1.
Units of measurement
–
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity, the metre is a unit of length that represents a definite predetermined length. When we say 10 metres, we actually mean 10 times the definite predetermined length called metre, the definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common, now there is a global standard, the International System of Units, the modern form of the metric system. In trade, weights and measures is often a subject of regulation, to ensure fairness. The International Bureau of Weights and Measures is tasked with ensuring worldwide uniformity of measurements, metrology is the science for developing nationally and internationally accepted units of weights and measures. In physics and metrology, units are standards for measurement of quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method, a standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights, science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving, in the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement. A unit of measurement is a quantity of a physical property. Units of measurement were among the earliest tools invented by humans, primitive societies needed rudimentary measures for many tasks, constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Weights and measures are mentioned in the Bible and it is a commandment to be honest and have fair measures. As of the 21st Century, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, however, the United States is the only industrialized country that has not yet completely converted to the Metric System. The systematic effort to develop an acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. After this treaty was signed, a General Conference of Weights, the CGPM produced the current SI system which was adopted in 1954 at the 10th conference of weights and measures. Currently, the United States is a society which uses both the SI system and the US Customary system
2.
Dimensional analysis
–
Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822, Physical quantities that are measurable have the same dimension and can be directly compared to each other, even if they are originally expressed in differing units of measure. If physical quantities have different dimensions, they cannot be compared by similar units, hence, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the dimensions on their left and right sides. Checking for dimensional homogeneity is an application of dimensional analysis. Dimensional analysis is routinely used as a check of the plausibility of derived equations and computations. It is generally used to categorize types of quantities and units based on their relationship to or dependence on other units. Many parameters and measurements in the sciences and engineering are expressed as a concrete number – a numerical quantity. Often a quantity is expressed in terms of other quantities, for example, speed is a combination of length and time. Compound relations with per are expressed with division, e. g.60 mi/1 h, other relations can involve multiplication, powers, or combinations thereof. A base unit is a unit that cannot be expressed as a combination of other units, for example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the units of length. Sometimes the names of units obscure that they are derived units, for example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs per second, so 1 A =1 C/s. Similarly, one newton is 1 kg⋅m/s2, percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as 1/100, derivatives with respect to a quantity add the dimensions of the variable one is differentiating with respect to on the denominator. Thus, position has the dimension L, derivative of position with respect to time has dimension LT−1 – length from position, time from the derivative, the second derivative has dimension LT−2. In economics, one distinguishes between stocks and flows, a stock has units of units, while a flow is a derivative of a stock, in some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions
3.
Contract
–
A contract is a voluntary arrangement between two or more parties that is enforceable by law as a binding legal agreement. Contract is a branch of the law of obligations in jurisdictions of the civil law tradition, Contract law concerns the rights and duties that arise from agreements. A contract arises when the parties agree that there is an agreement, formation of a contract generally requires an offer, acceptance, consideration, and a mutual intent to be bound. Each party to a contract must have capacity to enter the agreement, minors, intoxicated persons, and those under a mental affliction may have insufficient capacity to enter a contract. Some types of contracts may require formalities, such as a memorialization in writing, at common law, the elements of a contract are offer, acceptance, intention to create legal relations, and consideration. Not all agreements are necessarily contractual, as the parties generally must be deemed to have an intention to be legally bound, a so-called gentlemens agreement is one which is not intended to be legally enforceable, and which is binding in honour only. In order for a contract to be formed, the parties must reach mutual assent and this is typically reached through offer and an acceptance which does not vary the offers terms, which is known as the mirror image rule. An offer is a statement of the offerors willingness to be bound should certain conditions be met. If a purported acceptance does vary the terms of an offer, it is not an acceptance but a counteroffer and, therefore, the Uniform Commercial Code disposes of the mirror image rule in §2-207, although the UCC only governs transactions in goods in the USA. As a court cannot read minds, the intent of the parties is interpreted objectively from the perspective of a reasonable person and it is important to note that where an offer specifies a particular mode of acceptance, only an acceptance communicated via that method will be valid. Contracts may be bilateral or unilateral, a bilateral contract is an agreement in which each of the parties to the contract makes a promise or set of promises to each other. For example, in a contract for the sale of a home, less common are unilateral contracts in which one party makes a promise, but the other side does not promise anything. In these cases, those accepting the offer are not required to communicate their acceptance to the offeror, in a reward contract, for example, a person who has lost a dog could promise a reward if the dog is found, through publication or orally. The payment could be conditioned on the dog being returned alive. Those who learn of the reward are not required to search for the dog, but if someone finds the dog and delivers it, the High Court of Australia stated that the term unilateral contract is unscientific and misleading. In certain circumstances, a contract may be created. A contract is implied in fact if the circumstances imply that parties have reached an agreement even though they have not done so expressly, quantum meruit claims are an example. Carbolic, a firm, advertised a smoke ball marketed as a wonder drug that would, according to the instructions
4.
Accuracy and precision
–
Precision is a description of random errors, a measure of statistical variability. The two concepts are independent of other, so a particular set of data can be said to be either accurate, or precise. In the fields of science, engineering and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantitys true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are contrasted in the context of the scientific method. A measurement system can be accurate but not precise, precise but not accurate, neither, for example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment, eliminating the systematic error improves accuracy but does not change precision. A measurement system is considered if it is both accurate and precise. Related terms include bias and error, the terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data. Statistical literature prefers to use the terms bias and variability instead of accuracy and precision, bias is the amount of inaccuracy and variability is the amount of imprecision. In military terms, accuracy refers primarily to the accuracy of fire, ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units and maintained by national organizations such as the National Institute of Standards. This also applies when measurements are repeated and averaged, further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements. With regard to accuracy we can distinguish, the difference between the mean of the measurements and the value, the bias. Establishing and correcting for bias is necessary for calibration, the combined effect of that and precision. A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures, here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m, while a recording of 8,436 m would imply a margin of error of 0.5 m
5.
