User:Rktect/Imperial units
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Imperial units or the Imperial system are a collection of English units, first defined in the UK and the US not in the Weights and Measures Acts of 1816,1824and 1879 but centuries earlier. Original definitions were later refined (until 1959). The units were introduced in the United Kingdom and its colonies, including Commonwealth of Nations countries, and the then already independent United Statesin 1816. The United States did not participate in the acts of 1824 and 1879 having already adopted the metric system shortly after the civil war. From at least 732 [Roman] measures were the [British] standard in common use. Only in 960 was it first decreed that all measures must agree with standards kept in London and Winchester. In 1215 an agreement to have a national standard of weights and measures was incorporated into the magna carta. In 1266 an act established that a penny should weigh the same as 32 grains of wheat, twenty pennies to make one ounce, and twelve ounces to the pound. Eight pounds was to be the weight of a gallon of wine. 240 pennies thus equaled one pound.
- The 1215 magna carta agreement resulted in the act of 1266 establishing
- 8 pounds = 1 gallon = 1920 pennies
- 1 pound = 12 ounces = 240 pennies = 32 grains of wheat
- 1 ounce = 20
In 1304 a statute declared that for medicines a pound would be of 20 shillings, or 12 ounces differing from a standard pound of 15 ounces but with both pounds equaling 20 pennies. In 1352 a statute established the stone as 14lb. In 1532 it became law that butchers should sell meat by the French avoirdupois weight. In 1707 Queen Anne fixed Edwards wine gallon at 231 cubic inches becoming what is still the US gallon. In 1824 the weights and measures act established the Imperial system of weights and measures and it was passed into law in 1826. In 1878 the troy pound was declared illegal meaning that for commercial avoirdupois weights, only the system below of 56lb, 28lb, 14lb, 7lb, 4lb, 2lb, 1lb, 8oz, 4oz, 2oz, 1oz, 1/2oz, 1/4oz, 2dr, 1dr was allowed. This had the effect of removing the eight pound gallon from the doubling system. In 1969 the apothecaries system was outlawed for dispensing medicines, in favour of the metric system. In 1971 the 'L.s.d.' system of money was replaced with the 'decimal' system. In 1972 the passing of the European Communities act passed the responsibility for weights and measures legislation to Brussels. The Law of 1824 defined the following "Imperial Standards"
- 1 drachm fluid British .023281 cu in (24/2024 cu in)unit netto
- 1 drachm fluid US .024233 cu in (25/2024 cu in)unit brutto
- 1 noggin British 8.669 cu in
- 1 quartern = 1/2 Imperial gallon = 138.71 cu in cube with side 5.18"
- 1 bucket = 4 Imperial gallons = 1,109.7 cu in cube with side 10.35" 1/8 crc (Old English fote)
- 1 cubic foot = 1728 cu in = side 12" = 64 cubic palms of 3"
- 1 bushel (dry)= 2219.3 cu in = 1/4 cubic royal cubit, cube with side of 13"
- 1 cubic remen = 3375 cu in = side 15" = 2 cu ft = 125 cubic palms of 3"
- 1 strike = 2 bushels (dry)= 4438.6 cu in = 1/2 crc cube with side of 16.43"
- 1 cu Roman cubit = 5184 cu in = side 17.3" = 3 cu ft = 125 cubic hands of 3.46"
- 1 cu Egyptian cubit = 5428.68 cu in = side 17.58 = pi cu ft
- (nice for circular graineries, baskets, barrels,and amphorae.
- 1 Biblical cubit = 5832 cu in = side 18" = 3.375 cu ft = 216 cubic palms of 3"
- 1 bag or sock = 3 bushels (dry)= 6657.9 cu in = 3/4 crc cube with side of 18.81"
- 1 English cubit "(the diamond on the Stanley tape measure = 6912 cu in
- 1 English cubit = side 19.05" = 4 cu ft = 8 cubic spans of 9.52" (now 9.25")
- 1 cu royal cubit = 8640 cu in = side 20.5" = 5 cu ft = 512 cubic palms of 2.57"
- 1 coomb (cubit) = 4 bushels (dry) = 8877.2 = crc with side 20.7" = 32 Imperial gallons
- 1 barrel (dry = 36 Imperial gallons =9987.01704 cu in with side 21.53"
- 1 barley kus (30 Roman digits) = 10368 cu in = side 21.8" = 6 cu ft
- 1 wheat kus = 10852.6 cu in = side 22.14" = 2 pi cu ft.
