Why shouldn't there be an all-decimal streamlined
version of the traditional units for use in scientific
work? There is a power-vacuum here which BMWA could
step in and fill.

SI metric has an official governing body (CGPM, the
general conference on weights and measures) which
decides what the official SI units are. It performs
useful functions such as pruning dead wood from the
system. It does not seriously restrict freedom, I
believe, because scientists go right ahead and ignore
CGPM reccomendations on terminology. But at least
there is something on record you can refer to.

On the other hand, correct me if I am wrong, what
constitutes a traditional unit seems to be a matter
of common usage. (Paul Birch said something along those
lines I think.) There is, it seems, no official
Imperial System Board of Governors the way there is
in the case of SI metric.

What would be wrong with declaring an "official BWMA"
all decimal version for scientific work?

Maybe no scientist would use it. So what? I think it
would be good to have an all-decimal streamlined
version of the customary units on record.

If there were to be a recommended version of
traditional units for scientific work, I would favor
keeping it really spare: mostly just pound and inch.

No feet, no yards, no miles, no calories, no BTUs.
Cut out all redundancy. Use decimal multiples of
inch, cubic inch, pound per square inch, etc.

For scientific work there do not have to be
a whole lot of specially named units. Just a
few basic ones from which any others can be
constructed.

And what matters more is just having SOME recommended
decimal alternative to SI metric on record. To puncture
fools who talk as if metric had a monopoly on
the number ten and also to have something to which
one could refer. What the units actually are (the ones
I favor or some different ones) is of secondary
importance.

We do have tens and hundreds, as in thous and links and chain, but I know what you mean. I personally, would sponsor this sytem so long as it did not overide the measurements used by most ordinary people. Also, I do not think that this deciaml imperial suld be completely decimal, as ten is not always the best number even when dealing with maths and science.

What address do I write to to subscribe to the yardstick or any other bwma journal? What journals are there? How much are they?

Hello Bryan, I agree strongly with you that
no for-science-only version of traditional
should impinge on everyday life and certainly
not "override" good things like the numbers 12,
and 36, and 16 and feet and yards and so on.

But realistically who would use such a system?
It would be primarily just a matter of record
that there was an all decimal version available.
So I don't think there is any danger of it
overriding anything we care about.

Do you understand what "anonymous" means by
saying "OT" which I believe means "over the top."
What can he mean? You and I are sensible people
and not at all over the top. Maybe it his way
of expressing happiness.

There SHOULD be journals and stuff for him to
subscribe to, to the full extent of his desire.

BWMA's main journal is the Yardstick and is published 3-4 times a year. Annual membership is £10, obtainable from 45 Montgomery St, Edinburgh EH7 5JX.

With regards to the other issue on this thread, a main problem to overcome in the minds of many people is that the imperial system does not have an equivalent to the millimetre. A tenth of an inch just isn't fine enough, whereas a hundredth is virtually invisible to the naked eye. A twentieth or twenty-fifty of an inch is about right but something of a mouthful, and not decimal.

^ BWMA, Maybe the 16th of an inch can be "called" millimetre, or allowed to be called so colloquially. Maybe the 32nd can be, as I know, below eigth, especially 16th, no one uses the decimal or binary division colloquially although there is undoubtedly a demand for a mesure of that size. Maybe we could "nick", "borrow" call it what you will, the metre, redefine it on our terms (40 inches) and say a 1000th of *that* is an imperial millimetre. This works out as being 1 "milimetre"= 0.64 of a 16th of an inch; an immensly interesting coincidence, considering 64 already fits in with the current and proposed Imperial scheme of things.


In other words, maybe we can *recognise* that the "milimetre" is a measure, but not reallt have any of our standard measures based on it.

"...but not really have any of our standard measures based on it..."

- by this I mean that we oughtn't redefine the yard to be 40 inches or anything, or change the length of the inch so that it equals 40 old inches 36 new ones.

I mean that this new "mill" (as the milimetre is known colloquially) could be the basis for the scientific Imperial set of measures that you propose, Leonard. In order to define it from the metric milimetre, it could be known officially as the English milimetre, International milimetre or the Imperial milimetre, but could be refered to, if any scientist so wishes to use it, a miliyard or miliard (I know a "miliard" is the name by which the "thousand million" goes in Europe, or what goes for billion in America.)