Measurement uncertainty
–
In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is only when it is accompanied by a statement of the associated uncertainty. By international agreement, this uncertainty has a basis and reflects incomplete knowledge of the quantity value. The measurement uncertainty is taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty is the measurement uncertainty relative to the magnitude of a single choice for the value for the measured quantity. This particular single choice is called the measured value, which may be optimal in some well-defined sense. Thus, the measurement uncertainty is the measurement uncertainty divided by the absolute value of the measured value. The purpose of measurement is to provide information about a quantity of interest – a measurand, when a quantity is measured, the outcome depends on the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. The dispersion of the values would relate to how well the measurement is performed. Their average would provide an estimate of the value of the quantity that generally would be more reliable than an individual measured value. The dispersion and the number of measured values would provide information relating to the value as an estimate of the true value. However, this information would not generally be adequate, the measuring system may provide measured values that are not dispersed about the true value, but about some value offset from it. Suppose it is not set to zero when there is nobody on the scale. Then, no matter how many times the mass were re-measured. Measurement uncertainty has important economic consequences for calibration and measurement activities, the American Society of Mechanical Engineers has produced a suite of standards addressing various aspects of measurement uncertainty. ASME B89.7.3.2, Guidelines for the Evaluation of Dimensional Measurement Uncertainty, ASME B89.7.4, Measurement Uncertainty and Conformance Testing, Risk Analysis, provides guidance on the risks involved in any product acceptance/rejection decision. The Guide to the Expression of Uncertainty in Measurement, commonly known as the GUM, is the document on this subject. See Joint Committee for Guides in Metrology, the above discussion concerns the direct measurement of a quantity, which incidentally occurs rarely
6.
Confidence interval
–
In statistics, a confidence interval is a type of interval estimate of a population parameter. It is an interval, in principle different from sample to sample. How frequently the observed interval contains the true parameter if the experiment is repeated is called the confidence level, whereas two-sided confidence limits form a confidence interval, and one-sided limits are referred to as lower/upper confidence bounds. Confidence intervals consist of a range of values that act as good estimates of the population parameter. However, the interval computed from a sample does not necessarily include the true value of the parameter. After any particular sample is taken, the parameter is either in the interval or not. Since the observed data are random samples from the true population, the 99% confidence level means that 99% of the intervals obtained from such samples will contain the true parameter. The desired level of confidence is set by the researcher, If a corresponding hypothesis test is performed, the confidence level is the complement of the level of significance, i. e. a 95% confidence interval reflects a significance level of 0.05. The confidence interval contains the values that, when tested. Confidence intervals of difference parameters not containing 0 imply that there is a significant difference between the populations. In applied practice, confidence intervals are typically stated at the 95% confidence level, however, when presented graphically, confidence intervals can be shown at several confidence levels, for example, 90%, 95%, and 99%. Factors affecting the width of the confidence interval include the size of the sample, the level. A larger sample size normally will lead to an estimate of the population parameter. Confidence intervals were introduced to statistics by Jerzy Neyman in a paper published in 1937, Interval estimates can be contrasted with point estimates. A point estimate is a value given as the estimate of a population parameter that is of interest, for example. An interval estimate specifies instead a range within which the parameter is estimated to lie, Confidence intervals are commonly reported in tables or graphs along with point estimates of the same parameters, to show the reliability of the estimates. For example, an interval can be used to describe how reliable survey results are. In a poll of election–voting intentions, the result might be that 40% of respondents intend to vote for a certain party, a 99% confidence interval for the proportion in the whole population having the same intention on the survey might be 30% to 50%
7.
Engineering tolerance
–
In engineering and safety, a physical distance or space, as in a truck, train or boat under a bridge as well as a train in a tunnel. In mechanical engineering the space between a bolt and a nut or a hole, etc, dimensions, properties, or conditions may have some variation without significantly affecting functioning of systems, machines, structures, etc. A variation beyond the tolerance is said to be noncompliant, rejected, a primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a process. This can be by the use of principles, engineering knowledge. Experimental investigation is very useful to investigate the effects of tolerances, Design of experiments, formal engineering evaluations, a good set of engineering tolerances in a specification, by itself, does not imply that compliance with those tolerances will be achieved. Actual production of any product involves some inherent variation of input and output, measurement error and statistical uncertainty are also present in all measurements. With a normal distribution, the tails of measured values may extend well beyond plus and minus three standard deviations from the process average, appreciable portions of one tails might extend beyond the specified tolerance. The process capability of systems, materials, and products needs to be compatible with the engineering tolerances. Process controls must be in place and an effective Quality management system, such as Total Quality Management, a process capability index is used to indicate the relationship between tolerances and actual measured production. The choice of tolerances is also affected by the statistical sampling plan. This relates to the question of whether tolerances must be rigid or whether some small percentage of being out-of-tolerance may sometimes be acceptable. The alternative is that the best product has a measurement which is precisely on target, there is an increasing loss which is a function of the deviation or variability from the target value of any design parameter. The greater the deviation from target, the greater is the loss and this is described as the Taguchi loss function or quality loss function, and it is the key principle of an alternative system called inertial tolerancing. Research and development work conducted by M. Pillet and colleagues at the Savoy University has resulted in industry-specific adoption, recently the publishing of the French standard NFX 04-008 has allowed further consideration by the manufacturing community. Dimensional tolerance is related to, but different from fit in mechanical engineering, tolerances are assigned to parts for manufacturing purposes, as boundaries for acceptable build. No machine can hold dimensions precisely to the value, so there must be acceptable degrees of variation. If a part is manufactured, but has dimensions that are out of tolerance, tolerances can be applied to any dimension. The commonly used terms are, Basic size, the diameter of the shaft
8.
