Crime mapping is used by analysts in law enforcement agencies to map, visualize, and analyze crime incident patterns.  It is a key component of crime analysis and the CompStat policing strategy.  Mapping crime, using Geographic Information Systems (GIS), allows crime analysts to identify crime hot spots, along with other trends and patterns.

Overview
Using GIS, crime analysts can overlay other datasets such as census demographics, locations of pawn shops, schools, etc., to better understand the underlying causes of crime and help law enforcement administrators to devise strategies to deal with the problem.  GIS is also useful for law enforcement operations, such as allocating police officers and dispatching to emergencies.

Underlying theories that help explain spatial behavior of criminals include environmental criminology, which was devised in the 1980s by Patricia and Paul Brantingham, routine activity theory, developed by Lawrence Cohen and Marcus Felson and originally published in 1979, and rational choice theory, developed by Ronald V. Clarke and Derek Cornish, originally published in 1986.  In recent years, crime mapping and analysis has incorporated spatial data analysis techniques that add statistical rigor and address inherent limitations of spatial data, including spatial autocorrelation and spatial heterogeneity.  Spatial data analysis helps one analyze crime data and better understand why and not just where crime is occurring.

Research into computer-based crime mapping started in 1986, when the National Institute of Justice (NIJ) funded a project in the Chicago Police Department to explore crime mapping as an adjunct to community policing. That project was carried out by the CPD in conjunction with the Chicago Alliance for Neighborhood Safety, the University of Illinois at Chicago, and Northwestern University, reported on in the book, Mapping Crime in Its Community Setting: Event Geography Analysis.  The success of this project prompted NIJ to initiate the Drug Market Analysis Program (with the appropriate acronym D-MAP) in five cities, and the techniques these efforts developed led to the spread of crime mapping throughout the US and elsewhere, including the New York City Police Department's CompStat.

Applications
Crime analysts use crime mapping and analysis to help law enforcement management (e.g. the police chief) to make better decisions, target resources, and formulate strategies, as well as for tactical analysis (e.g. crime forecasting, geographic profiling).  New York City does this through the CompStat approach, though that way of thinking deals more with the short term.  There are other, related approaches with terms including Information-led policing, Intelligence-led policing, Problem-oriented policing, and Community policing.  In some law enforcement agencies, crime analysts work in civilian positions, while in other agencies, crime analysts are sworn officers.

From a research and policy perspective, crime mapping is used to understand patterns of incarceration and recidivism, help target resources and programs, evaluate crime prevention or crime reduction programs (e.g. Project Safe Neighborhoods, Weed & Seed and as proposed in Fixing Broken Windows), and further understanding of causes of crime.

The boom of internet technologies, particularly web-based geographic information system (GIS) technologies, is opening new opportunities for use of crime mapping to support crime prevention. Research indicates that the functions provided in web-based crime mapping are less than in most traditional crime mapping software. In conclusion, existing works of web-based crime mapping focus on supporting community policing rather than analytical functions such as pattern analysis and prediction.

See also
 Crime analysis
 Geographic profiling

Programs and projects
 CrimeView
 Criminal Reduction Utilising Statistical History
 CrimeAnalyst
 RAIDS Online
 RiskAhead
 ATACRAIDS

Individuals
 André-Michel Guerry
 Michael Maltz

Public access
 RAIDS Online
 SpotCrime.com
 Trulia, US real estate site with crime mapping
 YourMapper, open data crime mapping
 CitySafe, crime mapping for travelers & tourists

General
 Public Participation GIS

References

Further reading

Applications of geographic information systems
Criminology
Human geography
Law enforcement techniques
Crime statistics
Map types

Crime mapping


The Ashes is the symbol of international cricket  matches played between England and Australia. The Ashes were supposedly what remained of English cricket after the Australians had beaten them in the first test match played in England.

The name comes from a small pot (known as an "urn") of ashes, which was made and presented to the England captain in 1882. It was based on a joke printed in The Sporting Times, an English newspaper. Someone placed an advertisement in the pages of the paper, describing how English cricket had died and its body had been cremated.

Related pages
 Soccer Ashes
 The Women's Ashes

Cricket

The Ashes


Tuesday is the day of the week between Monday and Wednesday. In some countries, for example the United States of America, Tuesday is the third day of the week. In other parts of the world, Tuesday is the second day of the week.

History of the name
The name Tuesday comes from a Middle English word, Tiwesday. This word came from the Old English word Tiwes dæg. This was named after the Nordic god Tyr. Tyr was the God of War, like the Roman war god Mars, and Greek god Ares.

