The metric system is an internationally recognised decimalised system of measurement. It is in widespread use, where it is adopted, it is the only or most common system of weights and measures, it is now known as the International System of Units. It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, the volume of fuel in its tank, it is used in science and trade. In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, a few others, which together with their derived units, can measure any physical quantity. Metric system may refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today; the metric system was designed to have properties that make it easy to use and applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, a structure of base and derived units.
It is a coherent system, which means that its units do not introduce conversion factors not present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics; the units of the metric system taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which measures seconds. One unit, the kilogram, remains defined in terms of a man-made artefact, but scientists voted to change the definition to one based on Planck's constant via a Kibble balance; the new definition is expected to be formally propagated on 20 May 2019. While there are numerous named derived units of the metric system, such as watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity. Though other or widespread systems of weights and measures continue to exist, such as the British imperial system and the US customary system of weights and measures, in those systems most or all of the units are now defined in terms of the metric system, such as the US foot, now a defined decimal fraction of a metre.
The metric system is extensible, new base and derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry; the modern metric system consists of four electromechanical base units representing seven fundamental dimensions of measure: length, time, thermodynamic temperature, luminous intensity, quantity of substance. The units are: the metre for length kilogram for mass second for time ampere for electromagnetism kelvin for temperature candela for luminous intensity mole for quantityTogether they are sufficient for measuring any known quantity, without reference to further quantities or phenomena; the metre, ampere and mole are all defined in terms of other base units. For example, the speed of light is defined as 299,792,458 metres per second, the metre is derived from that constant and the definition of a second.
As a result, in dimensional analysis, they remain wholly separate concepts. There are 22 derived units with special names in the metric system, these are defined in terms of the base units or other named derived units. Eight of these units are electromagnetic quantities: volt, a unit of electrical potential ohm, a unit of electrical resistance tesla, a unit of magnetic flux density weber, a unit of magnetic flux farad, a unit of electrical capacitance henry, a unit of electrical inductance siemens, a unit of electrical conductance coulomb, a unit of electrical chargeFour of these units are mechanical quantities: watt, a unit of mechanical or electrical power newton, a unit of mechanical force joule, a unit of mechanical, electrical or thermodynamic energy pascal, a unit of pressureFive units represent measures of electromagnetic radiation and radioactivity: becquerel, a unit of radioactive decay sievert, a unit of absorbed ionising radiation gray, a unit of ionising radiation lux, a unit of luminous flux lumen, a unit of luminous intensityTwo units are measures of circular arcs and spherical surfaces: radian, a unit of circular arc steradian, a unit of spherical surface areaThree units are miscellaneous: degree Celsius, a unit of thermodynamic temperature katal, a unit of catalytic activity hertz, a unit of cycles per second Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce and technology, certain customary units of measure have acquired established positions within the world community.
In order that such units are used around the world, the CGPM catalogued such units in Tables 6 to 9 of the SI brochure. These categories are: Non-SI units accepted for use with the International System of Units; this list includes the hour and minute, the angular measures, the historic metric units, the litre and hectare Non-SI units whose values in SI units must be obtained experimentally. This list includes various units of measure used in atomic and nuclear physics and in astronomy such as the dalton, the electron mass, the electron volt, the astronomical unit
Medieval Greek known as Byzantine Greek, is the stage of the Greek language between the end of Classical antiquity in the 5th–6th centuries and the end of the Middle Ages, conventionally dated to the Ottoman conquest of Constantinople in 1453. From the 7th century onwards, Greek was the only language of administration and government in the Byzantine Empire; this stage of language is thus described as Byzantine Greek. The study of the Medieval Greek language and literature is a branch of Byzantine studies, the study of the history and culture of the Byzantine Empire; the beginning of Medieval Greek is dated back to as early as the 4th century, either to 330 AD, when the political centre of the Roman Empire was moved to Constantinople, or to 395 AD, the division of the Empire. However, this approach is rather arbitrary as it is more an assumption of political, as opposed to cultural and linguistic, developments. Indeed, by this time the spoken language pronunciation, had shifted towards modern forms.
