Institute Metric

## Overview

The Institute Metric (*Ilunitsystum*) is the standard unit of measurement used in the Institute that encompasses Length, Time, Weight, and Temperature into a unified system. It is made with 3 general principles in mind:

1. All units must be derived from unchanging natural constants, or other units within the Metric.
2. All units must be easily divisible, by 2, 3 and 4.
3. All units must be easily converted between them without significant calculations necessary.

## The Numeric System

The Institute Metric uses a Base-12 system, using 0,1,2,3,4,5,6,7,8,9,#,$ as their digits. As such, 1012 would be 1210, and 10012 would be 14410. This also goes into the decimals as well. As such, 0.112 would be 1/1210, and 0.0112 would be 1/14412.

Prefixes are added to existing units to create larger or smaller denominations of units. The table of Prefixes are as such:

Conversions between Decimal Systems and Base-10 Systems:

#12 = 1010

0.412 = 0.333...10

8412 = 10010

$#.812 = 142.666...10

## The Metrum: Length, Area, and Volume

The Metrum is a unit of length, measured to be 1/(2\*10612 ) of the Earth's radius. The Metrum is approximately 1.067 metres. It is denoted by the unit 'm', such that 1 metrum is 1m, and 1012 metrum is 10 m, or 1 Dm. Because it is difficult to measure the earth's radius every time a measurement is to be made, the Archives calculated how long the Metrum is defined to be and created a bronze rod to act as its base. This is called the Metrum Rod. The most widely used variations of the Metrum are the Kilometrum (km) for long-distance measurements, and the Centimetrum (cm) for measuring lengths of trinkets.

Area is measured in Square Metrum (m2) where 1 Square Metrum is equal to the area of a square with 1 metrum as its length. Here, the Prefix rules follow the squaring, such that km2 represents not 103m2, but 106m2. The same principle applies for Volumes. The most widely used variations of the Square Metrum are the Square Hectometrum (hm2) for areas of farms, and Square Centimetrum (cm2) for areas of little trinkets.

Volume is measured in Cubic Metrum (m3) where 1 Cubic Metrum is equal to the volume of a cube with 1 metrum as its length. The most widely used variations of the Cubic Metrum are Cubic Decimetrum (dm3) for volumes of large liquid containers, and Cubic Centimetrum (cm3) for volumes of cups.

## The Nium: Time

The Nium is a unit of time, measured to be exactly a day, or the time it takes for the sun to move from zenith to zenith. The most widely used variations of the Nium are the Decinium (dn, 2 hours), the Centinium (cn, 10 minutes), and the Secum (sec, 10-412 n. 4.167 seconds). 10012 Secae is a Centinium, and 1012 Centiniae is a Decinium. Time is written in decimals, such as: 0.$108 n (22:10:32).

### The Annum

Each year is, depending on whether or not it is a leap year, 26512 or 26612 days. The Annum, or the Year, is not a unit of time, but is commonly used by historians and geologists to refer to events and ages of thousands and millions of years old. Here, the 1 Nium difference is negligible, and is therefore accepted as not within the Institute Metric but of Traditionally Accepted Units.

### The Calendar

Each year is divided into 12 Lunae (2612 Niae, or a full phase transition of the moon), with each Lunum divided into 5 Hexiniae (612 Niae). This leaves 5 or 6 days out, from which an imaginary 'Lunum 13' is created, and are celebrated. The 6th day of the Lunum 13 only comes every 4 years, and is a day of religious festivities. All babies born on this day are considered as being especially lucky, and they commonly receive birthday gifts on the 5th day of Lunum 13.

Dates are written as such: Annum/Lunum/Hexinium/Nium. Example: 1#2/$/1/3.

### Timekeeping

The Institute has 3 different forms of clocks that aid in their timekeeping, which displays time in varying degrees of accuracy. The first form is that given by the **Interface Unit**, an artifact of unknown origin that has the capacity to correctly keep time by the Secum. It is the time that is used to correct any errors that may occur with other forms of clocks. The second form is the Sun Dial, placed at the centre of the courtyard of the First Bastion. The third form is the Water Clock, which rings a bronze bell every Decinium. The Institute's expertise in creating the last two forms of clocks is exported to its surrounding neighbors for accurate timekeeping.

