From dwells@fits.cx.nrao.edu Wed Jan 29 18:07:02 1992
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	["2771" "Thu" "23" "January" "1992" "14:31:07" "GMT" "Don Wells" "dwells@fits.cx.nrao.edu " nil "59" "SI Units (was Re: AAS meeting, Atlanta)" "^From:" nil nil "1"])
Newsgroups: sci.astro
In-Reply-To: metares@well.sf.ca.us's message of 23 Jan 92 06: 07:42 GMT
Organization: National Radio Astronomy Observatory, Charlottesville, VA
Distribution: sci
From: dwells@fits.cx.nrao.edu (Don Wells)
Subject: SI Units (was Re: AAS meeting, Atlanta)
Date: Thu, 23 Jan 1992 14:31:07 GMT

In article <29569@well.sf.ca.us> metares@well.sf.ca.us (Tom Van
Flandern) gives a glossary of certain astronomical units and
terminology. Some corrections are needed:

TVF> Angstrom: A unit of length equal to 10^-10 meters = 10^-8 cm.
     ^^^^^^^^                               ^^^                ^^

TVF> Used primarily to measure the wavelengths of photons of visible
TVF> light.  

The IAU Style Manual (1989, "The Preparation of Astronomical Papers
and Reports", prepared by G.A. Wilkins, President of Commission 5, on
behalf of the Executive Committee of the International Astronomical
Union) recommends use of SI (MKS) units, which in this context means
the *nanometer*, 10^-9 meters. The Angstrom is listed in Table 7
("Non-SI units and symbols whose continued use is deprecated", p.S24).

TVF> Electron Volt: A unit of energy equal to 1.60 x 10^-12 ergs...  
                                              ^^^^^^^^^^^^^^^^^^
                                              0.1602177 aJ (attoJoule)
                                                     ("atto" = 10^-18)

The eV is listed in Table 6 ("Non-SI units that are recognised for use
in astronomy", p.S23), and "atto" is listed in Table 5 ("SI prefixes
and symbols for multiples and submultiples").

TVF> Electromagnetic Spectrum: ... range of possible energies or
TVF> wavelengths of photons... Visible light..	wavelengths.. 3,000
TVF> and 10,000 Angstroms..	infrared.. wavelength.. 1 micron and
     ^^^^^^^^^^^^^^^^^^^^
     300 and 1000 nm

TVF> 1000 microns (= 1 millimeter).  Microwave.. 1 mm and 10 cm.
     ^^^^^^^^^^^^      ^^^^^^^^^^                  ^^        ^^
     1-1000 {\mu}m      mm                (both are legitimate SI units)
     
TVF> Radio waves..  10 cm and 10 meters... ultraviolet.. 100 Angstroms
                                 ^^^^^^
                                  m

TVF> and 3000 Angstroms... 
     ^^^^^^^^^^^^^^^^^^
       10-300 nm

Section 5.11 of the Manual ("SI Units", p.S20) says: "... The units of
the centimetre-gram-second (CGS) system and other non-SI units, which
will be unfamiliar to most young scientists, should not be used even
though they may be considered to have some advantages over SI units by
some astronomers. The IAU Executive Committee has recommended (see
Appendix B) that astronomers should complete the change-over quickly,
and so, for example, reports and papers for the IAU General Assembly
in 1991 should all use SI units or other recognised units."

--

Donald C. Wells             Associate Scientist        dwells@nrao.edu
National Radio Astronomy Observatory                   +1-804-296-0277
520 Edgemont Road                                 Fax= +1-804-296-0278
Charlottesville, Virginia 22903-2475 USA            78:31.1W, 38:02.2N 

From dwells@fits.cx.nrao.edu Wed Jan 29 18:07:34 1992
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	["4892" "Fri" "24" "January" "1992" "18:08:43" "GMT" "Don Wells" "dwells@fits.cx.nrao.edu " nil "96" "Re: SI Units (was Re: AAS meeting, Atlanta)" "^From:" nil nil "1"])
Newsgroups: sci.astro
In-Reply-To: dwells@fits.cx.nrao.edu's message of Thu, 23 Jan 1992 14: 31:07 GMT
Organization: National Radio Astronomy Observatory, Charlottesville, VA
Distribution: sci
From: dwells@fits.cx.nrao.edu (Don Wells)
Subject: Re: SI Units (was Re: AAS meeting, Atlanta)
Date: Fri, 24 Jan 1992 18:08:43 GMT

In article <DWELLS.92Jan23093107@fits.cx.nrao.edu>
dwells@fits.cx.nrao.edu (Don Wells) writes:

"...  The IAU Style Manual (1989, "The Preparation of Astronomical
Papers and Reports", prepared by G.A. Wilkins, President of Commission
5, on behalf of the Executive Committee of the International
Astronomical Union) recommends use of SI (MKS) units..."

I have received several Email messages in response to my posting on SI
units, and after reading them (and answering some) I offer the
following additional remarks:

1. Undergraduate Training vs. Graduate Training

I was an undergraduate physics student in the early 60s, 30 years ago,
and was taught in MKS (SI) units. Later in that decade, in graduate
school, I encountered the CGS approach. I thought at that time that
both systems were rational, each in its own way. I assumed that SI was
destined to be the accepted standard, but that in that era one still
needed to be bilingual. As a result of my posting on this subject I
have received Email from recent graduate students who tell me that the
situation I experienced 20-30 years ago still persists!  I.e., physics
undergraduates are still taught MKS and must still learn CGS in
astronomy graduate school. The persistence of this anomaly over such a
timespan is telling us something.

2. SI Units in the IAU Style Manual

It is, of course, true that IAU standards are only recommendations,
and that adherance to them is voluntary. However --- if the
recommendation to use SI units is opposed by a large fraction (a
majority?)  of our community, why isn't that fraction represented in
Commission 5 and/or the IAU Executive Committee? Is the persistence of
usage of both MKS and CGS units purely a phenomenon of (North)
American graduate departments, or is it present in astronomy
departments elsewhere in the world? The IAU is *the* international
organization of professional astronomers; in the end the practices it
recommends should really represent the consensus of astronomers
everywhere, or else those recommendations should be changed. 

3. Importance of Standard Units

Several decades of experience demonstrate that astronomers are able to
operate with both systems of units, and that few problems are caused
by the potential ambiguities. I myself don't particularly prefer
either system over the other. What I *do* care about is that
inconsistencies and ambiguities should be minimized in astronomical
archives (both observational data and published text) as much as
possible, in order to facilitate robust automated search and retrieval
technology in the years to come. My worries about this problem are the
real motivation for my posting on this subject.

For example, if the TUNITn keywords of FITS tables do not use a
consistent system of units we will surely find that it will be harder
to write our data analysis software. In March 1979 Eric Greisen and I
decides that the Basic FITS Agreement would specify that SI units
should be used in FITS files, and that decision was recently endorsed
by members of the IAU FITS Working Group and the NASA Technical Panel
during the NASA-supported codification of the FITS agreements. These
decisions were made precisely because of the worry that software will
prove to be less robust than humans in interpreting ambiguous or
inconsistent situations in our future archives.

4. Brief Bibliography

* "A Physicist's Desk Reference" (The Second Edition of Physics Vade
Mecum, H.L. Anderson, Editor in Chief, Am. Inst. Physics 1989) gives a
detailed tabulation of SI and units conversions in section 1.02 ("The
International System of Units", pp.5-10). It also contains a
convenient summary of the real MKS-vs-CGS (Gaussian units) issues in
section 1.05 (Physics Formulary), subsection C (Electricity and
Magnetism), where the notations are compared for E&M case by case. It
is clear that both systems are rational, and attractive, each in its
own way.

* Chicago Manual of Style says: "[section] 14.41 The International
System of Units (..abbreviated "SI") is used generally by scientists
around the world...". 

* Astrophysical Journal Instructions to Authors (1992 December 1, p.i)
says: "... 3. The standard abbreviations (without periods) for SI units
and some cgs units may be used..."

* Monthly Notices RAS Notice to Authors (recent issue) says: "... 7.
UNITS. Authors are strongly encouraged to use SI units."

* Document NOST-100-0.3b (6-November-1991, "Implementation of the
Flexible Image Transport System [FITS]", section 8.1.2, p.34, "TUNITn
Keywords") says: "...Use of the units defined in the IAU Style Manual
is recommended."
--

Donald C. Wells             Associate Scientist        dwells@nrao.edu
National Radio Astronomy Observatory                   +1-804-296-0277
520 Edgemont Road                                 Fax= +1-804-296-0278
Charlottesville, Virginia 22903-2475 USA            78:31.1W, 38:02.2N 

From njzy@vax5.cit.cornell.edu Wed Jan 29 18:07:48 1992
Status: RO
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	["2272" "" "24" "January" "92" "09:38:33" "EST" "T. Joseph Lazio, Cornell University" "njzy@vax5.cit.cornell.edu " nil "50" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro
Distribution: sci
Organization: Cornell University
From: njzy@vax5.cit.cornell.edu (T. Joseph Lazio, Cornell University)
Subject: Re: SI Units vs cgs units
Date: 24 Jan 92 09:38:33 EST

Keywords:  SI vs cgs
Summary:  Oh, no, not another change!