The conquests of Alexander the Great, the ensuing Hellenistic period, had caused Greek to spread to peoples throughout Anatolia and the Eastern Mediterranean, altering the spoken language's pronunciation and structure. Medieval Greek is the link between this vernacular, known as Koine Greek, Modern Greek. Though Byzantine Greek literature was still influenced by Attic Greek, it was influenced by vernacular Koine Greek, the language of the New Testament and the liturgical language of the Greek Orthodox Church. Constantine moved to Byzantium in 330; the city, though a major imperial residence like other cities such as Trier and Sirmium, was not a capital until 359. Nonetheless the imperial court resided there and the city was the political centre of the eastern parts of the Roman Empire where Greek was the dominant language. At first, Latin remained the language of the army, it was used for official documents. From the beginning of the 6th century, amendments to the law were written in Greek. Furthermore, parts of the Roman Corpus Iuris Civilis were translated into Greek.
Under the rule of Emperor Heraclius, who assumed the Greek title Basileus in 629, Greek became the official language of the Eastern Roman Empire. This was in spite of the fact that the inhabitants of the empire still considered themselves Rhomaioi until its end in 1453, as they saw their State as the perpetuation of Roman rule. Despite the absence of reliable demographic figures, it has been estimated that less than one third of the inhabitants of the Eastern Roman Empire, around eight million people, were native speakers of Greek; the number of those who were able to communicate in Greek may have been far higher. The native Greek speakers consisted of many of the inhabitants of the southern Balkan Peninsula, south of the Jireček Line, all of the inhabitants of Asia Minor, where the native tongues, except Armenian in the east, had become extinct, replaced by Greek, by the 5th century. In any case, all cities of the Eastern Roman Empire were influenced by the Greek language. In the period between 603 and 619, the southern and eastern parts of the empire were occupied by Persian Sassanids and, after being recaptured by Heraclius in the years 622 to 628, they were conquered by the Arabs in the course of the Muslim conquests a few years later.
Alexandria, a center of Greek culture and language, fell to the Arabs in 642. During the seventh and eighth centuries, Greek was replaced by Arabic as an official language in conquered territories such as Egypt; as more people gained a knowledge of Arabic. Thus, the use of Greek declined early on in Egypt; the invasion of the Slavs into the Balkan peninsula reduced the area where Greek was spoken and Latin. Sicily and parts of Magna Graecia, Asia Minor and more Anatolia, parts of the Crimean Peninsula remained Greek-speaking; the southern Balkans which would henceforth be contested between Byzantium and various Slavic kingdoms or empires. The Greek language spoken by one-third of the population of Sicily at the time of the Norman conquest 1060-90 remained vibrant for more than a century, but died out to a deliberate policy of Latinization in language and religion from the mid-1160s. From the late 11th century onwards, the interior of Anatolia was invaded by Seljuq Turks, who advanced westwards.
With the Ottoman conquests of Constantinople in 1453, the Peloponnese in 1459/1460, the Empire of Trebizond in 1461, Athens in 1465, two centuries the Duchy of Candia in 1669, the Greek language lost its status as a national language until the emergence of modern Greece in the year 1821. Language varieties after 1453 are referred to as Modern Greek; as early as in the Hellenistic period, there was a tendency towards a state of diglossia between the Attic literary language and the developing vernacular Koiné. By late antiquity, the gap had become impossible to ignore. In the Byzantine era, written Greek manifested itself in a whole spectrum of divergent registers, all of which were consciously archaic in comparison with the contemporary spoken vernacular, but in different degrees, they ranged from a moderately archaic style employed for most every-day writing and based on the written Koiné of the Bible and early Christian literature, to a artificial learned style, employed by authors with higher literary ambitions and imitating the model of classical Attic, in continuation of the movement of Atticism
Coins of the United States dollar
Coins of the United States dollar were first minted in 1792. New coins have been produced annually since and they make up a valuable aspect of the United States currency system. Today, circulating coins exist in denominations of 1¢, 5¢, 10¢, 25¢, 50¢, $1.00. Minted are bullion and commemorative coins. All of these are produced by the United States Mint; the coins are sold to Federal Reserve Banks which in turn are responsible for putting coins into circulation and withdrawing them as demanded by the country's economy. Today, four mints operate in the United States producing billions of coins each year; the main mint is the Philadelphia Mint, which produces circulating coinage, mint sets and some commemorative coins. The Denver Mint produces circulating coinage, mint sets and commemoratives; the San Francisco Mint produces regular and silver proof coinage, produced circulating coinage until the 1970s. The West Point Mint produces bullion coinage. Philadelphia and Denver produce the dies used at all of the mints.