In Latin, Tuesday is called Martis dies which means "Mars's Day". In French, Spanish, Italian and Romanian, the (Romance languages), the word for "Tuesday" is nearly the same as the Latin name. Tuesday is mardi in French, martes in Spanish, martedì in Italian, dimarts in Catalan, and marţi in Romanian.

The Celtic languages still spoken use the Latin names, even though none of these languages came from Latin. Tuesday is dé máirt in Irish, Meurzh in Breton, dydd Mawrth in Welsh and Dimàirt in Scottish Gaelic.

The English and Scandinavian names for Tuesday come from the Nordic god Tyr (Old English Tiw):

 Old Frisian: tîesdei
 Modern West Frisian: tiisdei
 Old English: tíwesdæg
 Anglo-Norman:
 Middle English: tíesdæi, tywesdai, twysday
 Early Modern English: towesday, Twesdaie, Tyisday, Tiseday,
 Modern English: Tuesday
 Old High German: zîestag
 Middle High German: zîstag
 Alemannic German: ziischtig
 Old Norse: týrsdagr
 Swedish: Tisdag
 Danish: Tirsdag
 Norwegian: Tirsdag or Tysdag
 Icelandic: Týsdagur

References

02

Tuesday


Chakib Benmoussa () (born 1958, Fes) is a Moroccan diplomat and politician. He previously served as the interior minister of Morocco and has been the lead negotiator for the Moroccan side in the Western Sahara conflict. Since December 2012, he is serving as the Moroccan ambassador to France. On October 7,2021 he was appointed as the education and sports minister.

Education
Benmoussa was born in Fes. He graduated from École Polytechnique of Paris, one of the most selective engineering schools in France, in 1979 and from École Nationale des Ponts et Chaussées in Paris in 1981 and a holder of Master of Science from Massachusetts Institute of Technology (MIT).

Career
Between 1989 and 1995 he worked as an executive at the Ministry of Equipment and Transportation, then as the secretary general of the prime minister (1995–98) and president of SONASID (1998-2000), a state-owned steel company based in Nador. In 2000, he became a member of the executive board of ONA Group, where Morocco's royal family is one of the main shareholders, and CEO of Brasseries du Maroc. He joined the Ministry of the Interior in 2002.

Interior Minister and crackdown on terrorism
The Moroccan Interior Ministry arrested 56 suspected terrorists in six cities on August 7, 2006. The suspects, believed to be members of the Jammaat Ansar El Mehdi terrorist organization, include soldiers, and wives of two pilots for Royal Air Maroc, the Moroccan state airline. Explosives, laboratory materials and propaganda leaflets were seized by police. In 2003 suicide bombings killed 45 people in Casablanca. Human rights activists accuse the Moroccan government of detaining innocent people and using torture. Commenting on the arrests on September 1, Minister Benmoussa said in a statement, "The members of this group were planning terrorist attacks targeting tourist sites, strategic government facilities and foreign holdings, and assassinations of prominent figures for political or moral reasons."

Mohammed Darif, a University of Mohammedia professor who studies Islamic terrorism, said the women's role was probably financing the terror cell.

He was, in a January 2010 cabinet reshuffle, succeeded as Interior Minister by Taib Cherkaoui.

Other roles
In December 2019, he was appointed by the King of Morocco as the President of the Commission in charge of elaborating the New Model of Development of Morocco.

References

1958 births
People from Fez, Morocco
Massachusetts Institute of Technology alumni
Living people
Government ministers of Morocco
Moroccan chief executives
Ambassadors of Morocco
Ambassadors of Morocco to France

Chakib Benmoussa


Peripheral Component Interconnect Express (PCI Express), officially abbreviated as PCIe or PCI-e, is a high-speed serial computer expansion bus standard, designed to replace the older PCI, PCI-X and AGP bus standards. It is the common motherboard interface for personal computers' graphics cards, hard disk drive host adapters, SSDs, Wi-Fi and Ethernet hardware connections.

Computer hardware

PCI Express


Raymond Gunn (January 11, 1904 – January 12, 1931) was a black man killed by a mob in Maryville, Missouri, United States, after being accused of killing a white woman.

The case received massive national publicity because it occurred outside the Southern "lynch belt," because of its brazen and planned nature, and because the county sheriff did not activate the Missouri National Guard troops that had been specifically deployed to prevent the lynching.

