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UNITS(1)										 UNITS(1)

       units - unit conversion program

       The  `units'  program converts quantities expressed in various scales to their equivalents
       in other scales.  The `units' program can handle multiplicative scale changes as  well  as
       nonlinear conversions such as Fahrenheit to Celsius.

       The  units are defined in an external data file.  You can use the extensive data file that
       comes with this program, or you can provide your own data file to suit your needs.

       You can use the program interactively with prompts, or you can use  it  from  the  command

       To  invoke units for interactive use, type `units' at your shell prompt.  The program will
       print something like this:

	   2131 units, 53 prefixes, 24 nonlinear units

	   You have:

       At the `You have:' prompt, type the quantity and units that you are converting from.   For
       example,  if you want to convert ten meters to feet, type `10 meters'.  Next, `units' will
       print `You want:'.  You should type the type of units you want to convert to.  To  convert
       to feet, you would type `feet'.

       The  answer will be displayed in two ways.  The first line of output, which is marked with
       a `*' to indicate multiplication, gives the result of the conversion you have  asked  for.
       The  second  line  of  output,  which is marked with a `/' to indicate division, gives the
       inverse of the conversion factor.  If you convert 10 meters to feet, `units' will print

	       * 32.808399
	       / 0.03048

       which tells you that 10 meters equals about 32.8 feet.  The second number gives	the  con-
       version	in  the  opposite  direction.  In this case, it tells you that 1 foot is equal to
       about 0.03 dekameters since the dekameter is 10 meters.	It also tells you that 1/32.8  is
       about .03.

       The  `units'  program prints the inverse because sometimes it is a more convenient number.
       In the example above, for example, the inverse value is an exact  conversion:  a  foot  is
       exactly .03048 dekameters.  But the number given the other direction is inexact.

       If you try to convert grains to pounds, you will see the following:

	   You have: grains
	   You want: pounds
		   * 0.00014285714
		   / 7000

       From  the  second  line	of  the output you can immediately see that a grain is equal to a
       seven thousandth of a pound.  This is not so obvious from the first line  of  the  output.
       If you find  the output format  confusing, try using the `--verbose' option:

	   You have: grain
	   You want: aeginamina
		   grain = 0.00010416667 aeginamina
		   grain = (1 / 9600) aeginamina

       If  you	request  a  conversion	between  units	which measure reciprocal dimensions, then
       `units' will display the conversion results with an extra note indicating that  reciprocal
       conversion has been done:

	   You have: 6 ohms
	   You want: siemens
		   reciprocal conversion
		   * 0.16666667
		   / 6

       Reciprocal conversion can be suppressed by using the `--strict' option.	As usual, use the
       `--verbose' option to get more comprehensible output:

	   You have: tex
	   You want: typp
		   reciprocal conversion
		   1 / tex = 496.05465 typp
		   1 / tex = (1 / 0.0020159069) typp

	   You have: 20 mph
	   You want: sec/mile
		   reciprocal conversion
		   1 / 20 mph = 180 sec/mile
		   1 / 20 mph = (1 / 0.0055555556) sec/mile

       If you enter incompatible unit types, the `units' program will print a message  indicating
       that the units are not conformable and it will display the reduced form for each unit:

	   You have: ergs/hour
	   You want: fathoms kg^2 / day
	   conformability error
		   2.7777778e-11 kg m^2 / sec^3
		   2.1166667e-05 kg^2 m / sec

       If  you only want to find the reduced form or definition of a unit, simply press return at
       the `You want:' prompt.	Here is an example:

	   You have: jansky
	   You want:
		   Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2

       The output from `units' indicates that the jansky is defined to be  equal  to  a  fluxunit
       which  in  turn	is  defined to be a certain combination of watts, meters, and hertz.  The
       fully reduced (and in this case somewhat more cryptic) form appears on the far right.

       If you want a list of options you can type `?' at the `You  want:'  prompt.   The  program
       will display a list of named units which are conformable with the unit that you entered at
       the `You have:' prompt above.  Note that conformable unit combinations will not appear  on
       this list.

       Typing  `help'  at  either prompt displays a short help message.  You can also type `help'
       followed by a unit name.  This will invoke a pager on the units data  base  at  the  point
       where  that  unit is defined.  You can read the definition and comments that may give more
       details or historical information about the unit.