Foot (unit)
–
The foot is a unit of length in the imperial and US customary systems of measurement. Since 1959, both units have been defined by international agreement as equivalent to 0.3048 meters exactly, in both systems, the foot comprises 12 inches and three feet compose a yard. Historically the foot was a part of local systems of units, including the Greek, Roman, Chinese, French. It varied in length from country to country, from city to city and its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits. The United States is the industrialized nation that uses the international foot and the survey foot in preference to the meter in its commercial, engineering. The foot is legally recognized in the United Kingdom, road signs must use imperial units, the measurement of altitude in international aviation is one of the few areas where the foot is widely used outside the English-speaking world. The length of the international foot corresponds to a foot with shoe size of 13,14,15.5 or 46. Historically the human body has been used to provide the basis for units of length. The foot of a male is typically about 15. 3% of his height, giving a person of 160 cm a foot of 245 mm. These figures are less than the used in most cities over time. Archeologists believe that the Egyptians, Ancient Indians and Mesopotamians preferred the cubit while the Romans, under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches and a cubit of 20.8 inches. The Egyptian equivalent of the measure of four palms or 16 digits—was known as the djeser and has been reconstructed as about 30 cm. The Greek foot had a length of 1⁄600 of a stadion, one stadion being about 181.2 m, the standard Roman foot was normally about 295.7 mm, but in the provinces, the pes Drusianus was used, with a length of about 334 mm. Originally both the Greeks and the Romans subdivided the foot into 16 digits, but in later years, after the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD790 Charlemagne attempted to reform the units of measure in his domains and his units of length were based on the toise and in particular the toise de lÉcritoire, the distance between the fingertips of the outstretched arms of a man. The toise has 6 pieds each of 326.6 mm, at the same time, monastic buildings used the Carolingian foot of 340 mm. The procedure for verification of the foot as described in the 16th century by Jacob Koebel in his book Geometrei, the measures of Iron Age Britain are uncertain and proposed reconstructions such as the Megalithic Yard are controversial. Later Welsh legend credited Dyfnwal Moelmud with the establishment of their units, the Belgic or North German foot of 335 mm was introduced to England either by the Belgic Celts during their invasions prior to the Romans or by the Anglo-Saxons in the 5th & 6th century
9.
Free software movement
–
Although drawing on traditions and philosophies among members of the 1970s hacker culture and academia, Richard Stallman formally founded the movement in 1983 by launching the GNU Project. Stallman later established the Free Software Foundation in 1985 to support the movement, the philosophy of the movement is that the use of computers should not lead to people being prevented from cooperating with each other. Stallman notes that this action will promote rather than hinder the progression of technology and this effort can go instead into advancing the state of the art. Members of the free software movement believe that all users of software should have the freedoms listed in The Free Software Definition, while social change may occur as an unintended by-product of technological change, advocates of new technologies often have promoted them as instruments of positive social change. This quote by San Jose State professor Joel West explains much of the philosophy, if it is assumed that social change is not only affected, but in some points of view, directed by the advancement of technology, is it ethical to hold these technologies from certain people. If not to make a change, this movement is in place to raise awareness about the effects that take place because of the physical things around us. A computer, for instance, allows us so many more freedoms than we have without a computer, the debate over the morality of both sides to the free software movement is a difficult topic to compromise respective opposition. Within the free movement, the FLOSS Manuals foundation specialises on the goal of providing such documentation. Members of the free software movement advocate that works which serve a practical purpose should also be free, the core work of the free software movement focused on software development. The free software movement also rejects proprietary software, refusing to install software that does not give them the freedoms of free software, some supporters of the free software movement take up public speaking, or host a stall at software-related conferences to raise awareness of software freedom. The ideas sparked by the GNU associates are an attempt to promote an environment that understands the benefits of having a local community. A lot of lobbying work has been done against software patents, other lobbying focusses directly on use of free software by government agencies and government-funded projects. The Venezuelan government implemented a free software law in January 2006, decree No.3,390 mandated all government agencies to migrate to free software over a two-year period. Congressmen Edgar David Villanueva and Jacques Rodrich Ackerman have been instrumental in introducing free software in Peru, the incident invited the attention of got Microsoft Inc, Peru, whose general manager wrote a letter to Villanueva. His response received worldwide attention and is seen as a piece of argumentation favouring use of free software in governments. In the United States, there have been efforts to pass legislation at the state level encouraging use of software by state government agencies. Like many social movements, the free movement has ongoing internal conflict between the many FOSS organizations and their personalities. For instance there is disagreement about the amount of compromises and pragmatism needed versus the need for strict adherence to values, after this Eric Raymond and Bruce Perens founded the Open Source Initiative, to promote the term open source software as an alternative term for free software
10.
