Units: I symbol for international einheit, the German name for the international unit (IU). IGPM abbreviation for Imperial gallons per minute. immi a traditional Swiss unit of liquid volume. The immi has been brought into the metric system and now equals exactly 1.5 liters (about 3.17 U.S. liquid pints). imperial a large wine bottle holding about 6 liters, 8 times the volume of a regular bottle . Also called a methuselah. Imperial gallon (gal or IG) a traditional unit of volume equal to about 1.201 U.S. liquid gallon or 4.546 liters. See gallon [3]. In Canada, the term "Imperial" is used frequently to distinguish the British Imperial units from the corresponding U.S. units. Imperial units the units of the British Imperial system, adopted by Parliament in 1824. The basic units of the system are the foot , the avoirdupois pound , and the Imperial pint . The Weights and Measures Acts of 1963 and 1985 have redefined the Imperial units in term of the SI units.

The Imperial units remain in varying degrees of use in Britain, Canada, Australia, and other areas of British heritage despite the introduction of metric units there. Americans should note that the Imperial foot and pound are essentially the same as the units used in the U.S., but the Imperial pint is significantly larger than the U.S. liquid and dry pints. inch (in or ") [1] a traditional unit of distance equal to 1/12 foot or exactly 2.54 centimeters. The Old English word ynce is derived from the Latin uncia, meaning a 1/12 part; thus "inch" and "ounce" actually have the same root. The inch was originally defined in England in two ways: as the length of three barleycorns laid end to end, or as the width of a man's thumb at the base of the nail. The barleycorn definition is peculiarly English, but the thumb-width definition is generic. In fact, in many European languages the word for inch also means thumb: examples include the Dutch duim, Swedish tum, French pouce, and Spanish pulgada.

In the history of English units the inch seems to come before the foot: after the Norman conquest of 1066 the foot was defined to equal 12 inches, rather than the inch being defined as 1/12 foot. inch (in or ") [2] one of several traditional units of pressure. Air pressure is measured traditionally in inches of mercury (next entry) and water pressure in inches of water column (following entry). inch of mercury (in Hg) a traditional unit of atmospheric pressure. In the United States, atmospheric pressure is customarily expressed as the height of a column of mercury exerting the same pressure as the atmosphere. When a traditional mercury barometer is used, this height is read directly as the height of the mercury column. These readings must be corrected for temperature since mercury, like most liquids, tends to expand as it warms. The conventional equivalent of one inch of mercury is 0.491 153 pounds per square inch or 3.386 38 kilopascals (33.8638 millibars ).

In the symbol for the unit, Hg is the chemical symbol for mercury; it comes from the Latin word hydrargyrum ("water-silver") for the liquid metal. inch of water column (in WC) a traditional unit of pressure, used in plumbing to describe both water and gas pressures. The conventional equivalent of one inch of water is 249.0889 pascals , which is 2.490 889 millibars , about 0.036 127 pounds per square inch (psi) or about 0.073 556 inches (1.868 32 millimeters) of mercury. inch of water gauge (in wg or "wg) another common name for the inch of water column. The word "gauge" (or "gage") after a pressure reading indicates that the pressure stated is actually the difference between the absolute, or total, pressure and the air pressure at the time of the reading.

inch pound (in·lbf or in lb) a traditional unit of work or energy, equal to 1/12 foot pound, about 0.112 985 joule or 1.0709 x 10-4 Btu . in d. abbreviation for the Latin in die, daily, a unit of frequency used in medical prescriptions. inhour (ih or inhr) a unit used in nuclear engineering to describe the "reactivity" of a nuclear reactor. In a reactor, fast-moving neutrons break apart atoms of uranium or plutonium; the fission of these atoms releases additional neutrons which keep the reaction going. The ratio R between the number of neutrons created and the number consumed in each cycle of fission must be very close to 1 in order for the reaction to be controlled. The reactivity is the difference k = R - 1 between this ratio and 1. One inhour is the reactivity which will cause the number of neutrons to increase by a factor of e = 2.71828 in one hour; a reactivity of t inhours will cause the number of neutrons to increase by a factor of e in 1/t hours.

The exact size of the unit varies according to the design of the reactor. Enrico Fermi (1901-1954), the Italian-American physicist who built the first nuclear reactor, introduced this unit in 1947; its name is an acronym for "inverse hours." Other reactivity measures include the dollar and the milli-k . international foot the current foot unit of the English-speaking countries, equal to exactly 30.48 centimeters. See survey foot for additional information. international nautical mile the nautical mile as currently defined by international agreement, equal to exactly 1852 meters or 6076.11549 feet. This long name is sometimes used to distinguish the current nautical mile from older units. international rubber hardness degree (IRHD) a unit used to measure the hardness of rubber and similar materials (technically known as elastomers). Measurements are made using an IRHD durometer , and the results are usually similar, but not identical, to readings made with the older Shore "A" durometer. The International Organization for Standardization (ISO) and the American Society for Testing and Materials (ASTM), among other standards agencies, have published IRHD test procedures.

