 mm  353 mm
+B5paper                 176 mm  250 mm
+B6paper                 125 mm  176 mm
+B7paper                  88 mm  125 mm
+B8paper                  62 mm   88 mm
+B9paper                  44 mm   62 mm
+B10paper                 31 mm   44 mm
+
+C0paper                 917 mm 1297 mm   # The basic C size has an area
+C1paper                 648 mm  917 mm   # of sqrt(sqrt(2)) square meters.
+C2paper                 458 mm  648 mm
+C3paper                 324 mm  458 mm   # Intended for envelope sizes
+C4paper                 229 mm  324 mm
+C5paper                 162 mm  229 mm
+C6paper                 114 mm  162 mm
+C7paper                  81 mm  114 mm
+C8paper                  57 mm   81 mm
+C9paper                  40 mm   57 mm
+C10paper                 28 mm   40 mm
+
+# gsm (Grams per Square Meter), a sane, metric paper weight measure
+
+gsm                     grams / meter^2
+
+# In the USA, a collection of crazy historical paper measures are used.  Paper
+# is measured as a weight of a ream of that particular type of paper.  This is
+# sometimes called the "substance" or "basis" (as in "substance 20" paper).
+# The standard sheet size or "basis size" varies depending on the type of
+# paper.  As a result, 20 pound bond paper and 50 pound text paper are actually
+# about the same weight.  The different sheet sizes were historically the most
+# convenient for printing or folding in the different applications.  These
+# different basis weights are standards maintained by American Society for
+# Testing Materials (ASTM) and the American Forest and Paper Association
+# (AF&PA).
+
+poundbookpaper          lb / 25 inch 38 inch ream
+lbbook                  poundbookpaper
+poundtextpaper          poundbookpaper
+lbtext                  poundtextpaper
+poundoffsetpaper        poundbookpaper    # For offset printing
+lboffset                poundoffsetpaper
+poundbiblepaper         poundbookpaper    # Designed to be lightweight, thin,
+lbbible                 poundbiblepaper   # strong and opaque.
+poundtagpaper           lb / 24 inch 36 inch ream
+lbtag                   poundtagpaper
+poundbagpaper           poundtagpaper
+lbbag                   poundbagpaper
+poundnewsprintpaper     poundtagpaper
+lbnewsprint             poundnewsprintpaper
+poundposterpaper        poundtagpaper
+lbposter                poundposterpaper
+poundtissuepaper        poundtagpaper
+lbtissue                poundtissuepaper
+poundwrappingpaper      poundtagpaper
+lbwrapping              poundwrappingpaper
+poundwaxingpaper        poundtagpaper
+lbwaxing                poundwaxingpaper
+poundglassinepaper      poundtagpaper
+lbglassine              poundglassinepaper
+poundcoverpaper         lb / 20 inch 26 inch ream
+lbcover                 poundcoverpaper
+poundindexpaper         lb / 25.5 inch 30.5 inch ream
+lbindex                 poundindexpaper
+poundindexbristolpaper  poundindexpaper
+lbindexbristol          poundindexpaper
+poundbondpaper          lb / 17 inch 22 inch ream  # Bond paper is stiff and
+lbbond                  poundbondpaper             # durable for repeated
+poundwritingpaper       poundbondpaper             # filing, and it resists
+lbwriting               poundwritingpaper          # ink penetration.
+poundledgerpaper        poundbondpaper
+lbledger                poundledgerpaper
+poundcopypaper          poundbondpaper
+lbcopy                  poundcopypaper
+poundblottingpaper      lb / 19 inch 24 inch ream
+lbblotting              poundblottingpaper
+poundblankspaper        lb / 22 inch 28 inch ream
+lbblanks                poundblankspaper
+poundpostcardpaper      lb / 22.5 inch 28.5 inch ream
+lbpostcard              poundpostcardpaper
+poundweddingbristol     poundpostcardpaper
+lbweddingbristol        poundweddingbristol
+poundbristolpaper       poundweddingbristol
+lbbristol               poundbristolpaper
+poundboxboard           lb / 1000 ft^2
+lbboxboard              poundboxboard
+poundpaperboard         poundboxboard
+lbpaperboard            poundpaperboard
+
+# When paper is marked in units of M, it means the weight of 1000 sheets of the
+# given size of paper.  To convert this to paper weight, divide by the size of
+# the paper in question.
+
+paperM                  lb / 1000
+
+# In addition paper weight is reported in "caliper" which is simply the
+# thickness of one sheet, typically in inches.  Thickness is also reported in
+# "points" where a point is 1|1000 inch.  These conversions are supplied to
+# convert these units roughly (using an approximate density) into the standard
+# paper weight values.
+
+pointthickness          0.001 in
+paperdensity            0.8 g/cm^3        # approximate--paper densities vary!
+papercaliper            in paperdensity
+paperpoint              pointthickness paperdensity
+
+#
+# Printing
+#
+
+fournierpoint           0.1648 inch / 12  # First definition of the printers
+                                          # point made by Pierre Fournier who
+                                          # defined it in 1737 as 1|12 of a
+                                          # cicero which was 0.1648 inches.
+olddidotpoint           1|72 frenchinch   # Francois Ambroise Didot, one of
+                                          # a family of printers, changed
+                                          # Fournier's definition around 1770
+                                          # to fit to the French units then in
+                                          # use.
+bertholdpoint           1|2660 m          # H. Berthold tried to create a
+                                          # metric version of the didot point
+                                          # in 1878.
+INpoint                 0.4 mm            # This point was created by a
+                                          # group directed by Fermin Didot in
+                                          # 1881 and is associated with the
+                                          # imprimerie nationale.  It doesn't
+                                          # seem to have been used much.
+germandidotpoint        0.376065 mm       # Exact definition appears in DIN
+                                          # 16507, a German standards document
+                                          # of 1954.  Adopted more broadly  in
+                                          # 1966 by ???
+metricpoint             3|8 mm            # Proposed in 1977 by Eurograf
+oldpoint                1|72.27 inch      # The American point was invented
+printerspoint           oldpoint          # by Nelson Hawks in 1879 and
+texpoint                oldpoint          # dominates USA publishing.
+                                          # It was standardized by the American
+                                          # Typefounders Association at the
+                                          # value of 0.013837 inches exactly.
+                                          # Knuth uses the approximation given
+                                          # here (which is very close).  The
+                                          # comp.fonts FAQ claims that this
+                                          # value is supposed to be 1|12 of a
+                                          # pica where 83 picas is equal to 35
+                                          # cm.  But this value differs from
+                                          # the standard.
+texscaledpoint          1|65536 texpoint  # The TeX typesetting system uses
+texsp                   texscaledpoint    # this for all computations.
+computerpoint           1|72 inch         # The American point was rounded
+point                   computerpoint
+computerpica            12 computerpoint  # to an even 1|72 inch by computer
+postscriptpoint         computerpoint     # people at some point.
+pspoint                 postscriptpoint
+twip                    1|20 point        # TWentieth of an Imperial Point
+Q                       1|4 mm            # Used in Japanese phototypesetting
+                                          # Q is for quarter
+frenchprinterspoint     olddidotpoint
+didotpoint              germandidotpoint  # This seems to be the dominant value
+europeanpoint           didotpoint        # for the point used in Europe
+cicero                  12 didotpoint
+
+stick                   2 inches
+
+# Type sizes
+
+excelsior               3 oldpoint
+brilliant               3.5 oldpoint
+diamondtype             4 oldpoint
+pearl                   5 oldpoint
+agate                   5.5 oldpoint  # Originally agate type was 14 lines per
+                                      #   inch, giving a value of 1|14 in.
+ruby                    agate         # British
+nonpareil               6 oldpoint
+mignonette              6.5 oldpoint
+emerald                 mignonette    # British
+minion                  7 oldpoint
+brevier                 8 oldpoint
+bourgeois               9 oldpoint
+longprimer              10 oldpoint
+smallpica               11 oldpoint
+pica                    12 oldpoint
+english                 14 oldpoint
+columbian               16 oldpoint
+greatprimer             18 oldpoint
+paragon                 20 oldpoint
+meridian                44 oldpoint
+canon                   48 oldpoint
+
+# German type sizes
+
+nonplusultra            2 didotpoint
+brillant                3 didotpoint
+diamant                 4 didotpoint
+perl                    5 didotpoint
+nonpareille             6 didotpoint
+kolonel                 7 didotpoint
+petit                   8 didotpoint
+borgis                  9 didotpoint
+korpus                  10 didotpoint
+corpus                  korpus
+garamond                korpus
+mittel                  14 didotpoint
+tertia                  16 didotpoint
+text                    18 didotpoint
+kleine_kanon            32 didotpoint
+kanon                   36 didotpoint
+grobe_kanon             42 didotpoint
+missal                  48 didotpoint
+kleine_sabon            72 didotpoint
+grobe_sabon             84 didotpoint
+
+#
+# Information theory units.  Note that the name "entropy" is used both
+# to measure information and as a physical quantity.
+#
+
+INFORMATION             bit
+
+nat                     (1/ln(2)) bits       # Entropy measured base e
+hartley                 log2(10) bits        # Entropy of a uniformly
+ban                     hartley              #   distributed random variable
+                                             #   over 10 symbols.
+dit                     hartley              # from Decimal digIT
+
+#
+# Computer
+#
+
+bps                     bit/sec              # Sometimes the term "baud" is
+                                             #   incorrectly used to refer to
+                                             #   bits per second.  Baud refers
+                                             #   to symbols per second.  Modern
+                                             #   modems transmit several bits
+                                             #   per symbol.
+byte                    8 bit                # Not all machines had 8 bit
+B                       byte                 #   bytes, but these days most of
+                                             #   them do.  But beware: for
+                                             #   transmission over modems, a
+                                             #   few extra bits are used so
+                                             #   there are actually 10 bits per
+                                             #   byte.
+octet                   8 bits               # The octet is always 8 bits
+nybble                  4 bits               # Half of a byte. Sometimes
+                                             #   equal to different lengths
+                                             #   such as 3 bits.
+nibble                  nybble
+nyp                     2 bits               # Donald Knuth asks in an exercise
+                                             #   for a name for a 2 bit
+                                             #   quantity and gives the "nyp"
+                                             #   as a solution due to Gregor
+                                             #   Purdy.  Not in common use.
+meg                     megabyte             # Some people consider these
+                                             # units along with the kilobyte
+gig                     gigabyte             # to be defined according to
+                                             # powers of 2 with the kilobyte
+                                             # equal to 2^10 bytes, the
+                                             # megabyte equal to 2^20 bytes and
+                                             # the gigabyte equal to 2^30 bytes
+                                             # but these usages are forbidden
+                                             # by SI.  Binary prefixes have
+                                             # been defined by IEC to replace
+                                             # the SI prefixes.  Use them to
+                                             # get the binary units KiB, MiB,
+                                             # GiB, etc.
+jiffy                   0.01 sec     # This is defined in the Jargon File
+jiffies                 jiffy        # (http://www.jargon.org) as being the
+                                     # duration of a clock tick for measuring
+                                     # wall-clock time.  Supposedly the value
+                                     # used to be 1|60 sec or 1|50 sec
+                                     # depending on the frequency of AC power,
+                                     # but then 1|100 sec became more common.
+                                     # On linux systems, this term is used and
+                                     # for the Intel based chips, it does have
+                                     # the value of .01 sec.  The Jargon File
+                                     # also lists two other definitions:
+                                     # millisecond, and the time taken for
+                                     # light to travel one foot.
+cdaudiospeed      44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2
+                                     # samples of sixteen bits each.
+cdromspeed       75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read
+                                     # each second with 2048 bytes per sector.
+                                     # Audio CDs do not have sectors, but
+                                     # people sometimes divide the bit rate by
+                                     # 75 and claim a sector length of 2352.
+                                     # Data CDs have a lower rate due to
+                                     # increased error correction overhead.
+                                     # There is a rarely used mode (mode2) with
+                                     # 2336 bytes per sector that has fewer
+                                     # error correction bits than mode1.
+dvdspeed                 1385 kB/s   # This is the "1x" speed of a DVD using
+                                     # constant linear velocity (CLV) mode.
+                                     # Modern DVDs may vary the linear velocity
+                                     # as they go from the inside to the
+                                     # outside of the disc.
+                       # See http://www.osta.org/technology/dvdqa/dvdqa4.htm
+
+FIT         / 1e9 hour # Failures In Time, number of failures per billion hours
+
+#
+# The IP address space is divided into subnets.  The number of hosts
+# in a subnet depends on the length of the subnet prefix.  This is
+# often written as /N where N is the number of bits in the prefix.
+#
+# https://en.wikipedia.org/wiki/Subnetwork
+#
+# These definitions gives the number of hosts for a subnet whose
+# prefix has the specified length in bits.
+#
+
+ipv4subnetsize(prefix_len) units=[1;1]  domain=[0,32] range=[1,4294967296] \
+                         2^(32-prefix_len) ; 32-log2(ipv4subnetsize)
+ipv4classA               ipv4subnetsize(8)
+ipv4classB               ipv4subnetsize(16)
+ipv4classC               ipv4subnetsize(24)
+
+ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \
+                         range=[1,340282366920938463463374607431768211456] \
+                         2^(128-prefix_len) ; 128-log2(ipv6subnetsize)
+
+#
+# Musical measures.  Musical intervals expressed as ratios.  Multiply
+# two intervals together to get the sum of the interval.  The function
+# musicalcent can be used to convert ratios to cents.