The proof and mint sets are manufactured each year and contain examples of all of the year's circulating coins. The producing mint of each coin may be identified, as most coins bear a mint mark; the identifying letter of the mint can be found on the front side of most coins, is placed near the year. Unmarked coins are issued by the Philadelphia mint. Among marked coins, Philadelphia coins bear a letter P. Denver coins bear a letter D, San Francisco coins bear a letter S, West Point coins bear a letter W. S and W coins are if found in general circulation, although S coins bearing dates prior to the mid-1970s are in circulation; the CC, O, C, D mint marks were used on gold and silver coins for various periods in the mid-nineteenth century until the early twentieth century by temporary mints in Carson City, Nevada. The mass and composition of the cent changed to the current copper plated zinc core in 1982. Both types were minted in 1982 with no distinguishing mark. Cents minted in 1943 were struck on planchets punched from zinc coated steel which left the resulting edges uncoated.
This caused many of these coins to rust. These "steel pennies" are not to be found in circulation today, as they were intentionally removed from circulation for recycling the metal. However, cents minted from 1944 to 1946 were made from a special salvaged WWII brass composition to replace the steel cents, but still save material for the war effort, are more common in circulation than their 1943 counterparts; the wheat cent was common during its time. Some dates are rare; this is due to the fact that unlike the silver denominations, the composition of the pre-1982 cent, nearly pure copper, is not so much more valuable over face value for it to be hoarded to the extreme extent of the silver denominations. Nickels produced from mid-1942 through 1945 were manufactured from 56% copper, 35% silver and 9% manganese; this allowed the saved nickel metal to be shifted to industrial production of military supplies during World War II. Few of these are still found in circulation. Prior to 1965 and passage of the Coinage Act of 1965 the composition of the dime, half-dollar and dollar coins was 90% silver and 10% copper.
The half-dollar continued to be minted in a 40% silver-clad composition between 1965 and 1970. Dimes and quarters from before 1965 and half-dollars from before 1971 are not in circulation due to being removed for their silver content. In 1975 and 1976 bicentennial coinage was minted. Regardless of date of coining, each coin bears the dual date "1776-1976"; the Quarter-Dollar, Half-Dollar and Dollar coins were issued in the copper 91.67% nickel 8.33% composition for general circulation and the Government issued 6-coin Proof Set. A special 3-coin set of 40% silver coins were issued by the U. S. Mint in both Uncirculated and Proof. Use of the half-dollar is not as widespread as that of other coins in general circulation; when found, many 50¢ coins are hoarded, spent, or brought to banks. The Presidential Dollar series features portraits of all deceased U. S. Presidents with four coin designs issued each year in the order of the president's inauguration date; these coins began circulating on February 15, 2007.
Starting 2012, these coins have been minted only for collectible sets because of a large stockpile. The Susan B. Anthony dollar coin was minted from 1979–1981 and 1999; the 1999 minting was in response to Treasury supplies of the dollar becoming depleted and the inability to accelerate the minting of the Sacagawea dollars by a year. 1981 Anthony dollars can sometimes be found in circulation from proof sets that were broken open, but these dollars were not minted with the intent that they circulate. Non-circulating bullion coins have been produced each year since 1986, they can be found in gold and silver, since 1997 platinum. In 2017, the Mint introduced palladium bullion; the face value of these coins is legal as tender, but does not reflect the value of the precious metal contained therein. On May 11, 2011, Utah became the first state to accept these coins as the value of the precious metal in common transactions; the Utah State Treasurer assigns a numerical precious metal value to these coins each week based on the spot metal prices.
