Second

The second is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​186400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

Although the historical definition of the unit was based on this division of the Earth's rotation cycle, the formal definition in the International System of Units (SI) is a much steadier timekeeper: 1 second is defined to be exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K).[1][2][3] Because the Earth's rotation varies and is also slowing ever so slightly, a leap second is periodically added to clock time[nb 1] to keep clocks in sync with Earth's rotation.

Multiples of seconds are usually counted in hours and minutes. Fractions of a second are usually counted in tenths or hundredths. In scientific work, small fractions of a second are counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera shutter speeds usually range from ​160 second to ​1250 second.

Sexagesimal divisions of the day from a calendar based on astronomical observation have existed since the third millennium BC, though they were not seconds as we know them today. Small divisions of time could not be counted back then, so such divisions were figurative. The first timekeepers that could count seconds accurately were pendulum clocks invented in the 17th century. Starting in the 1950s, atomic clocks became better timekeepers than earth's rotation, and they continue to set the standard today.

Second
Clock-pendulum
A pendulum-governed escapement of a clock, ticking every second
General information
Unit systemSI base unit
Unit ofTime
Symbols 

Clocks and solar time

A mechanical clock, one which does not depend on measuring the relative rotational position of the earth, keeps uniform time called mean time, within whatever accuracy is intrinsic to it. That means that every second, minute and every other division of time counted by the clock will be the same duration as any other identical division of time. But a sundial which measures the relative position of the sun in the sky called apparent time, does not keep uniform time. The time kept by a sundial varies by time of year, meaning that seconds, minutes and every other division of time is a different duration at different times of the year. The time of day measured with mean time versus apparent time may differ by as much as 15 minutes, but a single day will differ from the next by only a small amount; 15 minutes is a cumulative difference over a part of the year. The effect is due chiefly to the obliqueness of earth's axis with respect to its orbit around the sun.

The difference between apparent solar time and mean time was recognized by astronomers since antiquity, but prior to the invention of accurate mechanical clocks in the mid-17th century, sundials were the only reliable timepieces, and apparent solar time was the generally accepted standard.

Events and units of time in seconds

Fractions of a second are usually denoted in decimal notation, for example 2.01 seconds, or two and one hundredth seconds. Multiples of seconds are usually expressed as minutes and seconds, or hours, minutes and seconds of clock time, separated by colons, such as 11:23:24, or 45:23 (the latter notation can give rise to ambiguity, because the same notation is used to denote hours and minutes). It rarely makes sense to express longer periods of time like hours or days in seconds, because they are awkwardly large numbers. For the metric unit of second, there are decimal prefixes representing 10−24 to 1024 seconds.

Some common units of time in seconds are: a minute is 60 seconds; an hour is 3,600 seconds; a day is 86,400 seconds; a week is 604,800 seconds; a year (other than leap years) is 31,536,000 seconds; and a (Gregorian) century averages 3,155,695,200 seconds; with all of the above excluding any possible leap seconds.

Some common events in seconds are: a stone falls about 4.9 meters from rest in one second; a pendulum of length about one meter has a swing of one second, so pendulum clocks have pendulums about a meter long; the fastest human sprinters run 10 meters in a second; an ocean wave in deep water travels about 23 meters in one second; sound travels about 343 meters in one second in air; light takes 1.3 seconds to reach Earth from the surface of the Moon, a distance of 384,400 kilometers.

Other units incorporating seconds

A second is part of other units, such as frequency measured in hertz (inverse seconds or second−1), speed (meters per second) and acceleration (meters per second squared). The metric system unit becquerel, a measure of radioactive decay, is measured in inverse seconds. The meter is defined in terms of the speed of light and the second; definitions of the metric base units ampere and candela also depend on the second. Of the 22 named derived units of the SI, only three: degree Celsius, radian, and steradian, do not depend on the second. Many derivative units for everyday things are reported in terms of larger units of time, not seconds, such as clock time in hours and minutes, velocity of a car in miles per hour or kilometers per hour, kilowatt hours of electricity usage, and speed of a turntable in rotations per minute.

Timekeeping standards

A set of atomic clocks throughout the world keeps time by consensus: the clocks "vote" on the correct time, and all voting clocks are steered to agree with the consensus, which is called International Atomic Time (TAI). TAI "ticks" atomic seconds.[4]

Civil time is defined to agree with the rotation of the earth. The international standard for timekeeping is Coordinated Universal Time (UTC). This time scale "ticks" the same atomic seconds as TAI, but inserts or omits leap seconds as necessary to correct for variations in the rate of rotation of the earth.[5]

A time scale in which the seconds are not exactly equal to atomic seconds is UT1, a form of universal time. UT1 is defined by the rotation of the earth with respect to the sun, and does not contain any leap seconds.[6] UT1 always differs from UTC by less than a second.

