Some Help Developing Fictional Measurements

[stickmaker]

Here are my notes for how things are measured in the Kingdom of the Compact:

Measurements

Length

Solar Mile, aka Sol = Unit of length. Originally defined as one hundred-millionth of the average distance between the Earth and the Sun. Today the standard definition is one thousand times the distance between two fine, incised lines in the polished top surface of a slab of quartz in the Department of Measures building in Avignon. From this standard most other official measurements in the Compact are derived.

1 Solar Mile = 1 Sol = one thousand New Toise = 4600 Solar Feet ( = 0.93 statute miles = 4910.4 statute feet = 58924.8 statute inches = 1.5 kilometers = 1500 meters)
1 New Toise (pronounced "toys," plural: toises) = 1/1000 of a Solar Mile = 4.6 Solar Feet ( = 4.9104 statute feet = 1.497 meter)
(The old toise - well, one of the most common of them - was 1.949 meter, the same as the fathom - well, one of them.)
1 Solar Foot = 12 Solar Inches ( = 32.6 cm = 1.07 statute feet = 12.84 statute inches)
1 Solar Inch ( = 2.72 cm = 1.07 statute inches)

Volume

1 Dram = 0.5 cubic Solar Inch ( = 2.52 ml)
1 Roquille = 1 cubic Solar Inch = 8 Drams ( = 20.16 ml)
1 Pinte = 3 cubic Solar Inches = 27 Roquilles = 216 Drams ( = 544.32 ml)
1 Velte = 10 cubic Solar Inches = 1000 Roquilles = 37.037 Pinte ( = 20.16 liters)
1 Cubique = 1 cubic Solar Foot = 1.728 Velte = 64 Pinte ( = 34.837 liters)
1 Cubic Toise = 1 cubic New Toise = 97.336 Cubique = 168.2 Velte = 6229.5 Pinte ( = 3391 liters)

Weight/Mass/Force

1 Grain = 1/10th Roquille of water ( = ~2 mg)
10 Grains = 1 Roquille of water ( = ~20 mg)
1 Cinqcents Grain = 5 Roquille of water ( = ~1 g)
1 Once = 20 Cinqcents = 100 Roquille of water ( = ~20 g)
1 Livre = 25 Ounces ( = ~500 g)
1 Talent = 2500 Livre ( = ~50 kg)
1 Millelivre = 10 Talents ( = ~500 kg)
1 Ton = 2 Millelivre ( = ~1000 kg)

Time

Same as ours.

Money

1 Copper coin
1 Silver coin = 1 Sous = 100 Copper coins
1 Silver bar = 1 Livre = 20 Silver coins (historically, one pound of silver; here 500 grams or 1 livre weight)
1 Gold coin = 1 Crown = 10 Silver coins = 1/2 Silver bar
Small gold bar = ? = 10 Gold coins
Large gold bar = ? = 10 Small bars

It's largely based on pre-Revolutionary French units. I'd appreciate comments on the system, especially if someone finds I've made a math error. I'd also appreciate names for the small gold bar and large gold bar.

Comments

[kengr]

I'm pretty sure they'd use a platinum/iridium alloy for the length standard rather than quartz.

Quartz isn't thermally stable enough (ie the distance would change too much as the temperature of the block changed). The Pt/Ir alloy still changes with temp but not nearly as much.

Also, the length of an AU is *really* hard to determine with any degree of accuracy until you have radars that can bounce signals off other planets. Even worse than the use of the Earth's circumference in the original definition of the meter.

[stickmaker.livejournal.com]

Quartz is *very* thermally stable, in terms of linear and volumetric expansion. Fused quartz was the first choice for the Palomar 200" mirror, before deciding that was beyond the then state of the art and settling on Pyrex. Now, that's not natural quartz, but the properties of that are similar.

Let's see... Checking my notes, I have platinum at 27, but not platinum iridium alloy. Don't have a number for quartz, either. Looking online.

On this page:

http://en.wikipedia.org/wiki/Thermal_expansion

Quartz is: 0.33 (that probably varies with purity)

Fused quartz: 0.59

Platinum: 9

Nothing for platinum iridium

Diamond: 1

Invar: 1.2

So, quartz is actually better than fused quartz, at least on that table.