Maybe a thousandth of a yard could be a miliyard, as opposed to a thousandth of an "Imperial metre"

If you really want a pared-down system, it's easy (so long as scientists aren't expected actually to use it). You could base it on the second (9,192,631,770 periods of the unperturbed microwave transition between the two hyperfine levels of the ground state of Caesium-133), measuring everything in powers of the unit of time, but since the various metric systems use the second too, perhaps you wouldn't consider it imperial enough?

So you could base it on the foot, the distance light travels in vacuo in 1/983,571,050 of a second (or the distance light travels in vacuo in 9.34617967 periods of the unperturbed microwave transition between the two hyperfine levels of the ground state of Caesium-133).

If you don't mind changing the size of the foot a little, you could make the speed of light exactly 1ft/ns (which would make the foot very close to the metric foot of 30cm (29.979cm) and the inch very close to 2.5cm (2.4983cm)).

Everything else could be measured in feet (or powers of feet), including mass, force, temperature, energy, even time. If we make the speed of light 1ft/ns, then 1s=1Gft. An hour is 3.6Tft. Acceleration due to gravity (32ft/s/s) is then 32/Eft. One pound mass is 1.1232x10**-27 ft (though a 1myft pound would be very close to 400g (403.76g) and one pound weight would then be a dimensionless 32x10**-45). The triple point of water (273.16K) is 1.0393x10**-64 ft.

I could go on, but it should be obvious by now that the size of imperial geometrodynamic units is massively inconvenient for most purposes (as is the metric version).

In practice (if indeed one ever intended to use the system in practice) one would choose a set of basic units directly comparable with those currently employed in the Systeme International. The second and foot, as defined above, then the pound for mass (defined as 1.1232x10**-27 ft x (c**2/G) as above) and the poundal (one pound foot per second per second) for force. Derived units using the pound as a pound weight would be deprecated (so no psi, for instance, the unit of pressure being the poundal per square foot or the pound per foot per second per second).

In reality, engineers would even less willing to stick to these basic imperial units than they are to stick to SI (the alternative of making the pound a unit of force is no better, because then the unit of mass is properly the slug, which almost no one can ever be bothered to use).

In my view the proper way to use imperial units is to recognise that they are customary units, used by different trades and professions in different ways; we shouldn't try squeezing them into the procrustean bed of a unified system. That is precisely the problem with SI, though it is also its strength - and we don't need another SI, because SI already does its own job superlatively.

Each traditional usage can very easily be referred back to definitions in terms of basic physics, if ever this is required, which it seldom is. Each usage has its own physical constants and standard data presented in its own preferred form, so conversion from data published in other units is rarely necessary.

To insist on having the same sort of definitional purity as SI aspires to is simply to pander to the fanaticism of the metricators; even metric, in ordinary use, isn't so streamlined (and there's no real reason why it ever should be).

I'm sorry Paul, but the goal is not to make our system more like metric.

The fact is, we need to change some of our scientific measures slightly, and btw Imperial can be used for science and I personally do not propose a "universal unified" Imperial system in a science, but an improved version of the current.

I don't think either you or Leonard have a clear idea of what you want. Any redefinition of a sparse imperial system would necessarily make it more like metric. The strength of traditional units is precisely that they're not like that; that the imperial system is not sparse but thick, and far from systematic, both in its units and its multiples. We regularly use inches and feet and yards and miles, and thousands of feet or kft, and thousands of yards or kyd, and tenth inches and twentieth inches and mils and eighth inches and twelfth inches and anything else that takes our fancy.

There is no need for any official-style systematisation because workable definitions already exist (in terms of other imperial units or basic physics, if you're prejudiced against definitions in terms of metric units) for all the traditional units currently employed. There are several systematic formulations available for use in science and engineering if you want such things (the foot-pound-poundal system and the foot-slug-pound system) but almost nobody uses them - the scientists and engineers who still use British units tend to prefer a non-systematic mixture. Let's just leave them be.

For reference, here are the definitions in terms of basic physics of the imperial foot-pound-poundal system:

Basic Units:

One second (s) is equal to 9,192,631,770 periods of the unperturbed microwave transition between the two hyperfine levels of the ground state of Caesium-133.

One foot (ft) is equal to the distance light travels in vacuo in 1/983,571,050 of a second.

