The Denary system of measurement is a system of units, calendar, and time-reckoning based on decimal notation. It was invented by Hellerick Ferlibay in 2003, and is designed after the Senary system of measurement (which uses system of notation based on number 6).
Definition of the basic mechanical units[]
The basic mechanical units are:
- tempa, unit of time, abbreviated dT;
- longa, unit of length, abbreviated dL;
- massa, unit of mass, abbreviated dM.
An abbreviation of a unit of the Denary system always is preceded by small letter d, which means “denary”. It precedes an abbreviation of a derived unit as well, e.g. the unit for velocity, longa per massa, is abbreviated dL/T ("Denary longa per tempa").
To define the basic units the next natural constants are used:
- Density of water (at 3.984 °C): 999.97495 kg/m³;
- Speed of light in vacuum: 299792458 m/s;
- Mean solar day: 86400.002 SI seconds.
The basic mechanical units are defined to make these constants match the next values in Denary units:
- Density of water (at 3.984 °C): 1 dM/L³;
- Speed of light in vacuum: 353815000 dL/T;
- Mean solar day: 1000000 dT.
This definition determines the basic mechanical units on the next values in SI units:
- tempa, 1 dT = 0.086400002 s (about one microday, ≈ 1/11.57 second);
- longa, 1 dL = 0.073207945 m;
- massa, 1 dM = 0.39234106 kg.
Additionally, the units of length and time are chosen to make other natural constants match round numbers:
- Gravitational acceleration: 1 dL/T² = 9.806876575 m/s² (one “gee”);
- The Earth’s meridian: 546500000 dL = 40008142 m.
Having both density of water and gravitational acceleration equal to 1 is very useful, because it simplifies many physical calculations:
- 1 massa of water is 1 cubic longa of water.
- A body with mass 1 dM weighs 1 dLM/T² (dLM/T² is the Denary unit of force).
- The system unit of pressure, dM/LT², is equal to pressure at the depth of one longa in water (that’s why the unit of pressure is informally known as “water longa”; normal atmospheric pressure is about 141 water longas).
- A body drowns in water when its mass (and weight) is numerically greater than its volume.
Multiple and submultiple units[]
The multiple and submultiple units are derived from main units by means of their multiplication or division by a power of number 10. Their names are derived from the names of the original units by means of the next prefixes:
Multiple prefixes | Submultiple prefixes | ||
---|---|---|---|
10^{1} | uno- | 10^{–1} | eni- |
10^{2} | du- | 10^{–2} | bi- |
10^{3} | tre- | 10^{–3} | terti- |
10^{4} | qua- | 10^{–4} | quarti- |
10^{5} | pe- | 10^{–5} | penti- |
10^{6} | se- | 10^{–6} | secti- |
10^{7} | he- | 10^{–7} | hepti- |
10^{8} | oco- | 10^{–8} | octi- |
10^{9} | no- | 10^{–9} | noni- |
10^{10} | de- | 10^{–10} | deci- |
10^{11} | deuno- | 10^{–11} | decieni- |
10^{12} | dedu- | 10^{–12} | decibi- |
10^{13} | detre- | 10^{–13} | deciterti- |
10^{14} | dequa- | 10^{–14} | deciquarti- |
10^{15} | depe- | 10^{–15} | decipenti- |
10^{16} | dese- | 10^{–16} | decisecti- |
10^{17} | dehe- | 10^{–17} | decihepti- |
10^{18} | deoco- | 10^{–18} | deciocti- |
10^{19} | deno- | 10^{–19} | decinoni- |
Note that all the diminutive prefixes end in -i-.
These prefixes are not used in abbreviations.
According to the “scientific notation”, to indicate the power of 10 used to multiplicate/diminute the original unit, it should be written between the small letter d and the rest of the abbreviation. Thus, 1 d2T means “one dutempa”, = 100 tempas = 8.64 seconds; 1 d4T means “one quatempa”, = 10000 tempas = 14.4 minutes. Similar notation may be used for non-Denary units, e.g. “12d6 people” means “twelve million people”. The small letter d is allowed to be combined with the next minus sign into ð character, e.g. 1 ð2L means “one bilonga”, = 0.01 longa = 0,7321 mm.
The “common notation” is used as well. According to it, the multiplicating and diminuting suffixes between 10^{–9} and 10^{9} are abbreviated by their first letter: capital letter for multiplicating prefixes and small letter for diminuting suffixes. In these cases the small letter d for “Denary” is dropped. Thus eL means “enilonga” (0.1 longa = 7.321 mm), and DL means “dulonga” (100 longas = 7.321 m).
The unit of temperature[]
The Denary system uses absolute thermodynamic scale of temperature (i.e. its zero is equal to 0 kelvins, –273.15 °C, or –459.67 °F). The system unit of temperature is therma, its abbreviation is dΘ. By definition, the temperature of crystallization of water (273.15 K, 0 °C, 32 °F) is equal to 250 dΘ. Therefore one therma is equal to 273.15/250 = 1.0926 K. The translation formulas are the next:
- Thermas = centigrade × 1.0926 + 250;
- Thermas = Fahrenheit × 1.96668 + 230.576.