- 1 cubit of Tyre = 12096 cu in = side 23" = 7 cu ft
- 1 elle = 13824 cu in = side 24" = 8 cu ft
- 1 seam or quarter = 8 bushels (dry)=17,754.4 cu in with side 26"
- 1 butt = 126 Imperial gallons = 34,954.9 cu in with side 32.7"
- 1 chaldron = 32 bushels (dry)= 71,017.6 cu in with side 41.4"
- 1 wey = 40 bushels = 88,772 cu in with side 44.6"
- 1 puncheon = 70 imperial gallons = 155,351 cu in with side 53.76"
- 1 register ton = 100 cubic feet = 172,800 cu in with side 55.7"
- 1 last British = 80 bushels (dry) = 177,544 cubic in with side 56.2"
- 1 rod British = 1000 cubic feet = 1,728,000 cu in with side 120"
In Linear measure not much changed. The definitions of volumes continued to be related to lengths as their cubes. The definitions used go back a long time before they were passed into law by the British. Many are designed to be part of a system of proportional units that for practical day to day measures turn a ruler into a pocket calculator. To find the cubic inches in any Imperial unit is just a matter of doubling the last cube. These are still used in board measure and computing the number of cords of wood in a tree [forestry]
What makes the classical problems of Greek antiquity and the Bible irrational is the requirement to use an unmarked straightedge. Using a marked straightedge such as a ruler they are trivial. Mechanical constructions were used by Pythagoras, Plato and Eratosthenes to find solutions. The Greeks had copied the problems from the Egyptians everyday math, but made them more rigorous and general (and irrational) by requiring the use of the straightegdge.
"In the Rhind papyrus Ahmes gives a rule to construct a square of area nearly equal to that of a circle. The rule is to cut 1/9 off the circle's diameter and to construct a square on the remainder. Although this is not really a geometrical construction as such it does show that the problem of constructing a square of area equal to that of a circle goes back to the beginnings of mathematics. This is quite a good approximation, corresponding to a value of 3.1605, (256/81 expressed as unit fractions) rather than 3.14159, for pi."
For the doubling the cube problems setting the sides or cubes at the standard unit measures of the various participants in the system. its not "exact" but its close enough as a "rule of thumb" to be of substantive assistance to anyone working with commercial calculations. The division of cubic feet into cubic fingers, palms, hands, spans etc; relates to board measure.
The doubling system of the British Imperial System begins with the Horus eye fractions such as the divisions of the Hekat into unit fractions ro '2,'4,'8,'16,'32,'64,'128,'256 etc; then continues with the Biblical Bath and Metrets systems, barrel measure, cloth yards, Stecchini is actually quite good at explaining this and adds in units brutto and netto, trimmed units, the artaba and quedet, profane and sacred Mina and shekle with the built in tithing, variations on the British and American System after 1816, and then there is the [barley mow song] (alternate words for the gill divisions include nip, niperkin, quite a few more listed in Klein)
[odometer solution] [pytqagoras] [rhind papyrus] [circle squaring] [trisecting]
Contents |
[edit] Relation to other systems
The distinction between this imperial system and the U.S. customary units (also called standard units there) or older British/English units/systems and newer additions (foot-pound-second systems) is often not drawn precisely. Most length units are shared among the Imperial and U.S. systems, albeit partially and temporally defined slightly differently. Capacity measures differ the most due to the introduction of the Imperial gallon and the unification of wet and dry measures. The avoirdupois system only applies to weights; it has a long flavour and a short flavour for the hundredweight and ton.
The term imperial should not be applied to English units that were outlawed in Weights and Measures Act of 1824 or earlier, or which had fallen out of use by that time, nor to post-imperial inventions such as the slug or poundal.
Although most of the units are defined in more than one system, some subsidiary units were used to a much greater extent, or for different purposes, in one area rather than the other.