Modern commemoratives have been minte
Medieval Latin was the form of Latin used in Roman Catholic Western Europe during the Middle Ages. In this region it served as the primary written language, though local languages were written to varying degrees. Latin functioned as the main medium of scholarly exchange, as the liturgical language of the Church, as the working language of science, literature and administration. Medieval Latin represented, in essence, a continuation of Classical Latin and Late Latin, with enhancements for new concepts as well as for the increasing integration of Christianity. Despite some meaningful differences from Classical Latin, Medieval writers did not regard it as a fundamentally different language. There is no real consensus on the exact boundary where Late Latin Medieval Latin begins; some scholarly surveys begin with the rise of early Ecclesiastical Latin in the middle of the 4th century, others around 500, still others with the replacement of written Late Latin by written Romance languages starting around the year 900.
The terms Medieval Latin and Ecclesiastical Latin are used synonymously, though some scholars draw distinctions. Ecclesiastical Latin refers to the form, used by the Roman Catholic Church, whereas Medieval Latin refers more broadly to all of the forms of Latin used in the Middle Ages; the Romance languages spoken in the Middle Ages were referred to as Latin, since the Romance languages were all descended from Classical, or Roman, Latin itself. Medieval Latin had an enlarged vocabulary, which borrowed from other sources, it was influenced by the language of the Vulgate, which contained many peculiarities alien to Classical Latin that resulted from a more or less direct translation from Greek and Hebrew. Greek provided much of the technical vocabulary of Christianity; the various Germanic languages spoken by the Germanic tribes, who invaded southern Europe, were major sources of new words. Germanic leaders became the rulers of parts of the Roman Empire that they conquered, words from their languages were imported into the vocabulary of law.
Other more ordinary words were replaced by coinages from Vulgar Latin or Germanic sources because the classical words had fallen into disuse. Latin was spread to areas such as Ireland and Germany, where Romance languages were not spoken, which had never known Roman rule. Works written in those lands where Latin was a learned language, having no relation to the local vernacular influenced the vocabulary and syntax of medieval Latin. Since subjects like science and philosophy, including Argumentation theory and Ethics, were communicated in Latin, the Latin vocabulary that developed for them became the source of a great many technical words in modern languages. English words like abstract, communicate, matter and their cognates in other European languages have the meanings given to them in medieval Latin; the influence of Vulgar Latin was apparent in the syntax of some medieval Latin writers, although Classical Latin continued to be held in high esteem and studied as models for literary compositions.
The high point of the development of medieval Latin as a literary language came with the Carolingian renaissance, a rebirth of learning kindled under the patronage of Charlemagne, king of the Franks. Alcuin was an important writer in his own right. Although it was developing into the Romance languages, Latin itself remained conservative, as it was no longer a native language and there were many ancient and medieval grammar books to give one standard form. On the other hand speaking there was no single form of "medieval Latin"; every Latin author in the medieval period spoke Latin as a second language, with varying degrees of fluency and syntax. Grammar and vocabulary, were influenced by an author's native language; this was true beginning around the 12th century, after which the language became adulterated: late medieval Latin documents written by French speakers tend to show similarities to medieval French grammar and vocabulary. For instance, rather than following the classical Latin practice of placing the verb at the end, medieval writers would follow the conventions of their own native language instead.