       The `units' program can perform units conversions non-interactively from the command line.
       To  do  this, type the command, type the original units expression, and type the new units
       you want.  You will probably need to protect the units expressions from interpretation  by
       the shell using single quote characters.

       If you type

	   units '2 liters' 'quarts'

       then `units' will print

	       * 2.1133764
	       / 0.47317647

       and  then  exit.  The output tells you that 2 liters is about 2.1 quarts, or alternatively
       that a quart is about 0.47 times 2 liters.

       If the conversion is successful, then `units' will return success(0) to the calling envi-
       ronment.   If  `units'  is given non-conformable units to convert, it will print a message
       giving the reduced form of each unit and it will return failure (nonzero) to  the  calling

       When  `units'  is  invoked with only one argument, it will print out the definition of the
       specified unit.	It will return failure if the unit is not defined and success if the unit
       is defined.

       In  order  to  enter  more complicated units or fractions, you will need to use operations
       such as powers, products and division.  Powers of units can be  specified  using  the  `^'
       character  as shown in the following example, or by simple concatenation: `cm3' is equiva-
       lent to `cm^3'.	If the exponent is more than one digit, the `^' is required.  An exponent
       like  `2^3^2'  is evaluated right to left.  The `^' operator has the second highest prece-

	   You have: cm^3
	   You want: gallons
		   * 0.00026417205
		   / 3785.4118

	   You have: arabicfoot-arabictradepound-force
	   You want: ft lbf
		   * 0.7296
		   / 1.370614

       Multiplication of units can be specified by using spaces, a hyphen (`-')  or  an  asterisk
       (`*').  Division of units is indicated by the slash (`/') or by `per'.

	   You have: furlongs per fortnight
	   You want: m/s
		   * 0.00016630986
		   / 6012.8727

       Multiplication  has  a  higher precedence than division and is evaluated left to right, so
       `m/s * s/day' is equivalent to `m / s s day' and has dimensions of length per time  cubed.
       Similarly, `1/2 meter' refers to a unit of reciprocal length equivalent to .5/meter, which
       is probably not what you would intend if you entered that expression.   You  can  indicate
       division  of  numbers  with the vertical dash (`|').  This operator has the highest prece-
       dence so the square root of two thirds could be written `2|3^1|2'.

	   You have: 1|2 inch
	   You want: cm
		   * 1.27
		   / 0.78740157

       Parentheses can be used for grouping as desired.

	   You have: (1/2) kg / (kg/meter)
	   You want: league
		   * 0.00010356166
		   / 9656.0833

       Prefixes are defined separately from base units.  In order to get centimeters,  the  units
       database  defines  `centi-'  and `c-' as prefixes.  Prefixes can appear alone with no unit
       following them.	An exponent applies only to the immediately preceding unit and its prefix
       so  that `cm^3' or `centimeter^3' refer to cubic centimeters but `centi-meter^3' refers to
       hundredths of cubic meters.  Only one prefix is permitted per unit,  so	`micromicrofarad'
       will fail, but `micro-microfarad' will work.

       For  `units', numbers are just another kind of unit.  They can appear as many times as you
       like and in any order in a unit expression.  For example, to find  the  volume  of  a  box
       which is 2 ft by 3 ft by 12 ft in steres, you could do the following:

	   You have: 2 ft 3 ft 12 ft
	   You want: stere
		   * 2.038813
		   / 0.49048148

	   You have: $ 5 / yard
	   You want: cents / inch
		   * 13.888889
		   / 0.072

       And  the  second example shows how the dollar sign in the units conversion can precede the
       five.  Be careful:  `units' will interpret `$5' with no space as equivalent to dollars^5.

       Outside of the SI system, it is often desirable to add values of different units together.
       Sums of conformable units are written with the `+' character.