Metric system
–
The metric system is an internationally agreed decimal system of measurement. Many sources also cite Liberia and Myanmar as the other countries not to have done so. Although the originators intended to devise a system that was accessible to all. Control of the units of measure was maintained by the French government until 1875, when it was passed to an intergovernmental organisation. From its beginning, the features of the metric system were the standard set of interrelated base units. These base units are used to larger and smaller units that could replace a huge number of other units of measure in existence. Although the system was first developed for use, the development of coherent units of measure made it particularly suitable for science. Although the metric system has changed and developed since its inception, designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. At the outbreak of the French Revolution in 1789, most countries, the metric system was designed to be universal—in the words of the French philosopher Marquis de Condorcet it was to be for all people for all time. However, these overtures failed and the custody of the metric system remained in the hands of the French government until 1875. In languages where the distinction is made, unit names are common nouns, the concept of using consistent classical names for the prefixes was first proposed in a report by the Commission on Weights and Measures in May 1793. The prefix kilo, for example, is used to multiply the unit by 1000, thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as,1 mg =0, however,1935 extensions to the prefix system did not follow this convention, the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι, was used as a multiplier for 10000, prefixes are not usually used to indicate multiples of a second greater than 1, the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the unit of volume. The base units used in the system must be realisable. Each of the units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured. In practice, such realisation is done under the auspices of a mutual acceptance arrangement, in the original version of the metric system the base units could be derived from a specified length and the weight of a specified volume of pure water
11.
Metric prefix
–
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
12.
International System of Units
–
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
13.
Length
–
In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance, in other contexts length is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness. Length may be distinguished from height, which is vertical extent, and width or breadth, length is a measure of one dimension, whereas area is a measure of two dimensions and volume is a measure of three dimensions. In most systems of measurement, the unit of length is a base unit, measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As society has become more technologically oriented, much higher accuracies of measurement are required in a diverse set of fields. One of the oldest units of measurement used in the ancient world was the cubit which was the length of the arm from the tip of the finger to the elbow. This could then be subdivided into shorter units like the foot, hand or finger, the cubit could vary considerably due to the different sizes of people. After Albert Einsteins special relativity, length can no longer be thought of being constant in all reference frames. Thus a ruler that is one meter long in one frame of reference will not be one meter long in a frame that is travelling at a velocity relative to the first frame. This means length of an object is variable depending on the observer, in the physical sciences and engineering, when one speaks of units of length, the word length is synonymous with distance. There are several units that are used to measure length, in the International System of Units, the basic unit of length is the metre and is now defined in terms of the speed of light. The centimetre and the kilometre, derived from the metre, are commonly used units. In U. S. customary units, English or Imperial system of units, commonly used units of length are the inch, the foot, the yard, and the mile. Units used to denote distances in the vastness of space, as in astronomy, are longer than those typically used on Earth and include the astronomical unit, the light-year. Dimension Distance Orders of magnitude Reciprocal length Smoot Unit of length
14.
Astronomical unit
–
The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
15.
Barleycorn (unit)
–
The barleycorn is a small English unit of length equal to 1⁄3 of an inch still used in Great Britain and Ireland as a determiner of shoe sizes. The notion of three barleycorns composing an inch certainly predates this statute, however, appearing in the 10th-century Welsh Laws of Hywel Dda. In practice, various weights and measures acts of the English kings were standardized with reference to some particular yard-length iron, brass, the formal barleycorn was 1/108 of its length. The English statute notwithstanding, the barleycorn was also taken as a measure of length equal to 1/4 inch. British and Irish shoe sizes differ from one another by the distance of a barleycorn, as modern studies show, the actual length of a kernel of barley varies from as short as 4–7 mm to as long as 12–15 mm depending on the cultivar. Older sources claimed the length of a grain of barley being 0.345 in. Line, 1/4 of a barleycorn or 1/12 of an inch poppyseed, 1/4 or 1/5 of a barleycorn
16.
Inch
–
The inch is a unit of length in the imperial and United States customary systems of measurement now formally equal to 1⁄36 yard but usually understood as 1⁄12 of a foot. Derived from the Roman uncia, inch is also used to translate related units in other measurement systems. The English word inch was a borrowing from Latin uncia not present in other Germanic languages. The vowel change from Latin /u/ to English /ɪ/ is known as umlaut, the consonant change from the Latin /k/ to English /tʃ/ or /ʃ/ is palatalisation. Both were features of Old English phonology, inch is cognate with ounce, whose separate pronunciation and spelling reflect its reborrowing in Middle English from Anglo-Norman unce and ounce. In many other European languages, the word for inch is the same as or derived from the word for thumb, the inch is a commonly used customary unit of length in the United States, Canada, and the United Kingdom. It is also used in Japan for electronic parts, especially display screens, for example, three feet two inches can be written as 3′ 2″. Paragraph LXVII sets out the fine for wounds of various depths, one inch, one shilling, an Anglo-Saxon unit of length was the barleycorn. After 1066,1 inch was equal to 3 barleycorns, which continued to be its legal definition for several centuries, similar definitions are recorded in both English and Welsh medieval law tracts. One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda which superseded those of Dyfnwal, both definitions, as recorded in Ancient Laws and Institutes of Wales, are that three lengths of a barleycorn is the inch. However, the oldest surviving manuscripts date from the early 14th century, john Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure. He noted that this process would not perfectly recover the standard, before the adoption of the international yard and pound, various definitions were in use. In the United Kingdom and most countries of the British Commonwealth, the United States adopted the conversion factor 1 metre =39.37 inches by an act in 1866. In 1930, the British Standards Institution adopted an inch of exactly 25.4 mm, the American Standards Association followed suit in 1933. By 1935, industry in 16 countries had adopted the industrial inch as it came to be known, in 1946, the Commonwealth Science Congress recommended a yard of exactly 0.9144 metres for adoption throughout the British Commonwealth. This was adopted by Canada in 1951, the United States on 1 July 1959, Australia in 1961, effective 1 January 1964, and the United Kingdom in 1963, effective on 1 January 1964. The new standards gave an inch of exactly 25.4 mm,1.7 millionths of a longer than the old imperial inch and 2 millionths of an inch shorter than the old US inch. The United States retains the 1/39. 37-metre definition for survey purposes and this is approximately 1/8-inch in a mile
17.