Optical lattice clock

While they are not yet part of any timekeeping standard, optical lattice clocks with frequencies in the visible light spectrum now exist and are the most accurate timekeepers of all. A strontium clock with frequency 430 THz, in the red range of visible light, now holds the accuracy record: it will gain or lose less than a second in 15 billion years, which is longer than the estimated age of the universe. Such a clock can measure a change in its elevation of as little as 2 cm by the change in its rate due to gravitational time dilation.[7]

History of definition

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a caesium atomic clock, and they have realized a sexagesimal division of the day from ancient astronomical calendars.

Sexagesimal divisions of calendar time and day

Civilizations in the classic period and before constructed divisions of the calendar as well as arcs according to a sexagesimal system of counting, but the second was a sexagesimal subdivision of the day, not of the hour like the modern second. Sundials and water clocks were among the earliest timekeeping devices, and units of time were measured in degrees of arc. Conceptual units of time smaller than realizable on sundials were also used.

There are references to 'second' as part of a lunar month in the writings of natural philosophers of the Middle Ages, but no evidence that 'seconds' were ever realizable or adopted as part of timekeeping based on the lunar calendar.[nb 2][nb 3]

Fraction of solar day

The earliest mechanical clocks which appeared starting in the 14th century had displays that divided the hour into halves, thirds, quarters and sometimes even 12 parts, but never by 60. In fact, the hour was not commonly understood to be the duration of 60 minutes. It was not practical for timekeepers to consider minutes until the first mechanical clocks that displayed minutes appeared near the end of the 16th century. By that time, sexagesimal divisions of time were well established in Europe.[nb 4]

The earliest clocks to display seconds appeared during the last half of the 16th century. The second became accurately measurable with the development of mechanical clocks keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a second hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection, dated between 1560 and 1570.[10]:417–418[11] During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute.[12] In 1579, Jost Bürgi built a clock for William of Hesse that marked seconds.[10]:105 In 1581, Tycho Brahe redesigned clocks that had displayed only minutes at his observatory so they also displayed seconds, even though those seconds were not accurate. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds.[10]:104

In 1656, Dutch scientist Christiaan Huygens invented the first pendulum clock. It had a pendulum length of just under a meter which gave it a swing of one second, and an escapement that ticked every second. It was the first clock that could accurately keep time in seconds. By the 1730s, 80 years later, John Harrison's maritime chronometers could keep time accurate to within one second in 100 days.

In 1832, Gauss proposed using the second as the base unit of time in his millimeter-milligram-second system of units. The British Association for the Advancement of Science (BAAS) in 1862 stated that "All men of science are agreed to use the second of mean solar time as the unit of time."[13] BAAS formally proposed the CGS system in 1874, although this system was gradually replaced over the next 70 years by MKS units. Both the CGS and MKS systems used the same second as their base unit of time. MKS was adopted internationally during the 1940s, defining the second as ​186,400 of a mean solar day.

Fraction of an ephemeris year

Some time in the late 1940s, quartz crystal oscillator clocks with an operating frequency of ~100 kHz advanced to keep time with accuracy better than 1 part in 108 over an operating period of a day. It became apparent that a consensus of such clocks kept better time than the rotation of the Earth. Metrologists also knew that Earth's orbit around the Sun (a year) was much more stable than earth's rotation. This led to proposals as early as 1950 to define the second as a fraction of a year.

The Earth's motion was described in Newcomb's Tables of the Sun (1895), which provided a formula for estimating the motion of the Sun relative to the epoch 1900 based on astronomical observations made between 1750 and 1892.[14] This resulted in adoption of an ephemeris time scale expressed in units of the sidereal year at that epoch by the IAU in 1952.[15] This extrapolated timescale brings the observed positions of the celestial bodies into accord with Newtonian dynamical theories of their motion.[14] In 1955, the tropical year, considered more fundamental than the sidereal year, was chosen by the IAU as the unit of time. The tropical year in the definition was not measured but calculated from a formula describing a mean tropical year that decreased linearly over time.

In 1956, the second was redefined in terms of a year relative to that epoch. The second was thus defined as "the fraction ​131,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time".[14] This definition was adopted as part of the International System of Units in 1960.