As for calculating the AU, Eratosthenes estimated the distance to the Sun as approximately 23,000 times the Earth's radius using pure geometry, which is pretty close.

Here are my notes:

SC 1773 In response to a famine relief disaster caused by two different people using two different definitions for a measure of weight - and a long perceived need to simplify and standardize the complicated system of measures in his kingdom - King Claud creates a panel to establish a system of reproducible standards for measurement. In this, he is successful where even Charlemagne failed.

After three years of often heated discussion, the panel recommends a new unit of length, defined as one hundred-millionth of the average distance between the Earth and the Sun. The deciding moment occurs when one of the scholars recalls that Eratosthenes estimated the distance to the Sun as approximately 23,000 times the Earth's radius. He then remarks that a hundred-millionth of the most widely accepted value for that great distance would be close to the long-used measure of a thousand toises (that unit, itself, varying widely throughout the Compact) as well as most definitions of mile. This sparks a program to accurately measure both the Earth's radius and the distance to the Sun. This work also obtains the distance to the Moon and size of the Earth, the Moon and the Sun.

Using this data, the scholars calculate a new standard unit of length, which is named the Solar Mile, or Sol. All other units of length and volume - and, later, weight and density - are based on this. Using long-baseline observations combined with trigonometry, this length is marked by two incised lines, filled with gold, in a continuous layer of granite in the side of a mountain. The result is named the Incised Solar Mile. Using similar methods, a smaller physical unit - the New Toise, defined as one-thousandth of a Sol - is then created by incising fine lines in a slab of polished quartz. Eventually, a special formula of porcelain is developed which is used to make Master Toise measures. To this day, these are the standard references for length in the Compact. Many other nations pay a fee to have their own copy of this standard made.

While the original Solar Mile is not quite reproducible - in large part due to astronomers repeatedly refining their astronomical measurements - the effort is deemed successful. From this standard, an entire system of metrics is created.

I hope this is coherent. One of my cats has been repeatedly and persistently pestering me for attention. :-)

[stickmaker.livejournal.com]

Oh; the reason the meter was so far off is that one of the men sent out to make measurements instead stayed in a fancy hotel eating and drinking the funds and sending back educated guesses. :-)

People who aren't familiar with the history of metrology (not meteorology) don't realize just how good our ancestors were with non-electronic equipment. (Yes, ancient humans really did measure and lay out the foundations of those pyramids. :-)

I'm an engineer, I've had surveying, this is also an interest of mine beyond what I needed for my career. So, I know a lot more about it than most people.

I do appreciate your comments. I have a bad habit of lazily skipping over things, and need to be kept on my toes. You not only caused me to check and reassure myself, in the process of checking I learned a couple of new things.

[kengr]

I've had an interest in dimensional analysis (ie what units or "dimensions" one should use to measure various things) ever since an article on it back in Analog in the mid 60s.

It also suggested some base units to derive things from, which does drag in metrology.

The suggested units were based on the mass of the electron, the speed of light, and a few other things.

As I recall the only measurement currently based on a physical standard is the kilogram. Length is now based on wavelengths of light generated by a specific quantum transition in s specific isotope. And the speed of light is now a defined constant, so time is derived from the definition of length & the speed of light.

Or I may have that backwards.

Current is the weird one, with the ampere having a truly bizarre (but more or less reproducible) definition, with the Coulumb (unit of charge) derived from that and the time definition.

Odd factiod: The US gallon is apparently legally *defined* as 231 cubic inches. And the inch is defined as 2.54 cm.

[stickmaker.livejournal.com]

One of the more interesting books in my home library is _Secrets of the Great Pyramid_. It's not by a pyramidiot, but by a professional metrologist. He does a good job of recounting the history of various projects in modern (post-medieval, that is) times to measure various things in Egypt, primarily the Great Pyramid, as well as the post-ancient history of exploration. He also goes into a lot of detail on the various measurement systems (there were at least two cubits, the sacred and the profane, both repeated endlessly in carvings and drawings) the ancient Egyptians used.