Since the normal temperatures usually lie in between 200 and 300 dΘ (–55 and +55 °C, –66 and +130 °F) the words “two hundred” are usually dropped when the value is pronounced aloud. Thus, “high seventies” means about 275–280 dΘ (27–33 °C, 81–91 °F).
The Denary calendar[]
The year is divided into ten months of 36 or 37 days.
The calendar uses 7-day week. Every month starts with Sunday. The final one or two days don’t belong to any week and are known as month-ends (every year has 15 or 16 days of month-ends). Most holidays are shifted to the closest month-end.
Therefore:
- 1 year = 10 months = 50 weeks = 250 working days (with 5-day working week);
- 1 month = 5 weeks = 25 working days.
All of the above are decimally round numbers.
Numeration of months within year, weeks within year, days within month, and days within week starts with zero. Thus, months are numbered from 0 to 9, and days are numbered from 0 to 35 or 36.
The year starts on the same day as in the Gregorian calendar, the leap year rule is the same as well. In leap years the Month 1 has 37 days instead of 36.
The calendar uses the Common Era.
To define a day, two systems of notation may be used: the month notation and the week notation. In month notation the day is defined by the number of its month and the number of the day within month (YYYY-M-DD). In week notation the day is defined by the number of its week and the number of the day within week (YYYY-WW-D). It’s easy to convert a date between the two systems:
- Given: 2008-3-14.
- 3 months = 15 weeks, 14 days = 2 weeks with no reminder; 15 + 2 = 17 weeks.
- Therefore, 2008-3-14 = 2008-17-0 (May 1st, 2008).
The months have no official names, but informally (and somewhat jokingly) they are known as:
- Month 0: Zerober
- Month 1: Primember
- Month 2: Secumber
- Month 3: Tertimber
- Month 4: Quartember
- Month 5: Quintember
- Month 6: Sextember
- Month 7: September
- Month 8: October
- Month 9: November
The decimal fraction of the year f (0 ≤ f < 1) may be converted into the Denary calendar by means of the next formulas:
- Month = int (10 × f)
- Day = int (36.6 × (10 × f – Month))
In common (non-leap years) these formulas make no errors.
Geographic coordinates system[]
The geographic coordinates of a point on the Earth’s surface consist of its longitude and latitude expressed in angle units.
The system unit of angle is circa, it is equal to one complete revolution, i.e. 360°; its abbreviation is dC. One circa consists of 100 bicircas (ð2C).
The basic meridian of the Denary system is defined to be 15/32 of the full circle to the west from Greenwich (W168°45'). This meridian goes through the Bering Strait, separating Asia and America. The longitude is counted from the basic meridian, from east to west.
The latitude is counted from the equator. Northern latitudes have positive values, southern latitudes have negative values.
Time-reckoning[]
One day consists of 100 quatempas (ð2T).
The universal time is solar time on the basic meridian. It varies through the day between 0 and 100 quatempas.
On all the other meridians the same time is used, but it can be 100 quatempas greater than the universal time in the western parts of the world, where it’s still the previous day. E.g. 31.12 of Monday in Australia is the same moment as 131.12 of Sunday in California. You have to keep in mind that 1 day = 100 quatempas; when you subtract 100 quatempas from time, you have to add 1 day to the date, et vice versa.
In every region the local universal time is varying within some range. Theoretically its lower limit should be equal to the longitude of the place, and its upper limit should be 100 quatempas greater. In practice the bottom margin is about 10 quatempas greater than longitude, and is rounded to tens. Thus, in most European countries, whose longitude is about 50 bicircas, the time is varying between 60 and 160 quatempas, i.e. after 159.99 the clock shows 60.00 of the next day.
The table below shows the ranges of local universal time adopted in some cities of the world, in quatempas:
Auckland | 10.00–110.00 |
Tokyo | 20.00–120.00 |
Beijing | 30.00–130.00 |
New Delhi | 40.00–140.00 |
Moscow | 50.00–150.00 |
London | 60.00–160.00 |
Reykjavik | 70.00–170.00 |
Rio de Janeiro | 80.00–180.00 |
Chicago | 90.00–190.00 |
Los Angeles | 100.00–200.00 |
To get local solar time you have to subtract the longitude of the place from the local universal time.
The next formula may be used to convert time in hours into Denary universal time
DUT = (100 × ((H – TZ) / 24 – 17/32) + 100) mod 100.
Where DUT is Denary universal time in quatempas, H is local time in hours, TZ is the time zones in hours (positive for eastern time zones, and negative for western time zones). When time is less than the lower limit for this area, the local universal time is DUT + 100 quatempas.