+#
+
+# Perfect intervals
+
+octave                  2
+majorsecond             musicalfifth^2 / octave
+majorthird              5|4
+minorthird              6|5
+musicalfourth           4|3
+musicalfifth            3|2
+majorsixth              musicalfourth majorthird
+minorsixth              musicalfourth minorthird
+majorseventh            musicalfifth majorthird
+minorseventh            musicalfifth minorthird
+
+pythagoreanthird        majorsecond musicalfifth^2 / octave
+syntoniccomma           pythagoreanthird / majorthird
+pythagoreancomma        musicalfifth^12 / octave^7
+
+# Equal tempered definitions
+
+semitone                octave^(1|12)
+musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
+                                      100 log(musicalcent)/log(semitone)
+
+#
+# Musical note lengths.
+#
+
+wholenote               !
+MUSICAL_NOTE_LENGTH     wholenote
+halfnote                1|2 wholenote
+quarternote             1|4 wholenote
+eighthnote              1|8 wholenote
+sixteenthnote           1|16 wholenote
+thirtysecondnote        1|32 wholenote
+sixtyfourthnote         1|64 wholenote
+dotted                  3|2
+doubledotted            7|4
+breve                   doublewholenote
+semibreve               wholenote
+minimnote               halfnote
+crotchet                quarternote
+quaver                  eighthnote
+semiquaver              sixteenthnote
+demisemiquaver          thirtysecondnote
+hemidemisemiquaver      sixtyfourthnote
+semidemisemiquaver      hemidemisemiquaver
+
+#
+# yarn and cloth measures
+#
+
+# yarn linear density
+
+woolyarnrun             1600 yard/pound # 1600 yds of "number 1 yarn" weighs
+                                        # a pound.
+yarncut                 300 yard/pound  # Less common system used in
+                                        # Pennsylvania for wool yarn
+cottonyarncount         840 yard/pound
+linenyarncount          300 yard/pound  # Also used for hemp and ramie
+worstedyarncount        1680 ft/pound
+metricyarncount         meter/gram
+denier                  1|9 tex            # used for silk and rayon
+manchesteryarnnumber    drams/1000 yards   # old system used for silk
+pli                     lb/in
+typp                    1000 yd/lb   # abbreviation for Thousand Yard Per Pound
+asbestoscut             100 yd/lb    # used for glass and asbestos yarn
+
+tex                     gram / km    # rational metric yarn measure, meant
+drex                    0.1 tex      # to be used for any kind of yarn
+poumar                  lb / 1e6 yard
+
+# yarn and cloth length
+
+skeincotton             80*54 inch   # 80 turns of thread on a reel with a
+                                     #  54 in circumference (varies for other
+                                     #  kinds of thread)
+cottonbolt              120 ft       # cloth measurement
+woolbolt                210 ft
+bolt                    cottonbolt
+heer                    600 yards
+cut                     300 yards    # used for wet-spun linen yarn
+lea                     300 yards
+
+sailmakersyard          28.5 in
+sailmakersounce         oz / sailmakersyard 36 inch
+
+silkmomme               momme / 25 yards 1.49 inch  # Traditional silk weight
+silkmm                  silkmomme        # But it is also defined as
+                                         # lb/100 yd 45 inch.  The two
+                                         # definitions are slightly different
+                                         # and neither one seems likely to be
+                                         # the true source definition.
+
+#
+# drug dosage
+#
+
+mcg                     microgram        # Frequently used for vitamins
+iudiptheria             62.8 microgram   # IU is for international unit
+iupenicillin            0.6 microgram
+iuinsulin               41.67 microgram
+drop                    1|20 ml          # The drop was an old "unit" that was
+                                         # replaced by the minim.  But I was
+                                         # told by a pharmacist that in his
+                                         # profession, the conversion of 20
+                                         # drops per ml is actually used.
+bloodunit               450 ml           # For whole blood.  For blood
+                                         # components, a blood unit is the
+                                         # quantity of the component found in a
+                                         # blood unit of whole blood.  The
+                                         # human body contains about 12 blood
+                                         # units of whole blood.
+
+#
+# misc medical measure
+#
+
+frenchcathetersize      1|3 mm           # measure used for the outer diameter
+                                         # of a catheter
+charriere               frenchcathetersize
+
+
+#
+# fixup units for times when prefix handling doesn't do the job
+#
+
+hectare                 hectoare
+megohm                  megaohm
+kilohm                  kiloohm
+microhm                 microohm
+megalerg                megaerg    # 'L' added to make it pronounceable [18].
+
+#
+# Money
+#
+# Note that US$ is the primitive unit so other currencies are
+# generally given in US$.
+#
+
+unitedstatesdollar      US$
+usdollar                US$
+$                       dollar
+mark                    germanymark
+#bolivar                 venezuelabolivar       # Not all databases are 
+#venezuelabolivarfuerte  1e-5 bolivar           #    supplying these
+#bolivarfuerte           1e-5 bolivar           # The currency was revalued 
+#oldbolivar              1|1000 bolivarfuerte   # twice
+peseta                  spainpeseta
+rand                    southafricarand
+escudo                  portugalescudo
+guilder                 netherlandsguilder
+hollandguilder          netherlandsguilder
+peso                    mexicopeso
+yen                     japanyen
+lira                    turkeylira
+rupee                   indiarupee
+drachma                 greecedrachma
+franc                   francefranc
+markka                  finlandmarkka
+britainpound            unitedkingdompound
+greatbritainpound       unitedkingdompound
+unitedkingdompound      ukpound
+poundsterling           britainpound
+yuan                    chinayuan
+
+# Unicode Currency Names
+
+!utf8
+icelandkróna            icelandkrona
+polandzłoty             polandzloty
+tongapa’anga            tongapa'anga
+#venezuelabolívar        venezuelabolivar
+vietnamđồng             vietnamdong
+mongoliatögrög          mongoliatugrik
+sãotomé&príncipedobra   saotome&principedobra
+!endutf8
+
+UKP                     GBP        # Not an ISO code, but looks like one, and
+                                   # sometimes used on usenet.
+
+!include currency.units
+
+# Money on the gold standard, used in the late 19th century and early
+# 20th century.
+
+olddollargold           23.22 grains goldprice  # Used until 1934
+newdollargold           96|7 grains goldprice   # After Jan 31, 1934
+dollargold              newdollargold
+poundgold               113 grains goldprice    # British pound
+
+# Precious metals
+
+goldounce               goldprice troyounce
+silverounce             silverprice troyounce
+platinumounce           platinumprice troyounce
+XAU                     goldounce
+XPT                     platinumounce
+XAG                     silverounce
+
+# Nominal masses of US coins.  Note that dimes, quarters and half dollars
+# have weight proportional to value.  Before 1965 it was $40 / kg.
+
+USpennyweight           2.5 grams         # Since 1982, 48 grains before
+USnickelweight          5 grams
+USdimeweight            US$ 0.10 / (20 US$ / lb)   # Since 1965
+USquarterweight         US$ 0.25 / (20 US$ / lb)   # Since 1965
+UShalfdollarweight      US$ 0.50 / (20 US$ / lb)   # Since 1971
+USdollarweight          8.1 grams         # Weight of Susan B. Anthony and
+                                          #   Sacagawea dollar coins
+
+# British currency
+
+quid                    britainpound        # Slang names
+fiver                   5 quid
+tenner                  10 quid
+monkey                  500 quid
+brgrand                 1000 quid
+bob                     shilling
+
+shilling                1|20 britainpound   # Before decimalisation, there
+oldpence                1|12 shilling       # were 20 shillings to a pound,
+farthing                1|4 oldpence        # each of twelve old pence
+guinea                  21 shilling         # Still used in horse racing
+crown                   5 shilling
+florin                  2 shilling
+groat                   4 oldpence
+tanner                  6 oldpence
+brpenny                 0.01 britainpound
+pence                   brpenny
+tuppence                2 pence
+tuppenny                tuppence
+ha'penny                halfbrpenny
+hapenny                 ha'penny
+oldpenny                oldpence
+oldtuppence             2 oldpence
+oldtuppenny             oldtuppence
+threepence              3 oldpence    # threepence never refers to new money
+threepenny              threepence
+oldthreepence           threepence
+oldthreepenny           threepence
+oldhalfpenny            halfoldpenny
+oldha'penny             oldhalfpenny
+oldhapenny              oldha'penny
+brpony                  25 britainpound
+
+# Canadian currency
+
+loony                   1 canadadollar    # This coin depicts a loon
+toony                   2 canadadollar
+
+# Cryptocurrency
+
+satoshi                 1e-8 bitcoin
+XBT                     bitcoin           # nonstandard code
+
+# Inflation.
+#
+# Currently US inflation as reported by the BLS CPI index is available.
+# The UScpi() table reports the USA consumer price index.  Note that 
+# if you specify a year like 2015, that refers to the CPI reported
+# for December of 2014 (which is released in mid January 2015),
+# so it refers to the point right at the start of the given year. 
+# Months are increments of 1|12 on the year, so the January 2015
+# release will be 2015+1|12 = 2015.08333.  
+
+!include cpi.units
+
+USCPI()            UScpi
+USCPI_now          UScpi_now
+USCPI_lastdate     UScpi_lastdate
+cpi()              UScpi
+CPI()              UScpi
+cpi_now            UScpi_now
+CPI_now            UScpi_now
+cpi_lastdate       UScpi_lastdate
+CPI_lastdate       UScpi_lastdate
+
+# These definitions hide the CPI index and directly convert US dollars
+# from a specified date to current dollars.  You can use this to convert
+# historical dollars to present value or to convert money in the past
+# between two dates.
+
+dollars_in()       USdollars_in
+US$in()            USdollars_in
+$in()              USdollars_in
+
+# This definition gives the dimensionless US inflation factor since the
+# specified date.
+
+inflation_since()  USinflation_since
+
+
+#
+# Units used for measuring volume of wood
+#
+
+cord                    4*4*8 ft^3   # 4 ft by 4 ft by 8 ft bundle of wood
+facecord                1|2 cord
+cordfoot                1|8 cord     # One foot long section of a cord
+cordfeet                cordfoot
+housecord               1|3 cord     # Used to sell firewood for residences,
+                                     #   often confusingly called a "cord"
+boardfoot               ft^2 inch    # Usually 1 inch thick wood
+boardfeet               boardfoot
+fbm                     boardfoot    # feet board measure
+stack                   4 yard^3     # British, used for firewood and coal [18]
+rick                    4 ft 8 ft 16 inches # Stack of firewood, supposedly
+                                     #   sometimes called a face cord, but this
+                                     #   value is equal to 1|3 cord.  Name
+                                     #   comes from an old Norse word for a
+                                     #   stack of wood.
+stere                   m^3
+timberfoot              ft^3         # Used for measuring solid blocks of wood
+standard                120 12 ft 11 in 1.5 in  # This is the St Petersburg or
+                                     #   Pittsburg standard.  Apparently the
+                                     #   term is short for "standard hundred"
+                                     #   which was meant to refer to 100 pieces
+                                     #   of wood (deals).  However, this
+                                     #   particular standard is equal to 120
+                                     #   deals which are 12 ft by 11 in by 1.5
+                                     #   inches (not the standard deal).
+hoppusfoot               (4/pi) ft^3 # Volume calculation suggested in 1736
+hoppusboardfoot      1|12 hoppusfoot #   forestry manual by Edward Hoppus, for
+hoppuston              50 hoppusfoot #   estimating the usable volume of a log.
+                                     #   It results from computing the volume
+                                     #   of a cylindrical log of length, L, and
+                                     #   girth (circumference), G, by V=L(G/4)^2.
+                                     #   The hoppus ton is apparently still in
+                                     #   use for shipments from Southeast Asia.
+
+# In Britain, the deal is apparently any piece of wood over 6 feet long, over
+# 7 wide and 2.5 inches thick.  The OED doesn't give a standard size.  A piece
+# of wood less than 7 inches wide is called a "batten".  This unit is now used
+# exclusively for fir and pine.
+
+deal              12 ft 11 in 2.5 in # The standard North American deal [OED]
+wholedeal        12 ft 11 in 1.25 in # If it's half as thick as the standard
+                                     #   deal it's called a "whole deal"!
+splitdeal         12 ft 11 in 5|8 in # And half again as thick is a split deal.
+
+
+# Used for shellac mixing rate
+
+poundcut            pound / gallon
+lbcut               poundcut
+
+#
+# Gas and Liquid flow units
+#
+
+FLUID_FLOW              VOLUME / TIME
+
+# Some obvious volumetric gas flow units (cu is short for cubic)
+
+cumec                   m^3/s
+cusec                   ft^3/s
+
+# Conventional abbreviations for fluid flow units
+
+gph                     gal/hr
+gpm                     gal/min
+mgd                     megagal/day
+brgph                   brgallon/hr
+brgpm                   brgallon/min
+brmgd                   mega brgallon/day
+usgph                   usgallon/hr
+usgpm                   usgallon/min
+usmgd                   mega usgallon/day
+cfs                     ft^3/s
+cfh                     ft^3/hour
+cfm                     ft^3/min
+lpm                     liter/min
+lfm                     ft/min     # Used to report air flow produced by fans.
+                                   # Multiply by cross sectional area to get a
+                                   # flow in cfm.
+
+pru                     mmHg / (ml/min)  # peripheral resistance unit, used in
+                                         # medicine to assess blood flow in
+                                         # the capillaries.