international unit (IU) a unit used to measure the activity (that is, the effect) of many vitamins and drugs. For each substance to which this unit applies, there is an international agreement specifying the biological effect expected with a dose of 1 IU. Other quantities of the substance are then expressed as multiples of this standard. Examples: 1 IU represents 45.5 micrograms of a standard preparation of insulin or 0.6 microgram of a standard preparation of penicillin. Consumers most often see IU's on the labels of vitamin packages: in standard preparations the equivalent of 1 IU is 0.3 microgram (0.0003 mg) for vitamin A, 50 micrograms (0.05 mg) for vitamin C, 25 nanograms (0.000 025 mg) for vitamin D, and 2/3 milligram for (natural) vitamin E. Please note: for many substances there is no definite conversion between international units and mass units (such as milligrams). This is because preparations of those substances vary in activity, so that the effect per milligram of one preparation is different from that of another.

Internet time a global decimal time system proposed by the Swatch Corporation. See beat for more information. ips an abbreviation for inches per second (in/s), a traditional unit of velocity equal to 2.54 centimeters per second. ipy ArcGIS Help 10.1 - About distance units and editing About distance units and editing When editing, the map units of your data frame are used when reporting and entering measurements and distances. The map units are the units in which the spatial data in the data frame is drawn. The map units are determined by the coordinate system of the data frame. When editing, all the values you enter will be in map units by default. You can find out the map units used by your coordinate system on the Data Frame Properties dialog box > General tab. Sometimes when creating features, you need to enter values that were recorded in different distance units than the coordinate system of your data. When you input measurements, in many cases it is possible to enter values in units other than map units by specifying a units abbreviation with the value. For example, suppose your data is in a State Plane coordinate system and the linear units are U.S. survey feet. You are given measurements in meters. Rather than convert all the measurements to U.S.

survey feet, you can type the abbreviation for meters, m, after the measurements, and the tools will convert the distance correctly. Whenever you are typing a distance into one of the editing tools, you have the option to specify the linear units or simply type a number, which the tool will interpret as being in map units. Unit abbreviations only work when your data frame uses a projected coordinate system rather than a geographic coordinate system. The following sections outline all the unit abbreviations supported when editing and describe how to implement them. Metric units ft 0.3048 Also known as international foot or imperial foot that was used in most non-U.S. countries before the metric system. Mile Also referred to as a statute mile, equal to 5,280 international feet. Nautical mile nm 1,852 The nautical mile is a unit of distance used primarily in sea travel and aviation. The nautical mile is defined as the average distance on the earth's surface represented by one minute of latitude. In 1929, the nautical mile was defined as exactly 1,852 meters, or 6,076.11549 feet, a distance known as the international nautical mile.

Chain 1/4 chain, or 16.5 international feet. Link 1/100 international chain, or 66/100 international feet. Inch ftUS 0.3048006096 The U.S. survey foot is used in the state plane coordinate systems. In the United States, fundamental survey units, such as rods, chains, statute miles, acres, sections, and townships, all depend on the U.S. survey foot. An exact conversion to meters can be accomplished by multiplying U.S. survey feet by the fraction 1,200/3,937. Survey mile U.S. survey units Entering specific locations (DD, DMS, DDM, MGRS, USNG, and UTM) In commands that require you to enter a specific location when editing, you can specify the location as a longitude-latitude coordinate pair, a Military Grid Reference System (MGRS) grid location, a U.S. National Grid (USNG) location, or a Universal Transverse Mercator (UTM) coordinate. Map units are the default, but you can click the Units button to choose the units in which to enter coordinates.

These are the same formats used by the Go To XY command . Below are some guidelines for specifying these values. These apply to Absolute XY and commands such as Move To that allows you to move a vertex or topology element to an exact location. Remember that x is longitude (East/West), and y is latitude (North/South)—the same order in which coordinates are listed in the status bar. Spherical coordinates aren't always specified in this order, so make sure you enter longitude first in this dialog box. For example, if someone asks you to plot 17.1325, -60.666 on the map, ask them if these coordinates are in longitude-latitude or latitude-longitude order. The only way to tell the order from the coordinates themselves is if they contain E, W, N, S characters to signify the hemisphere. When you are using decimal degrees (DD), degrees minutes seconds (DMS), or degrees decimal minutes (DM), coordinates can be entered by using a minus sign before the numeric value to signify the western or southern quadrants or using E, W, N, S characters before or after the numeric values.

