title: Citizenship of the United States

text: Naturalization fees were US$60 in 1989; US$90 in 1991; US$95 in 1994; US$225 in 1999; US$260 in 2002; US$320 in 2003; US$330 in 2005. In 2007 application fees were increased from US$330 to US$595 and an additional US$80 computerized fingerprinting fee was added. The biometrics fee was increased to US$85 in 2010. On December 23, 2014, the application fees were increased again from US$595 to US$640. The high fees have been criticized as putting up one more wall to citizenship. Increases in fees for citizenship have drawn criticism. Doris Meissner, a senior fellow at the Migration Policy Institute and former Immigration and Naturalization Service Commissioner, doubted that fee increases deter citizenship-seekers. In 2009, the number of immigrants applying for citizenship plunged 62%; reasons cited were the slowing economy and the cost of naturalization.


title: Citizenship of the United States

text: The citizenship process has been described as a ritual that is meaningful for many immigrants. Many new citizens are sworn in during Independence Day ceremonies. Most citizenship ceremonies take place at offices of the United States Citizenship and Immigration Services. However, one swearing-in ceremony was held at Arlington National Cemetery in Virginia in 2008. The judge who chose this venue explained: "I did it to honor our country's warriors and to give the new citizens a sense for what makes this country great". According to federal law, citizenship applicants who are also changing their names must appear before a federal judge.


title: Citizenship of the United States

text: The title of "Honorary Citizen of the United States" has been granted eight times by an act of Congress or by a proclamation issued by the president pursuant to authorization granted by Congress. The eight individuals are Sir Winston Churchill, Raoul Wallenberg, William Penn, Hannah Callowhill Penn, Mother Teresa, the Marquis de Lafayette, Casimir Pulaski, and Bernardo de Gálvez y Madrid, Viscount of Galveston and Count of Gálvez.


title: Citizenship of the United States

text: Sometimes, the government awarded non-citizen immigrants who died fighting for American forces with the posthumous title of United States citizen, but this is not considered honorary citizenship. In June 2003, Congress approved legislation to help families of fallen non-citizen soldiers.


title: Citizenship of the United States

text: There is a sense in which corporations can be considered "citizens". Since "corporations" are considered persons in the eyes of the law, it is possible to think of corporations as being like citizens. For example, the airline Virgin America asked the United States Department of Transportation to be treated as an American air carrier. The advantage of "citizenship" is having the protection and support of the United States government when jockeying with foreign governments for access to air routes and overseas airports. Alaska Airlines, a competitor of Virgin America, asked for a review of the situation; according to United States law, "foreign ownership in a United States air carrier is limited to 25% of the voting interest in the carrier", but executives at Virgin America insisted the airline met this requirement.


title: Citizenship of the United States

text: For the purposes of diversity jurisdiction in the United States civil procedure, corporate citizenship is determined by the principal place of business of the corporation. There is some degree of disagreement among legal authorities as to how exactly this may be determined.


title: Citizenship of the United States

text: Another sense of "corporate citizenship" is a way to show support for causes such as social issues and the environment and, indirectly, gain a kind of "reputational advantage".


title: Citizenship of the United States

text: The Immigration and Nationality Act of 1952 (INA) made a minor distinction between United States citizenship and United States nationality. Citizenship comprises a larger set of privileges and rights for those persons that are United States citizens which is not afforded to individuals that are only United States nationals by virtue of their rights under the INA. It is well-established that all United States citizens are United States nationals but not all United States nationals are United States citizens.


title: Citizenship of the United States

text: The Naturalization Act of 1790 () provided the first rules to be followed by the United States in the granting of national citizenship after the ratification of the Constitution. A number of other Acts and statutes followed the Act of 1790 that expanded or addressed specific situations but it was not until the Immigration and Nationality Act of 1952 (), codified under Title 8 of the United States Code (), that the variety of statutes governing citizenship law were organized within one single body of text. The Immigration and Nationality Act of 1952 set forth the legal requirements for the acquisition of American nationality. The Fourteenth Amendment (1868) addressed citizenship rights. The United States nationality law, despite its "nationality" title, comprises the statutes that embody the law regarding both American citizenship and American nationality.


title: Citizenship of the United States

text: The United States government takes the position that unincorporated territories of the United States are not "in the United States" for purposes of the Citizenship Clause, and thus individuals born in those territories are only United States citizens at birth if Congress has passed a citizenship statute in regards to that territory. Thus, people born in Puerto Rico, Guam, the United States Virgin Islands and the Northern Mariana Islands (after November 4, 1986) have United States citizenship at birth, while people in the Northern Mariana Islands who automatically gained U.S Citizenship on November 4, 1986 may elect to give up United States citizenship while retaining United States nationality at the age of 18 (or within six months of becoming US Citizens, if over 18). Meanwhile, per , people born in American Samoa are United States nationals but not United States citizens at birth, and must apply for naturalization if they wish to become US citizens, which requires them to pay a US$680 fee (as of February 11, 2014), pass a good moral character assessment, be fingerprinted and pass an English and civics examination. The nationality status of a person born in an unincorporated United States Minor Outlying Island is not specifically mentioned by law, but under international law and Supreme Court dicta, they are also regarded as non-citizen nationals of the United States.


title: Citizenship of the United States

text: The United States government position with regards to American Samoa began to be challenged in court in the 2010s. A 2016 ruling by the D.C. Circuit Court upheld the United States government's position interpretation that American Samoa is not "in the United States" for purposes of the Fourteenth Amendment and thus American Samoans are nationals but not citizens at birth, A 2021 ruling by the 10th Circuit Court similarly upheld the government's position and reversed a lower court ruling that said American Samoan plaintiffs were United States citizens at birth.


title: Citizenship of the United States

text: Non-citizen nationals of the United States may reside and work in the United States without restrictions, and may apply for United States citizenship under the same rules as permanent United States residents. Both of these groups are not allowed to vote in federal or state elections, although there is no constitutional prohibition against their doing so. Most nationals of the United States statutorily transmit nationality to children born outside the United States.


title: Citizenship of the United States

text: The United States passport issued to non-citizen nationals of the United States contains the endorsement code 9 which states: "The bearer is a United States national and not a United States citizen" on the annotations page.


title: Citizenship of the United States

text: The issue of citizenship naturalization is a highly contentious matter in United States politics, particularly regarding illegal immigrants. Candidates in the 2008 presidential election, such as Rudolph Giuliani, tried to "carve out a middle ground" on the issue of illegal immigration, but rivals such as John McCain advocated legislation requiring illegal immigrants to first leave the country before being eligible to apply as citizens. Some measures to require proof of citizenship upon registering to vote have met with controversy.


title: Citizenship of the United States

text: Controversy can arise when citizenship affects political issues. Whether to include questions about current citizenship status in the United States Census questions has been debated in the Senate. Census data affects state electoral clout; it also affects budgetary allocations. Including non-citizens in Census counts also shifts political power to states that have large numbers of non-citizens due to the fact that reapportionment of congressional seats is based on Census data, and including non-citizens in the census is mandated by the United States Constitution.


title: Citizenship of the United States

text: There have been controversies based on speculation about which way newly naturalized citizens are likely to vote. Since immigrants from many countries have been presumed to vote Democratic if naturalized, there have been efforts by Democratic administrations to streamline citizenship applications before elections to increase turnout; Republicans, in contrast, have exerted pressure to slow down the process. In 1997, there were efforts to strip the citizenship of 5,000 newly approved immigrants who, it was thought, had been "wrongly naturalized"; a legal effort to do this presented enormous challenges. An examination by the Immigration and Naturalization Service of 1.1 million people who were granted citizenship from September 1995 to September 1996 found 4,946 cases in which a criminal arrest should have disqualified an applicant or in which an applicant lied about his or her criminal history. Before the 2008 election, there was controversy about the speed of the USCIS in processing applications; one report suggested that the agency would complete 930,000 applications in time for the newly processed citizens to vote in the November 2008 election. Foreign-born naturalized citizens tend to vote at the same rates as natives. For example, in the state of New Jersey in the 2008 election, the foreign born represented 20.1% of the state's population of 8,754,560; of these, 636,000 were eighteen or older and hence eligible to vote; of eligible voters, 396,000 actually voted, which was about 62%. So foreign-born citizens vote in roughly the same proportion (62%) as native citizens (67%).


title: Citizenship of the United States

text: There has been controversy about the agency in charge of citizenship. The USCIS has been criticized as being a "notoriously surly, inattentive bureaucracy" with long backlogs in which "would-be citizens spent years waiting for paperwork". Rules made by Congress and the federal government regarding citizenship are highly technical and often confusing, and the agency is forced to cope with enforcement within a complex regulatory milieu. There have been instances in which applicants for citizenship have been deported on technicalities. One Pennsylvania doctor and his wife, both from the Philippines, who applied for citizenship, and one Mr. Darnell from Canada who was married to an American with two children from this marriage, ran afoul of legal technicalities and faced deportation. "The New York Times" reported that "Mr. Darnell discovered that a 10-year-old conviction for domestic violence involving a former girlfriend, even though it had been reduced to a misdemeanor and erased from his public record, made him ineligible to become a citizen — or even to continue living in the United States". Overworked federal examiners under pressure to make "quick decisions" as well as "weed out security risks" have been described as preferring "to err on the side of rejection". In 2000, 399,670 applications were denied (about of all applications); in 2007, 89,683 applications for naturalization were denied, about 12% of those presented.