+
+# Miner's inch:  This is an old historic unit used in the Western  United
+# States.  It is generally defined as the rate of flow through a one square
+# inch hole at a specified depth such as 4 inches.  In the late 19th century,
+# volume of water was sometimes measured in the "24 hour inch".  Values for the
+# miner's inch were fixed by state statues.  (This information is from a web
+# site operated by the Nevada Division of Water Planning:  The Water Words
+# Dictionary at http://water.nv.gov/WaterPlanDictionary.aspx, specifically
+# http://water.nv.gov/programs/planning/dictionary/wwords-M.pdf.  All
+# but minersinchNV are s.v.  Miner's Inch [Western United States])
+
+minersinchAZ            1.5 ft^3/min
+minersinchCA            1.5 ft^3/min
+minersinchMT            1.5 ft^3/min
+minersinchNV            1.5 ft^3/min
+minersinchOR            1.5 ft^3/min
+minersinchID            1.2 ft^3/min
+minersinchKS            1.2 ft^3/min
+minersinchNE            1.2 ft^3/min
+minersinchNM            1.2 ft^3/min
+minersinchND            1.2 ft^3/min
+minersinchSD            1.2 ft^3/min
+minersinchUT            1.2 ft^3/min
+minersinchCO            1 ft^3/sec / 38.4  # 38.4 miner's inches = 1 ft^3/sec
+minersinchBC            1.68 ft^3/min      # British Columbia
+
+# Oceanographic flow
+
+sverdrup                1e6 m^3 / sec   # Used to express flow of ocean
+                                        # currents.  Named after Norwegian
+                                        # oceanographer H. Sverdrup.
+
+# In vacuum science and some other applications, gas flow is measured
+# as the product of volumetric flow and pressure.  This is useful
+# because it makes it easy to compare with the flow at standard
+# pressure (one atmosphere).  It also directly relates to the number
+# of gas molecules per unit time, and hence to the mass flow if the
+# molecular mass is known.
+
+GAS_FLOW                PRESSURE FLUID_FLOW
+
+sccm                    atm cc/min     # 's' is for "standard" to indicate
+sccs                    atm cc/sec     # flow at standard pressure
+scfh                    atm ft^3/hour  #
+scfm                    atm ft^3/min
+slpm                    atm liter/min
+slph                    atm liter/hour
+lusec                   liter micron Hg / s  # Used in vacuum science
+
+# US Standard Atmosphere (1976)
+# Atmospheric temperature and pressure vs. geometric height above sea level
+# This definition covers only the troposphere (the lowest atmospheric
+# layer, up to 11 km), and assumes the layer is polytropic.
+# A polytropic process is one for which PV^k = const, where P is the
+# pressure, V is the volume, and k is the polytropic exponent.  The
+# polytropic index is n = 1 / (k - 1).  As noted in the Wikipedia article
+# https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
+# the definitions of "exponent" and "index."  The functions below assume
+# the following parameters:
+
+# temperature lapse rate, -dT/dz, in troposphere
+
+lapserate       6.5 K/km        # US Std Atm (1976)
+
+# air molecular weight, including constituent mol wt, given
+# in Table 3, p. 3; CH4 (16.04303) and N2O (44.0128) from
+# Table 15, p. 33. Values for molecular weights are slightly
+# different from current values, so the original numerical
+# values are retained.
+
+air_1976        78.084   %    28.0134 \
+              + 20.9476  %    31.9988 \
+              + 9340     ppm  39.948 \
+              +  314     ppm  44.00995 \
+              +   18.18  ppm  20.183 \
+              +    5.24  ppm   4.0026 \
+              +    1.5   ppm  16.04303 \
+              +    1.14  ppm  83.80 \
+              +    0.5   ppm   2.01594 \
+              +    0.27  ppm  44.0128 \
+              +    0.087 ppm 131.30
+
+# from US Standard Atmosphere, 1962, Table I.2.7, p. 9
+
+air_1962        78.084     %  28.0134 \
+              + 20.9476    %  31.9988 \
+              + 9340     ppm  39.948 \
+              +  314     ppm  44.00995 \
+              +  18.18   ppm  20.183 \
+              +   5.24   ppm   4.0026 \
+              +   2      ppm  16.04303 \
+              +   1.14   ppm  83.80 \
+              +   0.5    ppm   2.01594 \
+              +   0.5    ppm  44.0128 \
+              +   0.087  ppm 131.30
+
+# Average molecular weight of air
+#
+# Concentration of greenhouse gases CO2, CH4, and N20 are from
+# https://gml.noaa.gov/ccgg/trends/global.html (accessed 2023-04-10);
+# others are from NASA Earth Fact Sheet
+# https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html (accessed 2023-04-10)
+# Numbers do not add up to exactly 100% due to roundoff and uncertainty.  Water
+# is highly variable, typically makes up about 1%
+
+air_2023        78.08% nitrogen 2 \
+              + 20.95% oxygen 2 \
+              + 9340 ppm argon \
+              +  419 ppm (carbon + oxygen 2) \
+              +   18.18 ppm neon \
+              +    5.24 ppm helium \
+              +    1.92 ppm (carbon + 4 hydrogen) \
+              +    1.14 ppm krypton \
+              +    0.55 ppm hydrogen 2 \
+              +    0.34 ppm (nitrogen 2 + oxygen)
+
+# from NASA Earth Fact Sheet (accessed 28 August 2015)
+# http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
+
+air_2015        78.08% nitrogen 2 \
+              + 20.95% oxygen 2 \
+              + 9340 ppm argon \
+              +  400 ppm (carbon + oxygen 2) \
+              +   18.18 ppm neon \
+              +    5.24 ppm helium \
+              +    1.7  ppm (carbon + 4 hydrogen) \
+              +    1.14 ppm krypton \
+              +    0.55 ppm hydrogen 2
+
+air             air_2023
+
+# universal gas constant
+R_1976          8.31432e3 N m/(kmol K)
+
+# polytropic index n
+polyndx_1976    air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
+
+# If desired, redefine using current values for air mol wt and R
+
+polyndx         polyndx_1976
+# polyndx       air (kg/kmol) gravity/(R lapserate) - 1
+
+# for comparison with various references
+
+polyexpnt       (polyndx + 1) / polyndx
+
+# The model assumes the following reference values:
+# sea-level temperature and pressure
+
+stdatmT0        288.15 K
+stdatmP0        atm
+
+# "effective radius" for relation of geometric to geopotential height,
+# at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
+# relation to actual radius
+
+earthradUSAtm   6356766 m
+
+# Temperature vs. geopotential height h
+# Assumes 15 degC at sea level
+# Based on approx 45 deg latitude
+# Lower limits of domain and upper limits of range are those of the
+# tables in US Standard Atmosphere (NASA 1976)
+
+stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
+    stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
+
+# Temperature vs. geometric height z; based on approx 45 deg latitude
+stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
+    stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
+
+# Pressure vs. geopotential height h
+# Assumes 15 degC and 101325 Pa at sea level
+# Based on approx 45 deg latitude
+# Lower limits of domain and upper limits of range are those of the
+# tables in US Standard Atmosphere (NASA 1976)
+
+stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
+    atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
+    (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
+
+# Pressure vs. geometric height z; based on approx 45 deg latitude
+stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
+   stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
+
+# Geopotential height from geometric height
+# Based on approx 45 deg latitude
+# Lower limits of domain and range are somewhat arbitrary; they
+# correspond to the limits in the US Std Atm tables
+
+geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
+    (earthradUSAtm z) / (earthradUSAtm + z) ; \
+    (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
+
+# The standard value for the sea-level acceleration due to gravity is
+# 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
+# R_eff = 2 g_phi / denom
+# g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
+#   or
+# g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
+# denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
+# There is no inverse function; the standard value applies at a latitude
+# of about 45.543 deg
+
+g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror  \
+    980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
+
+# effective Earth radius for relation of geometric height to
+# geopotential height, as function of latitude (Harrison 1949)
+
+earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
+    m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
+    (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
+
+# References
+# Harrison, L.P. 1949.  Relation Between Geopotential and Geometric
+#   Height.  In Smithsonian Meteorological Tables. List, Robert J., ed.
+#   6th ed., 4th reprint, 1968.  Washington, DC: Smithsonian Institution.
+# NASA.  US National Aeronautics and Space Administration. 1976.
+#   US Standard Atmosphere 1976.  Washington, DC: US Government Printing Office.
+
+# Gauge pressure functions
+#
+# Gauge pressure is measured relative to atmospheric pressure.  In the English
+# system, where pressure is often given in pounds per square inch, gauge
+# pressure is often indicated by 'psig' to distinguish it from absolute
+# pressure, often indicated by 'psia'.  At the standard atmospheric pressure
+# of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
+# psia; an automobile tire inflated to 31 psig has an absolute pressure of
+# 45.696 psia.
+#
+# With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
+# bar)); with psig(), the units are taken as psi, so the example above of tire
+# pressure could be given as psig(31).
+#
+# If the normal elevation is significantly different from sea level, change
+# Patm appropriately, and adjust the lower domain limit on the gaugepressure
+# definition.
+
+Patm    atm
+
+gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
+                x + Patm ; gaugepressure+(-Patm)
+
+psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
+    gaugepressure(x psi) ; ~gaugepressure(psig) / psi
+
+
+# Pressure for underwater diving
+
+seawater             0.1 bar / meter
+msw                  meter seawater
+fsw                  foot seawater
+
+#
+# Wire Gauge
+#
+# This area is a nightmare with huge charts of wire gauge diameters
+# that usually have no clear origin.  There are at least 5 competing wire gauge
+# systems to add to the confusion.  The use of wire gauge is related to the
+# manufacturing method: a metal rod is heated and drawn through a hole.  The
+# size change can't be too big.  To get smaller wires, the process is repeated
+# with a series of smaller holes.  Generally larger gauges mean smaller wires.
+# The gauges often have values such as "00" and "000" which are larger sizes
+# than simply "0" gauge.  In the tables that appear below, these gauges must be
+# specified as negative numbers (e.g. "00" is -1, "000" is -2, etc).
+# Alternatively, you can use the following units:
+#
+
+g00                      (-1)
+g000                     (-2)
+g0000                    (-3)
+g00000                   (-4)
+g000000                  (-5)
+g0000000                 (-6)
+
+# American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
+# important gauge. ASTM B-258 specifies that this gauge is based on geometric
+# interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
+# which is 0.005 inches exactly.  Therefore, the diameter in inches of a wire
+# is given by the formula 1|200 92^((36-g)/39).  Note that 92^(1/39) is close
+# to 2^(1/6), so diameter is approximately halved for every 6 gauges.  For the
+# repeated zero values, use negative numbers in the formula.  The same document
+# also specifies rounding rules which seem to be ignored by makers of tables.
+# Gauges up to 44 are to be specified with up to 4 significant figures, but no
+# closer than 0.0001 inch.  Gauges from 44 to 56 are to be rounded to the
+# nearest 0.00001 inch.
+#
+# In addition to being used to measure wire thickness, this gauge is used to
+# measure the thickness of sheets of aluminum, copper, and most metals other
+# than steel, iron and zinc.
+
+wiregauge(g) units=[1;m] range=(0,) \
+             1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
+awg()        wiregauge
+
+# Next we have the SWG, the Imperial or British Standard Wire Gauge.  This one
+# is piecewise linear.  It was used for aluminum sheets but also shows up for
+# wire used in jewelry.  
+
+brwiregauge[in]  \
+       -6 0.5    \
+       -5 0.464  \
+       -3 0.4    \
+       -2 0.372  \
+        3 0.252  \
+        6 0.192  \
+       10 0.128  \
+       14 0.08   \
+       19 0.04   \
+       23 0.024  \
+       26 0.018  \
+       28 0.0148 \
+       30 0.0124 \
+       39 0.0052 \
+       49 0.0012 \
+       50 0.001
+
+swg()        brwiregauge  
+
+# The following is from the Appendix to ASTM B 258
+#
+#    For example, in U.S. gage, the standard for sheet metal is based on the
+#    weight of the metal, not on the thickness. 16-gage is listed as
+#    approximately .0625 inch thick and 40 ounces per square foot (the original
+#    standard was based on wrought iron at .2778 pounds per cubic inch; steel
+#    has almost entirely superseded wrought iron for sheet use, at .2833 pounds
+#    per cubic inch). Smaller numbers refer to greater thickness. There is no
+#    formula for converting gage to thickness or weight.
+#
+# It's rather unclear from the passage above whether the plate gauge values are
+# therefore wrong if steel is being used.  Reference [15] states that steel is
+# in fact measured using this gauge (under the name Manufacturers' Standard
+# Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
+# But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
+# closer).
+#
+# This gauge was established in 1893 for purposes of taxation.
+
+# Old plate gauge for iron
+
+plategauge[(oz/ft^2)/(480*lb/ft^3)] \
+      -5 300   \
+       1 180   \
+      14  50   \
+      16  40   \
+      17  36   \
+      20  24   \
+      26  12   \
+      31   7   \
+      36   4.5 \
+      38   4
+
+# Manufacturers Standard Gage
+
+stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \
+      -5 300   \
+       1 180   \
+      14  50   \
+      16  40   \
+      17  36   \
+      20  24   \
+      26  12   \
+      31   7   \
+      36   4.5 \
+      38   4
+
+# A special gauge is used for zinc sheet metal.  Notice that larger gauges
+# indicate thicker sheets.
+
+zincgauge[in]    \
+        1 0.002  \
+       10 0.02   \
+       15 0.04   \
+       19 0.06   \
+       23 0.1    \
+       24 0.125  \
+       27 0.5    \
+       28 1
+
+#
+# Imperial drill bit sizes are reported in inches or in a numerical or
+# letter gauge.