Values in DMS and DM coordinates can be separated with spaces or the °, ', " special characters (such as when you paste coordinates that you have copied from other dialog boxes or applications that use those characters) or both. Regardless of whether you are using DD, DMS, or DM in the dialog box, coordinates can be entered in any of these three longitude-latitude formats and are automatically converted to match your chosen format. When you are using DD and DM, coordinates you input are always converted to use a minus sign to signify W or S. When you are using DMS, coordinates you input are always converted to use E, W, N, S to signify quadrants and are given the °, ', ", special characters. When using MGRS, or USNG locations, make sure there are no spaces in the coordinate string. Valid longitude-latitude inputs Valid UTM coordinate notation input 17R 419230 2714967 13-digit coordinate Conversion constants You can use conversion constants to convert from one measurement system to another. The measurement system to be converted should be multiplied by the associated conversion constant.

For example, to convert feet to centimeters, multiply feet by the conversion constant of 30.48 (27 feet x 30.48 = 822.96 centimeters). For a list, refer to the PDF of conversion constants . If this link does not work, you can open the conversion_constants.pdf from the \Documentation folder in the directory where you installed ArcGIS. To view this document, you need a copy of Adobe Reader . About the U.S. survey foot In 1959, the directors of the National Bureau of Standards and the United States Coast and Geodetic Survey agreed on a redefinition of the inch-centimeter relationship. This redefinition defined 1 inch as equal to 2.54 centimeters exactly, or 1 foot as equal to 0.3048 meters exactly. However, their agreement stipulated that the older value for 1 meter equaling 39.37 inches exactly be retained for identifying the U.S. survey foot.

One of the reasons for this retention was that the state plane coordinate systems, which are derived from the national geodetic control network, are based on the relationship of 1 meter equaling 39.37 inches exactly. The difference between these two values for the foot is very small, two parts per million, which is hardly measurable, but not trivial when computational consistency is desired. Fundamental survey units, such as rods, chains, statute miles, acres, sections, and townships, all depend on the relationship of 1 meter equaling 39.37 inches exactly. The U.S. survey foot table represents the corrected values (or U.S. survey values), using the 39.37-inch conversion value. Related Topics Units: N a metric unit of mass equal to 10-9 gram, or one millionth of a milligram. nanogray (nGy) a unit of radiation dose equal to 10-9 gray or 0.1 micro rad (µrad). This unit often occurs in the study of inhalation exposures.

nanoliter (nl or nL) a metric unit of volume equal to 10-9 liter or 0.001 cubic millimeter. nanometer (nm) a metric unit of distance equal to 10-9 meter. Introduced in 1951, the nanometer replaced the millimicron. One nanometer equals 0.001 micrometer or 10 angstroms . nanomole a unit of amount of substance equal to 10-9 mole . This unit is common in biochemistry, since a mole of a large organic molecule can be quite a large amount. nanon an informal name for the nanometer. nanonewton (nN) a metric unit of force equal to 10-9 newton (see below) or 0.1 milli dyne . Nanonewtons measure the force of solar radiation and the tiny forces exerted within living cells. nanoradian (nrad) a unit of angle measure equal to 10-9 radian . The nanoradian equals about 0.208 533 milliarcsecond (mas). Such tiny angles are encountered in astronomy and in geological measurements.

nanosecond (ns) a unit of time equal to 10-9 second. nanosievert (nSv) a unit of radiation dose equal to 10-9 sievert or 0.1 micro rem . nanostrain (nstrain) an engineering unit measuring strain. An object under strain is typically deformed (extended or compressed), and the strain is measured by the amount of this deformation relative to the same object in an undeformed state. One nanostrain is the strain producing a deformation of one part per billion (10-9). Strains in geological formations are often measured in this unit. nanotesla (nT) a unit of magnetic field strength equal to 10-9 tesla or 10-5 gauss . The unit is used in geology to measure small changes in the Earth's magnetic field. nat or natural unit a unit of information content used in information and communications theory. The nat is similar to the shannon but uses the natural logarithm (to the base e) instead of the logarithm to the base 2. If the probability of receiving a particular message is p, then the information content of the message is -loge p nats.

For example, if a message is a string of 5 letters or numerals, with all combinations being equally likely, then a particular message has probability 1/365 and the information content of a message is 5(loge 36) = 17.9176 nats. One nat equals log2 e = 1.442 695 shannons or log10 e = 0.434 294 hartleys . nautical mile (nmi, naut mi, n mile, or NM) a unit of distance used primarily at sea and in aviation. The nautical mile is defined to be the average distance on the Earth's surface represented by one minute of latitude. This may seem odd to landlubbers, but it makes good sense at sea, where there are no mile markers but latitude can be measured. Because the Earth is not a perfect sphere, it is not easy to measure the length of the nautical mile in terms of the statute mile used on land.

For many years the British set the nautical mile at 6080 feet (1853.188 meters), exactly 800 feet longer than a statute mile ; this unit was called the Admiralty mile. Until 1954 the U.S. nautical mile was equal to 6080.20 feet (1853.249 meters). In 1929 an international conference in Monaco redefined the nautical mile to be exactly 1852 meters or 6076.115 49 feet, a distance known as the international nautical mile. The international nautical mile equals about 1.1508 statute miles. There are usually 3 nautical miles in a league . The unit is designed to equal 1/60 degree [2], although actual degrees of latitude vary from about 59.7 to 60.3 nautical miles.