	   You have: 2 hours + 23 minutes + 32 seconds
	   You want: seconds
		   * 8612
		   / 0.00011611705

	   You have: 12 ft + 3 in
	   You want: cm
		   * 373.38
		   / 0.0026782366

	   You have: 2 btu + 450 ft-lbf
	   You want: btu
		   * 2.5782804
		   / 0.38785542

       The expressions which are added together must reduce to identical expressions in primitive
       units, or an error message will be displayed:

	   You have: 12 printerspoint + 4 heredium
	   Illegal sum of non-conformable units

       Because `-' is used for products, it cannot also be used to form differences of units.  If
       a  `-' appears after `(' or after `+' then it will act as a negation operator.  So you can
       compute 20 degrees minus 12 minutes by entering `20 degrees + -12 arcmin'.  The `+'  char-
       acter  is  sometimes  used  in exponents like `3.43e+8'.  This leads to an ambiguity in an
       expression like `3e+2 yC'.  The unit `e' is a  small  unit  of  charge,	so  this  can  be
       regarded  as  equivalent  to `(3e+2) yC' or `(3 e)+(2 yC)'.  This ambiguity is resolved by
       always interpreting `+' as part of an exponent if possible.

       Several built in functions are provided: `sin', `cos', `tan', `ln', `log', `log2',  `exp',
       `acos',	`atan' and `asin'.  The `sin', `cos', and `tan' functions require either a dimen-
       sionless argument or an argument with dimensions of angle.

	   You have: sin(30 degrees)
	   You want:
		   Definition: 0.5

	   You have: sin(pi/2)
	   You want:
		   Definition: 1

	   You have: sin(3 kg)
	   Unit not dimensionless

       The other functions on the list require dimensionless arguments.  The inverse  trigonomet-
       ric functions return arguments with dimensions of angle.

       If you wish to take roots of units, you may use the `sqrt' or `cuberoot' functions.  These
       functions require that the argument have the  appropriate  root.   Higher  roots  can   be
       obtained by using fractional exponents:

	   You have: sqrt(acre)
	   You want: feet
		   * 208.71074
		   / 0.0047913202

	   You have: (400 W/m^2 / stefanboltzmann)^(1/4)
	   You have:
		   Definition: 289.80882 K

	   You have: cuberoot(hectare)
	   Unit not a root

       Nonlinear  units  are represented using functional notation.  They make possible nonlinear
       unit conversions such temperature.  This is different from the linear units  that  convert
       temperature differences.  Note the difference below.  The absolute temperature conversions
       are handled by units starting with `temp', and you must use functional notation.  The tem-
       perature  differences  are  done  using	units starting with `deg' and they do not require
       functional notation.

	   You have: tempF(45)
	   You want: tempC

	   You have: 45 degF
	   You want: degC
		   * 25
		   / 0.04

       In this case, think of `tempF(x)' not as a function but as a notation which indicates that
       `x' should have units of `tempF' attached to it.  @xref{Nonlinear units}.

       Some  other examples of nonlinears units are ring size and wire gauge.  There are numerous
       different gauges and ring sizes.  See the units database for more details.  Note that wire
       gauges  with  multiple zeroes are signified using negative numbers where two zeroes is -1.
       Alternatively, you can use the synonyms `g00', `g000', and so on that are defined  in  the
       units database.

	   You have: wiregauge(11)
	   You want: inches
		   * 0.090742002
		   / 11.020255

	   You have: brwiregauge(g00)
	   You want: inches
		   * 0.348
		   / 2.8735632

	   You have: 1 mm
	   You want: wiregauge

       You invoke `units' like this:


       If the FROM-UNIT and TO-UNIT are omitted, then the program will use interactive prompts to
       determine which conversions to perform.	If both FROM-UNIT and TO-UNIT are given,  `units'
       will  print the result of that single conversion and then exit.	If only FROM-UNIT appears
       on the command line, `units' will display the definition of that  unit  and  exit.   Units
       specified  on the command line will need to be quoted to protect them from shell interpre-
       tation and to group them into two arguments.  @xref{Command line use}.

       The following options allow you to read in an alternative units	file,  check  your  units
       file, or change the output format:

       -c, --check
	      Check  that  all units and prefixes defined in the units data file reduce to primi-
	      tive units.  Print a list of all units that cannot be reduced.  Also  display  some
	      other  diagnostics  about suspicious definitions in the units data file.	Note that
	      only definitions active in the current locale are checked.