+#
+
+drillgauge[in] \
+       1  0.2280 \
+       2  0.2210 \
+       3  0.2130 \
+       4  0.2090 \
+       5  0.2055 \
+       6  0.2040 \
+       7  0.2010 \
+       8  0.1990 \
+       9  0.1960 \
+      10  0.1935 \
+      11  0.1910 \
+      12  0.1890 \
+      13  0.1850 \
+      14  0.1820 \
+      15  0.1800 \
+      16  0.1770 \
+      17  0.1730 \
+      18  0.1695 \
+      19  0.1660 \
+      20  0.1610 \
+      22  0.1570 \
+      23  0.1540 \
+      24  0.1520 \
+      25  0.1495 \
+      26  0.1470 \
+      27  0.1440 \
+      28  0.1405 \
+      29  0.1360 \
+      30  0.1285 \
+      31  0.1200 \
+      32  0.1160 \
+      33  0.1130 \
+      34  0.1110 \
+      35  0.1100 \
+      36  0.1065 \
+      38  0.1015 \
+      39  0.0995 \
+      40  0.0980 \
+      41  0.0960 \
+      42  0.0935 \
+      43  0.0890 \
+      44  0.0860 \
+      45  0.0820 \
+      46  0.0810 \
+      48  0.0760 \
+      51  0.0670 \
+      52  0.0635 \
+      53  0.0595 \
+      54  0.0550 \
+      55  0.0520 \
+      56  0.0465 \
+      57  0.0430 \
+      65  0.0350 \
+      66  0.0330 \
+      68  0.0310 \
+      69  0.0292 \
+      70  0.0280 \
+      71  0.0260 \
+      73  0.0240 \
+      74  0.0225 \
+      75  0.0210 \
+      76  0.0200 \
+      78  0.0160 \
+      79  0.0145 \
+      80  0.0135 \
+      88  0.0095 \
+      104 0.0031 
+
+drillA    0.234 in
+drillB    0.238 in
+drillC    0.242 in
+drillD    0.246 in
+drillE    0.250 in
+drillF    0.257 in
+drillG    0.261 in
+drillH    0.266 in
+drillI    0.272 in
+drillJ    0.277 in
+drillK    0.281 in
+drillL    0.290 in
+drillM    0.295 in
+drillN    0.302 in
+drillO    0.316 in
+drillP    0.323 in
+drillQ    0.332 in
+drillR    0.339 in
+drillS    0.348 in
+drillT    0.358 in
+drillU    0.368 in
+drillV    0.377 in
+drillW    0.386 in
+drillX    0.397 in
+drillY    0.404 in
+drillZ    0.413 in
+
+#
+# Screw sizes
+#
+# In the USA, screw diameters for both wood screws and machine screws
+# are reported using a gauge number.  Metric machine screws are
+# reported as Mxx where xx is the diameter in mm.
+#
+
+screwgauge(g) units=[1;m] range=[0,) \
+              (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
+
+#
+# Abrasive grit size
+#
+# Standards governing abrasive grit sizes are complicated, specifying
+# fractions of particles that are passed or retained by different mesh
+# sizes.  As a result, it is not possible to make precise comparisons
+# of different grit standards.  The tables below allow the
+# determination of rough equivlants by using median particle size.
+#
+# Standards in the USA are determined by the Unified Abrasives
+# Manufacturers' Association (UAMA), which resulted from the merger of
+# several previous organizations.  One of the old organizations was
+# CAMI (Coated Abrasives Manufacturers' Institute).
+#
+# UAMA has a web page with plots showing abrasive particle ranges for
+# various different grits and comparisons between standards.
+#
+# https://uama.org/abrasives-101/
+#
+# Abrasives are grouped into "bonded" abrasives for use with grinding
+# wheels and "coated" abrasives for sandpapers and abrasive films.
+# The industry uses different grit standards for these two
+# categories.
+#
+# Another division is between "macrogrits", grits below 240 and
+# "microgrits", which are above 240.  Standards differ, as do methods
+# for determining particle size.  In the USA, ANSI B74.12 is the
+# standard governing macrogrits.  ANSI B74.10 covers bonded microgrit
+# abrasives, and ANSI B74.18 covers coated microgrit abrasives.  It
+# appears that the coated standard is identical to the bonded standard
+# for grits up through 600 but then diverges significantly.
+#
+# European grit sizes are determined by the Federation of European
+# Producers of Abrasives.  http://www.fepa-abrasives.org
+#
+# They give two standards, the "F" grit for bonded abrasives and the
+# "P" grit for coated abrasives.  This data is taken directly from
+# their web page.
+
+# FEPA P grit for coated abrasives is commonly seen on sandpaper in
+# the USA where the paper will be marked P600, for example.  FEPA P
+# grits are said to be more tightly constrained than comparable ANSI
+# grits so that the particles are more uniform in size and hence give
+# a better finish.
+
+grit_P[micron] \
+        12 1815 \
+        16 1324 \
+        20 1000 \
+        24 764 \
+        30 642 \
+        36 538 \
+        40 425 \
+        50 336 \
+        60 269 \
+        80 201 \
+        100 162 \
+        120 125 \
+        150 100 \
+        180 82 \
+        220 68 \
+        240 58.5 \
+        280 52.2 \
+        320 46.2 \
+        360 40.5 \
+        400 35 \
+        500 30.2 \
+        600 25.8 \
+        800 21.8 \
+        1000 18.3 \
+        1200 15.3 \
+        1500 12.6 \
+        2000 10.3 \
+        2500 8.4
+
+# The F grit is the European standard for bonded abrasives such as
+# grinding wheels
+
+grit_F[micron] \
+        4 4890 \
+        5 4125 \
+        6 3460 \
+        7 2900 \
+        8 2460 \
+        10 2085 \
+        12 1765 \
+        14 1470 \
+        16 1230 \
+        20 1040 \
+        22 885 \
+        24 745 \
+        30 625 \
+        36 525 \
+        40 438 \
+        46 370 \
+        54 310 \
+        60 260 \
+        70 218 \
+        80 185 \
+        90 154 \
+        100 129 \
+        120 109 \
+        150 82 \
+        180 69 \
+        220 58 \
+        230 53 \
+        240 44.5 \
+        280 36.5 \
+        320 29.2 \
+        360 22.8 \
+        400 17.3 \
+        500 12.8 \
+        600 9.3 \
+        800 6.5 \
+        1000 4.5 \
+        1200 3 \
+        1500 2.0 \
+        2000 1.2
+
+# According to the UAMA web page, the ANSI bonded and ANSI coated standards
+# are identical to FEPA F in the macrogrit range (under 240 grit), so these
+# values are taken from the FEPA F table.  The values for 240 and above are
+# from the UAMA web site and represent the average of the "d50" range
+# endpoints listed there.
+
+ansibonded[micron] \
+    4 4890 \
+    5 4125 \
+    6 3460 \
+    7 2900 \
+    8 2460 \
+    10 2085 \
+    12 1765 \
+    14 1470 \
+    16 1230 \
+    20 1040 \
+    22 885 \
+    24 745 \
+    30 625 \
+    36 525 \
+    40 438 \
+    46 370 \
+    54 310 \
+    60 260 \
+    70 218 \
+    80 185 \
+    90 154 \
+    100 129 \
+    120 109 \
+    150 82 \
+    180 69 \
+    220 58 \
+    240 50 \
+    280 39.5 \
+    320 29.5 \
+    360 23 \
+    400 18.25 \
+    500 13.9 \
+    600 10.55 \
+    800 7.65 \
+    1000 5.8 \
+    1200 3.8
+
+grit_ansibonded() ansibonded
+
+# Like the bonded grit, the coated macrogrits below 240 are taken from the
+# FEPA F table.  Data above this is from the UAMA site.  Note that the coated
+# and bonded standards are evidently the same from 240 up to 600 grit, but
+# starting at 800 grit, the coated standard diverges.  The data from UAMA show
+# that 800 grit coated has an average size slightly larger than the average
+# size of 600 grit coated/bonded.  However, the 800 grit has a significantly
+# smaller particle size variation.
+#
+# Because of this non-monotonicity from 600 grit to 800 grit this definition
+# produces a warning about the lack of a unique inverse.
+
+ansicoated[micron] noerror \
+    4 4890 \
+    5 4125 \
+    6 3460 \
+    7 2900 \
+    8 2460 \
+    10 2085 \
+    12 1765 \
+    14 1470 \
+    16 1230 \
+    20 1040 \
+    22 885 \
+    24 745 \
+    30 625 \
+    36 525 \
+    40 438 \
+    46 370 \
+    54 310 \
+    60 260 \
+    70 218 \
+    80 185 \
+    90 154 \
+    100 129 \
+    120 109 \
+    150 82 \
+    180 69 \
+    220 58 \
+    240 50 \
+    280 39.5 \
+    320 29.5 \
+    360 23 \
+    400 18.25 \
+    500 13.9 \
+    600 10.55 \
+    800 11.5 \
+    1000 9.5 \
+    2000 7.2 \
+    2500 5.5 \
+    3000 4 \
+    4000 3 \
+    6000 2 \
+    8000 1.2
+
+grit_ansicoated()  ansicoated
+
+
+#
+# Is this correct?  This is the JIS Japanese standard used on waterstones
+#
+jisgrit[micron] \
+     150 75 \
+     180 63 \
+     220 53 \
+     280 48 \
+     320 40 \
+     360 35 \
+     400 30 \
+     600 20 \
+     700 17 \
+     800 14 \
+     1000 11.5 \
+     1200 9.5 \
+     1500 8 \
+     2000 6.7 \
+     2500 5.5 \
+     3000 4 \
+     4000 3 \
+     6000 2 \
+     8000 1.2
+
+# The "Finishing Scale" marked with an A (e.g. A75).  This information
+# is from the web page of the sand paper manufacturer Klingspor
+# https://www.klingspor.com/ctemplate1.aspx?page=default/html/gritGradingSystems_en-US.html
+#
+# I have no information about what this scale is used for.
+
+grit_A[micron]\
+     16 15.3 \
+     25 21.8 \
+     30 23.6 \
+     35 25.75 \
+     45 35 \
+     60 46.2 \
+     65 53.5 \
+     75 58.5 \
+     90 65 \
+     110 78 \
+     130 93 \
+     160 127 \
+     200 156
+#
+# Grits for DMT brand diamond sharpening stones from
+# https://www.dmtsharp.com/resources/dmt-catalog-product-information.html
+# "DMT Diamond Grits" PDF download
+
+dmtxxcoarse  120 micron    # 120 mesh
+dmtsilver    dmtxxcoarse
+dmtxx        dmtxxcoarse
+dmtxcoarse   60 micron     # 220 mesh
+dmtx         dmtxcoarse
+dmtblack     dmtxcoarse
+dmtcoarse    45 micron     # 325 mesh
+dmtc         dmtcoarse
+dmtblue      dmtcoarse
+dmtfine      25 micron     # 600 mesh
+dmtred       dmtfine
+dmtf         dmtfine
+dmtefine     9 micron      # 1200 mesh
+dmte         dmtefine
+dmtgreen     dmtefine
+dmtceramic   7 micron      # 2200 mesh
+dmtcer       dmtceramic
+dmtwhite     dmtceramic
+dmteefine    3 micron      # 8000 mesh
+dmttan       dmteefine
+dmtee        dmteefine
+
+#
+# The following values come from a page in the Norton Stones catalog,
+# available at their web page, http://www.nortonstones.com.
+#
+
+hardtranslucentarkansas  6 micron     # Natural novaculite (silicon quartz)
+softarkansas             22 micron    #   stones
+
+extrafineindia           22 micron    # India stones are Norton's manufactured
+fineindia                35 micron    #   aluminum oxide product
+mediumindia              53.5 micron
+coarseindia              97 micron
+
+finecrystolon            45 micron    # Crystolon stones are Norton's
+mediumcrystalon          78 micron    #   manufactured silicon carbide product
+coarsecrystalon          127 micron
+
+# The following are not from the Norton catalog
+hardblackarkansas        6 micron
+hardwhitearkansas        11 micron
+washita                  35 micron
+
+#
+# Mesh systems for measuring particle sizes by sifting through a wire
+# mesh or sieve
+#
+
+# The Tyler system and US Sieve system are based on four steps for
+# each factor of 2 change in the size, so each size is 2^1|4 different
+# from the adjacent sizes.  Unfortunately, the mesh numbers are
+# arbitrary, so the sizes cannot be expressed with a functional form.
+# Various references round the values differently.  The mesh numbers
+# are supposed to correspond to the number of holes per inch, but this
+# correspondence is only approximate because it doesn't include the
+# wire size of the mesh.
+
+# The Tyler Mesh system was apparently introduced by the WS Tyler
+# company, but it appears that they no longer use it.  They follow the
+# ASTM E11 standard.