(Note: using data from the Geodetic Reference System 1980, the "true" length of a nautical mile would be 1852.216 meters.) Ncm a symbol for the newton centimeter, a metric unit of torque equal to 0.01 newton meter (see below) or about 1.416 12 inch ounces (in·oz) in traditional English units. Ndm3 a symbol sometimes used for the normal liter (see below). Recall that a liter is the same as a cubic decimeter (dm3). nebuchadnezzar a huge wine bottle holding about 15 liters, 20 times the volume of a regular bottle . neck (nk) an informal unit of distance used to measure the distance one horse leads another at the finish of a race. The neck is usually interpreted to be 1/4 length or a little less; this is roughly 2 feet or 0.6 meter. neper (Np) a unit expressing the ratio of two numbers as a natural logarithm; the ratio r corresponds to (1/2) ln r nepers.

Quantities differ by 1 neper if one is e2 = 7.389056 times the other. One neper is equal to about 8.685 890 decibels , and in general n nepers equal 20n/(ln 10) decibels. The neper is accepted for use with SI units, and it may become an SI unit in the future. The unit recognizes the Scottish mathematician John Napier (1550-1617), the inventor of the logarithm (Napier often spelled his name Jhone Neper, and he used the Latin form Ioanne Napero in his writings). nest an old English unit of quantity equal to 3. This unit was often, but not always, used for items that nest together, such as 3 bowls or 3 hampers. net ton (NT) the name "net ton" is used in at least two ways: (1) as another name for the U.S.

or short ton of 2000 pounds (see ton [1]), and (2) as another name for the register ton, a unit of volume equal to 100 cubic feet (see ton [3]), in describing the cargo-carrying capacity of a ship as opposed to the entire interior volume. To avoid confusion, it is better to use "short ton" for use (1) and "net register ton" for use (2). new candle an older name (introduced in 1937) for the candela , a unit of light intensity. new style (NS) a notation used after dates to indicate that the date is stated in the Gregorian calendar (the calendar now in general use) rather than in the Julian calendar (see year [2]). The notation is used primarily for Gregorian dates between 15 October 1582, when the Gregorian calendar was adopted in Catholic Europe, and 14 September 1752, when it was adopted in Britain. See also old style . newton (N) the SI unit of force. A force of one newton will accelerate a mass of one kilogram at the rate of one meter per second per second.

The corresponding unit in the CGS system is the dyne ; there are 105 dynes in one newton. In traditional English terms, one newton is about 0.224 809 pounds of force (lbf) or 7.233 01 poundals . The newton is also equal to about 0.101 972 kilograms of force (kgf) or kiloponds (kp). The newton is named for Isaac Newton (1642-1727), the British mathematician, physicist, and natural philosopher. He was the first person to understand clearly the relationship between force (F), mass (m), and acceleration (a) expressed by the formula F = ma. newton meter (N·m) the SI unit of torque. Torque, the tendency of a force to cause a rotation, is the product of the force and the distance from the center of rotation to the point where the force is applied. Torque has the same units as work or energy, but it is a different physical concept. To stress the difference, scientists measure torque in newton meters rather than in joules , the SI unit of work.

One newton meter is approximately 0.737 562 pound foot . newton second (N·s) the SI unit of impulse, equal to the amount of momentum added to an object if a force of one newton is applied for one second. The newton second equals about 0.224 809 pound second (lbf·s) in traditional English units. Impulse and momentum have the same dimensions, but momentum is measured in kilogram meters per second (kg·m/s) in the SI. ngarn a unit of land area in Thailand. The ngarn equals 1/4 rai , 100 talangwah (tw), or exactly 400 square meters (478.396 square yards or just under 0.1 acre ). niacin equivalent (NE) a unit used in nutrition. An essential nutrient, niacin is supplied in normal diets from tryptophan, an amino acid found in many foods. However, only a small fraction of tryptophan is converted into niacin in the body.

Accordingly, 1 niacin equivalent is equal to 1 milligram of actual niacin or to 60 milligrams of tryptophan. nibble a unit of information used in computer science. A nibble is 4 bits or 1/2 byte . The cuter spelling nybble, suggested by byte, is sometimes used. In different contexts, a group of 4 bits is sometimes called a quadbit or a hexit. nile a unit used in nuclear engineering to describe the "reactivity" of a nuclear reactor. One nile is a reactivity of 0.01 or 1%. Since this is a rather large amount, reactivity is measured for practical purposes in milliniles, with one millinile = 10-5. The nile was invented in the British nuclear power industry. For a discussion of reactivity, see inhour . nine [1] a measure of "fineness" or purity of gold and other materials. For example, gold that is 99.99% pure, or .9999 fine , is called "4 nines fine." nine [2] a measure of reliability, or "availability," used in computer engineering.

