Curt Fischer wrote:
> 
> Ken wrote:
> 
>>Curt Fischer wrote:
>>
>>>Brett Robson wrote:
>>>
>>>
>>>>>The last I heard, the Avoirdupois pound was defined as being the weight of
>>>>>27.7015 cubic inches of distilled water at 62 degrees F with the barometer
>>>>>being at 30 inches.
>>>>
>>>>1. avoirdupois pound is not an imperial pound
>>>
>>>You're right here.  Congratulations.  Don't let it go to your head
>>>though....
>>>
>>>
>>>>2. your definition is pound-force not pound
>>>
>>>A pound force is a pound.  So what are you talking about?
>>
>>Well, Kevin's obsolete definition might have been better if he had said
>>*mass* instead of "*weight* of 27.7015 cubic inches...".
> 
> 
> But since the pound has historically been a unit of force, it is
> definitely better to speak of "weight".

Yeah, it is obvious that the pound is a unit of force, which is why
we need expressions like "pound force" or "lbf", which explicitly add
the qualifier "force" to make sure that the obvious is not overlooked.


>>One might speak of weightlessness, e.g. in orbit.  It wouldn't occur to an
>>astronaut, however, to say that he/she's massless...  Astronauts composed
>>of non-baryonic matter, and hence travelling at light speed, would be an
>>interesting concept, indeed...
>>
>>For those confused about these notions, the pound-force is the weight, or
>>*force* exerted by a pound of mass subjected to an acceleration of 1G; as
>>such, its expression in SI units would be in Newtons.
>>The pound, OTOH, is a unit of *mass*, and would be expressed in SI units
>>in Kilograms.
> 
> According to every technical book I have ever used, the pound is a unit
> of force.  Ergo, pounds measure weight.  Kilograms measure mass.  This
> is the reason that, in English (Sepponian) units, there is a no
> non-unity non-dimensionless constant called  gc (g sub c), which relates
> force to mass.  Here's a quick review for those of you having
> difficulty:
> 
> http://gems.mines.edu/~mckinnon/DCGN209/Handouts/gc%20summary.pdf

The fact that you perceived "pound" only as a unit of force is *your*
problem.  Didn't it occur to you at all that the term might have been
used to refer to mass, then?  I guess this kind of confusion explains
a bit why Sepponians still mix up their units and lose e.g. the occasional
spacecraft doing so.

The fact that you quote a handout from some Sepponian college which has
no qualms calling the "gc" factor appearing in Newton's 2d law of motion
a "universal gravitational constant" also makes me wince.  One wonders
what that lecturer would call the constant found, say, in the inverted
square law expressing the gravitational attraction between massive bodies...

Anyway, you seem to be still quite confused about your units and your
dimensional equations.  The "32.2" gc conversion factor only derives from
the fact that 1G of acceleration happens to be, in the foot-pound-second
system, 32.2 ft/s**2.  If pound expresses mass and lbf expresses a force,
then to what extent is gc's *dimensionality* in the foot-pound-second system
different from the SI system's?

It would also be interesting to know whether you consider the pound, as
a mass unit, to be a unit derived from the lbf, a bit like pressure,
say, is a unit ultimately derived from mass, length and time...


> Further evidence that the pound is a unit of force comes from
> established terms like "ft-lbs", which I hope everyone will agree is a
> unit of torque, not some mysterious unit of dimension (mass)x(length).  

In English, "further" should be used when one has already presented a
modicum of evidence supporting an argument.  Why should the fact that
it's more expedient in everyday language to talk about foot-pounds rather
than foot-pounds-force be any more significant than, say, Shakespeare
musing about a "pound of flesh" or your local grocer selling foodstuffs
by the pound?


> You might also want to check out what a "slug" is.

Webster's definition:

slug: the gravitational unit of mass in the foot-pound-second system
 to which a pound force can impart an acceleration of one foot per
 second per second and which is equal to the mass of an object
 weighing 32 pounds.