"Atomic" second

But even the best mechanical, electric motorized and quartz crystal-based clocks develop discrepancies, and virtually none are good enough to realize an ephemeris second. Far better for timekeeping is the natural and exact "vibration" in an energized atom. The frequency of vibration (i.e., radiation) is very specific depending on the type of atom and how it is excited. Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K). This length of a second was selected to correspond exactly to the length of the ephemeris second previously defined. Atomic clocks use such a frequency to measure seconds by counting cycles per second at that frequency. Radiation of this kind is one of the most stable and reproducible phenomena of nature. The current generation of atomic clocks is accurate to within one second in a few hundred million years.

Atomic clocks now set the length of a second and the time standard for the world.[16]

SI multiples

SI prefixes are commonly used for times shorter than one second, but rarely for multiples of a second. Instead, certain non-SI units are permitted for use in SI: minutes, hours, days, and in astronomy Julian years.[17]

SI multiples for second (s)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name Human-readable
10−1 s ds decisecond 101 s das decasecond ten seconds
10−2 s cs centisecond 102 s hs hectosecond 1 minute 40 seconds
10−3 s ms millisecond 103 s ks kilosecond 16 minutes 40 seconds
10−6 s µs microsecond 106 s Ms megasecond 11.6 days
10−9 s ns nanosecond 109 s Gs gigasecond 31.7 years
10−12 s ps picosecond 1012 s Ts terasecond 31,700 years
10−15 s fs femtosecond 1015 s Ps petasecond 31.7 million years
10−18 s as attosecond 1018 s Es exasecond 31.7 billion years
10−21 s zs zeptosecond 1021 s Zs zettasecond
10−24 s ys yoctosecond 1024 s Ys yottasecond
Common prefixes are in bold

See also

Notes

  1. ^ Clock time (that is, civil time) is set, directly or indirectly, to Coordinated Universal Time, which includes leap seconds. Other time scales are used in scientific and technical fields which do not contain leap seconds.
  2. ^ Circa 1000, the Persian scholar al-Biruni, writing in Arabic, used the term second, and defined the division of time between new moons of certain specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.[8]
  3. ^ In 1267, the medieval English scientist Roger Bacon, writing in Latin, defined the division of time between full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates.[9]
  4. ^ It may be noted that 60 is the smallest multiple of the first 6 counting numbers. So a clock with 60 divisions would have a mark for thirds, fourths, fifths, sixths and twelfths (the hours); whatever units the clock would likely keep time in, would have marks.

References

  1. ^ "Unit of time (second)". SI Brochure. BIPM. Retrieved December 22, 2013.
  2. ^ Second. Merriam Webster Learner's Dictionary.
  3. ^ "Base unit definitions: Second". physics.nist.gov. Retrieved September 9, 2016.
  4. ^ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009). Time: From Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 207–218.
  5. ^ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009). Time: From Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 16–17, 207.
  6. ^ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009). Time: From Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 68, 232.
  7. ^ Vincent, James. "The most accurate clock ever built only loses one second every 15 billion years". TheVerge.
  8. ^ Al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past". translated by Sachau C. Edward. pp. 147–149.
  9. ^ Bacon, Roger (2000) [1928]. The Opus Majus of Roger Bacon. translated by Robert Belle Burke. University of Pennsylvania Press. table facing page 231. ISBN 978-1-85506-856-8.
  10. ^ a b c Landes, David S. (1983). Revolution in Time. Cambridge, Massachusetts: Harvard University Press. ISBN 0-674-76802-7.
  11. ^ Willsberger, Johann (1975). Clocks & watches. New York: Dial Press. ISBN 0-8037-4475-7. full page color photo: 4th caption page, 3rd photo thereafter (neither pages nor photos are numbered).
  12. ^ Selin, Helaine (July 31, 1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Science & Business Media. p. 934. ISBN 978-0-7923-4066-9.
  13. ^ Jenkin, Henry Charles Fleeming, ed. (1873). Reports of the committee on electrical standards. British Association for the Advancement of Science. p. 90.
  14. ^ a b c "Leap Seconds". Time Service Department, United States Naval Observatory. Retrieved November 22, 2015.
  15. ^ Nautical Almanac Offices of the United Kingdom and the United States of America (1961), Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, p. 9, ... defined ephemeris time ... [was] adopted by the International Astronomical Union in Sept. 1952.
  16. ^ McCarthy, Dennis D.; Seidelmann, P. Kenneth (2009). Time: From Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 231–232.
  17. ^ International Astronomical Union. "Recommendations Concerning Units". Archived from the original on February 16, 2007. Retrieved February 18, 2007. Reprinted from the "IAU Style Manual" by G.A. Wilkinson, Comm. 5, in IAU Transactions XXB (1987).

External links

2018–19 UEFA Champions League

The 2018–19 UEFA Champions League is the 64th season of Europe's premier club football tournament organised by UEFA, and the 27th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.