One pound (lb) is that mass such that any two inert bodies of one pound mass and negligible size placed one foot apart in a vacuum accelerate towards each other with an acceleration of 1.4779E-10 ft/s/s.

The Rankine scale of thermodynamic temperature is such that the Rankine degree (R°) is equal to 1/491.688 of the absolute thermodynamic temperature of the triple point of pure water. The Fahrenheit degree is equal to the Rankine degree, and the Fahrenheit temperature of the triple point of pure water is 31.982°F.

Derived Units:

One poundal (pl) is the force of one pound mass under an acceleration of one foot per second per second (1 pl = 1 lb ft/s/s).

One foot poundal (fl) is the work done in moving one poundal through one foot (1 fl = 1 lb(ft/s)**2).

One cycle per second (c/s) is the unit of frequency.

Prefixes:

yotta- (Y) 1E24 1 septillion
zetta- (Z) 1E21 1 sextillion
exa- (E) 1E18 1 quintillion
peta- (P) 1E15 1 quadrillion
tera- (T) 1E12 1 trillion
giga- (G) 1E9 1 billion
mega- (M) 1E6 1 million
kilo- (k) 1000 1 thousand
hecto- (h) 100 1 hundred
deka- (da) 10 (deprecated)
deci- (d) 0.1 1 tenth
centi- (c) 0.01 1 hundredth
milli- (m) .001 1 thousandth
micro- (µ) 1E-6 1 millionth
nano- (n) 1E-9 1 billionth
pico- (p) 1E-12 1 trillionth
femto- (f) 1E-15 1 quadrillionth
atto- (a) 1E-18 1 quintillionth
zepto- (z) 1E-21 1 sextillionth
yocto- (y) 1E-24 1 septillionth

General remarks:

Other measurements, such as for area, volume, power and pressure, can be obtained as combinations of those units and prefixes given above (the unit of pressure is thus the poundal per square foot, pl/ft/ft and 1 atmosphere pressure is equal to 68.087 kpl/ft/ft).

BWMA is welcome to use these definitions of a basic decimalised imperial system, which is already standard and requires no change to existing usage, as an alternative to the definitions more commonly given in terms of metric units.

Paul wrote:
"BWMA is welcome to use these definitions [the ones he offered] of a basic decimalised imperial system, which is already standard and requires no change to existing usage, as an alternative to the definitions more commonly given in terms of metric units."

TO AVOID ANY DIVISION OF OPINION I shall not offer BWMA the following alternative--a proposed pound-inch system which in certain limited ways is similar to the one Paul described but which is in other ways unconventional. But to allow a clear comparison, I list the definitions in a way that roughly parallels Paul's.

I imitate the recently proposed redefinition of the kilogram in defining the pound mass. The unit of force is the weight of a pound mass in standard gravity (so the half-ounce-sized "poundal" force does not appear.)

Purely for comparison, here are the definitions in terms of basic physics of the proposed pound-inch system:

Basic Units:

One trice (tr) is equal to 467 818 410.7 periods of the unperturbed microwave transition between the two hyperfine levels of the ground state of Caesium-133. Equivalently, it equals 1/19.65 of a conventional second.

One inch (ih) is equal to the distance light travels in vacuo in 1/600 654 080 of a trice.

A one pound mass (lb) is that mass whose energy
equivalent equals that of a collection of photons with
frequencies summing to 313104 x 10^43 cycles per
trice. [[imitating the proposed redefinition of the
kilogram, Mohr and Taylor 1999]]


Derived Units:

One pound force (pf) is the force of one pound mass under an acceleration of one inch per trice per trice (1 pf = 1 lb ih/tr^2).

One inchpound (ip = ihpf) is the work done by a pound
force exerted through one inch (1 ip = 1 lb(ih/tr)^2).

One cycle per trice (c/tr) is the unit of frequency.

