Tony,
Here's a way to link traditional and universal units together in a mutually validating way.

It involves redefining two traditional units, the quarter (at one time a weight of 28 pounds), and the talent (a Greek unit of mass used in Roman Britain and elsewhere)

You are invited to recognize two codenames
as options, should anyone wish to go by them:

Fortyeightpound Talent, and
Twentysevenpound Quarter.

If we can re-energize the unit-words talent and quarter we can use them to establish a kind of hybrid traditional+natural system.

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the pound mass will be (same size as before and) 1/48 of a talent

the natural mass unit, Planck mass, will be a billionth of a talent

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there will be a 27 pound force unit called the quarterforce, or quarter (for short) and

the natural force unit will be 10**42 quarters

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UNIVERSAL UNITS ON THE WEB

No set of physical quantities is more basic than the universal fundamental constants of nature. I will quote values from the National Institute of Standards and Technology website. If consulted, the British NPL or any European site would corroborate the NIST values since they represent a consensus. The NIST lists thirteen such constants of which three are the natural unts: planck mass, length, and time. The other natural units are definable in terms of these three.

To see the NIST values for these constants, use the Google search engine with the keyword [constants]. Simply typing "constants" into Google will get you the NIST site, where clicking on the first category "universal" will get you the short list of universal fundamental physical constants. What NIST lists are actually the recommended values from an international committee, CODATA, of scientists specializing in the natural constants.

You will see immediately for instance that the length unit is 1.616 x 10**-32 millimeter. Since 1.616 is about the thickness of a penny this means that the natural length unit is 10**-32 of a penny's thickness.

REINFORCING TRADITIONAL UNITS: THE FORTYEIGHT POUND TALENT

It happens that a billion times the natural unit of mass is 48 pounds. Rather surprisingly, the equality is exact to the accuracy with which the natural unit is measured. Nothing comparable to this close coincidence occurs in the metric system. In metric terms, the same mass, namely a billion times natural, is 21.767 kilograms with an uncertainty of 0.075 percent.

This odd coincidence allows us to validate and corroborate traditional units in an unexpected way: we simply give 48 pounds a name—-TALENT for instance—-and say that the avoirdupois pound shall be 1/48 of a talent. Nothing changes. But a billion times the natural mass unit, as accurately as may presently be measured, is now one talent. (Not terribly different from the Attic Greek talent of 57 pounds or 60 "minae" in widespread use at one time.)

The existing set of British units, with one additional unit adjoined, namely the 48 pound talent, is one possible example of a traditional+natural hybrid system. It is a traditional system which has been adjusted (in this case simply by addition of one unit) to make a coincidence with natural units visible.

THE MILLION-PENNY MILE

If you google with keyword "constants" the first thing that comes up is the NIST site. Selecting "universal" and then "planck length" will get you the current best estimate for the natural length unit: 1.616×10**-32 millimeters.

Well 1.616 millimeters is about the thickness of a PENNY. Ten pennies make a useful fingerwidth unit and a million pennies make a recognizable MILE, which is 5300 feet and under half a percent different from the conventional mile. No accidental fit between natural units and the metric system is anywhere near that close.

THE TWENTYSEVEN POUND FORCE: QUARTER

The natural force unit happens to be 27×10**42 pounds of force and a traditional weight unit, the quarter (most recently 25 pounds in the US and 28 pounds in Britain), has varied in the 27 pound neighborhood.

The quarter unit in English is connected to the Arabic unit ar-Rub, which means "the quarter", and the Spanish and Portuguese arroba units, roughly the same size as our quarter.

So here we have an at-one-time widespread unit which we can redefine as 27 pounds and call the quarterforce or simply quarter for short. This makes the natural force unit, Planck force, equal to 10**42 quarterforce.

In gravity typical at the earth's surface a talent mass will weigh about 7/4 quarters. A man whose mass is 4 talents will weigh about 7 quarters.

NATURALNESS OF TRADITIONAL UNITS

Traditional British units are "natural" in several different senses. They have evolved through use by linguistically inventive people for many centuries, and units have been added, combined and adjusted in various ways to suit their purposes. Inevitably these units have adapted to the dimensions and materials of life. But this is not the only way in which units can be natural.

The units (planck mass, length, time) listed as universal fundamental physical constants are natural in a different sense. These are units favored in certain branches of physics and cosmology which arise if one requires that the values of the main proportions in nature (G, c, h-bar) be one. Quantities such as the planck mass and planck length are implicitly present in light and gravity everywhere in the universe. Units such as mile, talent, quarterforce, and penny, which are power-of-ten multiples of planck units, are also natural in the sense that they are human-scale versions of the basic Planck units and arise if one arranges the main proportions in nature to be powers of ten.

So these units are natural in various senses. The objective is to put them together in a convenient way so that they can help each other collectively to be more understandable and enduring.

This post was adapted from the essay at the following webpage.

http://www.planck.com/British+NaturalHybridUnits/index.html

DO YOU HAVE ROOM AT THE TABLE FOR TWO NEW-OLD UNITS?
They (48pound talent, adjusted quarter force) will
make your own set more enduring by linking it to
the units which have been around for as long as
there has been light and gravity.

I revised the previous material. introduced a "troy minute"---1600 minutes to a day instead of the ordinary 1440 minutes to a day. changed some things by a fraction of a percent to see how it would work. the units in this post are not identical to those of other posts but vary from them by a fraction of a percent in certain cases.