title: Citizenship of the United States

text: Generally, eligibility for citizenship is denied for the millions of people living in the United States illegally, although from time to time, there have been amnesties. In 2006, there were mass protests numbering hundreds of thousands of people throughout the United States demanding United States citizenship for illegal immigrants. Many carried banners which read "We Have A Dream Too". One estimate is that there were 12 million illegal immigrants in the United States in 2006. Many American high school students have citizenship issues. In 2008, it was estimated that there were 65,000 illegal immigrant students. The number was less clear for post-secondary education. A 1982 Supreme Court decision, "Plyler v. Doe" , entitled illegal immigrants to free education from kindergarten through high school. Undocumented immigrants who get arrested face difficulties in the courtroom as they have no constitutional right to challenge the outcome of their deportation hearings. In 2009, writer Tom Barry of the "Boston Review" criticized the crackdown against illegal immigrants since it "flooded the federal courts with nonviolent offenders, besieged poor communities, and dramatically increased the United States prison population, while doing little to solve the problem itself". Barry criticized the United States' high incarceration rate as being "fives times greater than the average rate in the rest of the world". Virginia senator Jim Webb agreed that "we are doing something dramatically wrong in our criminal justice system".


title: Citizenship of the United States

text: United States citizens can relinquish their citizenship, which involves abandoning the right to reside in the United States and all the other rights and responsibilities of citizenship. "Relinquishment" is the legal term covering all seven different potentially-expatriating acts (ways of giving up citizenship) under . "Renunciation" refers to two of those acts: swearing an oath of renunciation before a United States diplomatic or consular officer abroad, or before an official designated by the attorney general within the United States during a state of war. Out of an estimated three to six million United States citizens residing abroad, between five and six thousand relinquished citizenship each year in 2015 and 2016. United States nationality law treats people who performs potentially-expatriating acts with intent to give up United States citizenship as ceasing to be United States citizens from the moment of the act, but United States tax law since 2004 treats such individuals as though they remain United States citizens until they notify the State Department and apply for a Certificate of Loss of Nationality (CLN).


title: Citizenship of the United States

text: Renunciation requires an oath to be sworn before a State Department officer and thus involves in-person attendance at an embassy or consulate, but applicants for CLNs on the basis of other potentially-expatriating acts must attend an in-person interview as well. During the interview, a State Department official assesses whether the person acted voluntarily, intended to abandon all rights of United States citizenship, and understands the consequences of their actions. The State Department strongly recommends that Americans intending to relinquish citizenship have another citizenship, but will permit Americans to make themselves stateless if they understand the consequences. There is a US$2,350 administrative fee for the process. In addition, an expatriation tax is imposed on some individuals relinquishing citizenship, but payment of the tax is not a legal prerequisite for relinquishing citizenship; rather, the tax and its associated forms are due on the normal tax due date of the year following relinquishment of citizenship. State Department officials do not seek to obtain any tax information from the interviewee, and instruct the interviewee to contact the IRS directly with any questions about taxes.


title: Citizenship of the United States

text: Citizenship can be revoked under certain circumstances. For instance, if held that a naturalized person has concealed material evidence, wilfully misrepresented themselves, or engaged in subversive activities, then they may have their naturalization revoked.


title: Citizenship of the United States

text: A citizen does not lose United States citizenship when they perform such acts like seeking office in a foreign state. However, the higher office and more important role a citizen holds in a foreign government, the more limited the exercise of consular rights of United States citizenship will be: "Serving as a foreign head of state/government or foreign minister may affect the level of immunity from United States jurisdiction that a dual national may be afforded. All such cases should be referred to the Office of the Assistant Legal Adviser for Consular Affairs".


title: Citizenship of the United States

text: From September 22, 1922, to the passage of Nationality Act of 1940, a woman holding United States citizenship could lose it simply by marriage to an alien or certain aliens ineligible for citizenship.


title: Dimensional analysis

text: In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units.


title: Dimensional analysis

text: Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. "Incommensurable" physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and kilograms, seconds and kilograms, metres and seconds. For example, asking whether a kilogram is larger than an hour is meaningless.


title: Dimensional analysis

text: Any physically meaningful equation, or inequality, "must" have the same dimensions on its left and right sides, a property known as "dimensional homogeneity". Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation.


title: Dimensional analysis

text: The concept of physical dimension, and of dimensional analysis, was introduced by Joseph Fourier in 1822.


title: Dimensional analysis

text: The Buckingham π theorem describes how every physically meaningful equation involving "n" variables can be equivalently rewritten as an equation of dimensionless parameters, where "m" is the rank of the dimensional matrix. Furthermore, and most importantly, it provides a method for computing these dimensionless parameters from the given variables.


title: Dimensional analysis

text: A dimensional equation can have the dimensions reduced or eliminated through nondimensionalization, which begins with dimensional analysis, and involves scaling quantities by characteristic units of a system or natural units of nature. This may give insight into the fundamental properties of the system, as illustrated in the examples below.


title: Dimensional analysis

text: The dimension of a physical quantity can be expressed as a product of the base physical dimensions such as length, mass and time, each raised to an integer (and occasionally rational) power. The "dimension" of a physical quantity is more fundamental than some "scale" or unit used to express the amount of that physical quantity. For example, "mass" is a dimension, while the kilogram is a particular reference quantity chosen to express a quantity of mass. The choice of unit is arbitrary, and its choice is often based on historical precedent. Natural units, being based on only universal constants, may be thought of as being "less arbitrary".


title: Dimensional analysis

text: There are many possible choices of base physical dimensions. The SI standard selects the following dimensions and corresponding symbols: time (T), length (L), mass (M), electric current (I), absolute temperature (Θ), amount of substance (N) and luminous intensity (J). The symbols are by convention usually written in roman sans serif typeface. Mathematically, the dimension of the quantity "Q" is given by


title: Dimensional analysis

text: where "a", "b", "c", "d", "e", "f", "g" are the dimensional exponents. Other physical quantities could be defined as the base quantities, as long as they form a linearly independent basis – for instance, one could replace the dimension (I) of electric current of the SI basis with a dimension (Q) of electric charge, since .


title: Dimensional analysis

text: The unit chosen to express a physical quantity and its dimension are related, but not identical concepts. The units of a physical quantity are defined by convention and related to some standard; e.g., length may have units of metres, feet, inches, miles or micrometres; but any length always has a dimension of L, no matter what units of length are chosen to express it. Two different units of the same physical quantity have conversion factors that relate them. For example, ; in this case 2.54 cm/in is the conversion factor, which is itself dimensionless. Therefore, multiplying by that conversion factor does not change the dimensions of a physical quantity.


title: Dimensional analysis

text: There are also physicists who have cast doubt on the very existence of incompatible fundamental dimensions of physical quantity, although this does not invalidate the usefulness of dimensional analysis.


title: Dimensional analysis

text: In dimensional analysis, Rayleigh's method is a conceptual tool used in physics, chemistry, and engineering. It expresses a functional relationship of some variables in the form of an exponential equation. It was named after Lord Rayleigh.


title: Dimensional analysis

text: As a drawback, Rayleigh's method does not provide any information regarding number of dimensionless groups to be obtained as a result of dimensional analysis.


title: Dimensional analysis

text: Many parameters and measurements in the physical sciences and engineering are expressed as a concrete number—a numerical quantity and a corresponding dimensional unit. Often a quantity is expressed in terms of several other quantities; for example, speed is a combination of length and time, e.g. 60 kilometres per hour or 1.4 kilometres per second. Compound relations with "per" are expressed with division, e.g. 60 km/1 h. Other relations can involve multiplication (often shown with a centered dot or juxtaposition), powers (like m for square metres), or combinations thereof.


title: Dimensional analysis

text: A set of base units for a system of measurement is a conventionally chosen set of units, none of which can be expressed as a combination of the others and in terms of which all the remaining units of the system can be expressed. For example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the base units of length (m), thus they are considered derived or compound units.


title: Dimensional analysis

text: Sometimes the names of units obscure the fact that they are derived units. For example, a newton (N) is a unit of force, which may be expressed as the product of mass (with unit kg) and acceleration (with unit m⋅s). The newton is defined as .


title: Dimensional analysis

text: Percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as "hundredths", since .


title: Dimensional analysis

text: Taking a derivative with respect to a quantity divides the dimension by the dimension of the variable that is differentiated with respect to. Thus:


title: Dimensional analysis

text: Likewise, taking an integral adds the dimension of the variable one is integrating with respect to, but in the numerator.


title: Dimensional analysis

text: In economics, one distinguishes between stocks and flows: a stock has a unit (say, widgets or dollars), while a flow is a derivative of a stock, and has a unit of the form of theis unit divided by one of time (say, dollars/year).


title: Dimensional analysis

text: In some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions. For example, debt-to-GDP ratios are generally expressed as percentages: total debt outstanding (dimension of currency) divided by annual GDP (dimension of currency)—but one may argue that, in comparing a stock to a flow, annual GDP should have dimensions of currency/time (dollars/year, for instance) and thus debt-to-GDP should have the unit year, which indicates that debt-to-GDP is the number of years needed for a constant GDP to pay the debt, if all GDP is spent on the debt and the debt is otherwise unchanged.


title: Dimensional analysis

text: For example, it makes no sense to ask whether 1 hour is more, the same, or less than 1 kilometre, as these have different dimensions, nor to add 1 hour to 1 kilometre. However, it makes sense to ask whether 1 mile is more, the same, or less than 1 kilometre, being the same dimension of physical quantity even though the units are different. On the other hand, if an object travels 100 km in 2 hours, one may divide these and conclude that the object's average speed was 50 km/h.