For example, a component has "3 nines" of reliability if it operates correctly 99.9% of the time, or, equivalently, if its failure rate is 0.1%. Thus each nine represents a reduction of 90% in the failure rate. If the probability of correct operation is p, then the reliability, in nines, is equal to -log10(1-p). nip an informal unit of liquid volume. The term "nip" often means "a small amount," with no precise equivalent. In U.S. bartending, a nip is often taken to be 2 fluid ounces (about 59 milliliters). In Britain, a nip of spirits is considered to be 1/6 gill (about 22.95 milliliters or 0.776 U.S. fluid ounce ); a nip of beer is 1/4 pint (the same as a gill, 4 fluid ounces or about 117.7 milliliters) or sometimes 1/3 pint (189.4 milliliters).

nit (nt) an MKS unit of luminance, equal to one candela per square meter, or 10-4 stilb . The nit is not approved as part of the SI , but it has been approved since 1947 by the International Commission on Illumination (CIE) and is in wide use. The name of the unit comes from the Latin niteo, to shine. This unit is sometimes called the meterlambert, by analogy with the footlambert . Nm or N·m [1] symbol for newton meter, a unit of torque (see above). Nm [2] abbrevation for normal metric, a symbol for the density of worsted yarns. Yarn is described as a/b Nm if it is a-ply (has a individual strands) and there are b kilometers of yarn per kilogram. An example might be 2/40 Nw, describing a 2-ply yarn having 40 kilometers per kilogram. If the yarn is single-ply, the a is often omitted, so a single-ply yarn is described as b Nm.

noeud the French word for the knot (1.852 km/h), the traditional unit of velocity at sea. This unit is still used officially in France; for example, Météo France uses it in maritime weather forecasts. noggin a traditional unit of liquid volume, used primarily in Ireland. Like the gill , the noggin is often taken to equal 1/4 pint ; sometimes it is taken to be 1/2 pint. noise criterion (NC), noise rating (NR) units used in enginering to measure the acceptability of sound levels in enclosed spaces. The noise rating (NR) system was introduced by Kosten and van Os in 1962. Numerically, the NR rating is equal to the sound level in decibels at a frequency of 1000 hertz , but the rating requires lower levels at the more objectionable higher frequencies. The noise criterion (NC) system, introduced by Beranek in 1957, is similar, but it is designed more toward preserving speech communication, requiring lower levels of both high and low frequencies. It was updated in 1971, and the updated system is called PNC (prefered noise criterion).

nonet a unit of quantity equal to 9, used mostly in music to describe an ensemble of 9 instruments. nook a traditional unit of land area in northern England. Originally the nook was 1/2 virgate ; a virgate, often called a yardland in the north, was about 30 acres in southern England but tended to be closer to 40 acres in the north. A nook of land thus came to be 20 acres or about 8.094 hectares . normal (N) a term used in chemistry to describe a solution having a concentration of 1 gram equivalent per liter. The normal concentration of an ion is effectively equal to the molar concentration divided by the valence (the number of free or missing electrons) of the ion. normal cubic meter (Nm3) a unit of mass for gases equal to the mass of 1 cubic meter (35.3147 ft3) at a pressure of 1 atmosphere and at a standard temperature, often 0 °C (32 °F) or 20 °C (68 °F). The term standard cubic meter is also used; sometimes both are used, with different temperatures.

Because industry practice varies, these terms should always be defined wherever they occur. The symbol Nm3, though common, is not permissible under the SI because that symbol means "newton cubic meter." An acceptable SI symbol would be "m3 normal." See also sccm . normal liter (NL or Nl or Ndm3) a unit of mass for gases equal to the mass of 1 liter (0.035 3147 ft3) at a pressure of 1 atmosphere and at a standard temperature, often 0 °C (32 °F) or 20 °C (68 °F). Air flow is often stated in normal liters per minute (Nl/min). nose an informal unit of length, equal to roughly half the length of a horse's head, used in expressing the results of a horse race. note a unit of relative time in music, also called a whole note, equal to 1/2 breve . nox a unit of (low) illumination equal to 0.001 lux . This unit was used in Germany during World War II to describe permitted levels of lighting during air raids.

"Nox" is the Latin word for "night." noy a unit of perceived noisiness introduced by the American acoustics engineer K. D. Kryter in 1959. An observer uses the unit to described the noise levels he or she experiences as multiples of a standard level. The standard level, one noy, is defined to be the noisiness of a random noise signal within the frequency band from 910 to 1090 hertz at a sound pressure level of 40 decibels . As you have already guessed, the unit's name is chosen so that its plural is pronounced "noise." A jet aircraft takeoff is rated at about 110 noys. NTU abbreviation for nephelometric turbidity unit, a unit used in measuring water quality. Turbidity is an optical property: the scattering and absorption of light by solids suspended in water. Turbid water has a cloudy or hazy appearance.