Notice how Webster explicitly uses the term "pound force" -- despite
the fact that "force" should have been redundant, since according to
you, the "pound is a unit of force" ?
Furthermore, note that Webster speaks of "the *mass* of an object
weighing 32 *pounds*"?  How dare they use terms like "pounds" when
talking about the mass of an object!  Surely they need a refresher
course in English language usage!


>>>>3. your definition is /less/ accurate than using a standard object
>>>>  (perhaps this would be an interesting homework project for you.
>>>>  Discuss a practical way of maintaining as constant the 3 variables,
>>>>  volume, temp, and atmospheric pressure. Be sure to mention the
>>>>  effect of measurement on values)
>>>
>>>Umm, why couldn't you use any number of commercially available devices
>>>to maintain the desired temperature, volume, and pressure?
>>
>>First, because mass definitions involving a measurement of pressure
>>might be circular, as the standard pressure definition relies on mass,
>>acceleration and surface units... (Hint: how is the Pascal defined?)
> 
> Yes, but the definition under discussion here was not a definition of
> mass.  Ergo, no tautology.

No tautology only if we assume that pound is a unit of force, a point
with which I, um, forcefully disagree.  Besides, one then wonders why
people have the strange idea of bringing up pounds in a thread discussing
mass and kilograms...


>  Your points about accuracy are well-taken; I
> do understand that there were reasons that the weights and measures
> people adopted the Pt-Ir standard.  But if 1893 levels of precision are
> what we're talking about, then the devices today would perform
> admirably.

Nope, in precision terms, today's devices are no better than 1893's, as
far as mass references are concerned.  THIS IS WHY METALLIC REFERENCES
ARE STILL IN USE EVEN IN 2003, BY THE WAY.


>>Second, because there's no practical way to measure and regulate the
>>volume, temperature and pressure with the required precision.
>>The Pt+Ir mass references have an estimated error in the 10**-9 to
>>10**-8 range, which is the major reason these seemingly quaint objects
>>are still used, well, as mass references...
> 
> If we updated the definition to be the weight of a certain volume of
> liquid water at its triple point, wouldn't that take care of the
> temperature and pressure problem?  How hard is it to measure volume
> precisely?

I think if there was a precise way of determining that a sample of water
was uniformly at its triple point, as well as a way of determining its
volume, such that the measurement errors (temp, pressure etc) would have a
combined accuracy better than, say, 10**-9, we'd already have heard of it,
and metrologists all over the world would have discarded their metallic
mass references long ago...

How the calibrated masses of water would then be reproduced and shipped
to the standard institutes all over the world, while maintaining a 10**-8
or 10**-9 accuracy, would also be an interesting challenge.  Weight
references, a bit like coordinated universal time references, have to be
statistically measured and adjusted against independent references to have
credibility...


>>There's no better mass reference system known as of yet, even though
>>some new ideas are being investigated -- e.g. the Avogadro crystal
>>lattice approach based on accurately estimating the number of Si
>>atoms in a "perfect" sphere, whose dimensions are controlled by
>>interferometry.
> 
> What is the current uncertainty in Avogadro's number?

Avogadro number's relative uncertainty: about 8 * 10**-8


>  Why can't the
> standard unit of mass be the nucleus of one atom of carbon-12, which
> already has an atomic mass of 12 amu by definition.

If we're talking about a large number (10**20+?) of C12 atoms, then to
obtain that bunch with an isotopic separation BETTER THAN 10**-8 or
10**-9 would be, I'm afraid, quite challenging.  (Damn isotopes!)

If we're talking about using a small sample of isotopically pure reference
C12 atoms, I suspect that decorrelating e.g. the Van der Waals effects (a
factor with atomic force microscopes) with the measurable effects of the
mass proper (with a mass spectrometer?) at 10**-9 would be also, um, quite
"difficult".

I also suspect the engineering costs required to manipulate and count
single C12 atoms as weight references in a non-contaminating manner would
make the current prices of high-purity fullerene or carbon nanotube samples
appear, well, utterly laughable.

If you can devise a practical way of using single atoms as an accurate and
practical mass standard, I wouldn't be surprised if you'd get a phone call
from a committee in Stockholm...  (I think there's a team working on it in
Sepponia, using the conductivity properties of Au aggregates)