New stuff
diff --git a/Units.app/Contents/MacOS/definitions.units b/Units.app/Contents/MacOS/definitions.units
new file mode 100644
index 0000000..ddc3423
--- /dev/null
+++ b/Units.app/Contents/MacOS/definitions.units
@@ -0,0 +1,8418 @@
+#
+# 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.
+#