	      Like the `-check' option, this option  prints  a	list  of  units  that  cannot  be
	      reduced.	But to help find unit  definitions that cause endless loops, it lists the
	      units as they are checked.  If `units' hangs, then the last unit to be printed  has
	      a  bad  definition.   Note  that	only definitions active in the current locale are

       -o format, --output-format format
	      Use the specified format for numeric output.  Format is the same as  that  for  the
	      printf  function	in  the ANSI C standard.  For example, if you want more precision
	      you might use `-o %.15g'.

       -f filename, --file filename
	      Use filename as the units data file rather than the default units data file.   This
	      option overrides the `UNITSFILE' environment variable.

       -h, --help
	      Print out a summary of the options for `units'.

       -q, --quiet, --silent
	      Suppress	prompting  of  the user for units and the display of statistics about the
	      number of units loaded.

       -s, --strict
	      Suppress conversion of units to their reciprocal units.

       -v, --verbose
	      Give slightly more verbose output when converting units.	When  combined	with  the
	      `-c' option this gives the same effect as `--check-verbose'.

       -V, --version
	      Print  program version number, tell whether the readline library has been included,
	      and give the location of the default units data file.

       The conversion information is read from a units data file which is called `units.dat'  and
       is  probably  located in the `/usr/local/share' directory.  If you invoke `units' with the
       `-V' option, it will print the location of this file.  The default file	includes  defini-
       tions  for  all	familiar units, abbreviations and metric prefixes.  It also includes many
       obscure or archaic units.

       Many constants of nature are defined, including these:

	   pi	     ratio of circumference to diameter
	   c	     speed of light
	   e	     charge on an electron
	   force     acceleration of gravity
	   mole      Avogadro's number
	   water     pressure per unit height of water
	   Hg	     pressure per unit height of mercury
	   au	     astronomical unit
	   k	     Boltzman's constant
	   mu0	     permeability of vacuum
	   epsilon0  permitivity of vacuum
	   G	     gravitational constant
	   mach      speed of sound

       The database includes atomic masses for all of the elements and numerous other  constants.
       Also  included  are  the  densities  of various ingredients used in baking so that `2 cups
       flour_sifted' can be converted to `grams'.  This is not an exhaustive list.   Consult  the
       units data file to see the complete list, or to see the definitions that are used.

       The  unit  `pound' is a unit of mass.  To get force, multiply by the force conversion unit
       `force' or use the shorthand `lbf'.  (Note that `g'  is	already  taken	as  the  standard
       abbreviation  for the gram.)  The unit `ounce' is also a unit of mass.  The fluid ounce is
       `fluidounce' or `floz'.	British capacity units that differ from  their	US  counterparts,
       such  as  the  British Imperial gallon, are prefixed with `br'.	Currency is prefixed with
       its country name: `belgiumfranc', `britainpound'.

       The US Survey foot, yard, and mile can be obtained by using the `US' prefix.  These  units
       differ slightly from the international length units.  They were in general use until 1959,
       and are still used for geographic surveys.  The acre is officially defined in terms of the
       US  Survey  foot.   If  you  want an acre defined according to the international foot, use
       `intacre'.  The difference between these units is about 4 parts per million.  The  British
       also used a slightly different length measure before 1959.  These can be obtained with the
       prefix `UK'.

       When searching for a unit, if the specified string does not appear exactly as a unit name,
       then  the  `units'  program will try to remove a trailing `s' or a trailing `es'.  If that
       fails, `units' will check for a prefix.	All of the standard metric prefixes are defined.

       To find out what units and prefixes are available, read the standard units data file.

       All of the units and prefixes that `units' can convert are defined in the units data file.
       If you want to add your own units, you can supply your own file.

       A  unit	is  specified  on  a single line by giving its name and an equivalence.  Comments
       start with a `#' character, which can appear anywhere in a line.  The backslash	character
       (`')  acts as a continuation character if it appears as the last character on a line, mak-
       ing it possible to spread definitions out over several lines if desired.

       Unit names must not contain any of the operator characters `+', `-', `*', `/', `|', `^' or
       the  parentheses.   They  cannot begin with a digit or a decimal point (`.'), nor can they
       end with a digit (except for zero).  Be careful to define new units in terms of	old  ones
       so  that  a  reduction leads to the primitive units, which are marked with `!' characters.
       When adding new units, be sure to use the `-c' option to check that the new  units  reduce
       properly.   If  you  define  any  units which contain `+' characters, carefully check them
       because the `-c' option will not catch non-conformable sums.  If you create a loop in  the
       units  definitions,  then  `units' will hang when invoked with the `-c' options.  You will
       need to use the `--check-verbose' option which prints out each unit  as	it  checks  them.
       The  program  will still hang, but the last unit printed will be the unit which caused the
       infinite loop.