Prefixes:

yotta- (Y) 1E24 1 septillion
zetta- (Z) 1E21 1 sextillion
exa- (E) 1E18 1 quintillion
peta- (P) 1E15 1 quadrillion
tera- (T) 1E12 1 trillion
giga- (G) 1E9 1 billion
mega- (M) 1E6 1 million
kilo- (k) 1000 1 thousand
hecto- (h) 100 1 hundred
deka- (da) 10 (deprecated)
deci- (d) 0.1 1 tenth
centi- (c) 0.01 1 hundredth
milli- (m) .001 1 thousandth
micro- (µ) 1E-6 1 millionth
nano- (n) 1E-9 1 billionth
pico- (p) 1E-12 1 trillionth
femto- (f) 1E-15 1 quadrillionth
atto- (a) 1E-18 1 quintillionth
zepto- (z) 1E-21 1 sextillionth
yocto- (y) 1E-24 1 septillionth

General remarks:

Other measurements, such as for area, volume, power and pressure, can be obtained as combinations of those units and prefixes given above (the unit of pressure is thus the pound per square inch, pf/ih^2 [= PSI} and 1 atmosphere pressure is equal to around 14.7 PSI, the usual).

Everybody is supposed to tell time in the usual terms
of hours, minutes and seconds! The only time you are
supposed to see the small (roughly twentieth of a second)
trice unit of time is in definitions, physics coursework, and
perhaps some technical contexts where
it might be handy. The acceleration of standard
sealevel gravity is one inch per trice per trice.

Having a purely decimal version of pound-inch units
on record, or SEVERAL versions, endorsed or not by
BWMA, is very easy to do (given the internet and
websites) and does not need to change anything much.
People of course go on using whatever units they like
often in defiance of august bodies like the General
Conference on Weights and Measures (CGPM.)

There are some interesting issues surrounding the
electrical units and the form of the Lorentz equation,
which is different in SI from how it is some of the
other systems used in teaching and research. But we
didn't get as far as electrical units here.

I think this thread may be finished at least for
the time being.

BWMA wrote:
"With regards to the other issue on this thread, a main problem to overcome in the minds of many people is that the imperial system does not have an equivalent to the millimetre. A tenth of an inch just isn't fine enough, whereas a hundredth is virtually invisible to the naked eye. A twentieth or twenty-fifty of an inch is about right but something of a mouthful, and not decimal."

As far as I can see this is a serious objection to
having INCH as the basic unit of length in an all-decimal system.
Tenth too coarse and hundredth too fine.

I wanted to see what it would be like to have a
decimal version of pound-inch purely for reference
(not expecting it to actually be used in scientific
work) and here is one of the first results of taking
a closer look! It doesn't produce something on the
borderline between too fine and too coarse in the
length category. That is interesting. I don't thing we
are compelled to try to fix that problem or work around
it, just learn from it.

And its not a fatal flaw in a system intended only for
scientific work. The "mil" which usually means a thousandth of an INCH (not, as someone suggested, a
nickname for millimeter) has worked out OK in quite a
few technical contexts and the 25th of an inch you
were talking about is just 40 mils. Technical folk
can handle that.

Now maybe the tread is finished.

Leonard: What you're offering here is a new and unconventional system (NOT a decimalised variant of imperial). No way anybody is going to use it, especially since the "trice" isn't even decimally related to the most fundamental and well-known unit of all - the second. We don't NEED a brand new pseudo-British system; we've already got several in active use. All I was doing was providing suitably up-to-date definitions for a standard system that's been in use for over a century (though defining the pound in terms of a collection of photons would also be a reasonable alternative).

Leonard, to set facts straight, in America the one thousandth of an inch measure is known as the mil, but in Britain that measure is called the thou- "mill" *is* the nickname for a millimetre in Britain.

Hi Paul,

You wrote:
"(though defining the pound in terms of a collection of photons would also be a reasonable alternative)."

I am glad you said that, and that you find it reasonable.

Mohr and Taylor's suggestion is to define the kilogram through its frequency equivalent of 135 639 274 × 10^42 cycles per second. Resolution 7 of the 1999 GCPM called for redefinition of kilogram along some such lines, but was vaguer and more general.

They are the ones who proposed the language about
"energy of a collection of photons with frequencies
summing to..." I just took their language over.

You might like to look at Mohr and Taylor's article
on-line (Electronic Journal of Differential Equations,
August 2000). Their kilogram proposal is in paragraph 8.

http://ejde.math.swt.edu/conf-proc/04/m1/mohr.pdf

Taylor is ex-chair and Mohr is chair of CODATA who are
the people who periodically provide the recommended values of the fundamental constants that NIST lists and
that everybody seems to use.

They are senior people at NIST and write pretty well.