The final will be played at the Wanda Metropolitano in Madrid, Spain. The winners of the 2018–19 UEFA Champions League will earn the right to play against the winners of the 2018–19 UEFA Europa League in the 2019 UEFA Super Cup. They will also automatically qualify for the 2019–20 UEFA Champions League group stage, and if they have already qualified through their league performance, the berth reserved will be given to the champions of the 2018–19 Austrian Bundesliga, the 11th-ranked association according to next season's access list.For the first time, the video assistant referee (VAR) system was used in the competition from the round of 16 onward.Real Madrid were the defending champions, having won the title for three successive seasons in 2015–16, 2016–17 and 2017–18. However, they were eliminated by Ajax in the round of 16.

Coordinated Universal Time

Coordinated Universal Time (abbreviated to UTC) is the primary time standard by which the world regulates clocks and time. It is within about 1 second of mean solar time at 0° longitude, and is not adjusted for daylight saving time. In some countries where English is spoken, the term Greenwich Mean Time (GMT) is often used as a synonym for UTC and predates UTC by nearly 300 years.The first Coordinated Universal Time was informally adopted on 1 January 1960 and was first officially adopted as CCIR Recommendation 374, Standard-Frequency and Time-Signal Emissions, in 1963, but the official abbreviation of UTC and the official English name of Coordinated Universal Time (along with the French equivalent) were not adopted until 1967.The system has been adjusted several times, including a brief period where time coordination radio signals broadcast both UTC and "Stepped Atomic Time (SAT)" before a new UTC was adopted in 1970 and implemented in 1972. This change also adopted leap seconds to simplify future adjustments. This CCIR Recommendation 460 "stated that (a) carrier frequencies and time intervals should be maintained constant and should correspond to the definition of the SI second; (b) step adjustments, when necessary, should be exactly 1 s to maintain approximate agreement with Universal Time (UT); and (c) standard signals should contain information on the difference between UTC and UT."A number of proposals have been made to replace UTC with a new system that would eliminate leap seconds. A decision whether to remove them altogether has been deferred until 2023.The current version of UTC is defined by International Telecommunications Union Recommendation (ITU-R TF.460-6), Standard-frequency and time-signal emissions, and is based on International Atomic Time (TAI) with leap seconds added at irregular intervals to compensate for the slowing of the Earth's rotation. Leap seconds are inserted as necessary to keep UTC within 0.9 seconds of the UT1 variant of universal time. See the "Current number of leap seconds" section for the number of leap seconds inserted to date.

EFL Championship

The English Football League Championship (often referred to as the Championship for short or the Sky Bet Championship for sponsorship reasons) is the highest division of the English Football League (EFL) and second-highest overall in the English football league system, after the Premier League.

Each season, the two top-finishing teams in the Championship are automatically promoted to the Premier League. The teams that finish the season in 3rd through 6th place enter a playoff tournament, with the winner also gaining promotion to the Premier League. The three lowest-finishing teams in the Championship are relegated to League One.

The Football League Championship, which was introduced for the 2004–05 season, was previously known as the Football League First Division (1992–2004), and before that was known as Division Two (1892–1992). The winners of the Championship receive the Football League Championship trophy, the same trophy as the old First Division champions were handed prior to the Premier League's inception in 1992. Similar to other divisions of professional English football, Welsh clubs can be part of the division, making it a cross-border league.

The Championship is the wealthiest non-top flight football division in the world and the seventh richest division in Europe. With an average match attendance for the 2016–17 season of 20,130 the Championship ranked second after the German 2. Bundesliga as the most-watched secondary league in the world.

Barnsley have spent more seasons at the second level of English football than any other team and on 3 January 2011 became the first club to achieve 1,000 wins in the second level of English football with a 2–1 home victory over Coventry City. Barnsley are also the first club to play 3,000 games in second-level league football (W1028, D747, L1224). At present, Ipswich Town hold the longest tenure in the Championship, last being out of the division in the 2001–02 season when they were relegated from the Premier League.

Elizabeth II

Elizabeth II (Elizabeth Alexandra Mary; born 21 April 1926) is Queen of the United Kingdom and the other Commonwealth realms.Elizabeth was born in London as the first child of the Duke and Duchess of York, later King George VI and Queen Elizabeth, and she was educated privately at home. Her father acceded to the throne on the abdication of his brother King Edward VIII in 1936, from which time she was the heir presumptive. She began to undertake public duties during the Second World War, serving in the Auxiliary Territorial Service. In 1947, she married Prince Philip, Duke of Edinburgh, a former prince of Greece and Denmark, with whom she has four children: Charles, Prince of Wales; Anne, Princess Royal; Prince Andrew, Duke of York; and Prince Edward, Earl of Wessex.