       Here is an example of a short units file that defines some basic units:

	 m	  !	    # The meter is a primitive unit
	 sec	  !	    # The second is a primitive unit
	 micro-   1e-6	    # Define a prefix
	 minute   60 sec    # A minute is 60 seconds
	 hour	  60 min    # An hour is 60 minutes
	 inch	  0.0254 m  # Inch defined in terms of meters
	 ft	  12 inches # The foot defined in terms of inches
	 mile	  5280 ft   # And the mile

       A unit which ends with a `-' character is a prefix.  If a prefix definition  contains  any
       `/' characters, be sure they are protected by parentheses.  If you define `half- 1/2' then
       `halfmeter' would be equivalent to `1 / 2 meter'.

       Some units conversions of interest are nonlinear;  for  example,  temperature  conversions
       between	the Fahrenheit and Celsius scales cannot be done by simply multiplying by conver-
       sions factors.

       When you give a linear unit definition such as `inch 2.54 cm' you are  providing  informa-
       tion  that  `units'  uses to convert values in inches into primitive units of meters.  For
       nonlinear units, you give a functional definition that provides the same information.

       Nonlinear units are represented using a functional notation.  It is best  to  regard  this
       notation  not  as  a function call but as a way of adding units to a number, much the same
       way that writing a linear unit name after a number adds units to that number.  Internally,
       nonlinear  units are defined by a pair of functions which convert to and from linear units
       in the data file, so that an eventual conversion to primitive units is possible.

       Here is an example nonlinear unit definition:

       tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

       A nonlinear unit definition comprises a unit name, a dummy parameter name, two  functions,
       and  two  corresponding	units.	The functions tell `units' how to convert to and from the
       new unit.  In order to produce valid results, the arguments of  these  functions  need  to
       have  the  correct  dimensions.	 To facilitate error checking, you may specify the dimen-

       The definition begins with the unit name followed immediately (with no spaces)  by  a  `('
       character.   In	parentheses is the name of the parameter.  Next is an optional specifica-
       tion of the units required by the functions in this definition.	In the example above, the
       `tempF'	function  requires  an input argument conformable with `1'.  For normal nonlinear
       units definitions the forward function will always take	a  dimensionless  argument.   The
       inverse	function requires an input argument conformable with `K'.  In general the inverse
       function will need units that match the quantity measured by  your  nonlinear  unit.   The
       sole  purpose of the expression in brackets to enable `units' to perform error checking on
       function arguments.

       Next the function definitions appear.  In the  example  above,  the  `tempF'  function  is
       defined by

	   tempF(x) = (x+(-32)) degF + stdtemp

       This gives a rule for converting `x' in the units `tempF' to linear units of absolute tem-
       perature, which makes it possible to convert from tempF to other units.

       In order to make conversions to Fahrenheit possible, you must give a rule for the  inverse
       conversions. The inverse will be `x(tempF)' and its definition appears after a `;' charac-
       ter.  In our example, the inverse is

	   x(tempF) = (tempF+(-stdtemp))/degF + 32

       This inverse definition takes an absolute temperature as its argument and converts  it  to
       the  Fahrenheit temperature.  The inverse can be omitted by leaving out the `;' character,
       but then conversions to the unit will be impossible.  If the inverse is omitted	then  the
       `--check'  option will display a warning.  It is up to you to calculate and enter the cor-
       rect inverse function to obtain	proper	conversions.   The  `--check'  option  tests  the
       inverse	at one point and print an error if it is not valid there, but this is not a guar-
       antee that your inverse is correct.