The case was frequently invoked in the unsuccessful attempt to pass the Wagner-Costigan Act during the presidency of Franklin Roosevelt, which would have made it a federal crime for law enforcement officials to refuse to try to prevent a lynching.

Early life
Raymond Gunn was the oldest of the eight children of Michael and Maymie Gunn, a farming family in Maryville. In the 1920 census, the family is described as mulatto. In the 1930 census, Raymond Gunn is described as laborer and widower.

In September 1925, Gunn was convicted of the attempted rape of a student at what is now Northwest Missouri State University, after accosting the young woman on a rural lane outside of Maryville. The student claimed that Gunn stuck his thumbs into her mouth to keep her from screaming. Gunn never confessed to the crime, and he claimed to have been beaten while in custody. He was released on January 28, 1928.

Following his release, Gunn married a local woman and moved with her to Omaha. However, his wife died of pneumonia, and he returned to Maryville, where he made a living as a hunter.

Murder of Velma Colter
On December 16, 1930, a 20-year-old teacher, Velma Colter, daughter of a local farmer, was murdered in the one-room Garrett schoolhouse, () a mile southwest of Maryville. When she failed to return home, her parents went to the school. They found her partly undressed body in a pool of blood inside the school; a bloody footprint left by her killer was on the floor.

Because of his earlier conviction, Raymond Gunn was immediately suspected. A farmer reported he had seen a black man near the school. The sheriff arrested several black men matching the description, before he found Gunn on December 18. Gunn had blood stains on his shirt (he claimed it was rabbit blood), and his footprint matched the one at the crime scene. Moreover, Gunn had a severe bite mark on his thumb, recalling the student's description of the 1925 rape attempt.

Gunn finally confessed, saying he had entered the school with a hedge club after seeing the teacher outside with a coal bucket. She resisted his assault, biting his thumb, so he hit her with the club. She struck him with the coal bucket, and he hit her again and again, killing her. He then stabbed her.

Lynch mob atmosphere
Anger and talk of a lynching began immediately after Gunn was taken into custody, and crowds began to assemble in Maryville. Gunn was transferred for safety to the Buchanan County, Missouri jail, 45 miles south in St. Joseph, Missouri. Crowds formed there as well, and the sheriff ordered a truck mounted with a machine gun to be backed to the door. The gunner appeared to aim the weapon at the crowd, though he said he was just oiling it, which caused the crowd to disperse.

Gunn was transferred a second time, 100 miles south of Maryville to Kansas City, Missouri. On December 26, at 3:30 a.m., Gunn returned to Maryville for arraignment, and then immediately taken back to Kansas City.

Velma Colter's mother was quoted as saying she could not bear a trial and would not testify. Her oldest son, Floyd Colter, had been killed in France during World War I.

The lynching
Gunn's court date was set for January 12. The Nodaway County prosecuting attorney insisted Gunn would get a fair trial and appealed (along with Maryville business leaders) to Missouri's governor, Henry S. Caulfield, to deploy the National Guard to prevent an anticipated lynching attempt.  Caulfield complied and 60 guardsmen were ordered at 7:30 a.m. to stand by at the National Guard a block north of the courthouse (today's Maryville Public Library). However, by law, the National Guard could only be deployed at the written request of the sheriff, which was never made.  Sheriff Harvey England later claimed he did not call up the guardsmen because he did not want them injured.

By this point a large crowd occupied the Maryville square, between the jail block to the northeast and the Nodaway County, Missouri courthouse. The sheriff was transporting Gunn by car, and he drove directly into the mob. When he opened the door, the sheriff was pulled aside and Gunn was dragged out of the car. Witnesses later said the mob leader told the sheriff, "Either you move out of the way or die with this man, either way he's going to die today."

Gunn was marched south down Main Street through the Maryville streets, avoiding the National Guard. After an hour and a half, Gunn and the crowd reached at the Garrett schoolhouse. Gunn's ears and nose were bleeding from being beaten on the way. The schoolhouse was emptied and all furniture placed on the lawn. The mob was estimated to have grown to between 2,000 and 4,000. Gunn was taken inside the schoolhouse, where he is reported to have confessed his guilt again, claiming he had an accomplice named "Shike" Smith.

Gunn was moved to the roof and tied to a ridge pole. Gunn and the building were then doused with gasoline. The mob leader, identified only as the "man in a red coat", threw a lighted piece of paper into the building. Gunn screamed but once and appeared lifeless in 11 minutes.