An instrument called a nephelometer (from a Greek word meaning "cloudy") measures turbidity directly by comparing the amount of light transmitted straight through a water sample with the amount scattered at an angle of 90° to one side; the ratio determines the turbidity in NTU's. The instrument is calibrated using samples of a standard solution such as formazin, a synthetic polymer. Drinking water should not have a turbidity above 1 NTU, although values up to 5 NTU are usually considered safe. Outside the U.S., this unit is usually called the FNU (formazin nephelometric unit). nu a measure of the dispersiveness (or constringence, as it is called) of a lens or prism. If b, y, and r are the indices of refraction at blue, yellow, and red wavelengths, respectively, then the nu value is (y - 1)/(b - r). The measure is represented by the Greek letter nu, and sometimes the symbol "nu" is used as if it were a unit, as in 65 nu. Nw symbol for normal worsted, a unit measuring the density of worsted yarns.

Worsted yarn is described as a/b Nw if it is a-ply (has a individual strands) and there are b 560-yard hanks of yarn per pound. An example might be 2/40 Nw, describing a 2-ply yarn having 40 hanks (22 400 yards) per pound. If the yarn is single-ply, the a is often omitted, so a single-ply worsted yarn is described as b Nw. nybble Old Units of Length Old Units of Length Units of weight and volume are also considered People have always found it necessary to measure time, distance, area, volume and weight, and have devised units that measure these quantities. For time, there is an absolute standard in the motions of the heavens, but for the other quantities the units have had to be chosen arbitrarily, and it is these that we talk about here. Only recently have we succeeded in creating natural units for length and time, but weight still is arbitrary. Let's now examine some of the ways things have been measured, concentrating on the measurement of length.

The metric system, originating in the French Revolution and propagated widely in the 19th century, has brought a dreary but convenient uniformity to units of measurement. Only the English foot-pound-second system put up resistance to this aggression, upholding an alternative comprehensive system. In engineering, English units were divided decimally just like metric ones, especially in the United States. The kilopound or kip, used in structural engineering, is an example, as is the decimal foot in engineering and geodetic surveying, which replaced all other units. Engineering has decided that the metre (if you go metric all the way, you must accept its spelling as well) is an inconvenient unit, and uses the millimetre as its standard instead. A small unit appears to be favored in practical use, without the definition of larger units. In all but precision engineering, one millimeter is sufficient accuracy. The basic English unit of length was the yard of three feet, or the fathom of six. Each English foot was divided into 12 inches, and each inch into 3 barleycorns or 12 lines.

Length units used in land surveying are discussed in the article "Chaining." Other units were defined for use in printing, textiles, and other areas of commerce. This proliferation of units for special applications was a very common phenomenon, and led to uncertainties in exact definitions. Eventually, one inch was defined as exactly 25.4 mm, which tied the English and metric units together. In the United States, a meter was sometimes defined as exactly 39.37 inches, which gave 1 inch = 25.40005 mm, just enough different to be annoying in geodesy. 12 such inches made a survey foot, used by the Coast and Geodetic Survey. 5 feet, 6 inches, and 7 lines was written 5' 6" 7"'. The single and double apostrophes have survived into modern times, but not the triple. Before the metric system, the French unit of length was the toise, which is about 1949 mm. The toise was divided into 6 Paris feet, each of which was divided into 12 pouces, that were further subdivided into 12 lignes.

The use of 'Paris' to modify the foot suggests that there were other feet, and there were. Differences between units of the same name at different locations were common in France, and the leading stimulus for the establishment of a uniform national system. The differences in units were sometimes used for swindling of consumers. The equality 1071 Paris feet = 1142 English feet, quoted by Poggendorff in his history, can be used to convert 17th century measurements into their equivalents. This makes the Paris pouce 27.1 mm. The ligne usuel was later defined as 0.09113 inches, and a toise as 78.74172 inches. The livre was 1.10258 pounds, the boisseau 2.7512 British gallons. The litron was 1.7608 British pint. These Système Usuel units were in use from 1812 to 1840, since the people refused to use the new metric units, and this at least gave some uniformity.

In 1840 the use of metric units was compelled (compulsion is a great part of French liberté) under penalty, and the traditional names were forbidden. This is similar to what is happening in Britain at the present time. In the Système Ancien, used before 1812, the ligne was 0.0888 inches, the toise 6.3946 feet, the lieue was 2282 toise or 2.7637 miles. However, the old units varied from place to place in a confused way. In Germany, the English and French feet competed as units of measurement of length, but there were local definitions as well. Germany was a patchwork of local jurisdictions at the time, each jealous of its individuality. The Prussian inch appears to have been 24.6 mm, since the wine gallon is reported to have been 254 cubic Prussian inches. It is difficult to assess the accuracy of old measurements because of the uncertainty in the size of the units, or even in their proper identification.