You write: "Leonard's system isn't imperial."

Yeah. I call it pound-inch, or sometimes pound-inch-trice, or pound-inch-pound. The point of it is that you get to rate mass in pounds (like buying bananas) and also force in pounds (like PSI for pressure.)

The two Imperial versions that have been used in engineering that I know about were pound-slug and
pound-poundal. But neither slug or poundal seemed to
make people happy.

So here is a pound-pound system. Anybody can take a
look and see what the advantages/disadvantages are and see if they like it. I don't think it is subversive or anything just to lay it out there. In fact I would like to see a list of data in it, like the fundamental constants, just to see what that would look like.

I imagine we can let this thread stop now so it
can drift down the page and get out of the heat. what say? I am not going to advocate of pound-inch at BWMA board. Let's have your poundal version of Imperial as the official one here!

Bryan, I stand corrected!
I'm very glad to know this.
I was puzzled by seeing the word "thou"
as a unit.

And in US the mil is very common, you
buy plastic sheet and metal foil that is
so-and-so many mils.

Leonard: You're right that people tend not to like the slug or poundal - they get around it by deliberately being non-systematic. Your pound-pound system unfortunately necessitates replacing the second by the "trice", which would obviously be even less popular. You can drag the second back in, but only by being non-systematic. Your system would also elevate the local acceleration due to gravity (an arbitrary figure) to a central role, which terrestrial engineers might appreciate but scientists would naturally dislike.

Don't misunderstand me; I've no objection to people playing around with units and seeing what they can come up with, but what you were talking about at the head of the thread was "an all-decimal streamlined version of the traditional units". I assumed that the point of this was to able to demonstrate to the metric fanatics a consistent set of imperial units defined without the help of metric, but no less logical and capable of scientific application - as the old foot-pound-poundal system, with such definitions as I provided, certainly is.

I incline to the view that using gravity to define the pound as I suggested is more "classical" and therefore more appropriate for imperial units than the Mohr and Taylor trick of using photons (although I'm aware that Planck's constant is known to greater precision than the Gravitational constant, which is an argument the other way). But I'm easy. Either will do well enough.

The mil (equal to one milli-inch) IS used in Britain too, though how widely I don't know. I have never heard "mill" used as a "nickname for the millimetre", but possibly some people do use it that way.

Hi Paul you might be interested in this.
I averaged the guesses of three smart people
(Russ Rowlett, Barry Taylor, Jim Carr) as
to when the kilo redefinition might
be in place. I had to ask two of them but the
other voiced his opinion on Usenet. It came
to 2009 or so.

Mohr and Taylor have an even better article than
the EFDE one I gave URL for. More recent but not
on line as far as I know.

The Role of Fundamental Constants in the International
System of Units (SI): Present and Future
IEEE Transactions on Instrumentation and Measurement
vol 50 no 2 April 2001.

Two reasons are working together to push this. One is they've been having trouble with the kilogram and the other is they've been having trouble with the 1990 electrical standards (very reliable but in imperfect
relation to older electrical defs which are still official). Moving to M&T frequency-based def of kilogram would FIX BOTH PROBLEMS. Would establish
an exact value of h which you just remarked is already
very accurately known. The connection with the defs of volt and amp is the unobvious part which this paper goes into.

Perhaps it strikes you as foolish to take 3 smart people's guesses and average but it is certainly better
than my personal guess. I don't even know what I would
guess!

So I am beginning to try to visualize what it might look like when the SI, say circa 2009, is based on
the atomic clock second, c, and h. Maybe there will
be an adopted exact value of Boltzmann's so we would
have a temperature scale compatible with the actual
instruments used to measure temperature over a wide
range and not have to base the scale on water's triplepoint. But that is a side issue. I sense something qualitatively different about an SI based
entirely on fundamental constants (plus the atomic
clock of course.) For one thing Time is so prominent.
But these are just musings.

The snag with the photon energy-equivalent definition is that you can't actually "weigh" (measure the mass of) a bundle of photons, whereas you can, for instance, measure the mutual attraction of lumps of metal or the mass of a cubic metre of water. Such an abstract definition therefore has to be supplemented with a secondary standard that is physically reproducible.

The snag with a Boltzmann's constant definition is that its value is only known to around 10 ppm, whereas the triple point of water can be measured to better than 1 ppm.