+
+meshtyler[micron] \
+          2.5 8000 \
+          3   6727 \
+          3.5 5657 \
+          4   4757 \
+          5   4000 \
+          6   3364 \
+          7   2828 \
+          8   2378 \
+          9   2000 \
+         10   1682 \
+         12   1414 \
+         14   1189 \
+         16   1000 \
+         20    841 \
+         24    707 \
+         28    595 \
+         32    500 \
+         35    420 \
+         42    354 \
+         48    297 \
+         60    250 \
+         65    210 \
+         80    177 \
+        100    149 \
+        115    125 \
+        150    105 \
+        170     88 \
+        200     74 \
+        250     63 \
+        270     53 \
+        325     44 \
+        400     37 
+
+# US Sieve size, ASTM E11
+#
+# The WS Tyler company prints the list from ASTM E11 in
+# A Calculator for ASTM E11 Standard Sieve Designations
+# https://blog.wstyler.com/particle-analysis/astm-e11-standard-designations
+
+sieve[micron] \
+          3.5   5600 \
+          4     4750 \
+          5     4000 \
+          6     3350 \
+          7     2800 \
+          8     2360 \
+         10     2000 \
+         12     1700 \
+         14     1400 \
+         16     1180 \
+         18     1000 \
+         20      850 \
+         25      710 \
+         30      600 \
+         35      500 \
+         40      425 \
+         45      355 \
+         50      300 \
+         60      250 \
+         70      212 \
+         80      180 \
+        100      150 \
+        120      125 \
+        140      106 \
+        170       90 \
+        200       75 \
+        230       63 \
+        270       53 \
+        325       45 \
+        400       38 \
+        450       32 \
+        500       25 \
+        625       20   # These last two values are not in the standard series
+                       # but were included in the ASTM standard because they
+meshUS()  sieve        # were in common usage.                               
+
+# British Mesh size, BS 410: 1986
+# This system appears to correspond to the Tyler and US system, but
+# with different mesh numbers.
+#
+# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
+# 
+
+meshbritish[micron] \
+          3    5657 \
+          3.5  4757 \
+          4    4000 \
+          5    3364 \
+          6    2828 \
+          7    2378 \
+          8    2000 \
+         10    1682 \
+         12    1414 \
+         14    1189 \
+         16    1000 \
+         18     841 \
+         22     707 \
+         25     595 \
+         30     500 \
+         36     420 \
+         44     354 \
+         52     297 \
+         60     250 \
+         72     210 \
+         85     177 \
+        100     149 \
+        120     125 \
+        150     105 \
+        170      88 \
+        200      74 \
+        240      63 \
+        300      53 \
+        350      44 \
+        400      37  
+
+# French system, AFNOR NFX11-501: 1970
+# The system appears to be based on size doubling every 3 mesh
+# numbers, though the values have been aggressively rounded.
+# It's not clear if the unrounded values would be considered
+# incorrect, so this is given as a table rather than a function.
+# Functional form:
+#    meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron
+#
+# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
+
+meshtamis[micron] \
+        17   40 \
+        18   50 \
+        19   63 \
+        20   80 \
+        21  100 \
+        22  125 \
+        23  160 \
+        24  200 \
+        25  250 \
+        26  315 \
+        27  400 \
+        28  500 \
+        29  630 \
+        30  800 \
+        31 1000 \
+        32 1250 \
+        33 1600 \
+        34 2000 \
+        35 2500 \
+        36 3150 \
+        37 4000 \
+        38 5000 
+
+#
+# Ring size. All ring sizes are given as the circumference of the ring.
+#
+
+# USA ring sizes.  Several slightly different definitions seem to be in
+# circulation.  According to [15], the interior diameter of size n ring in
+# inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5.  The
+# size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
+#
+# However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
+# diameter and list no special case for size 2.  (Or alternatively they are
+# 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.)  One
+# reference claimed that the original system was that each size was 1|10 inch
+# circumference, but that source doesn't have an explanation for the modern
+# system which is somewhat different.
+
+ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
+            (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
+
+# Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
+# specified alphabetically and based on the ring inside diameter in steps of
+# 1|64 inch.  This system was replaced in 1987 by British Standard 6820 which
+# specifies sizes based on circumference.  Each size is 1.25 mm different from
+# the preceding size.  The baseline is size C which is 40 mm circumference.
+# The new sizes are close to the old ones.  Sometimes it's necessary to go
+# beyond size Z to Z+1, Z+2, etc.
+
+sizeAring               37.50 mm
+sizeBring               38.75 mm
+sizeCring               40.00 mm
+sizeDring               41.25 mm
+sizeEring               42.50 mm
+sizeFring               43.75 mm
+sizeGring               45.00 mm
+sizeHring               46.25 mm
+sizeIring               47.50 mm
+sizeJring               48.75 mm
+sizeKring               50.00 mm
+sizeLring               51.25 mm
+sizeMring               52.50 mm
+sizeNring               53.75 mm
+sizeOring               55.00 mm
+sizePring               56.25 mm
+sizeQring               57.50 mm
+sizeRring               58.75 mm
+sizeSring               60.00 mm
+sizeTring               61.25 mm
+sizeUring               62.50 mm
+sizeVring               63.75 mm
+sizeWring               65.00 mm
+sizeXring               66.25 mm
+sizeYring               67.50 mm
+sizeZring               68.75 mm
+
+# Japanese sizes start with size 1 at a 13mm inside diameter and each size is
+# 1|3 mm larger in diameter than the previous one.  They are multiplied by pi
+# to give circumference.
+
+jpringsize(n)  units=[1;mm] domain=[1,) range=[0.040840704,) \
+               (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
+
+# The European ring sizes are the length of the circumference in mm minus 40.
+
+euringsize(n)  units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
+
+#
+# Abbreviations
+#
+
+mph                     mile/hr
+brmpg                   mile/brgallon
+usmpg                   mile/usgallon
+mpg                     mile/gal
+kph                     km/hr
+fL                      footlambert
+fpm                     ft/min
+fps                     ft/s
+rpm                     rev/min
+rps                     rev/sec
+mi                      mile
+smi                     mile
+nmi                     nauticalmile
+mbh                     1e3 btu/hour
+mcm                     1e3 circularmil
+ipy                     inch/year    # used for corrosion rates
+ccf                     100 ft^3     # used for selling water [18]
+Mcf                     1000 ft^3    # not million cubic feet [18]
+kp                      kilopond
+kpm                     kp meter
+Wh                      W hour
+hph                     hp hour
+plf                     lb / foot    # pounds per linear foot
+
+#
+# Compatibility units with Unix version
+#
+
+pa                      Pa
+ev                      eV
+hg                      Hg
+oe                      Oe
+mh                      mH
+rd                      rod
+pf                      pF
+gr                      grain
+nt                      N
+hz                      Hz
+hd                      hogshead
+dry                     drygallon/gallon
+nmile                   nauticalmile
+beV                     GeV
+bev                     beV
+coul                    C
+
+#
+# Radioactivity units
+#
+event !dimensionless
+becquerel    event           /s           # Activity of radioactive source
+Bq                      becquerel    #
+curie                   3.7e10 Bq    # Defined in 1910 as the radioactivity
+Ci                      curie        # emitted by the amount of radon that is
+                                     # in equilibrium with 1 gram of radium.
+rutherford              1e6 Bq       #
+
+RADIATION_DOSE          gray
+gray                    J/kg         # Absorbed dose of radiation
+Gy                      gray         #
+rad                     1e-2 Gy      # From Radiation Absorbed Dose
+rep                     8.38 mGy     # Roentgen Equivalent Physical, the amount
+                                     #   of radiation which , absorbed in the
+                                     #   body, would liberate the same amount
+                                     #   of energy as 1 roentgen of X rays
+                                     #   would, or 97 ergs.
+
+sievert                 J/kg         # Dose equivalent:  dosage that has the
+Sv                      sievert      #   same effect on human tissues as 200
+rem                     1e-2 Sv      #   keV X-rays.  Different types of
+                                     #   radiation are weighted by the
+                                     #   Relative Biological Effectiveness
+                                     #   (RBE).
+                                     #
+                                     #      Radiation type       RBE
+                                     #       X-ray, gamma ray     1
+                                     #       beta rays, > 1 MeV   1
+                                     #       beta rays, < 1 MeV  1.08
+                                     #       neutrons, < 1 MeV   4-5
+                                     #       neutrons, 1-10 MeV   10
+                                     #       protons, 1 MeV      8.5
+                                     #       protons, .1 MeV      10
+                                     #       alpha, 5 MeV         15
+                                     #       alpha, 1 MeV         20
+                                     #
+                                     #   The energies are the kinetic energy
+                                     #   of the particles.  Slower particles
+                                     #   interact more, so they are more
+                                     #   effective ionizers, and hence have
+                                     #   higher RBE values.
+                                     #
+                                     # rem stands for Roentgen Equivalent
+                                     # Mammal
+banana_dose           0.1e-6 sievert # Informal measure of the dose due to 
+                                     #   eating one average sized banana
+roentgen              2.58e-4 C / kg # Ionizing radiation that produces
+                                     #   1 statcoulomb of charge in 1 cc of
+                                     #   dry air at stp.
+rontgen                 roentgen     # Sometimes it appears spelled this way
+sievertunit             8.38 rontgen # Unit of gamma ray dose delivered in one
+                                     #   hour at a distance of 1 cm from a
+                                     #   point source of 1 mg of radium
+                                     #   enclosed in platinum .5 mm thick.
+
+eman                    1e-7 Ci/m^3  # radioactive concentration
+mache                   3.7e-7 Ci/m^3
+
+#
+# Atomic weights.  The atomic weight of an element is the ratio of the mass of
+# a mole of the element to 1|12 of a mole of Carbon 12.  For each element, we
+# list the atomic weights of all of the isotopes.  The Standard Atomic Weights
+# apply to the elements in the isotopic composition that occurs naturally on
+# Earth.  These are computed values based on the isotopic distribution, and
+# may vary for specific samples.  Elements which do not occur naturally do
+# not have Standard Atomic Weights.  For these elements, if data on the most
+# stable isotope is available, is given.  Otherwise, the user must specify the
+# desired isotope.  
+
+!include elements.units
+
+# Density of the elements
+#
+# Note some elements occur in multiple forms (allotropes) with different
+# densities, and they are accordingly listed multiple times.  
+
+# Density of gas phase elements at STP
+
+hydrogendensity            0.08988 g/l    
+heliumdensity              0.1786 g/l     
+neondensity                0.9002 g/l     
+nitrogendensity            1.2506 g/l     
+oxygendensity              1.429 g/l      
+fluorinedensity            1.696 g/l      
+argondensity               1.784 g/l      
+chlorinedensity            3.2 g/l        
+kryptondensity             3.749 g/l      
+xenondensity               5.894 g/l      
+radondensity               9.73 g/l       
+
+# Density of liquid phase elements near room temperature
+
+brominedensity             3.1028 g/cm^3  
+mercurydensity            13.534 g/cm^3  
+
+# Density of solid elements near room temperature
+
+lithiumdensity             0.534 g/cm^3  
+potassiumdensity           0.862 g/cm^3  
+sodiumdensity              0.968 g/cm^3  
+rubidiumdensity            1.532 g/cm^3  
+calciumdensity             1.55 g/cm^3   
+magnesiumdensity           1.738 g/cm^3  
+phosphorus_white_density   1.823 g/cm^3  
+berylliumdensity           1.85 g/cm^3   
+sulfur_gamma_density       1.92 g/cm^3   
+cesiumdensity              1.93 g/cm^3
+carbon_amorphous_density   1.95 g/cm^3   # average value
+sulfur_betadensity         1.96 g/cm^3   
+sulfur_alpha_density       2.07 g/cm^3   
+carbon_graphite_density    2.267 g/cm^3  
+phosphorus_red_density     2.27 g/cm^3   # average value
+silicondensity             2.3290 g/cm^3 
+phosphorus_violet_density  2.36 g/cm^3   
+borondensity               2.37 g/cm^3   
+strontiumdensity           2.64 g/cm^3   
+phosphorus_black_density   2.69 g/cm^3   
+aluminumdensity            2.7 g/cm^3    
+bariumdensity              3.51 g/cm^3   
+carbon_diamond_density     3.515 g/cm^3  
+scandiumdensity            3.985 g/cm^3  
+selenium_vitreous_density  4.28 g/cm^3   
+selenium_alpha_density     4.39 g/cm^3   
+titaniumdensity            4.406 g/cm^3  
+yttriumdensity             4.472 g/cm^3  
+selenium_gray_density      4.81 g/cm^3   
+iodinedensity              4.933 g/cm^3  
+europiumdensity            5.264 g/cm^3  
+germaniumdensity           5.323 g/cm^3  
+radiumdensity              5.5 g/cm^3    
+arsenicdensity             5.727 g/cm^3  
+tin_alpha_density          5.769 g/cm^3  
+galliumdensity             5.91 g/cm^3   
+vanadiumdensity            6.11 g/cm^3   
+lanthanumdensity           6.162 g/cm^3  
+telluriumdensity           6.24 g/cm^3   
+zirconiumdensity           6.52 g/cm^3   
+antimonydensity            6.697 g/cm^3  
+ceriumdensity              6.77 g/cm^3   
+praseodymiumdensity        6.77 g/cm^3   
+ytterbiumdensity           6.9 g/cm^3    
+neodymiumdensity           7.01 g/cm^3   
+zincdensity                7.14 g/cm^3   
+chromiumdensity            7.19 g/cm^3   
+manganesedensity           7.21 g/cm^3   
+promethiumdensity          7.26 g/cm^3   
+tin_beta_density           7.265 g/cm^3  
+indiumdensity              7.31 g/cm^3   
+samariumdensity            7.52 g/cm^3   
+irondensity                7.874 g/cm^3  
+gadoliniumdensity          7.9 g/cm^3    
+terbiumdensity             8.23 g/cm^3   
+dysprosiumdensity          8.54 g/cm^3   
+niobiumdensity             8.57 g/cm^3   
+cadmiumdensity             8.65 g/cm^3   
+holmiumdensity             8.79 g/cm^3   
+cobaltdensity              8.9 g/cm^3    
+nickeldensity              8.908 g/cm^3  
+erbiumdensity              9.066 g/cm^3  
+polonium_alpha_density     9.196 g/cm^3  
+thuliumdensity             9.32 g/cm^3   
+polonium_beta_density      9.398 g/cm^3  
+bismuthdensity             9.78 g/cm^3   
+lutetiumdensity            9.841 g/cm^3  
+actiniumdensity           10 g/cm^3      
+molybdenumdensity         10.28 g/cm^3   
+silverdensity             10.49 g/cm^3   
+technetiumdensity         11 g/cm^3      
+leaddensity               11.34 g/cm^3   
+thoriumdensity            11.7 g/cm^3    
+thalliumdensity           11.85 g/cm^3   
+americiumdensity          12 g/cm^3      
+palladiumdensity          12.023 g/cm^3  
+rhodiumdensity            12.41 g/cm^3   
+rutheniumdensity          12.45 g/cm^3   
+berkelium_beta_density    13.25 g/cm^3   
+hafniumdensity            13.31 g/cm^3   
+curiumdensity             13.51 g/cm^3   
+berkelium_alphadensity    14.78 g/cm^3   
+californiumdensity        15.1 g/cm^3    
+protactiniumdensity       15.37 g/cm^3   
+tantalumdensity           16.69 g/cm^3   
+uraniumdensity            19.1 g/cm^3    
+tungstendensity           19.3 g/cm^3    
+golddensity               19.30 g/cm^3   
+plutoniumdensity          19.816 g/cm^3  
+neptuniumdensity          20.45 g/cm^3 # alpha form, only one at room temp
+rheniumdensity            21.02 g/cm^3   
+platinumdensity           21.45 g/cm^3   
+iridiumdensity            22.56 g/cm^3   
+osmiumdensity             22.59 g/cm^3
+
+# A few alternate names
+
+tin_gray tin_alpha_density
+tin_white tin_beta_density
+graphitedensity carbon_graphite_density
+diamonddensity carbon_diamond_density
+
+# Predicted density of elements that have not been made in sufficient
+# quantities for measurement.  