title: Dimensional analysis

text: The rule implies that in a physically meaningful "expression" only quantities of the same dimension can be added, subtracted, or compared. For example, if "m", "m" and "L" denote, respectively, the mass of some man, the mass of a rat and the length of that man, the dimensionally homogeneous expression is meaningful, but the heterogeneous expression is meaningless. However, "m"/"L" is fine. Thus, dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions.


title: Dimensional analysis

text: Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension , they are fundamentally different physical quantities.


title: Dimensional analysis

text: To compare, add, or subtract quantities with the same dimensions but expressed in different units, the standard procedure is first to convert them all to the same unit. For example, to compare 32 metres with 35 yards, use 1 yard = 0.9144 m to convert 35 yards to 32.004 m.


title: Dimensional analysis

text: A related principle is that any physical law that accurately describes the real world must be independent of the units used to measure the physical variables. For example, Newton's laws of motion must hold true whether distance is measured in miles or kilometres. This principle gives rise to the form that a conversion factor between a unit that measures the same dimension must take: multiplication by a simple constant. It also ensures equivalence; for example, if two buildings are the same height in feet, then they must be the same height in metres.


title: Dimensional analysis

text: In dimensional analysis, a ratio which converts one unit of measure into another without changing the quantity is called a "conversion factor". For example, kPa and bar are both units of pressure, and . The rules of algebra allow both sides of an equation to be divided by the same expression, so this is equivalent to . Since any quantity can be multiplied by 1 without changing it, the expression "" can be used to convert from bars to kPa by multiplying it with the quantity to be converted, including the unit. For example, because , and bar/bar cancels out, so .


title: Dimensional analysis

text: Dimensional analysis is most often used in physics and chemistry – and in the mathematics thereof – but finds some applications outside of those fields as well.


title: Dimensional analysis

text: A simple application of dimensional analysis to mathematics is in computing the form of the volume of an "n"-ball (the solid ball in "n" dimensions), or the area of its surface, the "n"-sphere: being an "n"-dimensional figure, the volume scales as formula_5 while the surface area, being formula_6-dimensional, scales as formula_7 Thus the volume of the "n"-ball in terms of the radius is formula_8 for some constant formula_9 Determining the constant takes more involved mathematics, but the form can be deduced and checked by dimensional analysis alone.


title: Dimensional analysis

text: In finance, economics, and accounting, dimensional analysis is most commonly referred to in terms of the distinction between stocks and flows. More generally, dimensional analysis is used in interpreting various financial ratios, economics ratios, and accounting ratios.


title: Dimensional analysis

text: In fluid mechanics, dimensional analysis is performed to obtain dimensionless pi terms or groups. According to the principles of dimensional analysis, any prototype can be described by a series of these terms or groups that describe the behaviour of the system. Using suitable pi terms or groups, it is possible to develop a similar set of pi terms for a model that has the same dimensional relationships. In other words, pi terms provide a shortcut to developing a model representing a certain prototype. Common dimensionless groups in fluid mechanics include:


title: Dimensional analysis

text: The first written application of dimensional analysis has been credited to an article of François Daviet at the Turin Academy of Science. Daviet had the master Lagrange as teacher.


title: Dimensional analysis

text: This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually later formalized in the Buckingham π theorem.


title: Dimensional analysis

text: Simeon Poisson also treated the same problem of the parallelogram law by Daviet, in his treatise of 1811 and 1833 (vol I, p. 39). In the second edition of 1833, Poisson explicitly introduces the term "dimension" instead of the Daviet "homogeneity".


title: Dimensional analysis

text: In 1822, the important Napoleonic scientist Joseph Fourier made the first credited important contributions based on the idea that physical laws like should be independent of the units employed to measure the physical variables.


title: Dimensional analysis

text: James Clerk Maxwell played a major role in establishing modern use of dimensional analysis by distinguishing mass, length, and time as fundamental units, while referring to other units as derived. Although Maxwell defined length, time and mass to be "the three fundamental units", he also noted that gravitational mass can be derived from length and time by assuming a form of Newton's law of universal gravitation in which the gravitational constant "G" is taken as unity, thereby defining . By assuming a form of Coulomb's law in which the Coulomb constant "k" is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were , which, after substituting his equation for mass, results in charge having the same dimensions as mass, viz. .


title: Dimensional analysis

text: Dimensional analysis is also used to derive relationships between the physical quantities that are involved in a particular phenomenon that one wishes to understand and characterize. It was used for the first time in this way in 1872 by Lord Rayleigh, who was trying to understand why the sky is blue. Rayleigh first published the technique in his 1877 book "The Theory of Sound".


title: Dimensional analysis

text: The original meaning of the word "dimension", in Fourier's "Theorie de la Chaleur", was the numerical value of the exponents of the base units. For example, acceleration was considered to have the dimension 1 with respect to the unit of length, and the dimension −2 with respect to the unit of time. This was slightly changed by Maxwell, who said the dimensions of acceleration are TL, instead of just the exponents.


title: Dimensional analysis

text: What is the period of oscillation of a mass attached to an ideal linear spring with spring constant suspended in gravity of strength ? That period is the solution for of some dimensionless equation in the variables , , , and .


title: Dimensional analysis

text: The four quantities have the following dimensions: [T]; [M]; [M/T]; and [L/T]. From these we can form only one dimensionless product of powers of our chosen variables, formula_14 = formula_15 , and putting formula_16 for some dimensionless constant gives the dimensionless equation sought. The dimensionless product of powers of variables is sometimes referred to as a dimensionless group of variables; here the term "group" means "collection" rather than mathematical group. They are often called dimensionless numbers as well.


title: Dimensional analysis

text: Note that the variable does not occur in the group. It is easy to see that it is impossible to form a dimensionless product of powers that combines with , , and , because is the only quantity that involves the dimension L. This implies that in this problem the is irrelevant. Dimensional analysis can sometimes yield strong statements about the "irrelevance" of some quantities in a problem, or the need for additional parameters. If we have chosen enough variables to properly describe the problem, then from this argument we can conclude that the period of the mass on the spring is independent of : it is the same on the earth or the moon. The equation demonstrating the existence of a product of powers for our problem can be written in an entirely equivalent way: formula_17, for some dimensionless constant (equal to formula_18 from the original dimensionless equation).


title: Dimensional analysis

text: When faced with a case where dimensional analysis rejects a variable (, here) that one intuitively expects to belong in a physical description of the situation, another possibility is that the rejected variable is in fact relevant, but that some other relevant variable has been omitted, which might combine with the rejected variable to form a dimensionless quantity. That is, however, not the case here.


title: Dimensional analysis

text: When dimensional analysis yields only one dimensionless group, as here, there are no unknown functions, and the solution is said to be "complete" – although it still may involve unknown dimensionless constants, such as .


title: Dimensional analysis

text: Consider the case of a vibrating wire of length "ℓ" (L) vibrating with an amplitude "A" (L). The wire has a linear density "ρ" (M/L) and is under tension "s" (LM/T), and we want to know the energy "E" (LM/T) in the wire. Let "π" and "π" be two dimensionless products of powers of the variables chosen, given by


title: Dimensional analysis

text: The linear density of the wire is not involved. The two groups found can be combined into an equivalent form as an equation


title: Dimensional analysis

text: where "f" is some other unknown function. Here the unknown function implies that our solution is now incomplete, but dimensional analysis has given us something that may not have been obvious: the energy is proportional to the first power of the tension. Barring further analytical analysis, we might proceed to experiments to discover the form for the unknown function "f". But our experiments are simpler than in the absence of dimensional analysis. We'd perform none to verify that the energy is proportional to the tension. Or perhaps we might guess that the energy is proportional to "ℓ", and so infer that . The power of dimensional analysis as an aid to experiment and forming hypotheses becomes evident.


title: Dimensional analysis

text: The power of dimensional analysis really becomes apparent when it is applied to situations, unlike those given above, that are more complicated, the set of variables involved are not apparent, and the underlying equations hopelessly complex. Consider, for example, a small pebble sitting on the bed of a river. If the river flows fast enough, it will actually raise the pebble and cause it to flow along with the water. At what critical velocity will this occur? Sorting out the guessed variables is not so easy as before. But dimensional analysis can be a powerful aid in understanding problems like this, and is usually the very first tool to be applied to complex problems where the underlying equations and constraints are poorly understood. In such cases, the answer may depend on a dimensionless number such as the Reynolds number, which may be interpreted by dimensional analysis.


title: Dimensional analysis

text: Consider the case of a thin, solid, parallel-sided rotating disc of axial thickness "t" (L) and radius "R" (L). The disc has a density "ρ" (M/L), rotates at an angular velocity "ω" (T) and this leads to a stress "S" (TLM) in the material. There is a theoretical linear elastic solution, given by Lame, to this problem when the disc is thin relative to its radius, the faces of the disc are free to move axially, and the plane stress constitutive relations can be assumed to be valid. As the disc becomes thicker relative to the radius then the plane stress solution breaks down. If the disc is restrained axially on its free faces then a state of plane strain will occur. However, if this is not the case then the state of stress may only be determined though consideration of three-dimensional elasticity and there is no known theoretical solution for this case. An engineer might, therefore, be interested in establishing a relationship between the five variables. Dimensional analysis for this case leads to the following (5 − 3 = 2) non-dimensional groups:


title: Dimensional analysis

text: Through the use of numerical experiments using, for example, the finite element method, the nature of the relationship between the two non-dimensional groups can be obtained as shown in the figure. As this problem only involves two non-dimensional groups, the complete picture is provided in a single plot and this can be used as a design/assessment chart for rotating discs


title: Dimensional analysis

text: The dimensions that can be formed from a given collection of basic physical dimensions, such as T, L, and M, form an abelian group: The identity is written as 1; , and the inverse of L is 1/L or L. L raised to any integer power "p" is a member of the group, having an inverse of L or 1/L. The operation of the group is multiplication, having the usual rules for handling exponents (). Physically, 1/L can be interpreted as reciprocal length, and 1/T as reciprocal time (see reciprocal second).