In article <DWELLS.92Jan23093107@fits.cx.nrao.edu>,
dwells@fits.cx.nrao.edu (Don Wells) writes: 
> In article <29569@well.sf.ca.us> metares@well.sf.ca.us (Tom Van
> Flandern) gives a glossary of certain astronomical units and
> terminology. Some corrections are in order [...]
> 
> TVF> Electromagnetic Spectrum: ... range of possible energies or
> TVF> wavelengths of photons... Visible light..	wavelengths.. 3,000
> TVF> and 10,000 Angstroms..	infrared.. wavelength.. 1 micron and
>      ^^^^^^^^^^^^^^^^^^^^
>      300 and 1000 nm
> 
> TVF> 1000 microns (= 1 millimeter).  Microwave.. 1 mm and 10 cm.
>      ^^^^^^^^^^^^      ^^^^^^^^^^                  ^^        ^^
>      1-1000 {\mu}m      mm                (both are legitimate SI units)
>      
> TVF> Radio waves..  10 cm and 10 meters... ultraviolet.. 100 Angstroms
>                                  ^^^^^^
>                                   m
> 
> TVF> and 3000 Angstroms... 
>      ^^^^^^^^^^^^^^^^^^
>        10-300 nm
> 
> Section 5.11 of the Manual ("SI Units", p.S20) says: "... The units of
> the centimetre-gram-second (CGS) system and other non-SI units, which
> will be unfamiliar to most young scientists, should not be used even
> though they may be considered to have some advantages over SI units by
> some astronomers. The IAU Executive Committee has recommended (see
> Appendix B) that astronomers should complete the change-over quickly,
> and so, for example, reports and papers for the IAU General Assembly
> in 1991 should all use SI units or other recognised units."

 Sigh.  After spending all my undergraduate years learning SI units, 
 I have spent my years in grad. school changing over and becoming 
 quite comfortable with cgs units.  Am I going to have to change, 
 again?
 
-- 
 T. Joseph Lazio                | Why relativity? and Why  
 514 Space Sciences             | turbulence?  I really believe   
 Ithaca, NY  14853              | [God] will have an answer for the
 (607) 255-6420                 | first [question].
 lazio@astrosun.tn.cornell.edu  |   -- W. Heisenberg, on his death bed
ICBM:                           |
 42 deg. 20' 08" N              |              STOP RAPE
 76 deg. 28' 48" W              |

From cain@geomag.gly.fsu.edu Wed Jan 29 18:07:56 1992
Status: RO
X-VM-v5-Data: ([nil nil nil nil nil nil nil nil nil]
	["2435" "" "26" "January" "92" "15:40:35" "GMT" "Joe Cain" "cain@geomag.gly.fsu.edu " nil "45" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Followup-To: sci.astro
Distribution: sci
Organization: Florida State University Geology Dept.
From: cain@geomag.gly.fsu.edu (Joe Cain)
Subject: Re: SI Units vs cgs units
Date: 26 Jan 92 15:40:35 GMT

In article <1992Jan24.093833.10105@vax5.cit.cornell.edu> njzy@vax5.cit.cornell.edu (T. Joseph Lazio, Cornell University) writes:
>In article <DWELLS.92Jan23093107@fits.cx.nrao.edu>,
>dwells@fits.cx.nrao.edu (Don Wells) writes: 
>> In article <29569@well.sf.ca.us> metares@well.sf.ca.us (Tom Van
>> Flandern) gives a glossary of certain astronomical units and
>> terminology. Some corrections are in order [...]
>
> Sigh.  After spending all my undergraduate years learning SI units, 
> I have spent my years in grad. school changing over and becoming 
> quite comfortable with cgs units.  Am I going to have to change, 
> again?

	As one who indeed encountered MKS at Caltech in the 50's but
worked under Sydney Chapman at the U. of Alaska for graduate school
and found him a diehard cgs person, I can indeed empathize with this
uneeded confusion. However, I chose for my planetary geology text this
year what I thought was the latest published (Wagner's "Introduction
to the Solar System," 1991) which has a prominent table in cgs only. (He
also makes the mistake of equating to old English units throught the
text). Thus the emergence of SI seems slow and will require continued
pressure to keep stomping on the multiplicity of systems. It would
help a lot to also push hard in the US to get a complete conversion
>from the old English so students see it as useful and not just more
learning they should forget.

	The actual units can be SI compatible and still understandable
if they are kept fairly simple. For my course I use c = 300,000 km/sec
instead of 3x10**8 m/sec simply because it is easier to understand
compared with the 150,000 km AU. However, I doubt that the SI units of
density (kg/m**3) will ever supplant gm/cc simply because 1, 3, 5, are
simple compared to 1000, 3000, 5000, etc. For radiation also the units
can be more or less SI and still useful. I have had to convert my
thinking that 5577A was apple green and 6300A red to 500, 600 nM, but
this is not so bad. Microns are hard to integrate into SI thinking,
but you are going to have a hard time getting radio astronomers to use
units they can't relate to waveguide and antenna sizes.

	In summary, I think you have to keep pushing SI, be kind to those
whose thinking was frozen decades ago, and try to use the smallest
number of units to promote the most interdisciplinary understanding. 

	

Joseph Cain		cain@geomag.gly.fsu.edu
cain@fsu.bitnet		scri::cain

From gill@physics.ubc.ca Wed Jan 29 18:07:57 1992
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	["448" "Mon" "27" "January" "1992" "17:35:12" "GMT" "Arnold Gill visiting astrophys phd std" "gill@physics.ubc.ca " nil "9" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro
Nntp-Posting-Host: physics.ubc.ca
Organization: University of British Columbia, Vancouver, B.C., Canada
Distribution: sci
From: gill@physics.ubc.ca (Arnold Gill visiting astrophys phd std)
Subject: Re: SI Units vs cgs units
Date: Mon, 27 Jan 1992 17:35:12 GMT

cain@geomag.gly.fsu.edu (Joe Cain) writes:
>	In summary, I think you have to keep pushing SI, be kind to those
>whose thinking was frozen decades ago, and try to use the smallest
>number of units to promote the most interdisciplinary understanding. 

     And everyone also has to stay `bilingual' so that one can understand papers
     written in the `Dark Ages'.
--
Arnold Gill --- astrophysician trainee in exile             gill@physics.ubc.ca

From gaetz@julian.uwo.ca Wed Jan 29 18:07:59 1992
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	["1510" "Mon" "27" "January" "1992" "22:35:05" "GMT" "Terry Gaetz" "gaetz@julian.uwo.ca " nil "32" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro
Organization: Dept. of Astronomy, Univ. of Western Ontario
Distribution: sci
From: gaetz@julian.uwo.ca (Terry Gaetz)
Subject: Re: SI Units vs cgs units
Date: Mon, 27 Jan 1992 22:35:05 GMT

In article <gill.696533712@physics.ubc.ca> gill@physics.ubc.ca (Arnold Gill visiting astrophys phd std) writes:
>cain@geomag.gly.fsu.edu (Joe Cain) writes:
>>	In summary, I think you have to keep pushing SI, be kind to those
>>whose thinking was frozen decades ago, and try to use the smallest
>>number of units to promote the most interdisciplinary understanding. 
>
>     And everyone also has to stay `bilingual' so that one can understand papers
>     written in the `Dark Ages'.

'Bilingualism' will stay important, too; too many standard reference 
tables have used (and new ones continue to use) non-SI units.

It is not only North American astronomers who persist in using non-SI 
units, either - see many physics papers and reference tables:

<Rooting through the shelves...>
  . "Atomic Transition Probabilities: Iron through Nickel" (1988) 
      - wavelengths in angstroms, energies in cm^-1
	(This is an NBS/NSRDS publication to boot!)
  . National Institute for Fusion Science (Nagoya, Japan) 
    "Total and Partial Cross Sections of Electron Transfer 
     Processes for Be^q+...", preprint, (Jun, 1991)
             - energy in eV, cross sections in cm^2
    "Observation of Parallel Viscosity in the CHS 
     Heliotron/Torsatron", preprint, (Jan, 1991)
	     - temperature in eV, density in 10^13 cm^-3, velocity in
	       km s^-1, viscosity in m^2 s^-1

SI may be the mandated standard, but I don't see cgs and non-SI units
going away anytime soon.
--
Terry Gaetz  --  gaetz@julian.uwo.ca

From mcdonald@aries.scs.uiuc.edu Wed Jan 29 18:08:00 1992
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	["2694" "Mon" "27" "January" "1992" "14:46:48" "GMT" "Doug McDonald" "mcdonald@aries.scs.uiuc.edu " nil "61" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: University of Illinois at Urbana
From: mcdonald@aries.scs.uiuc.edu (Doug McDonald)
Subject: Re: SI Units vs cgs units
Date: Mon, 27 Jan 1992 14:46:48 GMT


In article <1992Jan26.104035.19842@mailer.cc.fsu.edu> cain@geomag.gly.fsu.edu (Joe Cain) writes:
>In article <1992Jan24.093833.10105@vax5.cit.cornell.edu> njzy@vax5.cit.cornell.edu (T. Joseph Lazio, Cornell University) writes:
>>In article <DWELLS.92Jan23093107@fits.cx.nrao.edu>,
>>dwells@fits.cx.nrao.edu (Don Wells) writes: 


[SI flame wars] [Note: Im not an astronomer, I'm a physicist and chemist]

I have a very strong opinion on this, one shared my many (most?) of my
colleagues, including several Nobel Prize winners:

A plague on those who try to force pure SI units on everybody.