+
+franciumdensity            2.48 g/cm^3 # liquid, predicted melting point 8 degC
+astatinedensity            6.35 g/cm^3    
+einsteiniumdensity         8.84 g/cm^3    
+fermiumdensity             9.7 g/cm^3     
+nobeliumdensity            9.9 g/cm^3     
+mendeleviumdensity        10.3 g/cm^3    
+lawrenciumdensity         16 g/cm^3      
+rutherfordiumdensity      23.2 g/cm^3
+roentgeniumdensity        28.7 g/cm^3    
+dubniumdensity            29.3 g/cm^3    
+darmstadtiumdensity       34.8 g/cm^3    
+seaborgiumdensity         35 g/cm^3      
+bohriumdensity            37.1 g/cm^3    
+meitneriumdensity         37.4 g/cm^3    
+hassiumdensity            41 g/cm^3      
+
+#
+# population units
+#
+
+people                  1
+person                  people
+death                   people
+capita                  people
+percapita               per capita
+
+# TGM dozen based unit system listed on the "dozenal" forum
+# http://www.dozenalsociety.org.uk/apps/tgm.htm.  These units are
+# proposed as an allegedly more rational alternative to the SI system.
+
+Tim                     12^-4 hour         # Time 
+Grafut                  gravity Tim^2      # Length based on gravity
+Surf                    Grafut^2           # area
+Volm                    Grafut^3           # volume
+Vlos                    Grafut/Tim         # speed
+Denz                    Maz/Volm           # density
+Mag                     Maz gravity        # force
+Maz                     Volm kg / oldliter # mass based on water
+
+# Abbreviations
+
+# Tm                      Tim              # Conflicts with Tm = Terameter
+Gf                      Grafut
+Sf                      Surf
+Vm                      Volm
+Vl                      Vlos
+Mz                      Maz
+Dz                      Denz
+
+# Dozen based unit prefixes
+
+Zena-                   12
+Duna-                   12^2
+Trina-                  12^3
+Quedra-                 12^4
+Quena-                  12^5
+Hesa-                   12^6
+Seva-                   12^7
+Aka-                    12^8
+Neena-                  12^9
+Dexa-                   12^10
+Lefa-                   12^11
+Zennila-                12^12
+
+Zeni-                   12^-1
+Duni-                   12^-2
+Trini-                  12^-3
+Quedri-                 12^-4
+Queni-                  12^-5
+Hesi-                   12^-6
+Sevi-                   12^-7
+Aki-                    12^-8
+Neeni-                  12^-9
+Dexi-                   12^-10
+Lefi-                   12^-11
+Zennili-                12^-12
+
+#
+# Traditional Japanese units (shakkanhou)
+#
+# The traditional system of weights and measures is called shakkanhou from the
+# shaku and the ken.  Japan accepted SI units in 1891 and legalized conversions
+# to the traditional system.  In 1909 the inch-pound system was also legalized,
+# so Japan had three legally approved systems.  A change to the metric system
+# started in 1921 but there was a lot of resistance.  The Measurement Law of
+# October 1999 prohibits sales in anything but SI units.  However, the old
+# units still live on in construction and as the basis for paper sizes of books
+# and tools used for handicrafts.
+#
+# Note that units below use the Hepburn romanization system.  Some other
+# systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho".
+#
+#
+# http://hiramatu-hifuka.com/onyak/onyindx.html
+
+# Japanese Proportions.  These are still in everyday use.  They also
+# get used as units to represent the proportion of the standard unit.
+
+wari_proportion      1|10
+wari                 wari_proportion
+bu_proportion        1|100    # The character bu can also be read fun or bun
+                              # but usually "bu" is used for units.
+rin_proportion       1|1000
+mou_proportion       1|10000
+
+
+# Japanese Length Measures
+#
+# The length system is called kanejaku or
+# square and originated in China.  It was
+# adopted as Japan's official measure in 701
+# by the Taiho Code.  This system is still in
+# common use in architecture and clothing.
+
+shaku              1|3.3 m
+mou                1|10000 shaku
+rin                1|1000 shaku
+bu_distance        1|100 shaku
+sun                1|10 shaku
+jou_distance       10 shaku
+jou                jou_distance
+
+kanejakusun        sun      # Alias to emphasize architectural name
+kanejaku           shaku
+kanejakujou        jou
+
+# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
+taichi             shaku   # http://zh.wikipedia.org/wiki/台尺
+taicun             sun     # http://zh.wikipedia.org/wiki/台制
+!utf8
+台尺               taichi  # via Hanyu Pinyin romanizations
+台寸               taicun
+!endutf8
+
+# In context of clothing, shaku is different from architecture
+
+kujirajaku         10|8 shaku
+kujirajakusun      1|10 kujirajaku
+kujirajakubu       1|100 kujirajaku
+kujirajakujou      10 kujirajaku
+tan_distance       3 kujirajakujou
+
+ken                6 shaku  # Also sometimes 6.3, 6.5, or 6.6
+                            # http://www.homarewood.co.jp/syakusun.htm
+
+# mostly unused
+chou_distance      60 ken
+chou               chou_distance
+ri                 36 chou
+
+# Japanese Area Measures
+
+# Tsubo is still used for land size, though the others are more
+# recognized by their homonyms in the other measurements.
+
+gou_area             1|10 tsubo
+tsubo                36 shaku^2    # Size of two tatami = ken^2 ??
+se                   30 tsubo
+tan_area             10 se
+chou_area            10 tan_area
+
+# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
+ping                 tsubo     # http://zh.wikipedia.org/wiki/坪
+jia                  2934 ping # http://zh.wikipedia.org/wiki/甲_(单位)
+fen                  1|10 jia  # http://zh.wikipedia.org/wiki/分
+fen_area             1|10 jia  # Protection against future collisions
+!utf8
+坪                   ping      # via Hanyu Pinyin romanizations
+甲                   jia
+分                   fen
+分地                 fen_area  # Protection against future collisions
+!endutf8
+
+# Japanese architecture is based on a "standard" size of tatami mat.
+# Room sizes today are given in number of tatami, and this number
+# determines the spacing between colums and hence sizes of sliding
+# doors and paper screens.  However, every region has its own slightly
+# different tatami size.  Edoma, used in and around Tokyo and
+# Hokkaido, is becoming a nationwide standard.  Kyouma is used around
+# Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.
+# Note that the tatami all have the aspect ratio 2:1 so that the mats
+# can tile the room with some of them turned 90 degrees.
+#
+# http://www.moon2.net/tatami/infotatami/structure.html
+
+edoma                (5.8*2.9) shaku^2
+kyouma               (6.3*3.15) shaku^2
+chuukyouma           (6*3) shaku^2
+jou_area             edoma
+tatami               jou_area
+
+# Japanese Volume Measures
+
+# The "shou" is still used for such things as alcohol and seasonings.
+# Large quantities of paint are still purchased in terms of "to".
+
+shaku_volume         1|10 gou_volume
+gou_volume           1|10 shou
+gou                  gou_volume
+shou                 (4.9*4.9*2.7) sun^3   # The character shou which is
+                                           # the same as masu refers to a
+                                           # rectangular wooden cup used to
+                                           # measure liquids and cereal.
+                                           # Sake is sometimes served in a masu
+                                           # Note that it happens to be
+                                           # EXACTLY 7^4/11^3 liters.
+to                   10 shou
+koku                 10 to  # No longer used; historically a measure of rice
+
+# Japanese Weight Measures
+#
+# https://web.archive.org/web/20040927115452/http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html
+# https://en.wikipedia.org/wiki/Japanese_units_of_measurement
+
+# Not really used anymore.
+
+rin_weight           1|10 bu_weight
+bu_weight            1|10 monme
+fun                  1|10 monme
+monme                momme
+kin                  160 monme
+kan                  1000 monme
+kwan                 kan         # This was the old pronunciation of the unit.
+                                 # The old spelling persisted a few centuries
+                                 # longer and was not changed until around
+                                 # 1950.
+
+# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
+# says: "Volume measure in Taiwan is largely metric".
+taijin               kin      # http://zh.wikipedia.org/wiki/台斤
+tailiang             10 monme # http://zh.wikipedia.org/wiki/台斤
+taiqian              monme    # http://zh.wikipedia.org/wiki/台制
+!utf8
+台斤                 taijin # via Hanyu Pinyin romanizations
+台兩                 tailiang
+台錢                 taiqian
+!endutf8
+
+#
+# Australian unit
+#
+
+australiasquare         (10 ft)^2   # Used for house area
+
+
+#
+# A few German units as currently in use.
+#
+
+zentner                 50 kg
+doppelzentner           2 zentner
+pfund                   500 g
+
+# The klafter, which was used in central Europe, was derived from the span of
+# outstretched arms.
+#
+# https://en.wikipedia.org/wiki/Obsolete_Austrian_units_of_measurement
+# https://www.llv.li/files/abi/klafter-m2-en.pdf
+
+austriaklafter          1.89648384 m    # Exact definition, 23 July 1871 
+austriafoot             1|6 austriaklafter
+prussiaklafter          1.88 m
+prussiafoot             1|6 prussiaklafter
+bavariaklafter          1.751155 m
+bavariafoot             1|6 bavariaklafter
+hesseklafter            2.5 m
+hessefoot               1|6 hesseklafter
+switzerlandklafter      metricklafter
+switzerlandfoot         1|6 switzerlandklafter
+swissklafter            switzerlandklafter
+swissfoot               1|6 swissklafter
+metricklafter           1.8 m
+
+austriayoke             8 austriaklafter * 200 austriaklafter
+
+liechtensteinsquareklafter 3.596652 m^2 # Used until 2017 to measure land area 
+liechtensteinklafter  sqrt(liechtensteinsquareklafter)
+
+# The klafter was also used to measure volume of wood, generally being a stack
+# of wood one klafter wide, one klafter long, with logs 3 feet (half a klafter)
+# in length
+
+prussiawoodklafter      0.5 prussiaklafter^3
+austriawoodklafter      0.5 austriaklafter^3
+festmeter               m^3             # modern measure of wood, solid cube
+raummeter               0.7 festmeter   # Air space between the logs, stacked
+schuettraummeter        0.65 raummeter  # A cubic meter volume of split and cut
+                                        #   firewood in a loose, unordered
+                                        #   pile, not stacked.  This is called
+                                        #   "tipped".
+!utf8
+schüttraummeter         schuettraummeter
+!endutf8
+
+
+#
+# Swedish (Sweden) pre-metric units of 1739.
+# The metric system was adopted in 1878.
+# https://sv.wikipedia.org/wiki/Verkm%C3%A5tt
+#
+
+verklinje               2.0618125 mm
+verktum                 12 verklinje
+kvarter                 6 verktum
+fot                     2 kvarter
+aln                     2 fot
+famn                    3 aln
+
+#
+# Some traditional Russian measures
+#
+# If you would like to help expand this section and understand
+# cyrillic transliteration, let me know.  These measures are meant to
+# reflect common usage, e.g. in translated literature.  
+#
+
+dessiatine              2400 sazhen^2    # Land measure
+dessjatine              dessiatine
+
+funt                    409.51718 grams  # similar to pound
+zolotnik                1|96 funt        # used for precious metal measure
+pood                    40 funt          # common in agricultural measure
+
+arshin                  (2 + 1|3) feet
+sazhen                  3 arshin         # analogous to fathom
+verst                   500 sazhen       # of similar use to mile
+versta                  verst
+borderverst             1000 sazhen
+russianmile             7 verst
+
+
+
+
+#
+# Old French distance measures, from French Weights and Measures
+# Before the Revolution by Zupko
+#
+
+frenchfoot              144|443.296 m     # pied de roi, the standard of Paris.