title: Dimensional analysis

text: An abelian group is equivalent to a module over the integers, with the dimensional symbol corresponding to the tuple . When physical measured quantities (be they like-dimensioned or unlike-dimensioned) are multiplied or divided by one other, their dimensional units are likewise multiplied or divided; this corresponds to addition or subtraction in the module. When measurable quantities are raised to an integer power, the same is done to the dimensional symbols attached to those quantities; this corresponds to scalar multiplication in the module.


title: Dimensional analysis

text: A basis for such a module of dimensional symbols is called a set of base quantities, and all other vectors are called derived units. As in any module, one may choose different bases, which yields different systems of units (e.g., choosing whether the unit for charge is derived from the unit for current, or vice versa).


title: Dimensional analysis

text: The group identity, the dimension of dimensionless quantities, corresponds to the origin in this module, formula_22.


title: Dimensional analysis

text: In certain cases, one can define fractional dimensions, specifically by formally defining fractional powers of one-dimensional vector spaces, like formula_23. However, it is not possible to take arbitrary fractional powers of units, due to representation-theoretic obstructions.


title: Dimensional analysis

text: One can work with vector spaces with given dimensions without needing to use units (corresponding to coordinate systems of the vector spaces). For example, given dimensions M and L, one has the vector spaces formula_24 and formula_25, and can define formula_26 as the tensor product. Similarly, the dual space can be interpreted as having "negative" dimensions. This corresponds to the fact that under the natural pairing between a vector space and its dual, the dimensions cancel, leaving a dimensionless scalar.


title: Dimensional analysis

text: The set of units of the physical quantities involved in a problem correspond to a set of vectors (or a matrix). The nullity describes some number (e.g., "m") of ways in which these vectors can be combined to produce a zero vector. These correspond to producing (from the measurements) a number of dimensionless quantities, . (In fact these ways completely span the null subspace of another different space, of powers of the measurements.) Every possible way of multiplying (and exponentiating) together the measured quantities to produce something with the same unit as some derived quantity "X" can be expressed in the general form


title: Dimensional analysis

text: Consequently, every possible commensurate equation for the physics of the system can be rewritten in the form


title: Dimensional analysis

text: The dimension of physical quantities of interest in mechanics can be expressed in terms of base dimensions T, L, and M – these form a 3-dimensional vector space. This is not the only valid choice of base dimensions, but it is the one most commonly used. For example, one might choose force, length and mass as the base dimensions (as some have done), with associated dimensions F, L, M; this corresponds to a different basis, and one may convert between these representations by a change of basis. The choice of the base set of dimensions is thus a convention, with the benefit of increased utility and familiarity. The choice of base dimensions is not entirely arbitrary, because they must form a basis: they must span the space, and be linearly independent.


title: Dimensional analysis

text: For example, F, L, M form a set of fundamental dimensions because they form a basis that is equivalent to T, L, M: the former can be expressed as [F = LM/T], L, M, while the latter can be expressed as [T = (LM/F)], L, M.


title: Dimensional analysis

text: On the other hand, length, velocity and time do not form a set of base dimensions for mechanics, for two reasons:


title: Dimensional analysis

text: Depending on the field of physics, it may be advantageous to choose one or another extended set of dimensional symbols. In electromagnetism, for example, it may be useful to use dimensions of T, L, M and Q, where Q represents the dimension of electric charge. In thermodynamics, the base set of dimensions is often extended to include a dimension for temperature, Θ. In chemistry, the amount of substance (the number of molecules divided by the Avogadro constant, ≈ ) is also defined as a base dimension, N.


title: Dimensional analysis

text: In the interaction of relativistic plasma with strong laser pulses, a dimensionless relativistic similarity parameter, connected with the symmetry properties of the collisionless Vlasov equation, is constructed from the plasma-, electron- and critical-densities in addition to the electromagnetic vector potential. The choice of the dimensions or even the number of dimensions to be used in different fields of physics is to some extent arbitrary, but consistency in use and ease of communications are common and necessary features.


title: Dimensional analysis

text: Scalar arguments to transcendental functions such as exponential, trigonometric and logarithmic functions, or to inhomogeneous polynomials, must be dimensionless quantities. (Note: this requirement is somewhat relaxed in Siano's orientational analysis described below, in which the square of certain dimensioned quantities are dimensionless.)


title: Dimensional analysis

text: While most mathematical identities about dimensionless numbers translate in a straightforward manner to dimensional quantities, care must be taken with logarithms of ratios: the identity log("a"/"b") = log "a" − log "b", where the logarithm is taken in any base, holds for dimensionless numbers "a" and "b", but it does "not" hold if "a" and "b" are dimensional, because in this case the left-hand side is well-defined but the right-hand side is not.


title: Dimensional analysis

text: Similarly, while one can evaluate monomials ("x") of dimensional quantities, one cannot evaluate polynomials of mixed degree with dimensionless coefficients on dimensional quantities: for "x", the expression (3 m) = 9 m makes sense (as an area), while for "x" + "x", the expression (3 m) + 3 m = 9 m + 3 m does not make sense.


title: Dimensional analysis

text: However, polynomials of mixed degree can make sense if the coefficients are suitably chosen physical quantities that are not dimensionless. For example,


title: Dimensional analysis

text: This is the height to which an object rises in time "t" if the acceleration of gravity is 9.8 and the initial upward speed is 500 . It is not necessary for "t" to be in "seconds". For example, suppose "t" = 0.01 minutes. Then the first term would be


title: Dimensional analysis

text: The value of a dimensional physical quantity "Z" is written as the product of a unit ["Z"] within the dimension and a dimensionless numerical factor, "n".


title: Dimensional analysis

text: When like-dimensioned quantities are added or subtracted or compared, it is convenient to express them in the same unit so that the numerical values of these quantities may be directly added or subtracted. But, in concept, there is no problem adding quantities of the same dimension expressed in different units. For example, 1 metre added to 1 foot is a length, but one cannot derive that length by simply adding 1 and 1. A conversion factor, which is a ratio of like-dimensioned quantities and is equal to the dimensionless unity, is needed:


title: Dimensional analysis

text: The factor formula_34 is identical to the dimensionless 1, so multiplying by this conversion factor changes nothing. Then when adding two quantities of like dimension, but expressed in different units, the appropriate conversion factor, which is essentially the dimensionless 1, is used to convert the quantities to the same unit so that their numerical values can be added or subtracted.


title: Dimensional analysis

text: Only in this manner is it meaningful to speak of adding like-dimensioned quantities of differing units.


title: Dimensional analysis

text: Some discussions of dimensional analysis implicitly describe all quantities as mathematical vectors. (In mathematics scalars are considered a special case of vectors; vectors can be added to or subtracted from other vectors, and, inter alia, multiplied or divided by scalars. If a vector is used to define a position, this assumes an implicit point of reference: an origin. While this is useful and often perfectly adequate, allowing many important errors to be caught, it can fail to model certain aspects of physics. A more rigorous approach requires distinguishing between position and displacement (or moment in time versus duration, or absolute temperature versus temperature change).


title: Dimensional analysis

text: Consider points on a line, each with a position with respect to a given origin, and distances among them. Positions and displacements all have units of length, but their meaning is not interchangeable:


title: Dimensional analysis

text: This illustrates the subtle distinction between "affine" quantities (ones modeled by an affine space, such as position) and "vector" quantities (ones modeled by a vector space, such as displacement).


title: Dimensional analysis

text: Properly then, positions have dimension of "affine" length, while displacements have dimension of "vector" length. To assign a number to an "affine" unit, one must not only choose a unit of measurement, but also a point of reference, while to assign a number to a "vector" unit only requires a unit of measurement.


title: Dimensional analysis

text: Thus some physical quantities are better modeled by vectorial quantities while others tend to require affine representation, and the distinction is reflected in their dimensional analysis.


title: Dimensional analysis

text: This distinction is particularly important in the case of temperature, for which the numeric value of absolute zero is not the origin 0 in some scales. For absolute zero,


title: Dimensional analysis

text: where the symbol ≘ means "corresponds to", since although these values on the respective temperature scales correspond, they represent distinct quantities in the same way that the distances from distinct starting points to the same end point are distinct quantities, and cannot in general be equated.


title: Dimensional analysis

text: Unit conversion for temperature differences is simply a matter of multiplying by, e.g., 1 °F / 1 K (although the ratio is not a constant value). But because some of these scales have origins that do not correspond to absolute zero, conversion from one temperature scale to another requires accounting for that. As a result, simple dimensional analysis can lead to errors if it is ambiguous whether 1 K means the absolute temperature equal to −272.15 °C, or the temperature difference equal to 1 °C.


title: Dimensional analysis

text: Similar to the issue of a point of reference is the issue of orientation: a displacement in 2 or 3 dimensions is not just a length, but is a length together with a "direction". (This issue does not arise in 1 dimension, or rather is equivalent to the distinction between positive and negative.) Thus, to compare or combine two dimensional quantities in a multi-dimensional space, one also needs an orientation: they need to be compared to a frame of reference.


title: Dimensional analysis

text: This leads to the extensions discussed below, namely Huntley's directed dimensions and Siano's orientational analysis.


title: Dimensional analysis

text: Huntley has pointed out that a dimensional analysis can become more powerful by discovering new independent dimensions in the quantities under consideration, thus increasing the rank formula_35 of the dimensional matrix.