Whereas Latin had no definite or indefinite articles, medieval writers sometimes used forms of unus as an indefinite article, forms of ille as a definite article or quidam as something like an article. Unlike classical Latin, where esse was the only auxiliary verb, medieval Latin writers might use habere as an auxiliary, similar to constructions in Germanic and Romance languages; the accusative and infinitive construction in classical Latin was replaced by a subordinate clause introduced by quod or quia. This is identical, for example, to the use of que in similar constructions in French. In every age from the late 8th century onwards, there were learned writers who were familiar enough with classical syntax to be aware that these forms and usages were "wrong" and resisted their use, thus the Latin of a theologian like St Thomas Aquinas or of an erudite clerical historian such as William of Tyre tends to avoid most of the characteristics described above, showing its p
Chinese units of measurement
Chinese units of measurement, known in Chinese as the shìzhì, are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal since the Shang, several Chinese measures use hexadecimal. Local applications have varied, but the Chinese dynasties proclaimed standard measurements and recorded their predecessor's systems in their histories. In the present day, the People's Republic of China maintains some customary units based upon the market units but standardized to round values in the metric system, for example the common jin or catty of 500 g; the Chinese name for most metric units is based on that of the closest traditional unit. Taiwan, like Korea, saw its traditional units standardized to Japanese values and their conversion to a metric basis, such as the Taiwanese ping of about 3.306 m² based on the square ken. The Hong Kong SAR continues to use its traditional units, now defined based on a local equation with metric units. For instance, the Hong Kong catty is 604.78982 g.
Note: The names lí and fēn for small units are the same for length and mass. According to the Liji, the legendary Yellow Emperor created the first measurement units; the Xiao Erya and the Kongzi Jiayu state. According to the Records of the Grand Historian, these human body units caused inconsistency, Yu the Great, another legendary figure, unified the length measurements. Rulers with decimal units have been unearthed from Shang Dynasty tombs. In the Zhou Dynasty, the king conferred nobles with powers of the state and the measurement units began to be inconsistent from state to state. After the Warring States period, Qin Shi Huang unified China, standardized measurement units. In the Han Dynasty, these measurements were still being used, were documented systematically in the Book of Han. Astronomical instruments show little change of the length of chi in the following centuries, since the calendar needed to be consistent, it was not until the introduction of decimal units in the Ming Dynasty that the traditional system was revised.
On 7 January 1915, the Beiyang Government promulgated a measurement law to use not only metric system as the standard but a set of Chinese-style measurement. On 16 February 1929, the Nationalist Government adopted and promulgated The Weights and Measures Act to adopt the metric system as the official standard and to limit the newer Chinese units of measurement to private sales and trade in Article 11, effective on 1 January 1930; the Government of the People's Republic of China continued using the market system along with metric system, as decreed by the State Council of the People's Republic of China on 25 June 1959, but 1 catty being 500 grams, would become divided into 10 taels, instead of 16 taels, to be converted from province to province, while exempting Chinese prescription drugs from the conversion to prevent errors. On 27 February 1984, the State Council of the People's Republic of China decreed the market system to remain acceptable till the end of 1990 and ordered the transition to the national legal measures by that time, but farmland measures would be exempt from this mandatory metrication until further investigation and study.
In 1976 the Hong Kong Metrication Ordinance allowed a gradual replacement of the system in favor of the International System of Units metric system. The Weights and Measures Ordinance defines the metric and Chinese units; as of 2012, all three systems are in widespread use. On 24 August 1992, Macau published Law No. 14/92/M to order that Chinese units of measurement similar to those used in Hong Kong, Imperial units, United States customary units would be permissible for five years since the effective date of the Law, 1 January 1993, on the condition of indicating the corresponding SI values for three more years thereafter, Imperial, US units would be permissible as secondary to the SI. Traditional units of length include the chi, bu, li; the precise length of these units, the ratios between these units, has varied over time. 1 bu has consisted of either 6 chi, while 1 li has consisted of 300 or 360 bu. All "metric values" given in the tables are exact unless otherwise specified by the approximation sign'~'.