+pied                    frenchfoot        #   Half of the hashimicubit,
+frenchfeet              frenchfoot        #   instituted by Charlemagne.
+frenchinch              1|12 frenchfoot   #   This exact definition comes from
+frenchthumb             frenchinch        #   a law passed on 10 Dec 1799 which
+pouce                   frenchthumb       #   fixed the meter at
+                                          #   3 frenchfeet + 11.296 lignes.
+frenchline              1|12 frenchinch   # This is supposed to be the size
+ligne                   frenchline        #   of the average barleycorn
+frenchpoint             1|12 frenchline
+toise                   6 frenchfeet
+arpent                  180^2 pied^2      # The arpent is 100 square perches,
+                                          # but the perche seems to vary a lot
+                                          # and can be 18 feet, 20 feet, or 22
+                                          # feet.  This measure was described
+                                          # as being in common use in Canada in
+                                          # 1934 (Websters 2nd).  The value
+                                          # given here is the Paris standard
+                                          # arpent.
+frenchgrain             1|18827.15 kg     # Weight of a wheat grain, hence
+                                          # smaller than the British grain.
+frenchpound             9216 frenchgrain
+
+#
+# Before the Imperial Weights and Measures Act of 1824, various different
+# weights and measures were in use in different places.
+#
+
+# Scots linear measure
+
+scotsinch        1.00540054 UKinch
+scotslink        1|100 scotschain
+scotsfoot        12 scotsinch
+scotsfeet        scotsfoot
+scotsell         37 scotsinch
+scotsfall        6 scotsell
+scotschain       4 scotsfall
+scotsfurlong     10 scotschain
+scotsmile        8 scotsfurlong
+
+# Scots area measure
+
+scotsrood        40 scotsfall^2
+scotsacre        4 scotsrood
+
+# Irish linear measure
+
+irishinch       UKinch
+irishpalm       3 irishinch
+irishspan       3 irishpalm
+irishfoot       12 irishinch
+irishfeet       irishfoot
+irishcubit      18 irishinch
+irishyard       3 irishfeet
+irishpace       5 irishfeet
+irishfathom     6 irishfeet
+irishpole       7 irishyard      # Only these values
+irishperch      irishpole        # are different from
+irishchain      4 irishperch     # the British Imperial
+irishlink       1|100 irishchain # or English values for
+irishfurlong    10 irishchain    # these lengths.
+irishmile       8 irishfurlong   #
+
+#  Irish area measure
+
+irishrood       40 irishpole^2
+irishacre       4 irishrood
+
+# English wine capacity measures (Winchester measures)
+
+winepint       1|2 winequart
+winequart      1|4 winegallon
+winegallon     231 UKinch^3   # Sometimes called the Winchester Wine Gallon,
+                              # it was legalized in 1707 by Queen Anne, and
+                              # given the definition of 231 cubic inches.  It
+                              # had been in use for a while as 8 pounds of wine
+                              # using a merchant's pound, but the definition of
+                              # the merchant's pound had become uncertain.  A
+                              # pound of 15 tower ounces (6750 grains) had been
+                              # common, but then a pound of 15 troy ounces
+                              # (7200 grains) gained popularity.  Because of
+                              # the switch in the value of the merchants pound,
+                              # the size of the wine gallon was uncertain in
+                              # the market, hence the official act in 1707.
+                              # The act allowed that a six inch tall cylinder
+                              # with a 7 inch diameter was a lawful wine
+                              # gallon.  (This comes out to 230.9 in^3.)
+                              # Note also that in Britain a legal conversion
+                              # was established to the 1824 Imperial gallon
+                              # then taken as 277.274 in^3 so that the wine
+                              # gallon was 0.8331 imperial gallons.  This is
+                              # 231.1 cubic inches (using the international
+                              # inch).
+winerundlet    18 winegallon
+winebarrel     31.5 winegallon
+winetierce     42 winegallon
+winehogshead   2 winebarrel
+winepuncheon   2 winetierce
+winebutt       2 winehogshead
+winepipe       winebutt
+winetun        2 winebutt
+
+# English beer and ale measures used 1803-1824 and used for beer before 1688
+
+beerpint       1|2 beerquart
+beerquart      1|4 beergallon
+beergallon     282 UKinch^3
+beerbarrel     36 beergallon
+beerhogshead   1.5 beerbarrel
+
+# English ale measures used from 1688-1803 for both ale and beer
+
+alepint        1|2 alequart
+alequart       1|4 alegallon
+alegallon      beergallon
+alebarrel      34 alegallon
+alehogshead    1.5 alebarrel
+
+# Scots capacity measure
+
+scotsgill      1|4 mutchkin
+mutchkin       1|2 choppin
+choppin        1|2 scotspint
+scotspint      1|2 scotsquart
+scotsquart     1|4 scotsgallon
+scotsgallon    827.232 UKinch^3
+scotsbarrel    8 scotsgallon
+jug            scotspint
+
+# Scots dry capacity measure
+
+scotswheatlippy   137.333 UKinch^3    # Also used for peas, beans, rye, salt
+scotswheatlippies scotswheatlippy
+scotswheatpeck    4 scotswheatlippy
+scotswheatfirlot  4 scotswheatpeck
+scotswheatboll    4 scotswheatfirlot
+scotswheatchalder 16 scotswheatboll
+
+scotsoatlippy     200.345 UKinch^3    # Also used for barley and malt
+scotsoatlippies   scotsoatlippy
+scotsoatpeck      4 scotsoatlippy
+scotsoatfirlot    4 scotsoatpeck
+scotsoatboll      4 scotsoatfirlot
+scotsoatchalder   16 scotsoatboll
+
+# Scots Tron weight
+
+trondrop       1|16 tronounce
+tronounce      1|20 tronpound
+tronpound      9520 grain
+tronstone      16 tronpound
+
+# Irish liquid capacity measure
+
+irishnoggin    1|4 irishpint
+irishpint      1|2 irishquart
+irishquart     1|2 irishpottle
+irishpottle    1|2 irishgallon
+irishgallon    217.6 UKinch^3
+irishrundlet   18 irishgallon
+irishbarrel    31.5 irishgallon
+irishtierce    42 irishgallon
+irishhogshead  2 irishbarrel
+irishpuncheon  2 irishtierce
+irishpipe      2 irishhogshead
+irishtun       2 irishpipe
+
+# Irish dry capacity measure
+
+irishpeck      2 irishgallon
+irishbushel    4 irishpeck
+irishstrike    2 irishbushel
+irishdrybarrel 2 irishstrike
+irishquarter   2 irishbarrel
+
+# English Tower weights, abolished in 1528
+
+towerpound       5400 grain
+towerounce       1|12 towerpound
+towerpennyweight 1|20 towerounce
+towergrain       1|32 towerpennyweight
+
+# English Mercantile weights, used since the late 12th century
+
+mercpound      6750 grain
+mercounce      1|15 mercpound
+mercpennyweight 1|20 mercounce
+
+# English weights for lead
+
+leadstone     12.5 lb
+fotmal        70 lb
+leadwey       14 leadstone
+fothers       12 leadwey
+
+# English Hay measure
+
+newhaytruss 60 lb             # New and old here seem to refer to "new"
+newhayload  36 newhaytruss    # hay and "old" hay rather than a new unit
+oldhaytruss 56 lb             # and an old unit.
+oldhayload  36 oldhaytruss
+
+# English wool measure
+
+woolclove   7 lb
+woolstone   2 woolclove
+wooltod     2 woolstone
+woolwey     13 woolstone
+woolsack    2 woolwey
+woolsarpler 2 woolsack
+woollast    6 woolsarpler
+
+#
+# Ancient history units:  There tends to be uncertainty in the definitions
+#                         of the units in this section
+# These units are from [11]
+
+# Roman measure.  The Romans had a well defined distance measure, but their
+# measures of weight were poor.  They adopted local weights in different
+# regions without distinguishing among them so that there are half a dozen
+# different Roman "standard" weight systems.
+
+romanfoot    296 mm          # There is some uncertainty in this definition
+romanfeet    romanfoot       # from which all the other units are derived.
+pes          romanfoot       # This value appears in numerous sources. In "The
+pedes        romanfoot       # Roman Land Surveyors", Dilke gives 295.7 mm.
+romaninch    1|12 romanfoot  # The subdivisions of the Roman foot have the
+romandigit   1|16 romanfoot  #   same names as the subdivisions of the pound,
+romanpalm    1|4 romanfoot   #   but we can't have the names for different
+romancubit   18 romaninch    #   units.
+romanpace    5 romanfeet     # Roman double pace (basic military unit)
+passus       romanpace
+romanperch   10 romanfeet
+stade        125 romanpaces
+stadia       stade
+stadium      stade
+romanmile    8 stadia        # 1000 paces
+romanleague  1.5 romanmile
+schoenus     4 romanmile
+
+# Other values for the Roman foot (from Dilke)
+
+earlyromanfoot    29.73 cm
+pesdrusianus      33.3 cm    # or 33.35 cm, used in Gaul & Germany in 1st c BC
+lateromanfoot     29.42 cm
+
+# Roman areas
+
+actuslength  120 romanfeet     # length of a Roman furrow
+actus        120*4 romanfeet^2 # area of the furrow
+squareactus  120^2 romanfeet^2 # actus quadratus
+acnua        squareactus
+iugerum      2 squareactus
+iugera       iugerum
+jugerum      iugerum
+jugera       iugerum
+heredium     2 iugera          # heritable plot
+heredia      heredium
+centuria     100 heredia
+centurium    centuria
+
+# Roman volumes
+
+sextarius       35.4 in^3      # Basic unit of Roman volume.  As always,
+sextarii        sextarius      # there is uncertainty.  Six large Roman
+                               # measures survive with volumes ranging from
+                               # 34.4 in^3 to 39.55 in^3.  Three of them
+                               # cluster around the size given here.
+                               #
+                               # But the values for this unit vary wildly
+                               # in other sources.  One reference  gives 0.547
+                               # liters, but then says the amphora is a
+                               # cubic Roman foot.  This gives a value for the
+                               # sextarius of 0.540 liters.  And the
+                               # encyclopedia Britannica lists 0.53 liters for
+                               # this unit.  Both [7] and [11], which were
+                               # written by scholars of weights and measures,
+                               # give the value of 35.4 cubic inches.
+cochlearia      1|48 sextarius
+cyathi          1|12 sextarius
+acetabula       1|8 sextarius
+quartaria       1|4 sextarius
+quartarius      quartaria
+heminae         1|2 sextarius
+hemina          heminae
+cheonix         1.5 sextarii
+
+# Dry volume measures (usually)
+
+semodius        8 sextarius
+semodii         semodius
+modius          16 sextarius
+modii           modius
+
+# Liquid volume measures (usually)
+
+congius         12 heminae
+congii          congius
+amphora         8 congii
+amphorae        amphora      # Also a dry volume measure
+culleus         20 amphorae
+quadrantal      amphora
+
+# Roman weights
+
+libra           5052 grain   # The Roman pound varied significantly
+librae          libra        # from 4210 grains to 5232 grains.  Most of
+romanpound      libra        # the standards were obtained from the weight
+uncia           1|12 libra   # of particular coins.  The one given here is
+unciae          uncia        # based on the Gold Aureus of Augustus which
+romanounce      uncia        # was in use from BC 27 to AD 296.
+deunx           11 uncia
+dextans         10 uncia
+dodrans         9 uncia
+bes             8 uncia
+seprunx         7 uncia
+semis           6 uncia
+quincunx        5 uncia
+triens          4 uncia
+quadrans        3 uncia
+sextans         2 uncia
+sescuncia       1.5 uncia
+semuncia        1|2 uncia
+siscilius       1|4 uncia
+sextula         1|6 uncia
+semisextula     1|12 uncia
+scriptulum      1|24 uncia
+scrupula        scriptulum
+romanobol       1|2 scrupula
+
+romanaspound    4210 grain    # Old pound based on bronze coinage, the
+                              # earliest money of Rome BC 338 to BC 268.
+
+# Egyptian length measure
+
+egyptianroyalcubit      20.63 in    # plus or minus .2 in
+egyptianpalm            1|7 egyptianroyalcubit
+egyptiandigit           1|4 egyptianpalm
+egyptianshortcubit      6 egyptianpalm
+
+doubleremen             29.16 in  # Length of the diagonal of a square with
+remendigit       1|40 doubleremen # side length of 1 royal egyptian cubit.
+                                  # This is divided into 40 digits which are
+                                  # not the same size as the digits based on
+                                  # the royal cubit.
+
+# Greek length measures
+
+greekfoot               12.45 in      # Listed as being derived from the
+greekfeet               greekfoot     # Egyptian Royal cubit in [11].  It is
+greekcubit              1.5 greekfoot # said to be 3|5 of a 20.75 in cubit.
+pous                    greekfoot
+podes                   greekfoot
+orguia                  6 greekfoot
+greekfathom             orguia
+stadion                 100 orguia
+akaina                  10 greekfeet
+plethron                10 akaina
+greekfinger             1|16 greekfoot
+homericcubit            20 greekfingers  # Elbow to end of knuckles.
+shortgreekcubit         18 greekfingers  # Elbow to start of fingers.
+
+ionicfoot               296 mm
+doricfoot               326 mm
+
+olympiccubit            25 remendigit    # These olympic measures were not as
+olympicfoot             2|3 olympiccubit # common as the other greek measures.
+olympicfinger           1|16 olympicfoot # They were used in agriculture.