Atomic units
–
Atomic units form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of units, Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass. In Hartree units, the speed of light is approximately 137, atomic units are often abbreviated a. u. or au, not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts. Atomic units, like SI units, have a unit of mass, a unit of length, however, the use and notation is somewhat different from SI. Suppose a particle with a mass of m has 3.4 times the mass of electron, the value of m can be written in three ways, m =3.4 m e. This is the clearest notation, where the unit is included explicitly as a symbol. This notation is ambiguous, Here, it means that the m is 3.4 times the atomic unit of mass. But if a length L were 3.4 times the unit of length. The dimension needs to be inferred from context and this notation is similar to the previous one, and has the same dimensional ambiguity. It comes from setting the atomic units to 1, in this case m e =1. These four fundamental constants form the basis of the atomic units, therefore, their numerical values in the atomic units are unity by definition. Dimensionless physical constants retain their values in any system of units, of particular importance is the fine-structure constant α = e 2 ℏ c ≈1 /137. This immediately gives the value of the speed of light, expressed in atomic units, below are given a few derived units. Some of them have names and symbols assigned, as indicated in the table. There are two variants of atomic units, one where they are used in conjunction with SI units for electromagnetism. Although the units written above are the same way, the units related to magnetism are not. In the SI system, the unit for magnetic field is 1 a. u. = ℏ e a 02 =2. 35×105 T =2. 35×109 G, and in the Gaussian-cgs unit system, = e a 02 c =1. 72×103 T =1. 72×107 G
18.
Nautical mile
–
A nautical mile is a unit of measurement defined as exactly 1852 meters. Historically, it was defined as one minute of latitude, which is equivalent to one sixtieth of a degree of latitude. Today it is an SI derived unit, being rounded to a number of meters. The derived unit of speed is the knot, defined as one mile per hour. The geographical mile is the length of one minute of longitude along the Equator, there is no internationally agreed symbol. M is used as the abbreviation for the mile by the International Hydrographic Organization and by the International Bureau of Weights. NM is used by the International Civil Aviation Organization, nm is used by the U. S. National Oceanic and Atmospheric Administration. Nmi is used by the Institute of Electrical and Electronics Engineers, the word mile is from the Latin word for a thousand paces, mīlia. In 1617 the Dutch scientist Snell assessed the circumference of the Earth at 24,630 Roman miles, around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as the basis for a unit of measurement for distance, as one degree is 1/360 of a circle, one minute of arc is 1/21600 of a circle. These sexagesimal units originated in Babylonian astronomy, Gunter used Snells circumference to define a nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude.3 metres. Other countries measure the minute of arc at 45 degrees latitude, in 1929, the international nautical mile was defined by the First International Extraordinary Hydrographic Conference in Monaco as 1,852 meters. Imperial units and United States customary units used a definition of the nautical mile based on the Clarke Spheroid, the United States nautical mile was defined as 6,080.20 feet based in the Mendenhall Order foot of 1893. It was abandoned in favour of the nautical mile in 1954.181 meters. It was abandoned in 1970 and, legally, references to the unit are now converted to 1,853 meters. Conversion of units Orders of magnitude
19.
Chain (unit)
–
A chain is a unit of length. It measures 66 feet, or 22 yards, or 100 links, there are 10 chains in a furlong, and 80 chains in one statute mile. An acre is the area of 10 square chains, the chain has been used for several centuries in Britain and in some other countries influenced by British practice. By extension, chainage is the distance along a curved or straight line from a fixed commencing point. The chain was used with the mile to indicate land distances. Starting in the 19th century, the chain was used as a subdivision with the mile to show distances between stations, tunnels and bridges. The locally used units were often inconsistent from place to place, a rectangle of land one furlong in length and one chain in width has an area of one acre. His chain had 100 links, and the link is used as a subdivision of the chain as a unit of length, american surveyors sometimes used a longer chain of 100 feet, also of 100 links, known as the engineers chain or Ramsdens chain. The first such was constructed by Jesse Ramsden for the measurement of the Hounslow baseline at the start of the Anglo-French Survey. The term chain in this usually refers to the measuring instrument rather than a unit of length. Also in North America a modern variant of the chain as a tool is used in forestry for traverse surveys and this modern chain is a static cord,50 metres long, marked with a small tag at each metre, and also marked in the first metre every decimetre. When working in dense bush, an axe or hatchet is commonly tied to the end of the chain. Another version used extensively in forestry and surveying is the hip-chain, a hip-chain is a small box containing a string meter, worn on the hip. The user simply ties the spooled string off to a stake or tree and these instruments are available in both feet and meters. In Britain, the chain is no used for practical survey work. However it survives on the railways of the United Kingdom as a location identifier, since railways are entirely linear in topology, the mileage or chainage is sufficient to identify a place uniquely on any given route. Thus a certain bridge may be said to be at 112 mi 63 ch, in the case of the photograph the bridge is near Keynsham, that distance from London Paddington station. On new railway built in the United Kingdom such as High Speed 1
20.