Adapted from material at the following web-page.
http://www.planck.com/British+NaturalHybridUnits/index.html



REINFORCING TRADITIONAL UNITS WITH NATURAL ONES

THE FORTYEIGHT POUND TALENT

It happens that a billion times the natural unit of mass is 48 pounds. The equality is exact to the accuracy with which the natural unit is measured. This is an odd coincidence and nothing comparable to it occurs in the metric system. In metric terms, the same mass, namely a billion times natural, is 21.767 kilograms with an uncertainty of 0.075 percent. This experimental uncertainty in measuring the natural mass unit, an uncertainty of a thirteenth of a percent, means that a billion times the natural unit is indistinguisable from a mass of exactly 48 pounds.

This odd coincidence allows us to validate and corroborate traditional units in an unexpected way: we simply give 48 pounds a name—-talent for instance-—and say that the avoirdupois pound shall be 1/48 of a talent. Nothing changes. But a billion times the natural mass unit, as accurately as may presently be measured, is now one talent. (Not terribly different from the Attic Greek talent of 57 pounds or 60 "minae" in widespread use at one time.)

The existing set of British units, with one additional unit adjoined, namely the 48 pound talent, is an example of a traditional+natural hybrid system. It is a traditional system which has been adjusted (in this case simply by addition of one unit) to make a coincidence with natural units visible.

THE TROY MINUTE AND THE NATURAL TIME UNIT

The current best estimate for the natural time unit, if you scale it by 10**45 gives a minute-sized interval. One might call it a "troy minute" since it is about 10 percent shorter than the conventional minute (the medieval troy pound, from the French city of Troyes, was lighter than the now-prevailing pound avoirdupois.)

Although there are 1440 ordinary minutes in a day, there are some 1600 "troy minutes" because the troy minute is shorter. For definiteness, we can define the troy minute to be exactly 9/10 of an ordinary minute, or equivalently make it exactly 1/1600 of a day. A common highway speed (67 mph) is then a mile per minute, a typical speed for sound is ten miles per minute, the earth's average speed in orbit is 1000 miles per minute and the standard speed for light is ten million miles per minute. To make this last relationship exact all that is needed is a slight adjustment in the length of the mile.

THE THOUSAND-PACE MILE AND THE NATURAL LENGTH UNIT

If you google with keyword "constants" the first thing that comes up is the NIST site. Selecting "universal" and then "planck length" will get you the natural length unit: 1.62×10**-32 millimeters. So 10**32 the natural length unit is 1.62 millimeters—about the thickness of a penny. Ten pennies make a classic fingerwidth unit, a hundred are just over half a foot, and a thousand make an ordinary two-step PACE. A thousand such paces make a recognizable MILE, less than a percent different from the conventional mile in use today. No accidental fit between natural units and the metric system is anywhere near that close.

We can define the mile unambiguously so as to make the standard speed of light exactly ten million miles per minute—-it was already very close to that anyway—and that will stretch it out slightly and give the mile an exact value in metric terms of 1618.8…meters. Accordingly the pace 1.6188… meters. I won't belabor this in detail.

REDEFINING THE TALENT

Now that we have time and length scales unambigouously defined we can if we wish redefine the mass unit as follows.

talent = 10**34 h-bar minute/square pace.

This is in line with the previous definition which gave the speed of light an exact power-of-ten value—-it redefines the mass unit to make h-bar an exact power of ten as well. Doing so reduces the mass unit by TWO TENTHS OF A PERCENT changing it from 48 pounds to 47.9 pounds. The cost of not making this redefinition is merely that the mantissa of h-bar will be 0.998... instead of exactly one.


THE TWENTYSEVEN POUND QUARTERFORCE

The natural force unit happens to be 27.2 ×10**42 pounds of force and a traditional weight unit, the quarter (most recently 25 pounds in the US and 28 pounds in Britain), has varied in the 27.2 pound neighborhood. The English quarter is connected to the Arabic unit ar-Rub, which means "the quarter", and the Spanish and Portuguese arroba, roughly the same size as our quarter.

So here we have a once-widespread unit which we can redefine as 27.2 pounds and call the quarterforce or simply quarter for short. This makes the natural force unit, Planck force, equal to 10**42 quarters. The rigorous definition of the force unit, given the fact that the troy minute and the pace (a thousandth of a mile) and the talent mass unit have already been defined, is as follows.

quarterforce = 10,000 talent pace per square minute.

These definitions provide for a coherent system in which c and h-bar have exact power-of-ten values. Base units in the coherent system are a hundredth of a pace, a thousandth of a minute, and the talent mass itself. The quarter is the unit force in the system. The gravity constant G has a value which is approximately a power of ten, in fact G is very close to a millionth. In terms of the units introduced here it is 0.997 × 10**-6 cubic pace/square minute per talent. So it is G is within three tenths of a percent of being a power of thousand.

the fact that G is here not 1.000 millionth but rather 0.997 millionth is the price paid for simplifying the time scale so that there are exactly 1600 troy minutes in a day. the special minute is not intended as a replacement but as a technical time unit for certain very limited uses (definitions, physics problems). I wanted to see what it would be like if it was defined with the very simple number 1600 and allowed to co-exist with the ordinary minute (somewhat as troy and avoirdupois weight coexisted for some centuries.)