Point one:

The metric system was originally designed to have convenient multiples
of ten for every unit - grams, kilograms, gigagrams, meters, centimeters,
micrometers, seconds, milliseconds, picoseconds. Why not use that which is
convenient? I can remember the basic numbers (Planck's constant, mass
of proton, etc.) in both MKS and cgs units. I use whichever is easier.
It is trivial to convert. 

Point two:

In the actual world it is stupid to express everythings in say, meters and
seconds. Everybody I know expresses times in either picoseconds or femtoseconds
when relating to actual events, because that is the times that things actually
occur in our lab, for example, a laser pulse lasts roughly 1 picosecond,
always between .01 and 100 picoseconds. 

Consider lengths - teh wavelengths of light are often expressed in microns.
Now the micron happen to be one micrometer. Why worry? People express
energies in that unphysical unit the "wavenumber" which indeed is
not SI or cgs or anything - its not an energy unit at all, just a reciprocal
wavelength. Yet it is very convenient indeed. It is just silly to
try to talk about energies of molecular events induced by light in units
unreleated to the commonly used measure of light, the wavelength.


Then there are  pressure units used in vacuum work. You will note that
pressure gauges are calibrated in Torr. Everybody uses those units in the
lab. Really. Except for pressures greater than one atmosphere, where
they use atmospheres or even, heaven forbid, psi. I do admit to
removing psi from papers and putting in atmosphere.


I think that worrying about units is silly. I'd rather worry about the
science. In fact, using SI units in fields where they are not normally used,
such as mine, is counterproductive. IF somebody actually tries to give a talk
in SI units, they will invariably be asked to give, for example, the
pressures of their beam sources in either Torr or atmospheres. That is what
people think in. 


And to the astronomers: if you want to use SI units only please remember to
NEVER use AU or parsecs!!!


Doug McDonald

From dmark@acsu.buffalo.edu Wed Jan 29 18:08:04 1992
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	["771" "" "27" "January" "92" "22:44:15" "GMT" "David Mark" "dmark@acsu.buffalo.edu " nil "18" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: UB
Nntp-Posting-Host: autarch.acsu.buffalo.edu
From: dmark@acsu.buffalo.edu (David Mark)
Subject: Re: SI Units vs cgs units
Date: 27 Jan 92 22:44:15 GMT

>The metric system was originally designed to have convenient multiples
>of ten for every unit - grams, kilograms, gigagrams, meters, centimeters,
>micrometers, seconds, milliseconds, picoseconds. Why not use that which is
>convenient? I can remember the basic numbers (Planck's constant, mass
>of proton, etc.) in both MKS and cgs units. I use whichever is easier.
>It is trivial to convert. 

I'll ask the naive question; I hope I'm not the only sci.geo.geology 
subscriber who doesn't know this!

I thought I knew what the 'metric system' was, and also that SI was the
abbreviation for the scholarly or 'official' term for the metric system.

So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
system'?

David Mark
dmark@sun.acsu.buffalo.edu

From nick@sunburn.waterloo.edu Wed Jan 29 18:08:05 1992
Status: RO
X-VM-v5-Data: ([nil nil nil nil nil nil nil nil nil]
	["1841" "Tue" "28" "January" "1992" "00:56:35" "GMT" "Nick Fitzpatrick" "nick@sunburn.waterloo.edu " nil "34" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: University of Waterloo
From: nick@sunburn.waterloo.edu (Nick Fitzpatrick)
Subject: Re: SI Units vs cgs units
Date: Tue, 28 Jan 1992 00:56:35 GMT

In article <1992Jan27.224415.9284@acsu.buffalo.edu> dmark@acsu.buffalo.edu (David Mark) writes:
>>The metric system was originally designed to have convenient multiples
>>of ten for every unit - grams, kilograms, gigagrams, meters, centimeters,
>>micrometers, seconds, milliseconds, picoseconds. Why not use that which is
>>convenient? I can remember the basic numbers (Planck's constant, mass
>>of proton, etc.) in both MKS and cgs units. I use whichever is easier.
>>It is trivial to convert. 
>
>I'll ask the naive question; I hope I'm not the only sci.geo.geology 
>subscriber who doesn't know this!
>
>I thought I knew what the 'metric system' was, and also that SI was the
>abbreviation for the scholarly or 'official' term for the metric system.
>
>So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
>system'?

cgs, is a length-mass-time system, with cm, g, s as the base units, it is not
widely used anymore, except perhaps in the US which I here actually even
uses Imperial units on occasion  (I mean can you imagine!! (Flame me!)

MKS (if I remember correctly) is a length-force-time system, where metre, (that
is meter for our american cousins who can't spell) kg and s are the base units
Nobody uses this.  I even recall hearing that it is banned in some European 
countries!  (Mind you Imperial was banned here in Canada at one point, until
someone pointed out that with freedom of speech, one could not ban Imperial)

SI, or Systeme Internationale, which is what we often mistakenly call the
metric system, uses a length-mass-time with metres, kilograms, and seconds
as the base units (+ Celcius, and a few other special things that I
forget)..  Derived units include Litres for volume, Newtons for force
Pascals for pressure, ares, for area, etc,etc

Nicholas Fitzpatrick,  Waterloo, Ontario, Canada

From nick@sunburn.waterloo.edu Wed Jan 29 18:08:06 1992
Status: O
X-VM-v5-Data: ([nil t nil nil nil nil nil nil nil]
	["1822" "Tue" "28" "January" "1992" "03:56:26" "GMT" "Nick Fitzpatrick" "nick@sunburn.waterloo.edu " nil "37" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: nick@sunburn.waterloo.edu (Nick Fitzpatrick)
Subject: Re: SI Units vs cgs units
Organization: University of Waterloo
Date: Tue, 28 Jan 1992 03:56:26 GMT

In article <1992Jan28.005635.14025@watserv1.waterloo.edu> nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
>In article <1992Jan27.224415.9284@acsu.buffalo.edu> dmark@acsu.buffalo.edu (David Mark) writes:
>>>The metric system was originally designed to have convenient multiples
>>>of ten for every unit - grams, kilograms, gigagrams, meters, centimeters,
>>>micrometers, seconds, milliseconds, picoseconds. Why not use that which is
>>>convenient? I can remember the basic numbers (Planck's constant, mass
>>>of proton, etc.) in both MKS and cgs units. I use whichever is easier.
>>>It is trivial to convert. 
>>
>>I'll ask the naive question; I hope I'm not the only sci.geo.geology 
>>subscriber who doesn't know this!
>>
>>I thought I knew what the 'metric system' was, and also that SI was the
>>abbreviation for the scholarly or 'official' term for the metric system.
>>
>>So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
>>system'?
>
>cgs, is a length-mass-time system, with cm, g, s as the base units, it is not
>widely used anymore, except perhaps in the US which I here actually even
>uses Imperial units on occasion  (I mean can you imagine!! (Flame me!)
>
>MKS (if I remember correctly) is a length-force-time system, where metre, (that

Okay, before anyone else has the chance to flame me, let be the first!  MKS
is a length-mass-time system.  (Boy I'd look to meet the fool who thought 
it was force ;-)   So the question arises, what is the difference between
MKS and SI.