title: Dimensional analysis

text: As an example of the usefulness of the first approach, suppose we wish to calculate the distance a cannonball travels when fired with a vertical velocity component formula_36 and a horizontal velocity component formula_37, assuming it is fired on a flat surface. Assuming no use of directed lengths, the quantities of interest are then , the distance travelled, with dimension L, formula_37, formula_36, both dimensioned as TL, and the downward acceleration of gravity, with dimension TL.


title: Dimensional analysis

text: from which we may deduce that formula_42 and formula_43, which leaves one exponent undetermined. This is to be expected since we have two fundamental dimensions T and L, and four parameters, with one equation.


title: Dimensional analysis

text: However, if we use directed length dimensions, then formula_37 will be dimensioned as TL, formula_36 as TL, as L and as TL. The dimensional equation becomes:


title: Dimensional analysis

text: and we may solve completely as formula_47, formula_48 and formula_49. The increase in deductive power gained by the use of directed length dimensions is apparent.


title: Dimensional analysis

text: It also is often quite difficult to assign the L, L, L, L, symbols to the physical variables involved in the problem of interest. He invokes a procedure that involves the "symmetry" of the physical problem. This is often very difficult to apply reliably: It is unclear as to what parts of the problem that the notion of "symmetry" is being invoked. Is it the symmetry of the physical body that forces are acting upon, or to the points, lines or areas at which forces are being applied? What if more than one body is involved with different symmetries?


title: Dimensional analysis

text: Consider the spherical bubble attached to a cylindrical tube, where one wants the flow rate of air as a function of the pressure difference in the two parts. What are the Huntley extended dimensions of the viscosity of the air contained in the connected parts? What are the extended dimensions of the pressure of the two parts? Are they the same or different? These difficulties are responsible for the limited application of Huntley's directed length dimensions to real problems.


title: Dimensional analysis

text: In Huntley's second approach, he holds that it is sometimes useful (e.g., in fluid mechanics and thermodynamics) to distinguish between mass as a measure of inertia (inertial mass), and mass as a measure of the quantity of matter. Quantity of matter is defined by Huntley as a quantity (a) proportional to inertial mass, but (b) not implicating inertial properties. No further restrictions are added to its definition.


title: Dimensional analysis

text: For example, consider the derivation of Poiseuille's Law. We wish to find the rate of mass flow of a viscous fluid through a circular pipe. Without drawing distinctions between inertial and substantial mass, we may choose as the relevant variables:


title: Dimensional analysis

text: There are three fundamental variables, so the above five equations will yield two independent dimensionless variables:


title: Dimensional analysis

text: If we distinguish between inertial mass with dimension formula_52 and quantity of matter with dimension formula_53, then mass flow rate and density will use quantity of matter as the mass parameter, while the pressure gradient and coefficient of viscosity will use inertial mass. We now have four fundamental parameters, and one dimensionless constant, so that the dimensional equation may be written:


title: Dimensional analysis

text: where now only is an undetermined constant (found to be equal to formula_55 by methods outside of dimensional analysis). This equation may be solved for the mass flow rate to yield Poiseuille's law.


title: Dimensional analysis

text: Huntley's recognition of quantity of matter as an independent quantity dimension is evidently successful in the problems where it is applicable, but his definition of quantity of matter is open to interpretation, as it lacks specificity beyond the two requirements (a) and (b) he postulated for it. For a given substance, the SI dimension amount of substance, with unit mole, does satisfy Huntley's two requirements as a measure of quantity of matter, and could be used as a quantity of matter in any problem of dimensional analysis where Huntley's concept is applicable.


title: Dimensional analysis

text: Angles are, by convention, considered to be dimensionless quantities. As an example, consider again the projectile problem in which a point mass is launched from the origin at a speed and angle above the "x"-axis, with the force of gravity directed along the negative "y"-axis. It is desired to find the range , at which point the mass returns to the "x"-axis. Conventional analysis will yield the dimensionless variable , but offers no insight into the relationship between and .


title: Dimensional analysis

text: Siano has suggested that the directed dimensions of Huntley be replaced by using "orientational symbols" to denote vector directions, and an orientationless symbol 1. Thus, Huntley's L becomes L1 with L specifying the dimension of length, and specifying the orientation. Siano further shows that the orientational symbols have an algebra of their own. Along with the requirement that , the following multiplication table for the orientation symbols results:


title: Dimensional analysis

text: Note that the orientational symbols form a group (the Klein four-group or "Viergruppe"). In this system, scalars always have the same orientation as the identity element, independent of the "symmetry of the problem". Physical quantities that are vectors have the orientation expected: a force or a velocity in the z-direction has the orientation of . For angles, consider an angle that lies in the z-plane. Form a right triangle in the z-plane with being one of the acute angles. The side of the right triangle adjacent to the angle then has an orientation and the side opposite has an orientation . Since (using to indicate orientational equivalence) we conclude that an angle in the xy-plane must have an orientation , which is not unreasonable. Analogous reasoning forces the conclusion that has orientation while has orientation 1. These are different, so one concludes (correctly), for example, that there are no solutions of physical equations that are of the form , where and are real scalars. Note that an expression such as formula_56 is not dimensionally inconsistent since it is a special case of the sum of angles formula and should properly be written:


title: Dimensional analysis

text: which for formula_58 and formula_59 yields formula_60. Siano distinguishes between geometric angles, which have an orientation in 3-dimensional space, and phase angles associated with time-based oscillations, which have no spatial orientation, i.e. the orientation of a phase angle is formula_61.


title: Dimensional analysis

text: The assignment of orientational symbols to physical quantities and the requirement that physical equations be orientationally homogeneous can actually be used in a way that is similar to dimensional analysis to derive more information about acceptable solutions of physical problems. In this approach, one solves the dimensional equation as far as one can. If the lowest power of a physical variable is fractional, both sides of the solution is raised to a power such that all powers are integral, putting it into normal form. The orientational equation is then solved to give a more restrictive condition on the unknown powers of the orientational symbols. The solution is then more complete than the one that dimensional analysis alone gives. Often, the added information is that one of the powers of a certain variable is even or odd.


title: Dimensional analysis

text: As an example, for the projectile problem, using orientational symbols, , being in the xy-plane will thus have dimension and the range of the projectile will be of the form:


title: Dimensional analysis

text: Dimensional homogeneity will now correctly yield and , and orientational homogeneity requires that formula_63. In other words, that must be an odd integer. In fact, the required function of theta will be which is a series consisting of odd powers of .


title: Dimensional analysis

text: It is seen that the Taylor series of and are orientationally homogeneous using the above multiplication table, while expressions like and are not, and are (correctly) deemed unphysical.


title: Dimensional analysis

text: Siano's orientational analysis is compatible with the conventional conception of angular quantities as being dimensionless, and within orientational analysis, the radian may still be considered a dimensionless unit. The orientational analysis of a quantity equation is carried out separately from the ordinary dimensional analysis, yielding information that supplements the dimensional analysis.


title: Dimensional analysis

text: The dimensionless constants that arise in the results obtained, such as the C in the Poiseuille's Law problem and the formula_64 in the spring problems discussed above, come from a more detailed analysis of the underlying physics and often arise from integrating some differential equation. Dimensional analysis itself has little to say about these constants, but it is useful to know that they very often have a magnitude of order unity. This observation can allow one to sometimes make "back of the envelope" calculations about the phenomenon of interest, and therefore be able to more efficiently design experiments to measure it, or to judge whether it is important, etc.


title: Dimensional analysis

text: Paradoxically, dimensional analysis can be a useful tool even if all the parameters in the underlying theory are dimensionless, e.g., lattice models such as the Ising model can be used to study phase transitions and critical phenomena. Such models can be formulated in a purely dimensionless way. As we approach the critical point closer and closer, the distance over which the variables in the lattice model are correlated (the so-called correlation length, formula_65 ) becomes larger and larger. Now, the correlation length is the relevant length scale related to critical phenomena, so one can, e.g., surmise on "dimensional grounds" that the non-analytical part of the free energy per lattice site should be formula_66 where formula_67 is the dimension of the lattice.


title: Dimensional analysis

text: It has been argued by some physicists, e.g., M. J. Duff, that the laws of physics are inherently dimensionless. The fact that we have assigned incompatible dimensions to Length, Time and Mass is, according to this point of view, just a matter of convention, borne out of the fact that before the advent of modern physics, there was no way to relate mass, length, and time to each other. The three independent dimensionful constants: "c", "ħ", and "G", in the fundamental equations of physics must then be seen as mere conversion factors to convert Mass, Time and Length into each other.


title: Dimensional analysis

text: Just as in the case of critical properties of lattice models, one can recover the results of dimensional analysis in the appropriate scaling limit; e.g., dimensional analysis in mechanics can be derived by reinserting the constants "ħ", "c", and "G" (but we can now consider them to be dimensionless) and demanding that a nonsingular relation between quantities exists in the limit formula_68, formula_69 and formula_70. In problems involving a gravitational field the latter limit should be taken such that the field stays finite.


title: Dimensional analysis

text: Following are tables of commonly occurring expressions in physics, related to the dimensions of energy, momentum, and force.


title: Dimensional analysis

text: If , where "c" is the speed of light and "ħ" is the reduced Planck constant, and a suitable fixed unit of energy is chosen, then all quantities of time "T", length "L" and mass "M" can be expressed (dimensionally) as a power of energy "E", because length, mass and time can be expressed using speed "v", action "S", and energy "E":


title: Dimensional analysis

text: though speed and action are dimensionless ( and ) – so the only remaining quantity with dimension is energy. In terms of powers of dimensions:


title: Dimensional analysis

text: This is particularly useful in particle physics and high energy physics, in which case the energy unit is the electron volt (eV). Dimensional checks and estimates become very simple in this system.