Certain units are listed at List of Chinese classifiers → Measurement units. The Chinese word for metre is 米 mǐ. A kilometre, may be called 公里 gōnglǐ, i.e. a metric lǐ. In the engineering field, traditional units are rounded up to metric units. For example, the Chinese word 丝 sī is used to express 0.01 mm. These correspond to the measures listed as "China" in The Measures, Weights, & Moneys of All Nations Metric and other standard length units can be squared by the addition of the prefix 平方 píngfāng. For example, a square kilometre is 平方公里 píngfāng gōnglǐ; these units are used to measure cereal grains, among other things. In imperial times, the physical standard for these was the jialiang. In the case of volume, the market and metric shēng coincide, being equal to one litre as shown in the table; the Chinese standard SI prefixes may be added to this word shēng. Units of volume can be obtained from any standard unit of length using the prefix 立方 lìfāng, as in 立方米 lìfāng mǐ for a cubic metre; these units are used to measure the mas
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is used by scientists and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is known as "SCI" display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, the coefficient m is any real number; the integer n is called the order of magnitude and the real number m is called the significand or mantissa. However, the term "mantissa" may cause confusion because it is the name of the fractional part of the common logarithm. If the number is negative a minus sign precedes m. In normalized notation, the exponent is chosen so that the absolute value of the coefficient is at least one but less than ten. Decimal floating point is a computer arithmetic system related to scientific notation. Any given real number can be written in the form m×10^n in many ways: for example, 350 can be written as 3.5×102 or 35×101 or 350×100.
In normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3.5×102. This form allows easy comparison of numbers, as the exponent n gives the number's order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1; the 10 and exponent are omitted when the exponent is 0. Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized form, such as engineering notation, is desired. Normalized scientific notation is called exponential notation—although the latter term is more general and applies when m is not restricted to the range 1 to 10 and to bases other than 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3; the absolute value of m is in the range 1 ≤ |m| < 1000, rather than 1 ≤ |m| < 10. Though similar in concept, engineering notation is called scientific notation.
Engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. For example, 12.5×10−9 m can be read as "twelve-point-five nanometers" and written as 12.5 nm, while its scientific notation equivalent 1.25×10−8 m would be read out as "one-point-two-five times ten-to-the-negative-eight meters". A significant figure is a digit in a number; this includes all nonzero numbers, zeroes between significant digits, zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore, 1,230,400 has five significant figures: 1, 2, 3, 0, 4; when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, thus 1,230,400 would become 1.2304 × 106. However, there is the possibility that the number may be known to six or more significant figures, in which case the number would be shown as 1.23040 × 106.
Thus, an additional advantage of scientific notation is that the number of significant figures is clearer. It is customary in scientific measurements to record all the known digits from the measurements, to estimate at least one additional digit if there is any information at all available to enable the observer to make an estimate; the resulting number contains more information than it would without that extra digit, it may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements. Additional information about precision can be conveyed through additional notations, it is useful to know how exact the final digit are. For instance, the accepted value of the unit of elementary charge can properly be expressed as 1.6021766208×10−19 C, shorthand for ×10−19 C. Most calculators and many computer programs present large and small results in scientific notation invoked by a key labelled EXP, EEX, EE, EX, E, or ×10x depending on vendor and model.
Because superscripted exponents like 107 cannot always be conveniently displayed, the letter E is used to represent "times ten raised to the power of" and is followed by the value of the exponent. In this usage the character e is not related to the mathematical constant e or the exponential function ex. Although the E stands for exponent, the notation is referred to as E-notation rather than exponential notation; the use of E-notation facilitates data entry and readability in textual communication since it minimizes keystrokes, avoids reduced font sizes and provides a simpler and more concise display, but it is not encouraged in some publications. In most po
A grain is a unit of measurement of mass, in the troy weight and Apothecaries' system, equal to 64.79891 milligrams. It is nominally based upon the mass of a single virtual ideal seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definitions of units of mass. Rather, expressions such as "thirty-two grains of wheat, taken from the middle of the ear" appear to have been ritualistic formulas the premodern equivalent of legal boilerplate. Another source states that it was defined as the weight needed for 252.458 units to balance a cubic inch of distilled water at 30 inches of mercury pressure and 62 degrees Fahrenheit for both the air and water. Another book states that Captain Henry Kater, of the British Standards Commission, arrived at this value experimentally; the grain was the legal foundation of traditional English weight systems, is the only unit, equal throughout the troy and apothecaries' systems of mass. The unit was based on the weight of a single grain of barley, considered equivalent to 1 1⁄3 grains of wheat.