Edmund Gunter
–
Edmund Gunter, was an English clergyman, mathematician, geometer and astronomer of Welsh descent. He is best remembered for his contributions which include the invention of the Gunters chain, the Gunters quadrant. In 1620, he invented the first successful analog device which he developed to calculate logarithmic tangents and he was mentored in mathematics by Reverend Henry Briggs and eventually became a Gresham Professor of Astronomy, from 1619 until his death. Gunter was born in Hertfordshire in 1581 and he was educated at Westminster School, and in 1599 he matriculated at Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity and he became rector of St. Georges Church in Southwark. Mathematics, particularly the relationship between mathematics and the world, was the one overriding interest throughout his life. In 1619, Sir Henry Savile put up money to fund Oxford Universitys first two faculties, the chairs of astronomy and geometry. Gunter applied to become professor of geometry but Savile was famous for distrusting clever people, doe you call this reading of Geometric. This is mere showing of tricks, man, and, according to a contemporary account, dismissed him with scorne. He was shortly thereafter championed by the far wealthier Earl of Bridgewater and this post he held till his death. With Gunters name are associated several useful inventions, descriptions of which are given in his treatises on the sector, cross-staff, bow, quadrant and other instruments. He contrived his sector about the year 1606, and wrote a description of it in Latin, in 1620 he published his Canon triangulorum. In 1624 Gunter published a collection of his mathematical works and it was entitled The description and use of sector, the cross-staffe, and other instruments for such as are studious of mathematical practise. One of the most remarkable things about this book is that it was written and it was a manual not for cloistered university fellows but for sailors and surveyors in real world. There is reason to believe that Gunter was the first to discover that the needle does not retain the same declination in the same place at all times. By desire of James I he published in 1624 The Description and Use of His Majesties Dials in Whitehall Garden and he coined the terms cosine and cotangent, and he suggested to Henry Briggs, his friend and colleague, the use of the arithmetical complement. His practical inventions are briefly noted below, Gunters interest in geometry led him to develop a method of sea surveying using triangulation. Linear measurements could be taken between topographical features such as corners of a field, and using triangulation the field or other area could be plotted on a plane, and its area calculated
21.
Rod (unit)
–
The rod or perch or pole is a surveyors tool and unit of length equal to 5 1⁄2 yards, 16 1⁄2 feet, 1⁄320 of a statute mile or one-fourth of a surveyors chain and 5.0292 meters. The rod is useful as a unit of length because whole number multiples of it can equal one acre of square measure. The perfect acre is an area of 43,560 square feet, bounded by sides 660 feet by 66 feet long, or 220 yards by 22 yards long. Thus, an acre is 160 square rods, since the adoption of the international yard on 1 July 1959, the rod has been equal to exactly 5.0292 meters. Its name derives from the Ancient Roman unit, the pertica, the measure also has a relationship to the military pike of about the same size and both measures date from the sixteenth century, when that weapon was still utilized in national armies. Surveyors rods and chains are still utilized in rough terrains with heavy overgrowth where laser or other measurements are difficult or impossible. In old English, the lug is also used. In England, the perch was officially discouraged in favour of the rod as early as the 15th century, however, local customs maintained its use. In Ireland, a perch was standardized at 21 feet, making an Irish chain, furlong, until English King Henry VIII seized the lands of the Roman Catholic Church in 1536, land measures as we now know them were essentially unknown. Instead a narrative system of landmarks and lists was used, a chain is a larger unit of length measuring 66 feet, or 22 yards, or 100 links, or 4 rods. There are 10 chains or 40 rods in a furlong, and so 80 chains or 320 rods in one statute mile, by the time of the industrial revolution and the quickening of land sales, canal and railway surveys, et al. The rod as a measure was standardized by Edmund Gunter in England in 1607 as one-fourth of a chain. The perch as a measure in Rome was 10 feet. To confuse matters further, by ancient Roman definition, an arpent equalled 120 Roman feet, the related unit of square measure was the scrupulum or decempeda quadrata, equivalent to about 8.76 m2. They were subdivided in different ways, and were of many different lengths. Based on data from the following, N - Niemann, in England, the rod is first defined in law by the Composition of Yards and Perches, one of the statutes of uncertain date from the late 13th to early 14th centuries. The length of the chain was standardized in 1620 by Edmund Gunter at exactly four rods, fields were measured in acres, which were one chain by one furlong. Bars of metal one rod long were used as standards of length when surveying land, the rod was still in use as a common unit of measurement in the mid-19th century, when Henry David Thoreau used it frequently when describing distances in his work, Walden
22.
Cubit
–
The cubit is an ancient unit based on the forearm length from the middle finger tip to the elbow bottom. Cubits of various lengths were employed in many parts of the world in antiquity, during the Middle Ages, the term is still used in hedge laying, the length of the forearm being frequently used to determine the interval between stakes placed within the hedge. The English word cubit comes from the Latin noun cubitus elbow, from the verb cubo, cubare, cubui, cubitum to lie down, the ancient Egyptian royal cubit is the earliest attested standard measure. Cubit rods were used for the measurement of length, a number of these rods have survived, two are known from the tomb of Maya, the treasurer of the 18th dynasty pharaoh Tutankhamun, in Saqqara, another was found in the tomb of Kha in Thebes. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865. These cubit rods range from 523.5 to 529.2 mm in length, and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided. Use of the royal cubit is also known from Old Kingdom architecture, in 1916, during the last years of the Ottoman Empire and in the middle of World War I, the German assyriologist Eckhard Unger found a copper-alloy bar while excavating at Nippur. The bar dates from c.2650 BC and Unger claimed it was used as a measurement standard and this irregularly formed and irregularly marked graduated rule supposedly defined the Sumerian cubit as about 518.6 mm. The Near Eastern or Biblical cubit is usually estimated as approximately 457.2 mm, in ancient Greek units of measurement, the standard forearm cubit measured approximately 0.46 m. The short forearm cubit, from the wrist to the elbow, in ancient Rome, according to Vitruvius, a cubit was equal to 1 1⁄2 Roman feet or 6 palm widths. Other measurements based on the length of the forearm include some lengths of ell, the Chinese chi, the Japanese shaku, the Indian hasta, the Thai sok, the Tamil, the Telugu, a cubit arm in heraldry may be dexter or sinister. It may be vested and may be shown in positions, most commonly erect. It is most often used erect as a crest, for example by the families of Poyntz of Iron Acton, Rolle of Stevenstone, the Encyclopaedia of Ancient Egyptian Architecture. The Cubit, A History and Measurement Commentary, Journal of Anthropology doi,10. 1155/2014/489757,2014 Media related to Cubit arms at Wikimedia Commons The dictionary definition of cubit at Wiktionary
23.
