Dozenal Wiki

The Corn-Obol-Fecc or Primel system is an alternate system based on gravity, the specific gravity of water, and joule constant (specific heat of water), as unit values.  The particular choice of working base units allow for easier implementation, without destroying the design of the system.

There are some measures of matter which scale well: the density of atoms and stars are not much different to water.  Although the velocities do vary from what we experience, to thermal velocities (around 1000 kms) up to stellar velocities and then ultimately the speed of light, the variations here are five orders of magnitude in place of eighteen magnitudes for length and time.

We are ultimately human, and we walk around on the surface of a particular planet.  A number of rubbery constants have come to be accepted, such as the connection between mass and volume through capacity, mass and force through weight, and the connection between energy and the product of mass and temperature, through specific heat.  The basis of this system (there identical up to names), is then this.

Angle, Time and Calendar[]

The circle is taken as unit, and divided into powers of 12, into 100; degrees, of 100; minutes of 100; seconds.  The measure of angle in radians applies only when one has a small fraction of an incomplete circle.

The cycle of the day directly converts angle and time, by way of right ascession.  But the natural division usually advanced of the day is into powers of 12 also, as 10; hours of 100; minutes of 100; seconds.  This blink of an eye, the unit equal to the TGM scale, is 1/2 of these seconds.

The unit of time in this system is a fecc, "a period of time".  A decimal second is 34.56 of these units, a day is 1 000 000; of 1D6 feccs.

Calendar refers to grouping of days into weeks, months and years.  The change of that system has no part of this system: conversion to a duodecimal system does not need unwarranted distraction that the religious revolts would produce.

Length and Velocity from Time[]

At this time, there are five units of velocity in use: the foot per second, metre per second, mile per hour, kilometre per hour, and knot.  Although the units of the ratios vary by factors of 5000, the actual units lie between 1 and 3.3 ft/s.  This means that selecting a velocity unit as a means for selectiong time (time = velocity / gravity), and then use the formula that length = velocity × time to derive the length units from time.

The resulting units like 'foot/second / g'  gives a time unit like 1/32.175 seconds, while a km/h gives 1/35.3 s, which neatly brackets the time unit of 1/34.56 second.   A unit of this length gives the sorts of velocities one sees on land well in the range of 1 to 100; (90 mph or 140 kms).  Moreover, because the unit is near the km/h, simply converting the road signs and rounding will give a very close idea of the speeds involved.

The unit of length thus derived is then about 1/3 inch, or the length of a barleycorn.   Over 1 second, one travels a hand (4 inches, 100 mm), a minute gives (48 ft, or 14.4 m), and an hour gives a mile of 6912 feet or 2.0736 km,  A mile per hour is the same as a hand per second, or a corn per fecc, is a velo of velocity. 

One can still keep feet and inches, by making the yard as four feet or 100; corns.  The foot divides into 10; inches of 10; lines etc.  A mile would be at this rate, 1000; yards, of 100; corns.

The unit of area is a verge (yard) of land, being a rectangle of one yard long and one mile long, or one furlong wide, and one chain long. 

The knot, on the other hand, derives from a very different velocity: the speed of the rotating earth at some point, is 1000; knots, or 10000; minutes of arc in 10; hours.

Weight from Length[]

The units of mass (weight in metrological terms), is derived from a cube of water.  A cubic corn of water weights something like 5/9 gram, around the weight of a greek gold obol.  This unit is small, but one can build up either a traditional system, or steps of the obol to larger units.  A cubic hand of water gives a caddy or kilogram-size unit.

A volume of a caddy is a cubic hand, gives a unit near a litre.  This can be divided in the traditional cooking measures into 4 cups, of 48 teaspoons etc. 

Pressure from Length (head)[]

Although modern metrology defines pressure in terms of force per area, the actual measurement of this comes from a head of liquid, either mercury or water.   Even today, one measures the pressure that watches might withstand, in terms of metres of water. 

Atmospheric pressure is typically in the order of 890; corns of water (or 35 feet).  The unit of pressure is then pretty much near the metrologist's millibar, except that most of the weather that we have would stay in a three-digit arrange.

The Pendlebury 'Realities'[]

Tom Pendlebury wrote in the TGM, several 'realities' which can be included in the definitions. These generally are natural constants commonly used in engineering at the turn of the 20th C. It's worth noting that such a system has been considered some time before, and the various quantities are staples of new systems.