The units of length shown in the table were in use in Greek areas by the time of Herodotus (450 BC), who is our principal authority on units of his time. He is rather careful, and well aware of different definitions. The parasang is of Persian origin, the schoenus Egyptian. Herodotus explains how successively larger units are used by those richer and richer in land to survey their property. The relations between units are reliable, but the equivalents in modern units are only approximate. There were no universal standards in ancient times; indeed, there were none until recently. The fathom, for example, might more closely be 6 ft 1 in. The Greek foot was about 1% larger than the English foot. The later milion, milion, was a Roman mile of 1000 paces, 1680 modern yards, divided into 8 stadia (corresponding to modern furlongs), each stadion consisting of 100 orguiai, or 6 plethra, pleqra.

The stadion was from 200 to 210 yards in length, and would probably be laid out with a cord 10 orguiai (60 ft) in length, just as furlongs were later ten chains in length. The plethron was also a measure of area, a square one plethron on a side. It was common to express area measures in terms of the length of a square of equal area, so when reading one must determine whether length or area is meant. The square plethron was a little less than a quarter of an acre, equivalent to the Roman jugerum but not equal to it. Units are often translated as approximate equivalents, another source of uncertainty. The modern feet are descended from the Roman measurement of the same name and approximate value. The Roman foot, 11.65 modern inches (29.6 cm), was usually divided into 16 inches, not 12, however (as four palms of four Roman inches, about 3 modern inches, each). Divisions by powers of 2 are specially useful, since they are binary, and much more adapted to computers than powers of 10.

The English inch was later divided into halves, quarters, eighths, and so on, because of the utility and extendibility of this system, which completely replaced the use of lines. The Roman pound, libra (from which, lb.), was divided into 12 ounces, but the ounces were divided on the binary system down to 32nds, or oboli. Roman standards were relatively uniform, an interlude between times of confusion. Most Roman units of length survived in name or spirit in the English and other systems, even if changing somewhat in absolute value. For example, the stadium, which was 1/8 of a Roman mile, or 202 yards, became the furlong, 1/8 of an English mile, or 220 yards. The cubit, a forearm's length, was 1-1/2 Roman feet or 6 palms, and typically used in building. Some ancient cubits seem to have been longer than this, up to about 22 inches. Hands of 4 inches are still used to measure the height of a horse (at the shoulders). Note how length units were conveniently based on parts of the body used to measure distances.

The Roman mile consisted of 1000 double paces, or 5000 Roman feet, or 1480 metre, or 1619 yards. Distances on Roman roads were measured by odometers attached to carriage axles, as described in Vitruvius, and marked on mile stones. The English mile of 5280 feet is 1609 metre (a "metric mile" is, apparently, 1500 metre). As explained in the article "Chaining," it was defined as 80 chains of 66 ft each, and this is the reason for the odd number 5280. Gunter's chain of 100 links was a successful attempt to create a portable length standard that was not as stretchy as a cord. The English mile happened to come out a little larger than the Roman mile, to which it was intended to be an approximation. The nautical mile is 1852 metre, which corresponds to one minute of arc of latitude, approximately. The 'geographical' mile was 7420 metre, and the Prussian mile 7532 metre. These long miles were about five Roman miles.

The league was another measure of journeys, usually 3 English miles. France had an assortment of leagues: 2000 toise for the lieue de poste, 3 Roman miles for the lieue de terre, 4 kilometers for the lieue kilométrique, and 3 nautical miles for the lieue marine. The Greeks had the stadium of 580-622 feet, and the plethron of 97-100 feet. The ancient Persian parasang was 3.25 to 3.3 miles, 30 Greek stadia. Any great accuracy in the size of old units is illusory unless a critical study is made. The standards have, of course, disappeared, and their magnitude can be determined only by remeasuring a distance in modern terms. In the establishment of the metric system, the quadrant of the earth was measured as 5 130 738.62 toise, which was set equal to 10 000 000 metre.

This was a bad choice for defining a unit of length, worse than simply making a couple of arbitrary scratches on a bar, since it involved a difficult and tedious procedure, especially when the news arrived in France that the earth was not a sphere to a sufficient approximation. At any rate, a scratched bar was later adopted as standard, and the earth's quadrant allowed to be whatever it turned out to be in terms of metres. A similar mistake was made in defining the kilogram as the weight of a cubic decimetre (a litre) of water, since the density of water changes with temperature, and weight can be measured more accurately than a decilitre can be measured. Thus, both the litre and the kilogram were defined arbitrarily. The clumsiness was reflected in the slight difference between a cubic centimetre and a millilitre that thereby arose. The second of time remained 1/86400 of a mean solar day, with common units of time not related decimally, but by factors of 24 and 60. The decimal calendar was a ludicrous failure. The French also defined a right angle as 100 grads, another superfluity.