When her father died in February 1952, she became head of the Commonwealth and queen regnant of seven independent Commonwealth countries: the United Kingdom, Canada, Australia, New Zealand, South Africa, Pakistan and Ceylon. She has reigned as a constitutional monarch through major political changes, such as devolution in the United Kingdom, Canadian patriation, and the decolonisation of Africa. Between 1956 and 1992, the number of her realms varied as territories gained independence and realms, including South Africa, Pakistan, and Ceylon (renamed Sri Lanka), became republics. Her many historic visits and meetings include a state visit to the Republic of Ireland and visits to or from five popes. Significant events have included her coronation in 1953 and the celebrations of her Silver, Golden, and Diamond Jubilees in 1977, 2002, and 2012 respectively. In 2017, she became the first British monarch to reach a Sapphire Jubilee. She is the longest-lived and longest-reigning British monarch as well as the world's longest-reigning queen regnant and female head of state, the oldest and longest-reigning current monarch and the longest-serving current head of state.

Elizabeth has occasionally faced republican sentiments and press criticism of the royal family, in particular after the breakdown of her children's marriages, her annus horribilis in 1992 and the death in 1997 of her former daughter-in-law Diana, Princess of Wales. However, support for the monarchy has consistently been and remains high, as does her personal popularity.

German Empire

The German Empire (German: Deutsches Kaiserreich, officially Deutsches Reich), also known as Imperial Germany, was the German nation state that existed from the unification of Germany in 1871 until the abdication of Kaiser Wilhelm II in 1918.

It was founded in 1871 when the south German states, except for Austria, joined the North German Confederation. On 1 January 1871, the new constitution came into force that changed the name of the federal state and introduced the title of emperor for Wilhelm I, King of Prussia from the House of Hohenzollern. Berlin remained its capital, and Otto von Bismarck remained Chancellor, the head of government. As these events occurred, the Prussian-led North German Confederation and its southern German allies were still engaged in the Franco-Prussian War.

The German Empire consisted of 26 states, most of them ruled by royal families. They included four kingdoms, six grand duchies, five duchies (six before 1876), seven principalities, three free Hanseatic cities, and one imperial territory. Although Prussia was one of several kingdoms in the realm, it contained about two thirds of Germany's population and territory. Prussian dominance was also established constitutionally.

After 1850, the states of Germany had rapidly become industrialized, with particular strengths in coal, iron (and later steel), chemicals, and railways. In 1871, Germany had a population of 41 million people; by 1913, this had increased to 68 million. A heavily rural collection of states in 1815, the now united Germany became predominantly urban. During its 47 years of existence, the German Empire was an industrial, technological, and scientific giant, gaining more Nobel Prizes in science than any other country. By 1900, Germany was the largest economy in Europe, surpassing the United Kingdom, as well as the second-largest in the world, behind only the United States.From 1867 to 1878/9, Otto von Bismarck's tenure as the first and to this day longest reigning Chancellor was marked by relative liberalism, but it became more conservative afterwards. Broad reforms and the Kulturkampf marked his period in the office. Late in Bismarck's chancellorship and in spite of his personal opposition, Germany became involved in colonialism. Claiming much of the leftover territory that was yet unclaimed in the Scramble for Africa, it managed to build the third-largest colonial empire after the British and the French ones. As a colonial state, it sometimes clashed with other European powers, especially the British Empire.

Germany became a great power, boasting a rapidly developing rail network, the world's strongest army, and a fast-growing industrial base. In less than a decade, its navy became second only to Britain's Royal Navy. After the removal of Otto von Bismarck by Wilhelm II in 1890, the Empire embarked on Weltpolitik – a bellicose new course that ultimately contributed to the outbreak of World War I. In addition, Bismarck's successors were incapable of maintaining their predecessor's complex, shifting, and overlapping alliances which had kept Germany from being diplomatically isolated. This period was marked by various factors influencing the Emperor's decisions, which were often perceived as contradictory or unpredictable by the public. In 1879, the German Empire consolidated the Dual Alliance with Austria-Hungary, followed by the Triple Alliance with Italy in 1882. It also retained strong diplomatic ties to the Ottoman Empire. When the great crisis of 1914 arrived, Italy left the alliance and the Ottoman Empire formally allied with Germany.

In the First World War, German plans to capture Paris quickly in the autumn of 1914 failed. The war on the Western Front became a stalemate. The Allied naval blockade caused severe shortages of food. However, Imperial Germany had success on the Eastern Front; it occupied a large amount of territory to its east following the Treaty of Brest-Litovsk. The German declaration of unrestricted submarine warfare in early 1917, contributed to bringing the United States into the war.