The fundamental unit of the pre-1527 English weight system known as Tower weights, was a different sort of grain known as the "wheat grain". The Tower wheat grain was defined as 45⁄64 of a troy grain. Since the implementation of the international yard and pound agreement of 1 July 1959, the grain or troy grain measure has been defined in terms of units of mass in the International System of Units as 64.79891 milligrams. 1 gram is 15.43236 grains. The unit used by jewellers to measure pearls, diamonds, or other precious stones, called the jeweller's grain or pearl grain, is equal to 1⁄4 of a carat, or 50 mg; the grain was the name of a traditional French unit equal to 53.115 mg. In both British Imperial and U. S. customary units, there are 7,000 grains per avoirdupois pound, 5,760 grains per troy pound or apothecaries pound. The grain is used to measure the mass of bullets and propellants; the term refers to a single particle of gunpowder, the size of which varies according to requirements. In archery, the grain is the standard unit used to weigh arrows.
In dentistry, gold foil, used as a material to restore teeth, is measured in grains. In North America, the hardness of water is measured in grains per US gallon of calcium carbonate equivalents. Otherwise, water hardness is measured in the metric unit parts per million, equivalent to mg/L. One grain per US gallon is 17.1 ppm. Soft water contains 1 -- 4 gpg of calcium carbonate equivalents. Though no longer recommended, grains are still used in medicine as part of the apothecaries' system in prescriptions for older medicines such as aspirin or phenobarbital. For example, the dosage of a standard 325 mg tablet of aspirin is sometimes given as 5 grains. In that example the grain is approximated to 65 mg, though the grain can be approximated to 60 mg, depending on the medication and manufacturer; the apothecaries system has its own system of notation, in which the unit's symbol or abbreviation is followed by the quantity in lower case Roman numerals. For amounts less than one, the quantity is written for one half, ss.
Therefore, a prescription for tablets containing 325 mg of aspirin and 30 mg of codeine can be written "ASA gr. V c̄ cod. gr. ss tablets". The apothecaries' system has been replaced by the metric system, the use of the grain in prescriptions is now rare. Particulate emission levels, used to monitor and regulate pollution, are measured in grains per cubic foot; this is the same unit used to measure the amount of moisture in the air known as the absolute humidity. The SI unit used to measure particulate emissions and absolute humidity is mg/m3. One grain per cubic foot is 2288 mg/m3. At least since antiquity, grains of wheat or barley were used by Mediterranean traders to define units of mass. According to a longstanding tradition, 1 carat was equivalent to the weight of 4 wheat grains or 3 barleycorns. Since the weights of these seeds are variable that of the cereals as a function of moisture, this is a convention more than an absolute law; the history of the modern British grain can be traced back to a royal decree in thirteenth century England, re-iterating decrees that go back as far as King Offa.
The tower pound was one of many monetary pounds of 240 silver pennies. By consent of the whole Realm the King's Measure was made, so that an English Penny, called the Sterling, round without clipping, shall weigh Thirty-two Grains of Wheat dry in the midst of the Ear; the pound in question is the Tower pound. The Tower pound, abolished in 1527, consisted of 12 ounces like the troy pound, but was 1⁄16 lighter; the weight of the original sterling pennies was 22½ troy grains, or 32 "Tower grains". Physical grain weights were made and sold commercially at least as late as the early 1900s, took various forms, from squares of sheet metal to manufactured wire shapes and coin-like weights; the troy pound was only "the pound of Pence, Confections, as of Electuaries", as such goods might be measured by a troi or small balance. The old troy standard was set by King Offa's currency reform, was in full use in 1284, but was restricted to cu