Ell
–
In English-speaking countries, these included the Flemish ell, English ell and French ell, some of which are thought to derive from a double ell. In England, the ell was usually 45 in, or a yard and it was mainly used in the tailoring business but is now obsolete. Although the exact length was never defined in English law, standards were kept, the Viking ell was the measure from the elbow to the tip of the middle finger, about 18 inches. The Viking ell or primitive ell was used in Iceland up to the 13th century, by the 13th century, a law set the stika as equal to 2 ells which was the English ell of the time. An ell-wand or ellwand was a rod of length one ell used for official measurement, edward I of England required that every town have one. In Scotland, the Belt of Orion was called the Kings Ellwand, the Scottish ell was standardised in 1661, with the exemplar to be kept in the custody of Edinburgh. It comes from Middle English elle and it was used in the popular expression Gie im an inch, an hell tak an ell. The Ell Shop in Dunkeld, Perth and Kinross, is so called from the 18th century iron ell-stick attached to one corner, once used to measure cloth and other commodities in the adjacent market-place. The shaft of the old 17th century Kincardine Mercat cross stands in the square of Fettercairn, Scottish measures were made obsolete, and English measurements made standard in Scotland, by act of parliament in 1824. The Scottish ell was equivalent to, Scottish measures, 3 1⁄12 feet Metric system,94.1318 cm Imperial system,1.03 international yards,37.1 inches This article incorporates text from Dwellys Gaelic Dictionary. Collins Encyclopedia of Scotland Scottish National Dictionary and Dictionary of the Older Scottish Tongue Weights and Measures, by D. Richard Torrance, SAFHS, Edinburgh,1996, ISBN 1-874722-09-9
24.
Metric foot
–
International standard ISO2848 is an ISO standard used by the construction industry. It is based on multiples of 300 mm and 600 mm. making them easy to use in mental arithmetic and this system is known as modular coordination. A related standard is British Standards 6750, the standard unit of ISO2848 is a basic module, a length of 10 centimetres which is represented in the standards by the letter M. As dimensions increase, preference is given to lengths which are multiples of 3,6,12,15,30 and 60 basic modules, for smaller dimensions, the submodular increments 1⁄4 M and 1⁄2 M are preferred. A metric foot is a nickname for a preferred length of 3 basic modules. The 30 cm metric ruler was a length to the traditional imperial one-foot ruler. A metric foot is 4.8 millimetres shorter than an imperial foot, although the term metric foot is still occasionally used in the United Kingdom, in particular in the timber trade, dimensions are most likely to be quoted exclusively in metric units today. The sizes of the studios at BBC Television Centre in London, a metric inch is a nickname for a preferred 1⁄4 subdivision of an ISO2848 basic module, or 1⁄12 of a metric foot measuring 25 millimetres. A metric inch is 0.4 millimetres shorter than an inch, British Standard BS6750, Modular coordination in building
25.
Furlong
–
A furlong is a measure of distance in imperial units and U. S. customary units equal to one-eighth of a mile, equivalent to 660 feet,220 yards,40 rods, or 10 chains. Using the international definition of the inch as exactly 25.4 millimetres, however, the United States does not uniformly use this conversion ratio. Older ratios are in use for surveying purposes in some states and this variation is too small to have many practical consequences. Five furlongs are about 1.0 kilometre, the name furlong derives from the Old English words furh and lang. Dating back at least to early Anglo-Saxon times, it referred to the length of the furrow in one acre of a ploughed open field. The system of long furrows arose because turning a team of oxen pulling a heavy plough was difficult and this offset the drainage advantages of short furrows and meant furrows were made as long as possible. An acre is an area that is one long and one chain wide. For this reason, the furlong was once called an acres length. The term furlong, or shot, was used to describe a grouping of adjacent strips within an open field. Among the early Anglo-Saxons, the rod was the unit of land measurement. A furlong was forty rods, a four by 40 rods, or four rods by one furlong. At the time, the Saxons used the North German foot, when England changed to the shorter foot in the late 13th century, rods and furlongs remained unchanged, since property boundaries were already defined in rods and furlongs. The only thing changed was the number of feet and yards in a rod or a furlong. The definition of the rod went from 15 old feet to 16 1⁄2 new feet, the furlong went from 600 old feet to 660 new feet, or from 200 old yards to 220 new yards. The acre went from 36,000 old square feet to 43,560 new square feet, the furlong was historically viewed as being equivalent to the Roman stade, which in turn derived from the Greek system. In the Roman system, there were 625 feet to the stadium, eight stadia to the mile, a league was considered to be the distance a man could walk in one hour, and the mile consisted of 1,000 passus. After the fall of the Roman Empire, medieval Europe continued with the Roman system, around the year 1300, by royal decree England standardized a long list of measures. Among the important units of distance and length at the time were the foot, yard, rod, furlong, and the mile
26.