The high command under Paul von Hindenburg and Erich Ludendorff increasingly controlled the country, but in October after the failed offensive in spring 1918, the German armies were in retreat, allies Austria-Hungary and the Ottoman Empire had collapsed, and Bulgaria had surrendered. The Empire collapsed in the November 1918 Revolution with the abdications of its monarchs. This left a postwar federal republic and a devastated and unsatisfied populace, which later led to the rise of Adolf Hitler and Nazism.

Minute and second of arc

A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn (or complete rotation), one minute of arc is 1/21600 of a turn – it is for this reason that the Earth's circumference is almost exactly 21,600 nautical miles. A minute of arc is π/10800 of a radian.

A second of arc, arcsecond (arcsec), or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 (about 1/206265) of a radian. These units originated in Babylonian astronomy as sexagesimal subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship.

To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astronomy.

The number of square arcminutes in a complete sphere is 148510660 square arcminutes (the surface area of a unit sphere in square units divided by the solid angle area subtended by a square arcminute, also in square units – so that the final result is a dimensionless number).

The names "minute" and "second" have nothing to do with the identically named units of time "minute" or "second". The identical names reflect the ancient Babylonian number system, based on the number 60.

Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:

The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

A fourth law is often also described in the bibliography, which states that forces add up like vectors, that is, that forces obey the principle of superposition.

Second Boer War

The Second Boer War (11 October 1899 – 31 May 1902) was fought between the British Empire and two Boer states, the South African Republic (Republic of Transvaal) and the Orange Free State, over the Empire's influence in South Africa. It is also known variously as the Boer War, Anglo-Boer War, or South African War. Initial Boer attacks were successful, and although British reinforcements later reversed these, the war continued for years with Boer guerrilla warfare, until harsh British counter-measures brought them to terms.

The war started with the British overconfident and under-prepared. The Boers were well armed and struck first, besieging Ladysmith, Kimberley, and Mahikeng in early 1900, and winning important battles at Colenso, Magersfontein and Stormberg. Staggered, the British brought in large numbers of soldiers and fought back. General Redvers Buller was replaced by Lord Roberts and Lord Kitchener. They relieved the three besieged cities, and invaded the two Boer republics in late 1900. The onward marches of the British Army, well over 400,000 men, were so overwhelming that the Boers did not fight staged battles in defense of their homeland.

The British seized control of all of the Orange Free State and Transvaal, as the civilian leadership went into hiding or exile. In conventional terms, the war was over. The British officially annexed the two countries in 1900. Back home, Britain's Conservative government wanted to capitalize on this success and use it to maneuver an early general election, dubbed a "khaki election" to give the government another six years of power in London. British military efforts were aided by Cape Colony, the Colony of Natal and some native African allies, and further supported by volunteers from the British Empire, including Southern Africa, the Australian colonies, Canada, India and New Zealand. All other nations were neutral, but public opinion was largely hostile to the British. Inside the UK and its Empire there also was significant opposition to the Second Boer War.

The Boers refused to surrender. They reverted to guerrilla warfare under new generals Louis Botha, Jan Smuts, Christiaan de Wet and Koos de la Rey. Two years of surprise attacks and quick escapes followed. As guerrillas without uniforms, the Boer fighters easily blended into the farmlands, which provided hiding places, supplies, and horses.

The UK's response to guerilla warfare was to set up complex nets of block houses, strong points, and barbed wire fences, partitioning off the entire conquered territory. In addition, civilian farms and live stock were destroyed in the scorched earth strategy. Survivors were forced into concentration camps. Very large proportions of these civilians died of hunger and disease, especially the children.

British mounted infantry units systematically tracked down the highly mobile Boer guerrilla units. The battles at this stage were small operations. Few died during combat, though many of disease. The war ended in surrender and British terms with the Treaty of Vereeniging in May 1902. Both former republics were incorporated into the Union of South Africa in 1910, as part of the British Empire.

Second Sino-Japanese War

The Second Sino-Japanese War was a military conflict fought primarily between the Republic of China and the Empire of Japan from July 7, 1937, to September 2, 1945. It began with the Marco Polo Bridge Incident in 1937 in which a dispute between Japanese and Chinese troops escalated into a battle. Some sources in the modern People's Republic of China date the beginning of the war to the Japanese invasion of Manchuria in 1931.China fought Japan with aid from the Soviet Union and the United States. After the Japanese attack on Pearl Harbor in 1941, the war merged with other conflicts of World War II as a major sector known as the China Burma India Theater. Some scholars consider the start of the full-scale Second Sino-Japanese War in 1937 to have been the beginning of World War II. The Second Sino-Japanese War was the largest Asian war in the 20th century. It accounted for the majority of civilian and military casualties in the Pacific War, with between 10 and 25 million Chinese civilians and over 4 million Chinese and Japanese military personnel dying from war-related violence, famine, and other causes.