The units of time and angles were already uniform, and required no work. As has been mentioned above, the French population ignored the metric system until it was forced upon them. Britain introduced Imperial Units, based on the yard, pound, and second, in the 19th century to resist the metric system. The gallon was newly defined as the volume occupied by ten pounds of water, in stupid imitation of the metric system, which made the Imperial gallon (eight pints) somewhat larger than the previous, and American, wine gallon of 231 cubic inches. An Imperial gallon is 1.2032 US gallon, more exactly. A pint, which was now 20 ounces instead of 16, contained 25% more beer. In the Imperial system 1 gallon = 2 pottles = 4 quarts = 8 pints = 32 gills. Spirits were dispensed in gills. The basis of the US dry measure was the old Winchester struck bushel of 2150.42 cubic inches, equal to 4 pecks = 8 gallons = 32 quarts = 64 pints.

British dry measure was slightly different, a bushel being 2218.192 cubic inches, but divided like the American. Measures of weight are the same in Britain and the US. A grain is the same in troy (used for precious metals), avoirdupois and apothecary's systems. In the troy system, 5760 grains = 12 ounces = 1 pound (troy). An avoirdupois pound is 7000 grains or 16 ounces. Apothecary's weight is the same as troy, except that the ounce is divided into 8 drams of 3 scruples each, with 20 grains to the scruple. The stone of 14 pounds is used to measure the weights of people in Britain. A hundredweight is usually 112 pounds, and twenty hundredweight, 2240 pounds, is a ton. The units used to measure weights of coal in Britain were extremely various and local, and the hundredweight is the sole surviving representative of such units.

One might assume that a hundredweight would be 100 pounds, and a ton 2000 pounds, as in fact they are in the United States. The reason for the additional eighth seems to have originated to compensate for the stone and slack that would be included with a miner's coal. Then, 2240 pounds (or gross ton) weight delivered by the miner would be paid for as 2000 pounds (or net ton) of coal. The heavier ton was in common use in the United States before 1900, though the net ton is now understood when tons are mentioned. On the other hand, 112 pounds is exactly 8 stone, and stones did not originate in mining measurements. The gross ton is probably the original unit, the net ton derived from it by subtracting about an eighth. The Russian foot was the same as the English. The sachine was 7 feet, and the verst 500 sachine or 3500 feet (not far from a kilometer). The pood was 36.114 pounds. The Castilian vara was 32.8748 inches.

In California, it was legally 33.372 inches, and in Texas, I think it was 33 inches exactly. Land originally settled from Spain was surveyed in varas. The legua was 5000 varas, about 2.6335 miles. Many of the traditional units differed from locality to locality, which was the big problem with traditional units. The cántara of wine was 4.1 US gallons in Havana, 4.263 gallons in Castile. For precious metals, 1 marco = 50 castellanos = 400 tómine = 4800 Spanish gold grains. The castellano was from 71.07 to 71.04 grains avoirdupois. Three US gold dollars weighed 1.1 castellano. The marco was very close to 1/2 pound avoirdupois, but the figure varied from .50 to .54 pound.

For larger weights, the libra was 1.0161 pounds, the Madrid arroba 25.4025 pounds (25 libras), the quintal 101.61 pounds (100 libras), and the Castilian tonelada 2032.2 pounds (2000 libras). Length is now defined in terms of the speed of light, assumed to be an exact value (299792458 m/s), and time by the frequency of atomic vibrations, to a rather great precision. Weight is still defined by an arbitrary kilogram, or rather a collection of them. It is called mass, with undeserved dignity, since macroscopic comparisons are made by weighing. Masses on an atomic scale can be compared to better than one part in 108, which is better than weighing, so some atomic definition of the unit of mass is probably overdue so that uncertainties in the standard do not affect the values. Reference R. A. Young and T. J. Glover, Measure for Measure (Littleton, CO: Blue Willow, 1996).

An extensive table of equivalents, including many local units and curiosities. If you have a lot of converting to do, you might visit Online Length Unit Converter Composed by J. B. Calvert Created 3 July 1999 Math Dictionary - Nautical Mile MATH DICTIONARY Question: What is Nautical Mile ? Answer: A nautical mile is a measurement of distance at sea. It is 6083 feet, which is about 1.15 ordinary miles. A natural mile is one-sixtieth of the distance along the equator between two lines of longitude which differ by 1o. A speed of 1 nautical mile per hour is known as a knot. A nautical mile is also known as sea mile. It is a unit of length which corresponds approximately to one minute of latitude along any meridian. The international standard definition is: 1 nautical mile = 1,852 metres exactly. There is no commonly accepted international standard symbol for the unit nautical mile. The preferred abbreviation of the IEEE is nmi, while M is used by the BIPM and the maritime authorities of the USA and Canada. For aviation use, the preferred abbreviation of the ICAO is NM.

The abbreviation nm, though conflicting with the SI symbol for the nanometre is also in widespread use.

Question: Which unit of measurement is defined as being exactly 1,852 metres ?
Answer: NAUTICAL MILE