[edit] Measures of length
After the 1 July 1959 deadline, agreed upon in 1958, the U.S. and the British yard were defined identically (0.9144 m), the international yard. Metric equivalents in this article usually assume this latest official definition.
| 1 inch | = 25.4 mm | |||
|---|---|---|---|---|
| 1 foot | = 12 inches | = 304.8 mm | ||
| 1 yard | = 3 feet | = 36 inches | = 914.4 mm | |
| 1 rod, pole or perch | = 5½ yards | = 16½ feet | = 5.0292 m | |
| 1 chain | = 4 poles | = 22 yards | = 66 feet | = 20.1168 m |
| 1 furlong | = 10 chains | = 220 yards | = 660 feet | = 201.168 m |
| 1 mile | = 8 furlongs | = 1760 yards | = 5280 feet | = 1.609 344 km |
| 1 league | = 3 miles | = 5280 yards | = 15840 feet | = 4.828 032 km |
Until the adoption of the international definition of 1852 metres in 1970, the British nautical mile was defined as 6080 feet (1.85318 km). It was not readily expressible in terms of any of the intermediate units, because it was derived from the circumference of the Earth (like the original metre). Depth of water at sea was expressed in fathoms (6 feet = 1.8288 m).
[edit] Measures of area
| 1 rood | = 1 furlong × 1 rod | = 40 square rods | = 10890 square feet | = 0.10117141056 ha | = 1011.7141056 m² |
|---|---|---|---|---|---|
| 1 acre | = 1 furlong × 1 chain | = 160 square rods | = 1/640 square mile | = 0.40468564224 ha | = 4046.8564224 m² |
[edit] Measures of volume
In 1824, Britain adopted a close approximation to the ale gallon known as the Imperial gallon. The Imperial gallon was based on the volume of 10 lb of distilled water weighed in air with brass weights with the barometer standing at 30 in and at a temperature of 62 °F. In 1963, this definition was refined as the space occupied by 10 lb of distilled water of density 0.998 859 g/mL weighed in air of density 0.001 217 g/mL against weights of density 8.136 g/mL. This works out to exactly 4.545 964 591 L, or 277.420 in³. The Weights and Measures Act of 1985 finally switched to a gallon of exactly 4.546 09 L (approximately 277.419 43 cu in) [1].
| 1 fluid ounce | = 0.028 413 062 5 L | |||
|---|---|---|---|---|
| 1 gill | = 5 oz. | = 0.142 065 312 5 L | ||
| 1 pint | = 4 gills | = 20 oz. | = 0.568 261 25 L | |
| 1 quart | = 2 pints | = 40 oz. | = 1.136 522 5 L | |
| 1 gallon | = 4 quarts | = 8 pints | = 160 oz. | = 4.546 09 L |
| 1 peck | = 2 gal. | = 9.092 18 L | ||
|---|---|---|---|---|
| 1 kenning or bucket | = 2 pecks | = 4 gal. | = 18.184 36 L | |
| 1 bushel | = 2 kennings | = 4 pecks | = 8 gal. | = 36.368 72 L |
| 1 strike | = 2 bushels | = 16 gal. | = 72.737 44 L | |
| 1 quarter or pail | = 8 bushels | = 64 gal. | = 290.949 76 L | |
| 1 chaldron | = 4 quarters | = 32 bushels | = 256 gal. | = 1163.799 04 L |
| 1 last | = 10 quarters | = 80 bushels | = 640 gal. | = 2909.497 6 L |
| 1 firkin | = 9 gal. | = 40.914 81 L | ||
|---|---|---|---|---|
| 1 kilderkin | = 2 firkin | = 18 gal. | = 81.829 62 L | |
| 1 barrel | = 2 kilderkin | = 4 firkin | = 36 gal. | = 163.659 24 L |
| 1 hogshead (of beer) | = 3 kilderkin | = 6 firkin | = 54 gal. | = 245.488 86 L |
The full table of British apothecaries' measure is as follows:
| 1 minim | = 0.059 193 880 208¯3 mL | ||
|---|---|---|---|
| 1 fluid scruple | = 20 minims | = 1.183 877 604 1¯6 mL | |
| 1 fluid dram or fluidram | = 3 fluid scruples | = 60 minims | = 3.551 632 812 5 mL |
| 1 fluid ounce | = 8 fluid drachms | = 480 minims | = 28.413 062 5 mL |
| 1 pint | = 20 fluid ounces | = 568.261 25 mL | |
| 1 gallon | = 8 pints | = 160 fluid ounces | = 4.546 09 L |
For a comparison to the U.S. customary system see the article on English units
[edit] Measures of weight and mass
Britain has made some use of three different weight systems, troy weight, used for precious metals, avoirdupois weight, used for most other purposes, and apothecaries' weight, now virtually unused since the metric system is used for all scientific purposes.