And before anyone else writes me telling me how great cgs is for Gaussian
whatever, please note from the >> that I was following up a comment from
sci.geo.geology.  (sometimes I think the sci.space lot are from another
planet or something! :-)
>
>Nicholas Fitzpatrick,  Waterloo, Ontario, Canada
ditto


From gaetz@julian.uwo.ca Wed Jan 29 18:08:08 1992
Status: O
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	["2871" "Tue" "28" "January" "1992" "03:31:27" "GMT" "Terry Gaetz" "gaetz@julian.uwo.ca " nil "60" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: gaetz@julian.uwo.ca (Terry Gaetz)
Subject: Re: SI Units vs cgs units
Organization: Dept. of Astronomy, Univ. of Western Ontario
Date: Tue, 28 Jan 1992 03:31:27 GMT

In article <1992Jan27.224415.9284@acsu.buffalo.edu> dmark@acsu.buffalo.edu (David Mark) writes:
>>The metric system was originally designed to have convenient multiples
>>of ten for every unit - grams, kilograms, gigagrams, meters, centimeters,
>>micrometers, seconds, milliseconds, picoseconds. Why not use that which is
>>convenient? I can remember the basic numbers (Planck's constant, mass
>>of proton, etc.) in both MKS and cgs units. I use whichever is easier.
>>It is trivial to convert. 
>
>I'll ask the naive question; I hope I'm not the only sci.geo.geology 
>subscriber who doesn't know this!
>
>I thought I knew what the 'metric system' was, and also that SI was the
>abbreviation for the scholarly or 'official' term for the metric system.
>
>So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
>system'?

metric system:  any decimal system of measures based on the metre
	        (e.g. SI, cgs, MKS, MKSA); often SI is meant.
cgs:  system of units based on centimetres (cm), grams (g), and 
      seconds (s).
      (also variants:  electrostatic, electromagnetic, Gaussian, and
		       Heaviside-Lorentz units, depending on the units
                       used for electromagnetic quantities)
MKS:  system of units based on metres (m), kilograms (kg), and 
      seconds (s).
      (variant:  rationalized MKSA adds the ampere)
SI:   Syst\`eme International d'Unit\'es:
         m     metre       (length)
         kg    kilogram    (mass)
         s     second      (time)
         K     kelvin      (temperature interval)
         A     ampere      (electric current)
         cd    candela     (luminous intensity)
         mol   mole        (amount of substance)

      Other units are formed as combinations of these basic units
      and selected powers of ten.  Permitted prefixes are
       E   exa     10^(18)            m   milli    10^(-3)
       P   peta    10^(15)          \mu   micro    10^(-6)
       T   tera    10^(12)            n   nano     10^(-9)
       G   giga    10^(9)             p   pico     10^(-12)
       M   mega    10^(6)             f   femto    10^(-15)
       k   kilo    10^(3)             a   atto     10^(-18)

   hecto (10^2), deca (10), deci (10^-1), and centi (10^-2) are allowed,
   but are to be used only where kilo- or milli- would be impractical.
   Thus, the centimetre (cm) is not a prefered SI unit.

[the above is based on: appendix to Chambers English Dictionary,
                        Jackson: "Classical Electrodynamics"]

SI is the adopted international standard, but (Gaussian) cgs units and 
others (e.g. various forms of 'natural' units) are also widely used in 
astronomy and physics.
--
Terry Gaetz  --  gaetz@julian.uwo.ca

"Without Units, dimensionless analysis itself would be impossible."
                   (somebody's .sig; sorry, I don't have the attribution)

From henry@zoo.toronto.edu Wed Jan 29 18:08:12 1992
Status: O
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	["1736" "Tue" "28" "January" "1992" "17:17:08" "GMT" "Henry Spencer" "henry@zoo.toronto.edu " nil "29" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: henry@zoo.toronto.edu (Henry Spencer)
Subject: Re: SI Units vs cgs units
Date: Tue, 28 Jan 1992 17:17:08 GMT
Organization: U of Toronto Zoology

In article <1992Jan27.224415.9284@acsu.buffalo.edu> dmark@acsu.buffalo.edu (David Mark) writes:
>I thought I knew what the 'metric system' was, and also that SI was the
>abbreviation for the scholarly or 'official' term for the metric system.
>So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
>system'?

They're all metric systems.  The question is, what is the unit of (say)
energy?  Is it kg-m^2/s^2, or g-cm^2/s^2, or what?  And what is its name?
In this case the units differ only by factors of ten, but the situation
can be worse -- there are some electromagnetic units which might or might
not have a factor of pi in them, for example, depending on what convention
you choose.  Over the years various groups chose various different sets of
conventions, and the result was difficult and troublesome conversion
problems when, say, a thermodynamicist wanted to talk to a magnet expert.
You had to be careful even when the names seemed similar; for example,
there were three or four subtly-different units named "calorie".

SI, Systeme International, is an attempt to pull all this together and
have *one* metric system, with *one* unit for expressing, say, magnetic
flux density, and a consistent set of conversions with as few magic
conversion factors as possible.

Although SI is essentially universally accepted as desirable, the switchover
was always expected to be a very long process, and indeed it is proving
to be so.  It takes an awfully long time to convert things like reference
books, not to mention all the problems of equipment.
-- 
"Breakthrough ideas are not             | Henry Spencer @ U of Toronto Zoology
>from teams."  -- Hans von Ohain         |  henry@zoo.toronto.edu  utzoo!henry

From a722756@pan.mc.ti.com Wed Jan 29 18:08:13 1992
Status: O
X-VM-v5-Data: ([nil t nil nil nil nil nil nil nil]
	["1988" "Tue" "28" "January" "1992" "21:51:29" "GMT" "W. D. Rolph" "a722756@pan.mc.ti.com " nil "39" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: a722756@pan.mc.ti.com (W. D. Rolph)
Subject: Re: SI Units vs cgs units
Organization: Texas Instruments Materials and Controls Group
Date: Tue, 28 Jan 1992 21:51:29 GMT

henry@zoo.toronto.edu (Henry Spencer) writes:

>In article <1992Jan27.224415.9284@acsu.buffalo.edu> dmark@acsu.buffalo.edu (David Mark) writes:
>>I thought I knew what the 'metric system' was, and also that SI was the
>>abbreviation for the scholarly or 'official' term for the metric system.
>>So, what are 'cgs' and 'MKS' and how do the differ from 'SI' and 'the metric
>>system'?

>They're all metric systems.  The question is, what is the unit of (say)
>energy?  Is it kg-m^2/s^2, or g-cm^2/s^2, or what?  And what is its name?
>In this case the units differ only by factors of ten, but the situation
>can be worse -- there are some electromagnetic units which might or might
>not have a factor of pi in them, for example, depending on what convention
>you choose.  Over the years various groups chose various different sets of
>conventions, and the result was difficult and troublesome conversion
>problems when, say, a thermodynamicist wanted to talk to a magnet expert.
>You had to be careful even when the names seemed similar; for example,
>there were three or four subtly-different units named "calorie".

>SI, Systeme International, is an attempt to pull all this together and
>have *one* metric system, with *one* unit for expressing, say, magnetic
>flux density, and a consistent set of conversions with as few magic
>conversion factors as possible.

>Although SI is essentially universally accepted as desirable, the switchover
>was always expected to be a very long process, and indeed it is proving
>to be so.  It takes an awfully long time to convert things like reference
>books, not to mention all the problems of equipment.
>-- 
>"Breakthrough ideas are not             | Henry Spencer @ U of Toronto Zoology
>from teams."  -- Hans von Ohain         |  henry@zoo.toronto.edu  utzoo!henry

The wonders of the "standard" metric system.  Now for grins is force in
kilograms, or newtons or what?
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263

From leb@gsfc.nasa.gov Wed Jan 29 18:08:14 1992
Status: O
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	["3292" "" "29" "January" "92" "02:32:11" "GMT" "Lee E. Brotzman" "leb@gsfc.nasa.gov " nil "56" "Re: SI Units vs cgs units" nil nil nil "1"])
From: leb@gsfc.nasa.gov (Lee E. Brotzman)
Newsgroups: sci.astro,sci.space
Subject: Re: SI Units vs cgs units
Date: 29 Jan 92 02:32:11 GMT
Organization: Goddard Space Flight Center
Nntp-Posting-Host: hypatia.gsfc.nasa.gov

>henry@zoo.toronto.edu (Henry Spencer) writes:
>>SI, Systeme International, is an attempt to pull all this together and
>>have *one* metric system, with *one* unit for expressing, say, magnetic
>>flux density, and a consistent set of conversions with as few magic
>>conversion factors as possible.

>>Although SI is essentially universally accepted as desirable, the switchover
>>was always expected to be a very long process, and indeed it is proving
>>to be so.  It takes an awfully long time to convert things like reference
>>books, not to mention all the problems of equipment.
>>-- 
>>"Breakthrough ideas are not             | Henry Spencer @ U of Toronto Zoology
>>from teams."  -- Hans von Ohain         |  henry@zoo.toronto.edu  utzoo!henry

I think that this thread has rapidly diverged from its original intent.  This
is sci.astro, and the discussion was about standardized units for use in
astronomy.  The International Astronomical Union has firmly come down on the
side of SI units.

I have spent my entire nine-year professional career providing data to the 
astronomical community under the auspices of the Astronomical Data Center at 
NASA Goddard Space Flight Center.  In the early 80's, individual requesters 
were provided with one or two datasets on magnetic tape and wrote their own 
analysis routines to reduce the data.  Now they can request large volumes of 
data over the networks or on CD-ROM and can access all of the data 
simultaneously.  Intercomparison of the data is essential to modern data
analysis, and that implies that the data should be in a common system of units.

As a data archive, the ADC must be responsive to the requirements of our
contributors and maintain the data in its original form as given.  On the other
hand, we must be responsive to our requesters and provide the data in the form
they require to complete their work.  The path that we chose was to select a 
standard nomenclature for the field names and for the units that those fields
appeared in.  The work that went into our CD-ROM of astronomical catalogs
was mostly directed to standardizing the nomenclature of fields names and
units.