title: Dimensional analysis

text: However, if electric charges and currents are involved, another unit to be fixed is for electric charge, normally the electron charge "e" though other choices are possible.


title: Dimensional analysis

text: Kennedy's 1996 thesis describes an implementation in Standard ML, and later in F#. There are implementations for Haskell, OCaml, and Rust, Python, and a code checker for Fortran.


title: Dimensional analysis

text: McBride and Nordvall-Forsberg show how to use dependent types to extend type systems for units of measure.


title: Night-vision device

text: A night-vision device (NVD), also known as a night optical/observation device (NOD), night-vision goggle (NVG), is an optoelectronic device that allows visualization of images in low levels of light, improving the user's night vision. The device enhances ambient visible light and converts near-infrared light into visible light which can be seen by the user; this is known as I (image intensification). By comparison, viewing of infrared thermal radiation is referred to as thermal imaging and operates in a different section of the infrared spectrum. A night vision device usually consists of an image intensifier tube, a protective housing, and may have some type of mounting system. Many NVDs also include a protective sacrificial lens, mounted over the front lens (ie. objective lens) on NVDs to protect the latter from damage by environmental hazards and some can incorporate telescopic lenses. The image produced by an NVD is typically monochrome green, as green was considered to be the easiest color to look at for prolonged periods in the dark. Night vision devices may be passive, relying solely on ambient light, or may be active, using an IR (infrared) illuminator to better visualize the environment.


title: Night-vision device

text: Night vision devices can be handheld but many are head-mounted and attach to helmets. When used with firearms, an IR laser sight is often mounted to the user's weapon. The laser sight produces an infrared beam that is only visible through an NVD and aids with aiming. Some night vision devices are specially made to be mounted to firearms. These can used in conjunction with weapon sights like rifle scopes or can be used as standalone sights; some thermal weapon sights have been designed to provide similar capabilities.<ref name="nv/therm clipon sights"></ref>


title: Night-vision device

text: These devices were first used in World War II and came into wide use during the Vietnam War. The technology has evolved greatly since its introduction, leading to several "generations" of night-vision equipment with performance increases and price reductions. Consequently, though they are commonly used by the military and law enforcement agencies, night vision devices are available to civilian users for a wide range of applications including aviation, driving, demining, etc.


title: Night-vision device

text: Early night vision technology used prior to the end of World War II has been described as Generation 0.


title: Night-vision device

text: In 1929 Hungarian physicist Kálmán Tihanyi invented an infrared-sensitive electronic television camera for anti-aircraft defense in the UK.


title: Night-vision device

text: Night-vision devices were introduced in the German Army as early as 1939 and were used in World War II. AEG started developing the first devices in 1935. In mid-1943, the German Army began the first tests with infrared night-vision () devices and telescopic rangefinders mounted on Panther tanks. Two different arrangements were constructed and used on Panther tanks. The Sperber FG 1250 ("Sparrow Hawk"), with a range of up to 600 m, had a 30 cm infrared searchlight and an image converter operated by the tank commander.


title: Night-vision device

text: From late 1944 to March 1945 the German military conducted successful tests of FG 1250 sets mounted on Panther Ausf. G tanks (and other variants). Before World War II ended in 1945, approximately 50 (or 63) Panthers had been equipped with the FG 1250 and saw combat on both the Eastern and Western Fronts. The "Vampir" man-portable system for infantry was used with StG 44 assault rifles.


title: Night-vision device

text: Parallel development of night-vision systems occurred in the US. The M1 and M3 infrared night-sighting devices, also known as the "sniperscope" or "snooperscope", saw limited service with the US Army in World War II and in the Korean War, to assist snipers. These were active devices, using a large infrared light source to illuminate targets. Their image-intensifier tubes used an anode and an S-1 photocathode, made primarily of silver, cesium, and oxygen, and electrostatic inversion with electron acceleration was used to achieve gain.


title: Night-vision device

text: After World War II, Vladimir K. Zworykin developed the first practical commercial night-vision device at Radio Corporation of America, intended for civilian use. Zworykin's idea came from a former radio-guided missile. At that time, infrared was commonly called "black light", a term later restricted to ultraviolet. Zworykin's invention was not a success due to its size and cost.


title: Night-vision device

text: First-generation passive devices developed and patented by the US Army in the 1960s, introduced during the Vietnam War, were an adaptation of earlier active GEN 0 technology and relied on ambient light instead of using an extra infrared light source. Using an S-20 photocathode, their image intensifiers produced a light amplification of around , but they were quite bulky and required moonlight to function properly.


title: Night-vision device

text: Second-generation devices developed in the 1970s, featuring an improved image-intensifier tube using a micro-channel plate (MCP) with an S-25 photocathode, and resulted in a much brighter image, especially around the edges of the lens. This led to increased clarity in low ambient-light environments, such as moonless nights. Light amplification was around . Image resolution and reliability were also improved.


title: Night-vision device

text: Later advances in GEN II technology brought the tactical characteristics of "GEN II+" devices (equipped with better optics, SUPERGEN tubes, improved resolution and better signal-to-noise ratios), though GEN II+ is not formally recognized by the NVESD.


title: Night-vision device

text: Third-generation night-vision systems, developed in the late 1980s, maintained the MCP from Gen II, but used a photocathode made with gallium arsenide, which further improved image resolution. Gallium arsenide photocathodes are primarily manufactured by L3Harris Technologies and Elbit Systems of America and image light from 500-900 nm. In addition, the MCP is coated with an ion barrier film to increase tube life. However, the ion barrier causes fewer electrons to pass through, thus diminishing the improvement that the gallium-arsenide photocathode provides. Because of the ion barrier, the "halo" effect around bright spots or light sources is larger as well. Light amplification with these devices is improved to around –. Power consumption is higher than in GEN II tubes.


title: Night-vision device

text: Autogating (ATG) is a function which rapidly switches the power supply's voltage to the photocathode on and off. However, these switches are rapid enough that they are not detectable to the human eye and peak voltage supplied to the night vision device is maintained. This achieves several purposes: first, it reduces the "duty cycle" (ie. the amount of time that the tube has power running through it) which increases the device's lifespan. Second, autogating enhances the BSP (Bright-Source Protection), which is the built-in system that reduces the voltage supplied to the photocathode in response to ambient light levels. ABC (Automatic Brightness Control) is a similar function which modulates the amount of voltage supplied to the microchannel plate (rather than the photocathode) in response to ambient light. Together, BSP and ABC (alongside the autogating function) serve to prevent temporary blindness for the user and prevent damage to the tube when the night vision device is exposed to sudden bright sources of light, like a muzzle flash or artificial lighting being switched on. These modulation systems also help maintain a steady illumination level in the user's view which improves the ability to keep "eyes on target" in spite of temporary flashes of light. These functions are especially useful for pilots, soldiers in urban environments, and special operations forces who may be exposed to dynamic, rapidly changing light levels.


title: Night-vision device

text: OMNI, or OMNIBUS, refers to a series of contracts through which the US Army purchased GEN III night vision devices. This started with OMNI I which procured AN/PVS-7A and AN/PVS-7B devices, then continued with OMNI II (1990), OMNI III (1992), OMNI IV (1996), OMNI V (1998), OMNI VI (2002), OMNI VII (2005), OMNI VIII, and OMNI IX.


title: Night-vision device

text: However, OMNI is not a specification in and of itself. The performance of a particular GEN III OMNI device generally depends upon the tube which is used. For example, a GEN III OMNI III MX-10160A/AVS-6 tube will perform similarly to a GEN III VII MX-10160A/AVS-6 tube, even though the former was manufactured in ~1992 and the latter ~2005.


title: Night-vision device

text: One particular technology, PINNACLE©, is often mentioned as well. It is a proprietary thin-film microchannel plate technology created by ITT (since combined with Exelis, acquired by Harris, then sold to Elbit Systems of America) that was included in the OMNI VII contract. The thin-film improves performance.


title: Night-vision device

text: That being said, GEN III OMNI V–IX devices developed in the 2000s and onward can differ from standard GEN III and earlier GEN III OMNI I-IV devices in one or both of two important ways:


title: Night-vision device

text: While the consumer market sometimes classifies this type of system as "generation 4", the United States military describes these systems as "generation 3 autogated" tubes (GEN III OMNI V-IX). Moreover, as autogating power supplies can now be added to any previous generation of night-vision devices, "autogating" capability does not automatically class the devices as belonging to a particular OMNI classification. Any postnominals appearing after a generation type (i.e., Gen II+, Gen III+) do not change the generation type of the device, but instead indicate improvement(s) over the original specification's requirements.


title: Night-vision device

text: Figure of merit (FoM) is a number which gives a quantitative measure of a night vision device's effectiveness and clarity. It is calculated using the number of line pairs per millimeter which a user can detect while using the device multiplied by the image intensifier's signal-to-noise ratio.


title: Night-vision device

text: In the late 1990s, innovations in photocathode technology significantly increased the signal-to-noise ratio, with newly developed tubes starting to surpass the performance of standard Gen 3 tubes.


title: Night-vision device

text: By 2001, the United States federal government concluded that a tube's "generation" was not a determinant factor of a tube's global performance, making the term "generation" irrelevant in determining the performance of an image-intensifier tube, and therefore eliminated the term as a basis of export regulations.