## The Pondum: Weight and Mass

The Pondum is a unit of weight, measured to be 10-312 m3 of distilled water (0.703 kg). It is denoted by the unit 'p'. The most widely used variations of the Pondum are the Kilopondum (kp, 1214.767 kg) and the Millipondum (mp, 0.407 g). The weight of the Institute *Aurolum* (Gold Coin) is weighed at about a Centipondum (4.8 g) of 99% gold, with enough value to feed a family of 5 for a month.

## The Degrum: Degrees of Angles

The Degrum is a unit of angle, of which a full circle is 10012 Degrae. It is mostly used without any addition of prefixes, and is denoted by the unit 'deg.' Each Degrum is 2.5°.

## The Tempum: Temperature

The Tempum is a unit of temperature, divided into 10012 equal intervals, with 0 being 10012 at the freezing point of water and at the boiling point of water. Though the concept of pressure did not exist at the time of the Tempum's addition to the Institute Metric, it is measured at 1 atm. Room temperature (25C) would be equivalent to 3012T.

## History of the Institute Metric

### First Speaker Clauron and The Standardisation Coucil

*'On Measuring the Earth's Radius'* by Exon was published on 43 PC, in which Head Archivist Exon described a potential process of measuring the Earth's radius by measuring shadows from poles in faraway cities. By measuring the distance from the First Bastion and the southern tip of Great Devin, and by measuring the length of the shadow cast by a pole at the southern tip of Great Devin when the sun was directly overhead in the First Bastion - so as to not cast a shadow - Head Archivist Exon was able to produce a fairly accurate calculation of the radius of the Earth. This would provide a foundation on which the Institute Metric would be founded a mere year later.

*'Theses on the Institute Metric'* by Clauron was published on 44 PC, in which First Speaker Clauron emphasised the need for a standardised system of measurement to provide a solid basis for flourishing science, industry, and commerce. Inspired by Exon's work a year prior, these theses were widely supported by all in the Institute, using the earth's radius as measured by Exon's method as the cornerstone on which the Institute Metric is founded. This would culminate in the Standardisation Council of 45 PC, from which the Institute Metric would finally be born. Interestingly, Clauron first mentioned the neccessity for the Metrum Papers in this paper, highlighting the importance of spreading the Institute Metric beyond its borders, to civilisations that do not have knowledge of the Institute Standard language.

After the completion of Exon's calculations, the Metrum Rod and the Metrum Papers were made by the Standardisation Council. This took about a year to complete, but allowed for easy export of the Institute Metric to civilisations outside Great Devin. The papers and the Metrum Rod was published on 49 PC.

### Head Archivist Exon and the measuring of the Metrum

After the decision was made to standardise the Institution in line with the new Institute Metric, Head Archivist Exon was tasked with measuring the radius of the Earth. He did this by measuring the distance from the northern tip to the southern tip of Great Devin, and by measuring the angles made by the shadows of a long, bronze stick. Thanks to its location in the tropics, cities of Great Devin periodically experiences a time in which the sun is directly overhead, so that no shadows are formed. This fact made it possible for Exon to carry out the task of measuring the Metrum.

### The Metrum Papers

The Metrum Papers are a set of papers that discuss the use of the **Institute Metric**, notable in its lack of written language, containing only simple symbols and diagrams to teach the reader on the Institute Metric. The paper was created in the hopes to spread the use of the Institute Metric without any need of linguistic barrier, though its success is questionable as the Pondum relied on a description of water. Its completion gave insight to the Institute of the nature of The Elder Texts, as it too featured imagery and symbolism that would be present when trying to communicate without an established translation.

### The Tempum

During the Little Ice Age of 451~456 PC, the need to increase agricultural productivity forced Institute Archivists to find ways to measure temperature in units. This method was devised by Archivist Clyron on 454 PC, and contributed greatly to research and development of the Greenhouse Method, increasing agricultural productivity throughout the Institute.