With a common set of field names (visual magnitude always V, hours of right
acsension always RAH, etc.) and a common set of units (mag always magnitude,
h always hours of time, etc.) it is possible to write software that can 
determine the correct operations to perform on a given datum.  The promulgation 
of these standards is an important function of the international astronomical 
data centers and of the North American and European FITS committees.

For further discussions of the standardized nomenclature proposed by the ADC,
we suggest that you stay in touch with the sci.astro and alt.sci.astro.fits
discussion groups.  The ADC CD-ROM of astronomical catalogs is currently
available from the National Space Science Data Center at NASA Goddard Space
Flight Center, and complete information on how to obtain the data will be
given in this forum as soon as the material is made available.

--
-- Lee E. Brotzman                    Internet:  brotzman@nssdca.gsfc.nasa.gov
-- Hughes STX                         SPAN:      NSSDCA::BROTZMAN
-- National Space Science Data Center BITNET:    ZMLEB@SCFVM
-- NASA Goddard Space Flight Center

From okunewck@psuvax1.cs.psu.edu Wed Jan 29 18:08:16 1992
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	["2144" "Wed" "29" "January" "1992" "18:07:46" "GMT" "Phil OKunewick" "okunewck@psuvax1.cs.psu.edu " nil "43" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: okunewck@psuvax1.cs.psu.edu (Phil OKunewick)
Subject: Re: SI Units vs cgs units
Nntp-Posting-Host: psuvax1.cs.psu.edu
Organization: Random, at best
Date: Wed, 29 Jan 1992 18:07:46 GMT

   This is an old debate.  And a stupid one.

   The "metric" versus "traditional" measuring debate has been going
on ever since the metric system was first introduced.  Since the
metric system is usually easier to use, it's gradually taking over.
But so what??

   If you can't handle all measurements currently used in your field
(including those in still-useful old texts), then you probably should
consider another line of work.  The information is what's important,
not the units it's expressed in.


   If you want to really improve things, then drop this stupid
base-ten system.  The factors are five and two.  Two is okay, but what
kind of a nut would want to work with fives?  Oh sure - you say you're
comfortable with bast ten.  That's because it's been drummed into your
head since you were a toddler - "Now junior, count to ten on your
eight fingers and two thumbs..."  But did you ever try to cut a pie
into five slices?  Damn near impossible.

   It's time to dump this nonsense, and start working with something
clean.  What's wrong with dividing by two's?  Dividing a pie into four
or eight slices is easy.

   Our entire civilization should start using Base-16 - it's a power
of two that people can easily deal with.  Measuring becomes infinitely
simpler - start with a standard that's one unit long, and keep
doubling it or dividing it in half.  Heck, some cultures already do
this - 1/8", 1/2", 1/32", pints, quarts, you get the idea.  Each time
you divide or multiply four times (see that power of two there?), you
shift a decimal place.  Simple as that.

   Still not convinced?  Then consider the alternative - someday in the
distant future we may encounter intelligent life in another part of the
universe.  And their first assessment of us will be, "Base-ten??  What
kind of a numbering system is that?  No wonder it took you earthlings so
long to get into space - you spend all your time measuring and no time
thinking.  What a bunch of nimrods."  And they'll tell all their buddies,
and earthlings will become the laughing stock of the universe.

   Now we don't really want that that to happen, do we?  I think not.


From gill@physics.ubc.ca Wed Jan 29 18:08:20 1992
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	["1320" "" "29" "January" "92" "21:43:49" "GMT" "Arnold Gill visiting astrophys phd std" "gill@physics.ubc.ca " nil "31" "Re: SI Units vs cgs units" nil nil nil "1"])
From: gill@physics.ubc.ca (Arnold Gill visiting astrophys phd std)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs cgs units
Date: 29 Jan 92 21:43:49 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
Nntp-Posting-Host: physics.ubc.ca

okunewck@psuvax1.cs.psu.edu (Phil OKunewick) writes:

>   If you can't handle all measurements currently used in your field
>(including those in still-useful old texts), then you probably should
>consider another line of work.  The information is what's important,
>not the units it's expressed in.

     Quite agreed - but it makes things easier if future generations
     didn't have to worry about what units a specific quantity is
     measured in.

     Of course, if you want really strange units, then look at some
     GR or QM papers where all of the standard constants are equal to 1.

>   If you want to really improve things, then drop this stupid
>base-ten system.  The factors are five and two.  Two is okay, but what
>kind of a nut would want to work with fives?  

[...and...]

>   Our entire civilization should start using Base-16 - it's a power
>of two that people can easily deal with.  

     I've read novels which were of the opinion that the most sensible
     base is actually base 12 -- a small number tht has lots of small 
     factors (2,3,4,6).  Potentially more useful.  However, its not going
     to happen, and base 16 is only useful for computers and people who
     can only say "Yes" and "No".  :-)

--
Arnold Gill --- astrophysician trainee in exile             gill@physics.ubc.ca

From dsc@gemini.tmc.edu Wed Jan 29 18:08:22 1992
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	["1879" "" "28" "January" "92" "14:57:43" "GMT" "Doug S. Caprette Bldg. 28 W191 x3892" "dsc@gemini.tmc.edu " nil "33" "SI Units vs others" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: NASA GSFC CDP VLBI
Nntp-Posting-Host: gemini.gsfc.nasa.gov
From: dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892)
Subject: SI Units vs others
Date: 28 Jan 92 14:57:43 GMT

In article <1992Jan28.005635.14025@watserv1.waterloo.edu> nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
>
>cgs, is a length-mass-time system, with cm, g, s as the base units, it is not
>widely used anymore, except perhaps in the US which I here actually even
>uses Imperial units on occasion  (I mean can you imagine!! (Flame me!)
>
The units customarily used by engineers in the US are properly refered to
as American Customary Units (ACU).  They include some SI and other metric 
units, as well as some Imperial units, and some uniquely American units 
e.g. the gallon.  There are also some bizarre 'hybrid' units like the
kip (kilopound).  This kind of thing seems to be very poorly organized
to the layman, but ACU are chosen to yield values in a reasonable range
for everyday use.  In particular, the use of a system based on unit force,
(the pound) is advantageous when doing analysis of stress and strain.
This probably dates back to slide rule days.

Bear in mind that the principle advantage to metric units is the simplifi-
cation of arithmetic, an advantage largely gone since the proliferation of
the electronic calculator.

It seems only reasonable for people to publish results in the units in which 
the work is customarily done.

As an aside, why is the angstrom considered an oddball unit?  Ten, raised to the
power of negative ten is about as metric as you can get.  Ten, raised to the 
power of negative nine, should be considered odd.  After all, nine is NOT an 
integral multiple of ten.
--
 |  Regards,         |   Hughes STX                |    Code 926.9 GSFC        |
 |  Doug Caprette    |   Lanham, Maryland          |    Greenbelt, MD  20771   |
 -------------------------------------------------------------------------------
"Le guard meurte, mais ne se donne pas." 
                 -- (falsely?) attributed to General Cambronne at Waterloo

From nick@sunburn.waterloo.edu Wed Jan 29 18:08:23 1992
Status: O
X-VM-v5-Data: ([nil t nil nil nil nil nil nil nil]
	["1917" "" "28" "January" "92" "21:37:10" "GMT" "Nick Fitzpatrick" "nick@sunburn.waterloo.edu " nil "31" "Re: SI Units vs others" nil nil nil "1"])
From: nick@sunburn.waterloo.edu (Nick Fitzpatrick)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 28 Jan 92 21:37:10 GMT
Organization: University of Waterloo

In article <1992Jan28.145743.23033@nsisrv.gsfc.nasa.gov> dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892) writes:
>In article <1992Jan28.005635.14025@watserv1.waterloo.edu> nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
>>
>>cgs, is a length-mass-time system, with cm, g, s as the base units, it is not
>>widely used anymore, except perhaps in the US which I here actually even
>>uses Imperial units on occasion  (I mean can you imagine!! (Flame me!)
>>
>The units customarily used by engineers in the US are properly refered to
>as American Customary Units (ACU).  They include some SI and other metric 
>units, as well as some Imperial units, and some uniquely American units 
>e.g. the gallon.  There are also some bizarre 'hybrid' units like the
>kip (kilopound).  This kind of thing seems to be very poorly organized
>to the layman, but ACU are chosen to yield values in a reasonable range
>for everyday use.  In particular, the use of a system based on unit force,
>(the pound) is advantageous when doing analysis of stress and strain.
>This probably dates back to slide rule days.
>
Yes it is very frustating when one comes along a US publication, where
they indicate concentrations in mg/L, and then present flows in
USgal/day  (ACK, ugh, painful), where if the units were in L/day (or m^3/day)
any fool can immediatly see that the flux is.

Pounds for stress?  The problems that get me with Imperial, is that
some people used pound force, and erg for mass (or was it slug, some
dead unit, I have to check it every time) and some used pound
mass, and poundal force.  I'm not sure how one would use pound stress, surely 
you would need a force/area unit, like Pascals or something . . .