The war was the result of a decades-long Japanese imperialist policy to expand its influence politically and militarily in order to secure access to raw material reserves, food, and labor. The period after World War I brought about increasing stress on the Japanese polity. Leftists sought universal suffrage and greater rights for workers. Increasing textile production from Chinese mills was adversely affecting Japanese production. The Great Depression brought about a large slowdown in exports. All of this contributed to militant nationalism, culminating in the rise to power of a militarist fascist faction. This faction was led at its height by the Hideki Tojo cabinet of the Imperial Rule Assistance Association under edict from Emperor Hirohito. In 1931, the Mukden Incident helped spark the Japanese invasion of Manchuria. The Chinese were defeated and Japan created a new puppet state, Manchukuo; many historians cite 1931 as the beginning of the war. This view has been adopted by the PRC government. From 1931 to 1937, China and Japan continued to skirmish in small, localized engagements, so-called "incidents".

Initially the Japanese scored major victories, capturing both Shanghai and the Chinese capital of Nanjing in 1937. After failing to stop the Japanese in the Battle of Wuhan, the Chinese central government was relocated to Chongqing (Chungking) in the Chinese interior. By 1939, after Chinese victories in Changsha and Guangxi, and with Japan's lines of communications stretched deep into the Chinese interior, the war reached a stalemate. The Japanese were also unable to defeat the Chinese communist forces in Shaanxi, which waged a campaign of sabotage and guerrilla warfare against the invaders. While Japan ruled the large cities, they lacked sufficient manpower to control China's vast countryside. During this time, Chinese communist forces launched a counter offensive in Central China while Chinese nationalist forces launched a large scale winter offensive.

On December 7, 1941, the Japanese attacked Pearl Harbor, and the following day the United States declared war on Japan. The United States began to aid China by airlifting material over the Himalayas after the Allied defeat in Burma that closed the Burma Road. In 1944 Japan launched the invasion, Operation Ichi-Go, that conquered Henan and Changsha. However, this failed to bring about the surrender of Chinese forces. In 1945, the Chinese Expeditionary Force resumed its advance in Burma and completed the Ledo Road linking India to China. At the same time, China launched large counteroffensives in South China and retook West Hunan and Guangxi.

Despite continuing to occupy part of China's territory, Japan eventually surrendered on September 2, 1945, to Allied forces following the atomic bombings of Hiroshima and Nagasaki and the Soviet invasion of Japanese-held Manchuria. The remaining Japanese occupation forces (excluding Manchuria) formally surrendered on September 9, 1945, with the following International Military Tribunal for the Far East convened on April 29, 1946. At the outcome of the Cairo Conference of November 22–26, 1943, the Allies of World War II decided to restrain and punish the aggression of Japan by restoring all the territories that Japan annexed from China, including Manchuria, Taiwan/Formosa, and the Pescadores, to China, and to expel Japan from the Korean Peninsula. China was recognized as one of the Big Four of the Allies during the war and became one of the five permanent members of the United Nations Security Council.

Speed of light

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second (approximately 300,000 km/s (186,000 mi/s)). It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most commonly associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum (including electromagnetic radiation and gravitational waves). Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of electromagnetic waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s (124,000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 299,700 km/s (186,220 mi/s), which is about 90 km/s (56 mi/s) slower than c.

For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip. The speed of light can be used with time of flight measurements to measure large distances to high precision.

Ole Rømer first demonstrated in 1676 that light travels at a finite speed (as opposed to instantaneously) by studying the apparent motion of Jupiter's moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism. In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism.

After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s (983571056 ft/s; 186282.397 mi/s) with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units (SI) as the distance travelled by light in vacuum in 1/299792458 of a second.

Virginia Cavaliers men's basketball

The Virginia Cavaliers men's basketball program represents the University of Virginia in the Atlantic Coast Conference in Division I of the NCAA. The team is coached by Tony Bennett. Since 2006 the team has played at John Paul Jones Arena, an on-campus arena on the North Grounds of the university, in front of 14,593.

A consistent winner in the early years of college basketball under the tutelage of Pop Lannigan (254–95 from 1905 to 1929), the Cavalier program lay mostly dormant between 1930 and 1975 before Terry Holland arrived to win their first ACC Championship and earn their first NCAA Tournament appearance in his second year. UVA has since finished first in the ACC basketball standings nine times, third best all-time. They have won the ACC Tournament three times.