       If you wish to make synonyms for nonlinear units, you still need to define both	the  for-
       ward and inverse functions.  Inverse functions can be obtained using the `~' operator.  So
       to create a synonym for `tempF' you could write

	   fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)

       You may occasionally wish to define a function that operates on units.  This can  be  done
       using  a nonlinear unit definition.  For example, the definition below provides conversion
       between radius and the area of a circle.  Note that this definition requires a  length  as
       input and produces an area as output, as indicated by the specification in brackets.

	   circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)

       Sometimes  you  may  be	interested  in	a piecewise linear unit such as many wire gauges.
       Piecewise linear units can be defined by specifying conversions to linear units on a  list
       of  points.   Conversion  at other points will be done by linear interpolation.	A partial
       definition of zinc gauge is

	   zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1

       In this example, `zincgauge' is the name of the piecewise linear unit.  The definition  of
       such  a	unit  is  indicated by the embedded `[' character.  After the bracket, you should
       indicate the units to be attached to the numbers in  the  table.   No  spaces  can  appear
       before  the `]' character, so a definition like `foo[kg meters]' is illegal; instead write
       `foo[kg*meters]'.  The definition of the unit consists of a list of pairs optionally sepa-
       rated  by  commas.   This list defines a function for converting from the piecewise linear
       unit to linear units.  The first item in each pair is the function  argument;  the  second
       item  is  the value of the function at that argument (in the units specified in brackets).
       In this example, we define `zincgauge' at five points.  For example, we set `zincgauge(1)'
       equal  to `0.002 in'.  Definitions like this may be  more readable  if written using  con-
       tinuation characters as

	    zincgauge[in] \
	       1  0.002 \
	       10 0.02 \
	       15 0.04 \
	       19 0.06 \
	       23 0.1

       With the preceeding definition, the following conversion can be performed:

	   You have: zincgauge(10)
	   You want: in
	       * 0.02
	       / 50
	   You have: .01 inch
	   You want: zincgauge

       If you define a piecewise linear unit that is not strictly  monotonic,  then  the  inverse
       will  not  be  well  defined.   If  the inverse is requested for such a unit, `units' will
       return the smallest inverse.  The `--check' option will print a warning if a non-monotonic
       piecewise linear unit is encountered.

       Some units have different values in different locations.  The localization feature accomo-
       dates this by allowing the units database to specify  region  dependent	definitions.	A
       locale  region  in  the	units  database begins with `!locale' followed by the name of the
       locale.	The leading `!' must appear in the first  column  of  the  units  database.   The
       locale  region is terminated by `!endlocale'.  The following example shows how to define a
       couple units in a locale.

       !locale en_GB
       ton		       brton
       gallon		       brgallon

       The current locale is specified by the `LOCALE' environment variable.  Note that the  `-c'
       option only checks the definitions which are active for the current locale.

       The `units' programs uses the following environment variables.

       LOCALE Specifies  the locale.  The default is `en_US'.  Sections of the units database are
	      specific to certain locales.

       PAGER  Specifies the pager to use for help and for displaying the conformable units.   The
	      help function browses the units database and calls the pager using the `+nn' syntax
	      for specifying a line number.  The default pager is `more', but `less', `emacs', or
	      `vi' are possible alternatives.

	      Specifies  the  units  database  file to use (instead of the default). This will be
	      overridden by the `-f' option.

       If the `readline' package has been compiled in, then when `units' is  used  interactively,
       numerous command line editing features are available.  To check if your version of `units'
       includes the readline, invoke the program with the `--version' option.

       For complete information about readline, consult the documentation for the readline  pack-
       age.   Without  any  configuration,  `units' will allow editing in the style of emacs.  Of
       particular use with `units' are the completion commands.

       If you type a few characters and then hit `ESC' followed by the `?' key then `units'  will
       display	a  list  of all the units which start with the characters typed.  For example, if
       you type `metr' and then request completion, you will see something like this:

       You have: metr
       metre		 metriccup	   metrichorsepower  metrictenth
       metretes 	 metricfifth	   metricounce	     metricton
       metriccarat	 metricgrain	   metricquart	     metricyarncount
       You have: metr

       If there is a unique way to complete a unitname, you can hit the tab key and `units'  will
       provide	the  rest  of  the unit name.  If `units' beeps, it means that there is no unique
       completion.  Pressing the tab key a second time will print the list of all completions.

       /usr/share/units.dat - the standard units data file

       Adrian Mariano (adrian@cam.cornell.edu)

					   30 Jan 2001					 UNITS(1)
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