I suppose the one advantage we got in the Free trade pact with the US,
was that it provided protection for the (Canadian) metric system, however
there was no protection for the US system. (Thank the lord, )

From dsc@gemini.tmc.edu Wed Jan 29 18:08:27 1992
Status: O
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	["1614" "" "29" "January" "92" "00:21:37" "GMT" "Doug S. Caprette Bldg. 28 W191 x3892" "dsc@gemini.tmc.edu " nil "31" "Re: SI Units vs others" nil nil nil "1"])
From: dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 29 Jan 92 00:21:37 GMT
Organization: NASA GSFC CDP VLBI
Nntp-Posting-Host: gemini.gsfc.nasa.gov

In article <1992Jan28.213710.7334@watserv1.waterloo.edu> nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
>In article <1992Jan28.145743.23033@nsisrv.gsfc.nasa.gov> dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892) writes:
>> ...
>>for everyday use.  In particular, the use of a system based on unit force,
>>(the pound) is advantageous when doing analysis of stress and strain.
>>This probably dates back to slide rule days.
>>
>Yes it is very frustating when one comes along a US publication, where
>they indicate concentrations in mg/L, and then present flows in
>USgal/day  (ACK, ugh, painful), where if the units were in L/day (or m^3/day)
>any fool can immediatly see that the flux is.
>
>Pounds for stress?  The problems that get me with Imperial, is that
>
Of course not (layman).  PSI for stress, or, kPSI (kilopounds per square
inch).  The pound (force) is a basic unit in ACU.  The unit of mass (slug),
is a derived unit, as are pressure units.
>
>some people used pound force, and erg for mass (or was it slug, some
>
Erg is a metric unit (cgs: gm cm squared per second squared).  A slug is
that mass which accelerates at a rate of one foot per second squared when
acted on by a force of one pound.
>
>dead unit, I have to check it every time) and some used pound
>mass, and poundal force.  I'm not sure how one would use pound stress, surely 
>you would need a force/area unit, like Pascals or something . . .
>
You need a hell of a lot of them in fact, 350,150 or so Pascals for normal
atmospheric pressure at sea level and Mega or even Giga Pascals for real
world stresses and pressures.

From nick@sunburn.waterloo.edu Wed Jan 29 18:08:32 1992
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	["1243" "Wed" "29" "January" "1992" "03:15:32" "GMT" "Nick Fitzpatrick" "nick@sunburn.waterloo.edu " nil "26" "Re: SI Units vs others" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: nick@sunburn.waterloo.edu (Nick Fitzpatrick)
Subject: Re: SI Units vs others
Organization: University of Waterloo
Date: Wed, 29 Jan 1992 03:15:32 GMT

In article <1992Jan29.002137.20487@nsisrv.gsfc.nasa.gov> dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892) writes:
>>you would need a force/area unit, like Pascals or something . . .
>>
>You need a hell of a lot of them in fact, 350,150 or so Pascals for normal
>atmospheric pressure at sea level and Mega or even Giga Pascals for real
>world stresses and pressures.

Well of course you dont just use Pa (duhhh).  Anyone who has ever checked
the weather forecast in this country (Canada) will see the pressure listed
as 101.3 kPa (or something close, depending on the weather), pretty
simple atmospheric pressure = (about) 100 kPa.  Simple.

And when we get into engineering we use MPa, therefore, in Canada, a 
normal concrete is rated at (I believe) 20 MPa.

Thats the whole beauty of Metric, the prefixes.  
I go from Montreal to Toronto, 500 km
My height 1.75 m.
My pencil lead, 5mm.
and then we get all those microscopic things.

God when I see those US papers, I just die, volume in ft^3, volume in
fl oz, volume in ft^2*acre, volume in gal (US), volume in gal (IMP)
volume in pints, volume in quarts, volume in bushels.  God I could just
die, it so weird,  How anyone is supposed to get an intuitive feel for
it I don't know.  

From bthoen@teal.csn.org Wed Jan 29 18:08:33 1992
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	["1519" "" "29" "January" "92" "04:27:45" "GMT" "Bill Thoen" "bthoen@teal.csn.org " nil "28" "Re: SI Units vs others" nil nil nil "1"])
From: bthoen@teal.csn.org (Bill Thoen)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 29 Jan 92 04:27:45 GMT
Organization: Colorado SuperNet, Inc.
Nntp-Posting-Host: teal.csn.org

In article <1992Jan29.031532.14841@watserv1.waterloo.edu> nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
>
>God when I see those US papers, I just die, volume in ft^3, volume in
>fl oz, volume in ft^2*acre, volume in gal (US), volume in gal (IMP)
>volume in pints, volume in quarts, volume in bushels.  God I could just
>die, it so weird,  How anyone is supposed to get an intuitive feel for
>it I don't know.  

Well, it used to be even worse. In "A New and Complete System of Arithmetic
Composed for the Use of the Citizens of the United States" by Nicholas Pike,
A.M. published in 1797, you can see that we (Americans) have made some 
improvements.  For example, back then 7 92/100 inches was one link, 25 links
made one 1 pole, 4 poles made one chain, 10 chains made one furlong, 8 
furlongs were in every mile.  And another inportant measure was for beer. We
still have the quart and gallon, but did you know that 8 gallons make a firkin?
And 2 firkins make a kilderkin, and 2 kilderkins made a barrel, and 1 1/2 
barrels made a hogshead, 2 barrels equals a puncheon, and there was 3 barrels
to the butt. It goes on and on for all kinds of measures, and there was even
exchange rates for money between the various states!
 
So when you read American papers, you should count your blessings that this
isn't 1797 anymore, eh?   :-)

(The above information is mentioned in a more recent book by Isaac Asimov,
"Asimov on Numbers", 1977 edition by Pocket Books, ISBN 0-671-82134-2)

- Bill Thoen
  bthoen@csn.org

From henry@zoo.toronto.edu Wed Jan 29 18:08:35 1992
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	["1056" "Wed" "29" "January" "1992" "05:27:31" "GMT" "Henry Spencer" "henry@zoo.toronto.edu " nil "19" "Re: SI Units vs others" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: henry@zoo.toronto.edu (Henry Spencer)
Subject: Re: SI Units vs others
Date: Wed, 29 Jan 1992 05:27:31 GMT
Organization: U of Toronto Zoology

In article <1992Jan29.002137.20487@nsisrv.gsfc.nasa.gov> dsc@gemini.tmc.edu (Doug S. Caprette Bldg. 28 W191 x3892) writes:
>... The pound (force) is a basic unit in ACU.  The unit of mass (slug),
>is a derived unit, as are pressure units.

And of course, when you receive a hardware weight estimate in pounds,
it has to be converted to slugs before you can do anything with it.

>You need a hell of a lot of them in fact, 350,150 or so Pascals for normal
>atmospheric pressure at sea level and Mega or even Giga Pascals for real
>world stresses and pressures.

Yawn.  So what else is new?  The farad (unit of capacitance) is at the
other end of the scale, far too large for most practical purposes, so
electronics types have been using pF, nF, and uF for a long time.  It
is not difficult.  Normal atmospheric pressure is about 100 kPa; where
did you get 350?  Mess up a conversion factor? :-)
-- 
"Breakthrough ideas are not             | Henry Spencer @ U of Toronto Zoology
>from teams."  -- Hans von Ohain         |  henry@zoo.toronto.edu  utzoo!henry

From binkley@boulder.Colorado.EDU Wed Jan 29 18:08:36 1992
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	["738" "" "29" "January" "92" "06:58:09" "GMT" "Jon Binkley" "binkley@boulder.Colorado.EDU " nil "20" "Re: SI Units vs others" nil nil nil "1"])
From: binkley@boulder.Colorado.EDU (Jon Binkley)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 29 Jan 92 06:58:09 GMT
Organization: University of Colorado, Boulder
Nntp-Posting-Host: beagle.colorado.edu

Say what will about the Imperial System, but I learned of a cosmic
coincidence which revived it in my mind.

Don't even ask me how this inquiry came about, but it turns out that
the cubic attoparsec (atto = e-18) is almost exactly equal to
one fluid ounce (certainly to within the error of accurately
measuring an attoparsec!).

Now, would you rather live in the cold, heartless world where 
your cubic attoparsecs equaled 0.029 something litres, or the
warm, friendly world where your cubic attoparsecs equaled one
nice round fluid ounce?

Jon Binkley

The conversion, for those who are as geeky as myself:
1 parsec = 3.09e13 km = 3.09e18 cm
1 attoparsec = 3.09 cm
1 cubic attoparsec = 29.5 cubic cm = 0.998 fl. oz.
Close enough for me!