Virginia won the 2019 NCAA Tournament Championship, has been to the Final Four of the NCAA Tournament three times, and won the last third-place game ever played at the event. The Cavaliers have been in the Top 5 of the AP Poll a total of 96 weeks in the past four decades, ranking the program 9th since 1980. Never making the Top 5 from the first poll in 1949 until 1981, the program still ranks 16th all-time by this measure.

Watt

The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by .

World War II

World War II (often abbreviated to WWII or WW2), also known as the Second World War, was a global war that lasted from 1939 to 1945. The vast majority of the world's countries—including all the great powers—eventually formed two opposing military alliances: the Allies and the Axis. A state of total war emerged, directly involving more than 100 million people from over 30 countries. The major participants threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. World War II was the deadliest conflict in human history, marked by 50 to 85 million fatalities, most of whom were civilians in the Soviet Union and China. It included massacres, the genocide of the Holocaust, strategic bombing, premeditated death from starvation and disease, and the only use of nuclear weapons in war.Japan, which aimed to dominate Asia and the Pacific, was at war with China by 1937, though neither side had declared war on the other. World War II is generally said to have begun on 1 September 1939, with the invasion of Poland by Germany and subsequent declarations of war on Germany by France and the United Kingdom. From late 1939 to early 1941, in a series of campaigns and treaties, Germany conquered or controlled much of continental Europe, and formed the Axis alliance with Italy and Japan. Under the Molotov–Ribbentrop Pact of August 1939, Germany and the Soviet Union partitioned and annexed territories of their European neighbours, Poland, Finland, Romania and the Baltic states. Following the onset of campaigns in North Africa and East Africa, and the fall of France in mid 1940, the war continued primarily between the European Axis powers and the British Empire. War in the Balkans, the aerial Battle of Britain, the Blitz, and the long Battle of the Atlantic followed. On 22 June 1941, the European Axis powers launched an invasion of the Soviet Union, opening the largest land theatre of war in history. This Eastern Front trapped the Axis, most crucially the German Wehrmacht, into a war of attrition. In December 1941, Japan launched a surprise attack on the United States as well as European colonies in the Pacific. Following an immediate U.S. declaration of war against Japan, supported by one from Great Britain, the European Axis powers quickly declared war on the U.S. in solidarity with their Japanese ally. Rapid Japanese conquests over much of the Western Pacific ensued, perceived by many in Asia as liberation from Western dominance and resulting in the support of several armies from defeated territories.

The Axis advance in the Pacific halted in 1942 when Japan lost the critical Battle of Midway; later, Germany and Italy were defeated in North Africa and then, decisively, at Stalingrad in the Soviet Union. Key setbacks in 1943, which included a series of German defeats on the Eastern Front, the Allied invasions of Sicily and Italy, and Allied victories in the Pacific, cost the Axis its initiative and forced it into strategic retreat on all fronts. In 1944, the Western Allies invaded German-occupied France, while the Soviet Union regained its territorial losses and turned toward Germany and its allies. During 1944 and 1945 the Japanese suffered major reverses in mainland Asia in Central China, South China and Burma, while the Allies crippled the Japanese Navy and captured key Western Pacific islands.

The war in Europe concluded with an invasion of Germany by the Western Allies and the Soviet Union, culminating in the capture of Berlin by Soviet troops, the suicide of Adolf Hitler and the German unconditional surrender on 8 May 1945. Following the Potsdam Declaration by the Allies on 26 July 1945 and the refusal of Japan to surrender under its terms, the United States dropped atomic bombs on the Japanese cities of Hiroshima and Nagasaki on 6 and 9 August respectively. With an invasion of the Japanese archipelago imminent, the possibility of additional atomic bombings, the Soviet entry into the war against Japan and its invasion of Manchuria, Japan announced its intention to surrender on 15 August 1945, cementing total victory in Asia for the Allies. Tribunals were set up by fiat by the Allies and war crimes trials were conducted in the wake of the war both against the Germans and the Japanese.

World War II changed the political alignment and social structure of the globe. The United Nations (UN) was established to foster international co-operation and prevent future conflicts; the victorious great powers—China, France, the Soviet Union, the United Kingdom, and the United States—became the permanent members of its Security Council. The Soviet Union and United States emerged as rival superpowers, setting the stage for the nearly half-century long Cold War. In the wake of European devastation, the influence of its great powers waned, triggering the decolonisation of Africa and Asia. Most countries whose industries had been damaged moved towards economic recovery and expansion. Political integration, especially in Europe, emerged as an effort to end pre-war enmities and create a common identity.

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