title: Night-vision device

text: Though image-intensification technology employed by different manufacturers varies, from the tactical point of view, a night-vision system is an optical device that enables vision in conditions of low light. The US government itself has recognized the fact that the technology itself makes little difference, as long as an operator can see clearly at night. Consequently, the United States bases export regulations not on the generation, but on the figure of merit.


title: Night-vision device

text: ITAR regulations specify that US-made tubes with a FOM greater than 1400 are not exportable outside the US; however, the Defense Technology Security Administration (DTSA) can waive that policy on a case-by-case basis.


title: Night-vision device

text: Fusion night vision is a newer advance in night vision technology which combines I² (image intensification) with thermal imaging, which functions in the medium (MWIR 3-5 µm) and/or long (LWIR 8-14 µm) wavelength range. Initial models appeared in the 2000s and progressed in the 2010s. Some devices are dedicated fusion devices while others are clip-on thermal imagers which can add a thermal overlay to standard I² night vision devices. Fusion technologies combines the strengths of traditional I², which is excellent for navigation and discernment of fine details, with the strengths of thermal imaging, which excels in spotting the heat signatures of targets. Fusion systems have offered a number of different imaging modes including "fused" night vision with thermal overlay, night vision only, thermal only, and various special fusion modes like outline (which outlines objects that have thermal signatures) or "decamouflage", which highlights all objects that are of near-human temperatures. Fusion devices do struggle with weight and power usage and are often heavier and have shorter run times than contemporary I²-only devices.


title: Night-vision device

text: Aside from fusion of I² and thermal imaging within a single device, some users have tried using an I² device over one eye and a thermal device over the other eye, relying on the human visual system to provide a binocular combined view of the two. Some, but not all, thermal imaging systems can also be viewed through a night vision device (ie. lining up the thermal imager in front of the I² night vision device) to produce a form of fusion vision.


title: Night-vision device

text: Out of Band (OOB) refers to night vision technologies which operate outside of the 500-900 nm NIR (near infrared) range that traditional Gen III gallium arsenide tubes detect. Imaging outside the usual spectrum is possible with dedicated OOB image intensifier tubes or with clip-on devices. Two examples include Photonis' 4G HyMa (Hybrid Multi-Alkali) image intensifier tubes (bandwidth of 350-1100 nm, from near UV to IR) and Safran Optics 1's AN/PAS-34 E-COSI (Enhanced Clip-On SWIR Imager), which clips onto standard night vision devices and provides an overlay (in the 900-1700 nm range), respectively.


title: Night-vision device

text: OOB provides several advantages. First, OOB imaging makes better use of ambient light; while a standard Gen III/III+ device can only intensify light in the 500-900 nm NIR range, an OOB device also intensifies any UV light or SWIR light in the environment. As a result, an OOB device might be able to see more on a starlit night than a standard GEN III/III+ device could. Second, OOB imaging can help JTACs and other FACs when marking targets with a laser designator. Many laser designators use 1064nm light, which is barely visible to standard Gen III/III+ devices, so ground personnel may need to use a separate "see-spot" device to visually confirm that the designator's targeting laser is on target. OOB night vision devices, however, can easily image the 1064nm range.


title: Night-vision device

text: Third, OOB light is not visible to most commercially available night vision devices. Despite ITAR restrictions, night vision technologies have proliferated among peer and near-peer countries and have also made their way into terrorist hands. For example, there has been documented use of night vision equipment by the Taliban Red Unit. As a result, if friendly forces are using night vision equipment like IR illuminators, IR strobes, IR lasers, etc. then hostile forces using night vision equipment could spot them as well. OOB strobes, illuminators, and lasers, on the other hand, are easily visible when using OOOB night vision but much more difficult to spot with current Gen III/III+ night vision equipment as they appear faintly if at all (depending on wavelength and intensity).


title: Night-vision device

text: Additionally, depending on the wavelengths covered by an OOB imaging device, users might be able to observe the lasers used in laser rangefinders as they often operate in the 1550nm range.


title: Night-vision device

text: Night vision devices, whether monocular or binocular, typically have a limited field of view (FoV); the commonly used AN/PVS-14 has a FoV of 40° which is rather less than the 95° monocular horizontal FoV and 190° binocular horizontal FoV that humans possess. Due to the limited FoV, users must visually scan about to fully check their surroundings, which is a time consuming process. This limitation is particularly evident when using night vision devices for flying, driving, or CQB where split second decisions must be made. Because of these limitations, many SOF troops preferred to use white light rather than night vision when conducting CQB. As a result, much time and effort has gone into research to develop a wider FoV solution for night vision devices. As of 2021, there were three primary methods for increasing peripheral vision in night vision devices (each with their own advantages and disadvantages):


title: Night-vision device

text: Panoramic night vision goggles (PNVG) increase field of view by increasing the number of sensors: if tubes are generally limited to 40°, then one can add more tubes to increase peripheral vision. This solution works well and does not compromise device performance or visual clarity but comes at the cost of size, weight, power requirements, and complexity. A well-known set of peripheral NVGs is the GPNVG-18 (Ground Peripheral Night Vision Goggle), which was used in the raid in Abottabad that killed Osama Bin Laden. These goggles, and the aviation AN/AVS-10 PNVG from which they were derived, offer a 97° FoV.


title: Night-vision device

text: Foveated night vision (F-NVG) uses specialized WFoV optics to increase the field of view through a night vision intensifier tube. The fovea refers to the part of the retina which is responsible for central vision. These night vision devices have users still look "straight through" the tubes so light passing through the center of the tube falls on the foveal retina, as is the case with traditional binocular NVGs. While these devices increase FoV, it comes at the price of image quality and edge distortions. A US Naval contract for US$47.6 million was awarded to Kent Optronics to retrofit AN/PVS-15 units with WFoV optics that expanded them to 80° FoV with less than 4% distortion.


title: Night-vision device

text: Diverging image tube (DIT) night vision increases FoV by positioning the night vision tubes so they are no longer parallel but are angled slightly outward. This increases peripheral FoV but causes distortion and reduced image quality. Unfortunately, optical clarity is best when looking through the center of an image intensifier tube. With DIT, users are no longer looking "straight through" the center of the tubes (which provides the clearest images) and light passing through the center of the tubes no longer falls on the fovea (the area of clearest vision). The AN/PVS-25 was one such example of DIT night vision from the late 2000s. The WFoV BNVD is a variant of the AN/PVS-31A which incorporates both F-NVG and DIT-NVG concepts: the foveal WFoV optics increase the FoV of each tube from 40° to 55°, while the slight angulation of the tubes positions them so there is a 40° overlap of binocular vision in the center and a total 70° bi-ocular FoV. With the performance of the modified AN/PVS-31A tubes used, the WFoV BNVD has a FoM of 2706 which is better than the FoM in both the GPNVG-18 and the standard AN/PVS-31A.


title: Night-vision device

text: Some night vision devices, including several of the ENVG models, are digital, which allows electronic transmission of the device's night vision view, though this often comes at the price of size, weight, power usage.


title: Night-vision device

text: Ceramic Optical Ruggedized Engine (CORE) is a technology which was first shown at the 2012 SHOT Show in Las Vegas, NV by Armasight. CORE produces a higher-performance Gen 1 tubes. The main difference between CORE tubes and standard Gen 1 tubes is introduction of a ceramic plate instead of a glass one. This plate is produced from specially formulated ceramic and metal alloys. Edge distortion is improved, photo sensitivity is increased, and the resolution can be as high as 60 /mm. CORE is still considered Gen 1, as it does not utilize a microchannel plate.


title: Night-vision device

text: Scientists at the University of Michigan have developed a contact lens that can act as a night-vision device. The lens has a thin strip of graphene between layers of glass that reacts to photons to make dark images look brighter. Current prototypes only absorb 2.3% of light, so the percentage of light pickup has to rise before the lens can be viable. The graphene technology can be expanded into other uses, like car windshields, to improve night-driving. The US. Army is interested in the technology to potentially replace night-vision goggles.


title: Night-vision device

text: The Sensor and Electron Devices Directorate (SEDD) of the US Army Research Laboratory developed quantum-well infrared detector (QWID) technology. This technology's epitaxial layers, which result in diode formation, compose a gallium arsenide or aluminum gallium arsenide system (GaAs or AlGaAs). It is particularly sensitive to infrared waves that are mid-long lengths. The Corrugated QWIP (CQWIP) broadens detection capacity by using a resonance superstructure to orient more of the electric field parallel, so that it can be absorbed. Although cryogenic cooling between 77 K and 85 K is required, QWID technology is considered for constant surveillance viewing due to its claimed low cost and uniformity in materials.


title: Night-vision device

text: Materials from the II–VI compounds, such as HgCdTe, are used for high-performing infrared light-sensing cameras. In 2017 the US Army Research Labs in collaboration with Stony Brook University developed an alternative within the . InAsSb, a III–V compound, is commonly used commercially for opto-electronics in items such as DVDs and cell phones. To counteract this possibility in implementing InAsSb, scientists added a graded layer with increased atomic spacing and an intermediate layer of the substrate GaAs to trap any potential defects. This technology was designed with night-time military operations in mind.


title: Night-vision device

text: The Soviet Union, and after 1991 the Russian Federation, have developed a range of night-vision devices. Models used after 1960 by the Russian/Soviet Army are designated "1PNxx" (xx), where "1PN" is the GRAU index of night-vision devices. The PN stands for "pritsel nochnoy" (), meaning "night sight", and the "xx" is the model number. Different models introduced around the same time use the same type of batteries and mechanism for mounting on the weapon. The multi-weapon models have replaceable elevation scales, with one scale for the ballistic arc of each supported weapon. The weapons supported include the AK family, sniper rifles, light machine guns and hand-held grenade launchers.