From sacass@unix1.tcd.ie Wed Jan 29 18:08:50 1992
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	["1149" "" "29" "January" "92" "11:45:44" "GMT" "stephen andrew cass" "sacass@unix1.tcd.ie " nil "20" "Re: SI Units vs others" nil nil nil "1"])
From: sacass@unix1.tcd.ie (stephen andrew cass)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 29 Jan 92 11:45:44 GMT
Organization: Trinity College, Dublin
Nntp-Posting-Host: unix1.tcd.ie

In <binkley.696668289@beagle> binkley@boulder.Colorado.EDU (Jon Binkley) writes:
>Don't even ask me how this inquiry came about, but it turns out that
>the cubic attoparsec (atto = e-18) is almost exactly equal to
>one fluid ounce (certainly to within the error of accurately
>measuring an attoparsec!).
>Now, would you rather live in the cold, heartless world where 
>your cubic attoparsecs equaled 0.029 something litres, or the
>warm, friendly world where your cubic attoparsecs equaled one
>nice round fluid ounce?

Sorry, but what is an ounce? Those of us brought up in the brave new
world of the metric system simply have very little real conception of
what the Imperial units ARE inside our heads. If someones says something is 4
pounds for example, I will have no *real* understanding of the weight
untill I run some kind of conversion. For me I think of Yards as short
meters, and have a reasonable idea of inches and miles and pints, but
after that I really have no idea of imperial measures. I *KNOW* what a
litre is, but the same cannot be said of an ounce. Does anyone else out
there feel the same?
Stephen Cass ( sacass@unix1.tcd.ie) 

From nareid@imf.unit.no Wed Jan 29 18:08:52 1992
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	["1029" "" "29" "January" "92" "14:18:53" "GMT" "Helge Nareid" "nareid@imf.unit.no " nil "22" "Re: SI Units vs others" nil nil nil "1"])
From: nareid@imf.unit.no (Helge Nareid)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 29 Jan 92 14:18:53 GMT
Organization: The Norwegian Institute of Technology, Trondheim

In article <sacass.696685544@unix1.tcd.ie> sacass@unix1.tcd.ie (stephen andrew cass) writes:
>In <binkley.696668289@beagle> binkley@boulder.Colorado.EDU (Jon Binkley) writes:
>>Don't even ask me how this inquiry came about, but it turns out that
>>the cubic attoparsec (atto = e-18) is almost exactly equal to
>>one fluid ounce (certainly to within the error of accurately
>>measuring an attoparsec!).

>Sorry, but what is an ounce? Those of us brought up in the brave new
>world of the metric system simply have very little real conception of
>what the Imperial units ARE inside our heads. 

>Stephen Cass ( sacass@unix1.tcd.ie) 

And exactly what sort of fluid ounce is it - an imperial fluid ounce
(28.413 ml) or a US fluid ounce (29.574 ml) ??? Or is there a difference
between the US and UK parsec ?


--
Helge Nareid                             E-mail :    nareid@phys.unit.no
SINTEF Applied Physics                   Phone  :    + 47 - 7 - 59 34 18
Trondheim, Norway                        Fax    :    + 47 - 7 - 59 34 20

From jkohnen@comix.cs.uoregon.edu Wed Jan 29 18:08:53 1992
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	["1338" "" "28" "January" "92" "22:18:41" "GMT" "John Hamilton Kohnen" "jkohnen@comix.cs.uoregon.edu " nil "25" "Re: SI Units vs others" nil nil nil "1"])
From: jkohnen@comix.cs.uoregon.edu (John Hamilton Kohnen)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 28 Jan 92 22:18:41 GMT
Organization: The Max Robinson Institute


     "This kind of thing seems to be very poorly organized
     to the layman, but ACU are chosen to yield values in a
     reasonable range for everyday use."
 
   Producing values in a reasonable range for everyday use is the
key to choosing any system of measure. For virtually all of us
that means most of the time there are only three units: too
little, too much, and just right. A rational hierarchical scheme
is simply unnecessary to function in regular society. Traditional
units like feet-yards-miles, far from being as irrational as is
usually thought, are firmly grounded on this principle.
   Consider the beer drinking English and their traditional fluid
measures, the ounce, pint, and quart. An ounce is what one can
normally swallow easily and the pint about what is comfortable to
raise in one hand. Two pints, or a quart, and you have a pleasant
time with your chums, not too much and not too little. Imminently
sensible.
   But what if you are on the continent and must use the metric
system? Clearly a cubic centimeter won't satisfy anybody but the
company chemist, so your recourse is the liter. Larger even than
a quart and too much for one hand, that's a unit provocative of
athletic drinking. Little wonder both the French and the Germans
have tried to conquer the whole of Europe since metric units were
adopted.

From davem@ee.ubc.ca Thu Jan 30 09:48:36 1992
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	["240" "Thu" "30" "January" "1992" "00:59:48" "GMT" "david michelson" "davem@ee.ubc.ca " nil "6" "Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: University of BC, Electrical Engineering
From: davem@ee.ubc.ca (david michelson)
Subject: Re: SI Units vs cgs units
Date: Thu, 30 Jan 1992 00:59:48 GMT

Well, I for one don't like cgs *at all*.  I mean, how can anyone like
a system where capacitance is measured in units of *length*! :-)
 
Dave Michelson             "davem@ee.ubc.ca"
UBC Electrical Engineering
Applied Electromagnetics Group

From jokim@jarthur.claremont.edu Thu Jan 30 09:49:16 1992
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	["1298" "" "30" "January" "92" "03:26:23" "GMT" "John H. Kim" "jokim@jarthur.claremont.edu " nil "28" "Re: SI Units vs cgs units" nil nil nil "1"])
From: jokim@jarthur.claremont.edu (John H. Kim)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs cgs units
Date: 30 Jan 92 03:26:23 GMT
Followup-To: sci.astro,sci.geo.geology,sci.space
Organization: Harvey Mudd College, Claremont, CA 91711

In article <1992Jan28.033127.22112@julian.uwo.ca> gaetz@julian.uwo.ca (Terry Gaetz) writes:

>SI:   Syst\`eme International d'Unit\'es:
>         m     metre       (length)
>         kg    kilogram    (mass)
>         s     second      (time)
>         K     kelvin      (temperature interval)
>         A     ampere      (electric current)
>         cd    candela     (luminous intensity)
>         mol   mole        (amount of substance)

>      Other units are formed as combinations of these basic units
>      and selected powers of ten.  Permitted prefixes are
       ....
>       k   kilo    10^(3)             a   atto     10^(-18)

Except, because they made converting between units so much easier
than the english system, they decided to slip in KILO-grams just
to keep everyone on their toes.  Be careful of this if you've got
a whole mess of numbers and units and you try to simplify it by
canceling out prefixes like 'kilo' and 'Mega' when they're in both
the numerator and denominator.  (If you're careful, you'll notice
you have grams left over, not kg, but more often you'll end up
reading it as kg)
-- 
John H. Kim                 | (This space to be filled when I
jokim@jarthur.claremont.edu | think of something very clever 
uunet!jarthur!jokim         | to use as a disclaimer)

From userDHAL@mts.ucs.UAlberta.CA Thu Jan 30 09:51:13 1992
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	["1868" "" "30" "January" "92" "00:33:54" "GMT" "David Halliwell" "userDHAL@mts.ucs.UAlberta.CA " nil "41" "Re: SI Units vs others" nil nil nil "1"])
From: userDHAL@mts.ucs.UAlberta.CA (David Halliwell)
Newsgroups: sci.astro,sci.geo.geology,sci.space
Subject: Re: SI Units vs others
Date: 30 Jan 92 00:33:54 GMT
Organization: MTS Univ of Alberta

In article <1992Jan29.031532.14841@watserv1.waterloo.edu>, nick@sunburn.waterloo.edu (Nick Fitzpatrick) writes:
> 
>God when I see those US papers, I just die, volume in ft^3, volume in
>fl oz, volume in ft^2*acre, volume in gal (US), volume in gal (IMP)
>volume in pints, volume in quarts, volume in bushels.  God I could just
>die, it so weird,  How anyone is supposed to get an intuitive feel for
>it I don't know. 
   
     I have to agree with this one. One of the areas I work in
involves heat conduction. Have you ever seen the units that show of
for thermal conductivity? The worst one I can remember was one where
the flux density was in BTUs per square foot per second, and the
temperature gradient was in Fahrenheit degrees per inch. Put the
two linear measures into the same units? No way, Jose! It was left
as such, giving thermal conductivity in, wait...
  
    (BTU/sq.ft./sec)/(deg.F/inch)
  
    (In SI units, thermal conductivity is W/mK. Which is simpler? :-))
  
    And I'm glad that someone else has pointed out the difference
between Imperial fluid ounces and U.S. fluid ounces. That's one of
my favourite cocktail party pro-metric conversation pieces. It 
sometimes takes a LONG time to convince people of that one!
  
    By the way, is there anyone else out there who believes that
stresses should be left as N/sq.m, and that Pa should be used ONLY
for pressure?
 
    And now just for fun, the proverbial question (which I will
leave unanswered for now):
  
        Which weighs more?
            A pound of gold, or
            a pound of feathers?
 