Spig: This is the unit that corresponds to specific gravity, taken to be the density of a particular state of water. In practice, using a cube of water (as the kilogram is a decimetre cube of water), is used to define the unit of specific gravity (eg kg/dm³), rather than the other way around. Water measured in air is less dense, since it displaces air, and this is counted. Water in air is 997.07 kg/m³, + air itself (1.2 kg/m³) gives water (998.2). Water at its greatest density is 999.972 kg/m³, this was found by Beniot in 1895.

The derived mass is then m = d.l^3 = m.g^3 t^6. The ratio of m/t^6 has been observed in nature, in that the mass is proportional to the sixth power of urine discharge.

Leo: This unit appeared originally as 10 m/s², but is close enough to gravity, that we might define the unit as standard gravity. So while a pound-leo is the same size as a pound-force, the former is an exact value based on standard gravity, while the latter is based on local gravity.

The derived length is then l = g.t^2

Specific Heat: The unit of heat was derived by heating a unit mass by a unit temperature. Thus the B.Th.U. is a pound-fahrenheit, and the calorie is variously the CGS gram-celcius or the MKS kilogram-calcius. The fahrenheit part corresponds to an energy/mass relation, which equates to raising the mass 778 feet against gravity (James Prescott Joule). If we suppose that the ice-point to boiling point is 180 of these units (ie 140,000 feet), then we could convert this into the length unit derived from the leo.

The specific heat of water is 4186.8 J/kg °C. If we suppose that the degree-celcius divides sexagesimally, as do degrees of arc, then this corresponds to 1.163 J/kg "C. Redividing the 100°C into 116.3 °N, this becomes 1 J/kg "N, the heat to raise 1 kg by 1°N is then a Watt-hour. The IST calorie was defined as 0.86 international watt-hours = 1 kilogram-degree celcius.

Time: The day is the quantum of calendar, and its divisions reflect the 24-hour cycle. The TGM divides the hour into 144 minutes of 144 seconds, the unit called a 'timm'. The current second is 5.76 of these units, and the net effect is that g/5.76 m/s is quite a fast pace. Since the unit of length is g.t²,

Wendy Krieger's 'Realities'[]

Wendy Krieger takes a rather different view on the choice of base units. The basis here is that certain things hold the same rate from molecules to stars.

density: The atom in this range can be regarded as a fairly hard sphere, and most atoms, despite their weight, are very similar in size. For many solids, the molar-density is 1/10 spig-mole (eg gram-mole per cu cm). Liquids are somewhat less dense, but not much.

velocity: This value is most closely connected to specific energy. Thermal velocities, such as the speed of sound, are in the order of 100 to 1000 metres per second. Stellar velocities are of the order of 0.001 times the speed of light, which is something like 1000 times thermal velocities. But it is the same sort of range of heat from atoms to molecules.

time: This is a singular variable that determines the 'size' of things. Simply keeping the same density and velocity, but reducing time to 1 nanosecond, removes nearly all of the exponets of the atomic constants.

charge: electrical charge is taken as a surface feature. Thus, when something like a field induces polarisation, the internal dipoles all align, but the net effect is the unmatched charges where there is no facing dipole.

When these realities are combined with the leo, we see that the 'ideal unit' of time is the sort that produces a velocity in the ft/s, kph, knot, mph, m/s range. We evaluate 'g' in these units, to get g.1s =35.304 kph = 32.174 ft/s,= 19.0626 kn = 21.93685 mph = 9.80665 m/s.

Since a duodecimal division of the day is proposed, the day gives a unit at 1/34.56 seconds, and 1.s × g would be 34.56 kine.

The unit of length comes to 1 metre = 34.56²/9.80665 lengths, or 121.794 length units. This is about 1/3 inch, and the corn, or barley corn is suggested. Note that 12 corns is nearly 1 dm, and 12 dm makes the old french aune or yard of 1.2 metres.

The unit of mass is a cubic corn of water. The unit is close to 1/1800 kilogram, or 0.555 grams. This is very close to the old greek unit obol, that we select this name.

Although the length and mass units are near the CGS units, the velocity is 28.375 cm/s, which makes the derived units much bigger than their CGS units.

Section heading[]

Write the second section of your page here.