title: Night-vision device

text: The Russian army has also contracted the development of and fielded a series of so-called (). The counter-sniper night sight is an active system that uses laser pulses from a laser diode to detect reflections from the focal elements of enemy optical systems and estimate their range. The vendor claims that this system is unparalleled:


title: Geography of Japan

text: Japan is an archipelagic country comprising a stratovolcanic archipelago over along the Pacific coast of East Asia. It consists of 6,852 islands. The five main islands are Hokkaido, Honshu, Kyushu, Shikoku and Okinawa. There are 6,847 remote islands. The Ryukyu Islands and Nanpō Islands are south and east of the main islands.


title: Geography of Japan

text: The territory covers . It is the fourth largest island country in the world and the largest island country in East Asia. The country has the 6th longest coastline at and the 8th largest Exclusive Economic Zone of in the world.


title: Geography of Japan

text: The terrain is mostly rugged and mountainous with 66% forest. The population is clustered in urban areas on the coast, plains and valleys. Japan is located in the northwestern Ring of Fire on multiple tectonic plates. East of the Japanese archipelago are three oceanic trenches. The Japan Trench is created as the oceanic Pacific Plate subducts beneath the continental Okhotsk Plate. The continuous subduction process causes frequent earthquakes, tsunami and stratovolcanoes. The islands are also affected by typhoons. The subduction plates have pulled the Japanese archipelago eastward, created the Sea of Japan and separated it from the Asian continent by back-arc spreading 15 million years ago.


title: Geography of Japan

text: The climate varies from humid continental in the north to humid subtropical and tropical rainforest in the south. These differences in climate and landscape have allowed the development of a diverse flora and fauna, with some rare endemic species, especially in the Ogasawara Islands.


title: Geography of Japan

text: Japan extends from 20° to 45° north latitude (Okinotorishima to Benten-jima) and from 122° to 153° east longitude (Yonaguni to Minami Torishima). Japan is surrounded by seas. To the north the Sea of Okhotsk separates it from the Russian Far East, to the west the Sea of Japan separates it from the Korean Peninsula, to the southwest the East China Sea separates the Ryukyu Islands from China and Taiwan, to the east is the Pacific Ocean.


title: Geography of Japan

text: The Japanese archipelago is over long in a north-to-southwardly direction from the Sea of Okhotsk to the Philippine Sea in the Pacific Ocean. It is narrow, and no point in Japan is more than from the sea. There are 6,852 islands in total. The five main islands are (from north to south) Hokkaido, Honshu, Shikoku, Kyushu and Okinawa. Three of the four major islands (Honshu, Kyushu and Shikoku) are separated by narrow straits of the Seto Inland Sea and form a natural entity. The 6,847 smaller islands are called remote islands. This includes the Bonin Islands, Daitō Islands, Minami-Tori-shima, Okinotorishima, the Ryukyu Islands, the Volcano Islands, Nansei Islands, and the Nanpō Islands, as well as numerous islets, of which 430 are inhabited. The Senkaku Islands are administered by Japan but disputed by China. This excludes the disputed Northern Territories (Kuril islands) and Liancourt Rocks. In total, as of 2021, Japan's territory is , of which is land and water. Japan has the sixth longest coastline in the world (). It is the largest island country in East Asia and fourth largest island country in the world.


title: Geography of Japan

text: Because of Japan's many far-flung outlying islands and long coastline, the country has extensive marine life and mineral resources in the ocean. The Exclusive Economic Zone of Japan covers and is the 8th largest in the world. It is more than 11 times the land area of the country. The Exclusive Economic Zone stretches from the baseline out to from its coast. Its territorial sea is , but between in the international straits—La Pérouse (or Sōya Strait), Tsugaru Strait, Ōsumi, and Tsushima Strait.


title: Geography of Japan

text: Japan has a population of 126 million in 2019. It is the 11th most populous country in the world and second most populous island country. 81% of the population lives on Honshu, 10% on Kyushu, 4.2% on Hokkaido, 3% on Shikoku, 1.1% in Okinawa Prefecture and 0.7% on other Japanese islands such as the Nanpō Islands.


title: Geography of Japan

text: Japan is informally divided into eight regions from northeast (Hokkaidō) to southwest (Ryukyu Islands):


title: Geography of Japan

text: Each region contains several prefectures, except the Hokkaido region, which comprises only Hokkaido Prefecture.


title: Geography of Japan

text: The regions are not official administrative units, but have been traditionally used as the regional division of Japan in a number of contexts. For example, maps and geography textbooks divide Japan into the eight regions, weather reports usually give the weather by region, and many businesses and institutions use their home region as part of their name (Kinki Nippon Railway, Chūgoku Bank, Tohoku University, etc.). While Japan has eight High Courts, their jurisdictions do not correspond with the eight regions.


title: Geography of Japan

text: About 73% of Japan is mountainous, with a mountain range running through each of the main islands. Japan's highest mountain is Mount Fuji, with an elevation of . Japan's forest cover rate is 68.55% since the mountains are heavily forested. The only other developed nations with such a high forest cover percentage are Finland and Sweden.


title: Geography of Japan

text: Since there is little level ground, many hills and mountainsides at lower elevations around towns and cities are often cultivated. As Japan is situated in a volcanic zone along the Pacific deeps, frequent low-intensity earth tremors and occasional volcanic activity are felt throughout the islands. Destructive earthquakes occur several times a century. Hot springs are numerous and have been exploited by the leisure industry.


title: Geography of Japan

text: The Geospatial Information Authority of Japan measures Japan's territory annually in order to continuously grasp the state of the national land. As of July 1, 2021, Japan's territory is . It increases in area due to volcanic eruptions such as Nishinoshima (西之島), the natural expansion of the islands, and land reclamation.


title: Geography of Japan

text: The Japanese archipelago is relatively far away from the Asian continent. Kyushu is closest to the southernmost point of the Korean peninsula with a distance of , which is almost 6 times farther away than from England to France across the English Channel. Thus historically Kyushu was the gateway between Asia and Japan. China is separated by of sea from Japan's big main islands. Hokkaido is near Sakhalin, which was occupied by Japan from 1905 to 1945. Most of the population lives on the Pacific coast side of Honshū. The west coast facing the Sea of Japan is less densely populated.


title: Geography of Japan

text: The Japanese archipelago was difficult to reach since before ancient history. During the Paleolithic period around 20,000 BCE at the height of the Last Glacial Maximum, there was a land bridge between Hokkaido and Sakhalin which linked Japan with the Asian continent. The land bridge disappeared when the sea levels rose in the Jōmon period around 10,000 BCE.


title: Geography of Japan

text: Japan's remote location, surrounded by vast seas, rugged, mountainous terrain and steep rivers make it secure against invaders and uncontrolled migration from the Asian continent. The Japanese can close their civilization with an isolationist foreign policy. During the Edo period the Tokugawa Shogunate enforced the Sakoku policy which prohibited most foreign contact and trade from 1641 to 1853. In modern times, the inflow of people is managed via the seaports and airports. Thus Japan is fairly insulated from continental issues.


title: Geography of Japan

text: Throughout history, Japan was never fully invaded nor colonized by other countries. The Mongols tried to invade Japan twice and failed in 1274 and 1281. Japan capitulated only once after nuclear attacks in World War II. At the time Japan did not have nuclear technology. The insular geography is a major factor for the isolationist, semi-open and expansionist periods of Japanese history.


title: Geography of Japan

text: The mountainous islands of the Japanese archipelago form a crescent off the eastern coast of Asia. They are separated from the continent by the Sea of Japan, which serves as a protective barrier. Japan has 108 active volcanoes (10% of the world's active volcanoes) because of active plate tectonics in the Ring of Fire.


title: Geography of Japan

text: Around 15 million years ago, the volcanic shoreline of the Asian continent was pushed out into a series of volcanic island arcs. This created the "back-arc basins" known as the Sea of Japan and Sea of Okhotsk with the formal shaping of the Japanese archipelago. The archipelago also has summits of mountain ridges that were uplifted near the outer edge of the continental shelf. About 73 percent of Japan's area is mountainous, and scattered plains and intermontane basins (in which the population is concentrated) cover only about 27 percent. A long chain of mountains runs down the middle of the archipelago, dividing it into two halves, the "face", fronting on the Pacific Ocean, and the "back", toward the Sea of Japan. On the Pacific side are steep mountains 1,500 to 3,000 meters high, with deep valleys and gorges.


title: Geography of Japan

text: Central Japan is marked by the convergence of the three mountain chains—the Hida, Kiso, and Akaishi mountains—that form the Japanese Alps ("Nihon Arupusu"), several of whose peaks are higher than . The highest point in the Japanese Alps is Mount Kita at . The highest point in the country is Mount Fuji (Fujisan, also erroneously called Fujiyama), a volcano dormant since 1707 that rises to above sea level in Shizuoka Prefecture. On the Sea of Japan side are plateaus and low mountain districts, with altitudes of 500 to 1,500 meters.


title: Geography of Japan

text: There are three major plains in central Honshū. The largest is the Kantō Plain which covers in the Kantō region. The capital Tokyo and the largest metropolitan population is located there. The second largest plain in Honshū is the Nōbi Plain with the third-most-populous urban area Nagoya. The third largest plain in Honshū is the Osaka Plain which covers in the Kinki region. It features the second largest urban area of Osaka (part of the Keihanshin metropolitan area). Osaka and Nagoya extend inland from their bays until they reach steep mountains. The Osaka Plain is connected with Kyoto and Nara. Kyoto is located in the Yamashiro Basin and Nara is in the Nara Basin .