The use of the troy pound (373.241 721 6 g) was abolished in Britain on January 6, 1879, with only the troy ounce (31.103 476 8 g) and its decimal subdivisions retained. In all the systems, the fundamental unit is the pound, and all other units are defined as fractions or multiples of it.
| 1 mite | = 1/20 grain | = 3.239 945 5 mg | |
|---|---|---|---|
| 1 grain | = 64.798 91 mg | ||
| 1 drachm | = 1/16 ounce | = 1/256 pound | = 1.771 845 195 312 5 g |
| 1 ounce | = 1/16 pound | = 28.349 523 125 g | |
| 1 pound | = 7000 grains | = 453.592 37 g | |
| 1 stone | = 14 pounds | = 6.350 293 18 kg | |
| 1 quarter | = 2 stones | = 28 pounds | = 12.700 586 36 kg |
| 1 hundredweight | = 4 quarters | = 112 pounds | = 50.802 345 44 kg |
| 1 ton | = 20 hundredweight | = 2240 pounds | = 1016.046 908 8 kg |
Note that the British ton is 2240 pounds (the long ton), which is very close to a metric tonne, whereas the ton generally used in the United States is the "short ton" of 2000 pounds (907.184 74 kg), both are 20 hundredweights. For more on U.K.-U.S. differences see English unit.
[edit] Current use of Imperial units
British law now defines each Imperial unit entirely in terms of the metric equivalent. See the Units of Measurement Regulations 1995. This regulation effectively outlaws their usage in retail and trading except in previously established exceptions. This has now been proved by in court against the so called 'Metric Martyrs', a small group of market traders. Despite this, many small market traders still use the customary measures, citing customer preference especially among the older population.
In the United States and in a few Caribbean countries, the U.S. customary units, which are similar to Imperial units based upon older English units and in part share definitions, are still in common use. English units have been replaced elsewhere by the SI (metric) system. Most Commonwealth of Nations countries have switched entirely to the international system of units.
The United Kingdom completed its legal transition to SI units in 1995, but a few such units are still in official use: draught beer must still be sold in pints, most roadsign distances are still in yards and miles, and speed limits are in miles per hour, therefore interfaces in cars must have miles, and even though the troy pound was outlawed in Great Britain in the Weights and Measures Act of 1878, the troy ounce still may be used for the weight of precious stones and metals. The use of SI units is increasingly mandated by law for the retail sale of food and other commodities, but many British people still use Imperial units in colloquial discussion of distance (miles and yards), speed (miles per hour), weight (stones and pounds), liquid (pints and gallons) and height (feet and inches).
In Canada, the government's efforts to implement the metric system were more extensive: pretty much any agency, institution, or thing provided by the government will use SI units exclusively. Imperial units were eliminated from all road signs, although both systems of measurement will still be found on privately-owned signs (such as the height warnings at the entrance of a multi-storey parking facility). Temperatures in degrees Fahrenheit will occasionally be heard on English Canadian commercial radio stations, but only those that cater to older listeners. The law requires that measured products (such as fuel and meat) be priced in metric units, although there is leniency in regards to fruits and vegetables. Traditional units persist in ordinary conversation and may be experiencing a resurgence due to the reduction in trade barriers with the United States. Few Canadians would use SI units to describe their weight and height, although driver's licences use SI units. In livestock auction markets, cattle are sold in dollars per hundredweight (short, of course), whereas hogs are sold in dollars per hundred kilograms. Land is surveyed and registered in metric units, but imperial units still dominate in construction, house renovation and gardening talk ("two-by-fours" don't measure 2×4").
