International Units (Galhaf)

The standard international measurement system used on Galhaf evolved out of traditional units used in West Odirá and, unlike Earth's SI is not based on a decimal system. In this article, standard English translations will be used. There is no single naming system for the units, though standard symbols exist for each unit

Basic Units

Time

The basic unit of time is the daythird, historically defined as 1/216,000 of a day (25 hours, 26 minutes, and 55 seconds in Earth time), part of a sexagesimal system of dividing the day:

• 1 day = 60 daymins = 25 h, 26 m, 55 s
• 1 daymin = 60 daysecs = 25 m, 26.9 s (1/60 day)
• 1 daysec = 60 daythirds = 25.449 s (1/3600 day)
• 1 daythird = .42414 s (1/216,000 day)
• 1 dayfourth = ¹/₆₀ daythird = 7.0691 ms (1/12,960,000 day)

Historically, further sexagesimal divisions were used. In modern times, however, small units of time are usually given in fractions of the daythird. The dayfourth retains some minor usage, particularly in timing races and the like

Length

The basic unit of length is the fathom, historically defined as twice the distance that an object falls at sea level at 45 degrees north in a daythird, approximately 170 cm

• 1 League = 60 Furlongs = 12.2193 km
• 1 Furlong = 120 Fathoms = 203.656 m
• 1 Fathom = 4 Cubits = 169.713 cm
• 1 Cubit = 6 Hands = 42.4283 cm
• 1 Hand = 5 Grains = 7.07138 cm
• 1 Grain = 60 hairwidths = 1.41428 cm
• 1 Hairwidth = 235.713 μm

Area

In modern times, area is commonly measured by squared lengths, such as square league or square fathom, but a few traditional units were adopted:

• Houseland: 4 square furlongs (¹/₉₀₀

square league; 16.5903 ha, 40.9955 acres)

• Minuteland: ¹/₆₀

houseland, thus 1/15
square furlong or 960 square fathoms (2,765.05 m2, .683259 acres, 29,762.8 ft2) 

• Panel: 4 square cubits (¹/₄

square fathom, .720063 m2, 7.75069 ft2)

Panels are commonly used to measure the area of buildings, while houseland and minuteland are commonly used to measure small land areas, especially real estate

Volume

• 1 Octet = ¹/₈

Cubit fathom = 8 Barrels = 611.022 L (cube 2 cubits on a side)

• 1 Barrel = 64 Sesters = 76.3778 L (cubic cubit)
• 1 Sester = 8 Gills = 1.19340 L
• 1 Gill = 27 Drams = 149.175 mL
• 1 Dram = 60 Minims = 5.52501 mL
• 1 Minim = 92.0835 μL

Cubic measurements are also used, such as cubic fathom and so on.

Mass

The basic unit of mass is the talent, historically defined as the mass of 1 barrel of water

• 1 Talent = 8 Octals = 76.3778 kg
• 1 Octal = 12 Pounds = 9.54723 kg
• 1 Pound = 12 Ounces = 795.602 g
• 1 Ounce = 3600 Grains = 66.3002 g
• 1 Grain = 18.4167 mg

These units are also used for weight and force. In ambiguous contexts, the words "mass", "weight" or "force" can be affixed. When used as force, an acceleration of 1 fathom per daythird² is used, i.e., a pound-force is the force required to accelerate a mass of one pound at the rate of 1 fathom per daythird per daythird (7.5057 Newtons)

Temperature

As originally devised, the zero point was intended as the temperature achieved by a mixture of water, ice, and ammonium chloride and the boiling point was set at 60 (approximately 104 C in Galhaf's slightly-denser atmosphere). This set the freezing point of pure water at about 8.7 degrees. The scale was subsequently shifted to make the freezing point of water 10 degrees. For scientific purposes, a second temperature scale exists in which absolute zero is set at 0. The triple point of water is defined as 131.07 with the difference between Absolute and common being 121.07. The increment is thus about 2.084 Kelvin (273.16/131.07)

Angle

The most common way of measuring angles is by dividing a circle into 288 degrees. Radians are also used with the same definition as on Earth.

History

The International System was created at the First International Conference for Standardization. The Conference was held with the intent of reducing barriers to international trade and science caused by differing standards. At the time, there were different units in use in each nation, and even, quite frequently, in different parts of nations. Many were based on similar principles, such as the fathom of 4 cubits or 24 hands, but with differing values for the units. Several proposals were presented, including a completely decimalized system. The decimalized system was rejected as being too different from commonly-recognized units.

Even after it was accepted that common units would be used, it took months of debate to settle on a consensus agreement. It was accepted that adopting a particular national value would unfairly benefit that nation over the others, and thus, a "natural" basis major debate centered on how the unit of length should be defined, as most accepted the idea of mass being defined in terms of a volume of water. The main proposals were:

• The league set to 1/10 a degree along the equator (I.e., 1/2880 equatorial radius; 1 fathom = 185.346 cm = 1.09211 current fathoms)
• The league set to 1/1000 the diameter of Galhaf (1 fathom = 169.913 cm = 1.00118 current fathoms)
• The fathom set to 10 times the length of a pendulum with a half-period of 1 daythird (exactly 10/π², or 1.01321 current fathoms)
• The cubit set to the length of one side of a cubic volume of water with a mass equal to 100 Trade pounds. The trade pound was a weight historically defined as a particular volume of silver which had long been used in trade in East Odirá and had some familiarity in West Odirá as well. (1 fathom = 166.945 cm = .983690 current fathoms) - the only major proposal that used mass to define length
• The fathom set to twice the distance an object falls at 45 degrees north at sea level in one daythird

The last-listed was, of course, ultimately accepted. The pendulum was, however, used to measure the force of gravity. Namely, the standard fathom was measured by multiplying the length of a daythird-pendulum by π²

Use in science

For scientific purposes, a variant system is used which, similar to Earth's SI, uses decimal prefixes. In principle, the prefixes can be added to any of the units above, but in practice, only a few units are used:

• Time
  • For short increments, the daythird is used. For longer increments, days can be used, but rarely with prefixes, and years for very long periods of time
• Length
  • Typically, leagues are used for long distances, fathoms for middle distances, and hairwidths for small units, prefixes are rarely added to fathoms
• Mass
  • Pounds and grains are the most commonly-used units in science. Talents are often used for engineering purposes

Derived units

There are several systems of derived units, depending on which base units are used to define larger units:

• Daythird-fathom-pound: This has become the most commonly-accepted system
• Daythird-hairwidth-grain: Historically common in laboratory use

Due to the way that the fathom was defined, systems that use the fathom do not need to have distinct units for force and mass

Contemporary definitions

• The fathom is defined as the distance light travels in 1/74,922,857 daythird