  
Dave Halliwell                  |      "Learn from the mistakes of others;
Department of Geography         |       you'll not live long enough to make
University of Alberta           |       them all yourself..."
Edmonton, Alberta.              |       - Canada Aviation Safety Letter.

From henry@zoo.toronto.edu Thu Jan 30 14:53:13 1992
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	["886" "Thu" "30" "January" "1992" "18:47:57" "GMT" "Henry Spencer" "henry@zoo.toronto.edu " nil "14" "Re: SI Units vs cgs units" nil nil nil "1"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
From: henry@zoo.toronto.edu (Henry Spencer)
Subject: Re: SI Units vs cgs units
Date: Thu, 30 Jan 1992 18:47:57 GMT
Organization: U of Toronto Zoology

In article <gill.696721429@physics.ubc.ca> gill@physics.ubc.ca (Arnold Gill visiting astrophys phd std) writes:
>     Of course, if you want really strange units, then look at some
>     GR or QM papers where all of the standard constants are equal to 1.

An amusing side note on this:  in his JBIS paper on space warps (real ones
supported by current physics, not science-fictional ones), Robert Forward
complained loudly about this convention.  It makes the physics easier,
but translating the results back into normal units -- so you can decide
whether the engineering required is impossible or merely daunting -- is
tremendously difficult because it's hard to figure out where (and which)
conversion factors are needed.
-- 
"Breakthrough ideas are not             | Henry Spencer @ U of Toronto Zoology
>from teams."  -- Hans von Ohain         |  henry@zoo.toronto.edu  utzoo!henry

From paulz@hpspdla.spd.HP.COM Thu Jan 30 17:28:12 1992
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	["1121" "" "30" "January" "92" "01:19:42" "GMT" "Paul Zander" "paulz@hpspdla.spd.HP.COM " nil "27" "Re: Re: SI Units vs cgs units" nil nil nil "1"])
From: paulz@hpspdla.spd.HP.COM (Paul Zander)
Newsgroups: sci.astro
Subject: Re: Re: SI Units vs cgs units
Date: 30 Jan 92 01:19:42 GMT
Organization: HP Stanford Park - Palo Alto, CA

henry@zoo.toronto.edu (Henry Spencer) writes:

>The wonders of the "standard" metric system.  Now for grins is force in
>kilograms, or newtons or what?


For the benefit of readers who don't know the answer:

Kilograms is a unit of mass.  A kilogram will be a kilogram on the
earth, the moon, or deep space.  If there is some gravitational field,
a balance scale and a set of calibrated standards (popularly but
incorrectly called "weights") might be used to determine mass.  This
works because in a scale is balanced, equal masses will have equal
weights.

One type of force is the gravitational attraction of the earth (moon,
etc) on an object.  Force can be measured by a spring scale.  An
object with a mass of 1 kilogram will have a weight of 1 newton on the
earth's surface.  The weight will be different in different places in
the universe, but the mass is constant (ignoring relativistic
effects).

The difference between mass and force seems subtle to many beginning
physics students, but is especially important in astronomy.  More
detailed coverage can be found in almost elementary physics text.

Paul Zander

From stefano@orion.astro.uiuc.edu Thu Jan 30 18:15:19 1992
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	["1087" "" "30" "January" "92" "20:21:40" "GMT" "Stefano Casertano" "stefano@orion.astro.uiuc.edu " nil "24" "Re: SI Units vs cgs units" nil nil nil "1"])
From: stefano@orion.astro.uiuc.edu (Stefano Casertano)
Newsgroups: sci.astro
Subject: Re: SI Units vs cgs units
Date: 30 Jan 92 20:21:40 GMT
Organization: University of Illinois at Urbana

In <12990031@hpspdla.spd.HP.COM> paulz@hpspdla.spd.HP.COM (Paul Zander) writes:


>  (deleted about difference between mass and force)

>One type of force is the gravitational attraction of the earth (moon,
>etc) on an object.  Force can be measured by a spring scale.  An
>object with a mass of 1 kilogram will have a weight of 1 newton on the
                                                        ^^^^^^^^
>earth's surface.  The weight will be different in different places in
>the universe, but the mass is constant (ignoring relativistic
>effects).

No.  It will have a weight equal to the mass times the local gravitational
acceleration, typically about 9.81 m s^-2.  Since the newton (N) equals
1 kg m s^-2, the weigth of a mass of one kg will be around 9.81 N,
and it will be slightly different at different places on the Earth's 
surface.  

I commend your effort to clarify the difference between mass and weight,
better than I could do (and I have tried in the past...) but please
make sure of your facts next time...

Stefano Casertano         stefano@sirius.astro.uiuc.edu

From joe@astro.as.utexas.edu Fri Jan 31 09:40:27 1992
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	["163" "" "30" "January" "92" "21:07:48" "GMT" "Joe Wang" "joe@astro.as.utexas.edu " nil "5" "Re: SI Units (was Re: AAS meeting, Atlanta)" "^From:" nil nil "1"])
Newsgroups: sci.astro
Distribution: sci
Organization: McDonald Observatory, University of Texas @ Austin
From: joe@astro.as.utexas.edu (Joe Wang)
Subject: Re: SI Units (was Re: AAS meeting, Atlanta)
Date: 30 Jan 92 21:07:48 GMT

Speaking of which, my undergraduate training (only two years ago) was
completely in cgs units, which meant that I was in for a shock when I
took the GRE.

OUCH!!!

From paulz@hpspdla.spd.HP.COM Fri Jan 31 14:32:53 1992
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	["368" "" "30" "January" "92" "21:45:38" "GMT" "Paul Zander" "paulz@hpspdla.spd.HP.COM " nil "9" "Re: Re: SI Units vs cgs units" "^From:" nil nil "1"])
Newsgroups: sci.astro
Organization: HP Stanford Park - Palo Alto, CA
From: paulz@hpspdla.spd.HP.COM (Paul Zander)
Subject: Re: Re: SI Units vs cgs units
Date: 30 Jan 92 21:45:38 GMT

Correction:

In my previous comments, there was an error.  On the earth's surface, a
mass of 1 kilogram will have a weight of 9.8 Newtons.  That is because
the earths gravitaional field creates an acceleration of 9.8
meters/second.  

The key point remains, mass is unaffected by gravity (ignoring
relativistic effects) but weight is very much a function of gravity. 

From mehr@oskar.uchicago.edu Mon Feb  3 09:55:16 1992
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	["852" "" "1" "February" "92" "00:56:01" "GMT" "David Mehringer" "mehr@oskar.uchicago.edu " nil "22" "Re: Re: SI Units vs cgs units" "^From:" nil nil "2"])
Newsgroups: sci.astro
Organization: Department of Statistics
From: mehr@oskar.uchicago.edu (David Mehringer)
Subject: Re: Re: SI Units vs cgs units
Date: 1 Feb 92 00:56:01 GMT

In article <12990032@hpspdla.spd.HP.COM> paulz@hpspdla.spd.HP.COM (Paul Zander) writes:
>Correction:
>
>In my previous comments, there was an error.  On the earth's surface, a
>mass of 1 kilogram will have a weight of 9.8 Newtons.  That is because
>the earths gravitaional field creates an acceleration of 9.8
>meters/second.  
>
As long as we are being dimensionally correct, acceleration is 
measured in meters/(second)**2 in the mks system, not meters/second.

>The key point remains, mass is unaffected by gravity (ignoring
>relativistic effects) but weight is very much a function of gravity. 

The Newtonian relationship is weight = mass * gravity.


--
Dave Mehringer            | "There is a fine line between dignity and 
dmehring@zia.aoc.nrao.edu |  stupidity." 
National Radio Astronomy  |    -- Homey the Clown
Observatory, Socorro, NM  | 

From cbm@mrcnext.cso.uiuc.edu Mon Feb  3 09:56:33 1992
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	["758" "" "1" "February" "92" "18:35:28" "GMT" "Commodore Unix Support" "cbm@mrcnext.cso.uiuc.edu " nil "14" "Re: SI Units vs others" "^From:" nil nil "2"])
Newsgroups: sci.astro,sci.geo.geology,sci.space
Organization: University of Illinois at Urbana
From: cbm@mrcnext.cso.uiuc.edu (Commodore Unix Support)
Subject: Re: SI Units vs others
Date: 1 Feb 92 18:35:28 GMT

dan@rcdips.nrl.navy.mil (Dan Nagle) writes:

>If your car uses (say) 30 mpg, how many yards is that to the ounce?
>(Ignore, if you are sure you can, the issue of WHICH ounce...)
>Of course, if you only knew how many kilometers per liter, the
>conversion to meters per milliliter is (ahem) straightforward.

Of course, any physicist would represent it as meters per cubic meter
and cancel, giving a mileage estimate of 0.0042 m^-2.  Lets see.  Inverse
meters squared is inverse area, so we could really call it 0.0000432 acres^-1
or 0.0000432 erca's.  Better yet, subatomic physicists would want to use
barns for area, and represent it as 478329432 barns^-1, or 478329432 nrab's.

Now why dont we just use those convenient units on the gas mileage estimates?