Hand (unit)
–
The hand is a non-SI unit of measurement of length standardized to 4 inches. It is used to measure the height of horses in some English-speaking countries, including Australia, Canada, the Republic of Ireland, the United Kingdom and it was originally based on the breadth of a human hand. The adoption of the inch in 1959 allowed for a standardized imperial form. It may be abbreviated to h or hh, thus,62 inches is fifteen and a half hands, or 15.2 hh. Hands may be abbreviated to h, or hh, the hh form is sometimes interpreted as standing for hands high. When spoken aloud, hands are stated by numbers,15.0 is fifteen hands,15.2 is alternately fifteen-two or fifteen hands, to convert inches to hands, the number in inches is divided by four, then the remainder is added after the radix point. A designation of 15.5 hands is not halfway between 15 and 16 hands, but rather reads 15 hands and five inches, an impossibility in a base 4 radix numbering system, where a hand is four inches. On surviving Ancient Egyptian cubit-rods, the royal cubit is divided into seven palms of four digits or fingers each, five digits are equal to a hand, with thumb, and six to a closed fist. The royal cubit measured approximately 525 mm, so the length of the ancient Egyptian hand was about 94 mm. The hand is a unit in the UK. is four-fingers breadth, being the fist clenched, whereby the height of a horse is measured. Today the hand is used to measure the height of horses, ponies and it is used in the U. S. and also in some other nations that use the metric system, such as Canada, Ireland and the UK. In other parts of the world, including continental Europe, and in FEI-regulated international competition, horses are measured in metric units, usually metres or centimetres. In South Africa, measurements may be given in both hands and centimetres, while in Australia, the equestrian regulations stipulate that both measurements are to be given, a horse is measured from the ground to the top of the highest non-variable point of the skeleton, the withers. For official measurement, the process of the fifth thoracic vertebra may be identified by palpation. Miniature horses, but not miniature ponies, are measured at the base of the last true hairs of the rather than at the withers. For international competition regulated by the Fédération Équestre Internationale and for USEF competition in the US, in the United Kingdom, official measurement of horses is overseen by the Joint Measurement Board. For JMB purposes, the shoes must be removed and the hooves correctly prepared for shoeing prior to measurement, anthropic units List of horse breeds List of unusual units of measurement Pony Span
27.
Light-second
–
The light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance light travels in free space in one second. One light-nanosecond is almost 300 millimetres, which limits the speed of transfer between different parts of a large computer. One light-microsecond is about 300 metres, the mean distance, over land, between opposite sides of the Earth is 66.8 light-milliseconds. Communications satellites are typically 1.337 light-milliseconds to 119.4 light-milliseconds from the surface of the Earth, the light-second is a convenient unit for measuring distances in the inner Solar System, because it corresponds very closely to the radiometric data used to determine them.004786385 s. The mean diameter of the Earth is about 0.0425 light-seconds, the average distance from the Earth to the Moon is about 1.282 light-seconds. The diameter of the Sun is about 4.643 light-seconds, the average distance from the Earth to the Sun is 499.0 light-seconds. Multiples of the light-second can be defined, although apart from the light-year they are used in popular science publications than in research works. For example, a light-minute is 60 light-seconds and the distance from the Earth to the Sun is 8.317 light-minutes. Light-year 100 megametres Geometrized unit system
28.
Metre
–
The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
29.
SI base unit
–
The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011
30.
Mile
–
The mile is an English unit of length of linear measure equal to 5,280 feet, or 1,760 yards, and standardised as exactly 1,609.344 metres by international agreement in 1959. The Romans divided their mile into 5,000 feet but the importance of furlongs in pre-modern England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread to the British-colonized nations who continue to employ the mile, the US Geological Survey now employs the metre for official purposes but legacy data from its 1927 geodetic datum has meant that a separate US survey mile continues to see some use. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated as mph, mpg. The modern English word mile derives from Middle English myl and Old English mīl, the present international mile is usually what is understood by the unqualified term mile. When this distance needs to be distinguished from the nautical mile, in British English, the statute mile may refer to the present international miles or to any other form of English mile since the 1593 Act of Parliament which set it as a distance of 1,760 yards. Under American law, however, the statute mile refers to the US survey mile, the mile has been variously abbreviated—with and without a trailing period—as m, M, ml, and mi. The American National Institute of Standards and Technology now uses and recommends mi in order to avoid confusion with the SI metre and millilitre. Derived units such as miles per hour and miles per gallon, however, continue to be abbreviated in the United States, United Kingdom, the BBC style holds that There is no acceptable abbreviation for ‘miles’ and so it should be spelt out when used in describing areas. The Roman mile consisted of a thousand paces as measured by every other step—as in the distance of the left foot hitting the ground 1,000 times. The ancient Romans, marching their armies through uncharted territory, would push a carved stick in the ground after each 1000 paces. Well-fed and harshly driven Roman legionaries in good weather thus created longer miles, the distance was indirectly standardised by Agrippas establishment of a standard Roman foot in 29 BC, and the definition of a pace as 5 feet. An Imperial Roman mile thus denoted 5,000 Roman feet, surveyors and specialized equipment such as the decempeda and dioptra then spread its use. In modern times, Agrippas Imperial Roman mile was empirically estimated to have been about 1,481 metres in length, in Hellenic areas of the Empire, the Roman mile was used beside the native Greek units as equivalent to 8 stadia of 600 Greek feet. The mílion continued to be used as a Byzantine unit and was used as the name of the zero mile marker for the Byzantine Empire. The Roman mile also spread throughout Europe, with its local variations giving rise to the different units below, also arising from the Roman mile is the milestone. All roads radiated out from the Roman Forum throughout the Empire –50,000 miles of stone-paved roads, at every mile was placed a shaped stone, on which was carved a Roman numeral, indicating the number of miles from the center of Rome – the Forum. Hence, one knew how far one was from Rome