+olympicfeet             olympicfoot
+olympicdakylos          olympicfinger
+olympicpalm             1|4 olympicfoot
+olympicpalestra         olympicpalm
+olympicspithame         3|4 foot
+olympicspan             olympicspithame
+olympicbema             2.5 olympicfeet
+olympicpace             olympicbema
+olympicorguia           6 olympicfeet
+olympicfathom           olympicorguia
+olympiccord             60 olympicfeet
+olympicamma             olympiccord
+olympicplethron         100 olympicfeet
+olympicstadion          600 olympicfeet
+
+# Greek capacity measure
+
+greekkotyle             270 ml           # This approximate value is obtained
+xestes                  2 greekkotyle    # from two earthenware vessels that
+khous                   12 greekkotyle   # were reconstructed from fragments.
+metretes                12 khous         # The kotyle is a day's corn ration
+choinix                 4 greekkotyle    # for one man.
+hekteos                 8 choinix
+medimnos                6 hekteos
+
+# Greek weight.  Two weight standards were used, an Aegina standard based
+# on the Beqa shekel and an Athens (attic) standard.
+
+aeginastater            192 grain        # Varies up to 199 grain
+aeginadrachmae          1|2 aeginastater
+aeginaobol              1|6 aeginadrachmae
+aeginamina              50 aeginastaters
+aeginatalent            60 aeginamina    # Supposedly the mass of a cubic foot
+                                         # of water (whichever foot was in use)
+
+atticstater             135 grain        # Varies 134-138 grain
+atticdrachmae           1|2 atticstater
+atticobol               1|6 atticdrachmae
+atticmina               50 atticstaters
+attictalent             60 atticmina     # Supposedly the mass of a cubic foot
+                                         # of water (whichever foot was in use)
+
+# "Northern" cubit and foot.  This was used by the pre-Aryan civilization in
+# the Indus valley.  It was used in Mesopotamia, Egypt, North Africa, China,
+# central and Western Europe until modern times when it was displaced by
+# the metric system.
+
+northerncubit           26.6 in           # plus/minus .2 in
+northernfoot            1|2 northerncubit
+
+sumeriancubit           495 mm
+kus                     sumeriancubit
+sumerianfoot            2|3 sumeriancubit
+
+assyriancubit           21.6 in
+assyrianfoot            1|2 assyriancubit
+assyrianpalm            1|3 assyrianfoot
+assyriansusi            1|20 assyrianpalm
+susi                    assyriansusi
+persianroyalcubit       7 assyrianpalm
+
+
+# Arabic measures.  The arabic standards were meticulously kept.  Glass weights
+# accurate to .2 grains were made during AD 714-900.
+
+hashimicubit            25.56 in          # Standard of linear measure used
+                                          # in Persian dominions of the Arabic
+                                          # empire 7-8th cent.  Is equal to two
+                                          # French feet.
+
+blackcubit              21.28 in
+arabicfeet              1|2 blackcubit
+arabicfoot              arabicfeet
+arabicinch              1|12 arabicfoot
+arabicmile              4000 blackcubit
+
+silverdirhem            45 grain  # The weights were derived from these two
+tradedirhem             48 grain  # units with two identically named systems
+                                  # used for silver and used for trade purposes
+
+silverkirat             1|16 silverdirhem
+silverwukiyeh           10 silverdirhem
+silverrotl              12 silverwukiyeh
+arabicsilverpound       silverrotl
+
+tradekirat              1|16 tradedirhem
+tradewukiyeh            10 tradedirhem
+traderotl               12 tradewukiyeh
+arabictradepound        traderotl
+
+# Miscellaneous ancient units
+
+parasang                3.5 mile # Persian unit of length usually thought
+                                 # to be between 3 and 3.5 miles
+biblicalcubit           21.8 in
+hebrewcubit             17.58 in
+li                      10|27.8 mile  # Chinese unit of length
+                                      #   100 li is considered a day's march
+liang                   11|3 oz       # Chinese weight unit
+
+
+# Medieval time units.  According to the OED, these appear in Du Cange
+# by Papias.
+
+timepoint               1|5 hour  # also given as 1|4
+timeminute              1|10 hour
+timeostent              1|60 hour
+timeounce               1|8 timeostent
+timeatom                1|47 timeounce
+
+# Given in [15], these subdivisions of the grain were supposedly used
+# by jewelers.  The mite may have been used but the blanc could not
+# have been accurately measured.
+
+mite                    1|20 grain
+droit                   1|24 mite
+periot                  1|20 droit
+blanc                   1|24 periot
+
+#
+# Localization
+#
+
+!var UNITS_ENGLISH US
+hundredweight           ushundredweight
+ton                     uston
+scruple                 apscruple
+fluidounce              usfluidounce
+gallon                  usgallon
+bushel                  usbushel
+quarter                 quarterweight
+cup                     uscup
+tablespoon              ustablespoon
+teaspoon                usteaspoon
+dollar                  US$
+cent                    $ 0.01
+penny                   cent
+minim                   minimvolume
+pony                    ponyvolume
+grand                   usgrand
+firkin                  usfirkin
+hogshead                ushogshead
+cable                   uscable
+!endvar
+
+!var UNITS_ENGLISH GB
+hundredweight           brhundredweight
+ton                     brton
+scruple                 brscruple
+fluidounce              brfluidounce
+gallon                  brgallon
+bushel                  brbushel
+quarter                 brquarter
+chaldron                brchaldron
+cup                     brcup
+teacup                  brteacup
+tablespoon              brtablespoon
+teaspoon                brteaspoon
+dollar                  US$
+cent                    $ 0.01
+penny                   brpenny
+minim                   minimnote
+pony                    brpony
+grand                   brgrand
+firkin                  brfirkin
+hogshead                brhogshead
+cable                   brcable
+!endvar
+
+!varnot UNITS_ENGLISH GB US
+!message Unknown value for environment variable UNITS_ENGLISH.  Should be GB or US.
+!endvar
+
+
+!utf8
+⅛-                      1|8
+¼-                      1|4
+⅜-                      3|8
+½-                      1|2
+⅝-                      5|8
+¾-                      3|4
+⅞-                      7|8
+⅙-                      1|6
+⅓-                      1|3
+⅔-                      2|3
+⅚-                      5|6
+⅕-                      1|5
+⅖-                      2|5
+⅗-                      3|5
+⅘-                      4|5
+# U+2150-               1|7  For some reason these characters are getting
+# U+2151-               1|9  flagged as invalid UTF8.
+# U+2152-               1|10
+#⅐-               1|7   # fails under MacOS
+#⅑-               1|9   # fails under MacOS
+#⅒-               1|10  # fails under MacOS
+ℯ                       exp(1)      # U+212F, base of natural log
+µ-                      micro       # micro sign U+00B5
+μ-                      micro       # small mu U+03BC
+ångström                angstrom
+Å                       angstrom    # angstrom symbol U+212B
+Å                       angstrom    # A with ring U+00C5
+röntgen                 roentgen
+°C                      degC
+°F                      degF
+°K                      K           # °K is incorrect notation
+°R                      degR
+°                       degree
+℃                       degC
+℉                       degF
+K                       K          # Kelvin symbol, U+212A
+ℓ                       liter      # unofficial abbreviation used in some places
+Ω                       ohm       # Ohm symbol U+2126
+Ω                       ohm       # Greek capital omega U+03A9
+℧                       mho
+G₀                      G0
+H₀                      H0              
+Z₀                      Z0
+a₀                      a0
+n₀                      n0
+ε₀                      epsilon0
+μ₀                      mu0
+Φ₀                      Phi0
+R∞                      Rinfinity
+R_∞                     Rinfinity
+λ_C                     lambda_C
+μ_B                     mu_B
+ν_133Cs                 nu_133Cs  
+ʒ                        dram     # U+0292
+℈                       scruple
+℥                       ounce
+℔                       lb
+ℎ                       h
+ℏ                       hbar
+τ                       tau    
+π                       pi      # Greek letter pi
+𝜋                       pi      # mathematical italic small pi
+α                       alpha  
+σ                       sigma  
+‰                       1|1000
+‱                       1|10000
+′                       '        # U+2032
+″                       "        # U+2033
+
+#
+# Unicode currency symbols
+#
+
+¢                       cent
+£                       britainpound
+¥                       japanyen
+€                       euro
+₩                       southkoreawon
+₪                       israelnewshekel
+₤                       lira
+# ₺                       turkeylira  # fails under MacOS
+₨                       rupee           # unofficial legacy rupee sign
+# ₹                       indiarupee      # official rupee sign # MacOS fail
+#؋                       afghanafghani    # fails under MacOS
+฿                       thailandbaht
+₡                       costaricacolon
+₣                       francefranc
+₦                       nigerianaira
+₧                       spainpeseta
+₫                       vietnamdong
+₭                       laokip 
+₮                       mongoliatugrik
+₯                       greecedrachma
+₱                       philippinepeso
+# ₲                       paraguayguarani # fails under MacOS
+#₴                       ukrainehryvnia   # fails under MacOS
+#₵                       ghanacedi        # fails under MacOS
+#₸                       kazakhstantenge  # fails under MacOS
+#₼                       azerbaijanmanat # fails under MacOS
+#₽                       russiaruble     # fails under MacOS
+#₾                       georgialari     # fails under MacOS
+﷼                       iranrial
+﹩                      $
+￠                      ¢
+￡                      £
+￥                      ¥
+￦                      ₩
+
+#
+# Square Unicode symbols starting at U+3371
+#
+
+㍱                      hPa
+㍲                      da
+㍳                      au
+㍴                      bar
+# ㍵                          oV???
+㍶                      pc
+#㍷                      dm      invalid on Mac
+#㍸                      dm^2    invalid on Mac
+#㍹                      dm^3    invalid on Mac
+㎀                      pA
+㎁                      nA
+㎂                      µA
+㎃                      mA
+㎄                      kA
+㎅                      kB
+㎆                      MB
+㎇                      GB
+㎈                      cal
+㎉                      kcal
+㎊                      pF
+㎋                      nF
+㎌                      µF
+㎍                      µg
+㎎                      mg
+㎏                      kg
+㎐                      Hz
+㎑                      kHz
+㎒                      MHz
+㎓                      GHz
+㎔                      THz
+㎕                      µL
+㎖                      mL
+㎗                      dL
+㎘                      kL
+㎙                      fm
+㎚                      nm
+㎛                      µm
+㎜                      mm
+㎝                      cm
+㎞                      km
+㎟                      mm^2
+㎠                      cm^2
+㎡                      m^2
+㎢                      km^2
+㎣                      mm^3
+㎤                      cm^3
+㎥                      m^3
+㎦                      km^3
+㎧                      m/s
+㎨                      m/s^2
+㎩                      Pa
+㎪                      kPa
+㎫                      MPa
+㎬                      GPa
+㎭                      rad
+㎮                      rad/s
+㎯                      rad/s^2
+㎰                      ps
+㎱                      ns
+㎲                      µs
+㎳                      ms
+㎴                      pV
+㎵                      nV
+㎶                      µV
+㎷                      mV
+㎸                      kV
+㎹                      MV
+㎺                      pW
+㎻                      nW
+㎼                      µW
+㎽                      mW
+㎾                      kW
+㎿                      MW
+㏀                      kΩ
+㏁                      MΩ
+㏃                      Bq
+㏄                      cc
+㏅                      cd
+㏆                      C/kg
+㏈()                    dB
+㏉                      Gy
+㏊                      ha
+# ㏋  HP??
+㏌                      in
+# ㏍                      KK??
+# ㏎                      KM???
+㏏                      kt
+㏐                      lm
+# ㏑                      ln
+# ㏒                      log
+㏓                      lx
+㏔                      mb
+㏕                      mil
+㏖                      mol
+㏗()                    pH
+㏙                      ppm
+#   ㏚     PR???
+㏛                      sr
+㏜                      Sv
+㏝                      Wb
+#㏞                      V/m     Invalid on Mac
+#㏟                      A/m     Invalid on Mac
+#㏿                      gal     Invalid on Mac
+
+!endutf8
+
+############################################################################
+#
+# Unit list aliases
+#
+# These provide a shorthand for conversions to unit lists.
+#
+############################################################################
+
+!unitlist uswt lb;oz
+!unitlist hms hr;min;sec
+!unitlist time year;day;hr;min;sec
+!unitlist dms deg;arcmin;arcsec
+!unitlist ftin ft;in;1|8 in
+!unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
+!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
+                tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
+
+############################################################################
+#
+# The following units were in the Unix units database but do not appear in
+# this file:
+#
+#      wey        used for cheese, salt and other goods.  Measured mass or
+#      waymass    volume depending on what was measured and where the measuring
+#                 took place.  A wey of cheese ranged from 200 to 324 pounds.
+#
+#      sack       No precise definition
+#
+#      spindle    The length depends on the type of yarn
+#
+#      block      Defined variously on different computer systems
+#
+#      erlang     A unit of telephone traffic defined variously.
+#                 Omitted because there are no other units for this
+#                 dimension.  Is this true?  What about CCS = 1/36 erlang?
+#                 Erlang is supposed to be dimensionless.  One erlang means
+#                 a single channel occupied for one hour.
+#
+############################################################################
+#
+# The following have been suggested or considered and deemed out of scope.
+# They will not be added to GNU units.  
+#
+# Conversions between different calendar systems used in different countries or
+# different historical periods are out of scope for units and will not be added.
+#
+# Wind chill and heat index cannot be handled because they are bivarite,
+# with dependence on both the temperature and wind speed or humidity.  
+#
+# Plain english text output like "one hectare is equivalent to one hundred
+# million square centimeters" is out of scope.  
+#