A reporter for the St. Joseph Gazette gave the following gruesome description:

He twisted and revealed a huge blister ballooning on his left upper arm. Pieces of his skin blew away to the wind as the blistering heat became more intense and soon his torso was splotched with white patches of exposed flesh. His hair burned like a torch for moment then his head sagged. His body writhed. It took the appearance of a mummy.

The building's roof collapsed within 16 minutes. Burnt fragments of the schoolhouse were taken by the crowd as souvenirs.

Aftermath
No charges were ever filed in the lynching. Attempts to identify the "man in the red coat" have been answered by the claim he was an outsider. However, newspapers said all the others were local.

Gunn's lynching was universally condemned by newspapers across the United States. The Atlanta Constitution published an editorial cartoon with the caption of "The Torch of Civilization in Missouri."

After the brutal incident, Maryville residents heard rumors that African Americans from Kansas City were coming to attack the city in retaliation. Townsmen reportedly set up machine gun nests on Main Street. The Gunn family's home was also burned.

The 1930 census showed 90 African Americans living in Maryville, with 35 enrolled in the town's school. By 1931, the number of African Americans had dropped to six, and eventually almost all left the town in fear.

Franklin Roosevelt campaigned in 1932, saying he was going to take steps to stop all lynchings. Ironically, he did not back the proposed Wagner-Costigan Act, though he did add a Civil Rights Section to the Justice Department.

References

External links
Northwest Missouri State University resources on the case
The Tragedy of Lynching by Arthur F. Raper
Time Magazine, 1931 article

1931 deaths
1931 murders in the United States
American people convicted of murder
American rapists
People murdered in Missouri
Lynching deaths in Missouri
Racially motivated violence against African Americans
Murdered African-American people
People from Maryville, Missouri
January 1931 events
African-American history of Missouri
African-American history between emancipation and the civil rights movement
1931 in Missouri
Prisoners murdered in custody
Anti-black racism in Missouri
Nodaway County, Missouri
Crimes in Missouri

Lynching of Raymond Gunn


Concord Hymn est un poème de Ralph Waldo Emerson écrit en 1837 pour un monument de Concord, un obélisque commémorant la bataille de Concord en 1775 au début de la Révolution américaine.

Poème
By the rude bridge that arched the flood,
Their flag to April's breeze unfurled,
Here once the embattled farmers stood,
And fired the shot heard round the world.

The foe long since in silence slept;
Alike the conqueror silent sleeps;
And Time the ruined bridge has swept
Down the dark stream which seaward creeps.

On this green bank, by this soft stream,
We set to-day a votive stone;
That memory may their deed redeem,
When, like our sires, our sons are gone.

Spirit, that made those heroes dare
To die, and leave their children free,
Bid Time and Nature gently spare
The shaft we raise to them and thee.

Poème américain
Poésie du XIXe siècle
Chanson de 1837

Concord Hymn


The siege of Trichinopoly (1751–1752) was conducted by Chanda Sahib, who had been recognized as the Nawab of the Carnatic by representatives of the French East India Company, against the fortress town of Trichinopoly, held by Muhammed Ali Khan Wallajah.

Background

Following the Battle of Ambur in 1749, in which Muhammed's father Anwaruddin Muhammed Khan was slain, Muhammed fled to Trichinopoly.  Chanda, assisted by Joseph François Dupleix, had planned to besiege Muhammed there in 1749, but the need for funding and provisions led him to instead besiege Tanjore first, and movements of Chanda's Maratha enemies prompted him to lift that siege and move north to face the new threat.  Muhammed had in the meantime opened separate negotiations with both the French and British for support.  In response to these, the British sent several hundred Europeans to Trichinopoly.

Siege
In March 1751 Chanda again began moving south from the Carnatic capital of Arcot, again with French support.  The size of his force prompted the British at Madras to send additional troops toward Trichinopoly to intercept Chanda.  After a brief encounter near Valikondapuram in July, the outnumbered British retreated to Trichinopoly.  Chanda followed with his main army, and began besieging the fortress town.  Siege operations were principally conducted by the French contingent, first under D'Auteuil, and the later under Law.

In an attempt to relieve the siege, the British in Madras sent Captain Robert Clive with a small force to occupy Arcot, which Chanda had left inadequately defended.  Chanda detached 4,000 of his siege force in an attempt to recover Arcot; this attempt famously failed, propelling Clive into a more prominent role in India.

The siege was eventually lifted, and the tables turned, in April 1752 with the arrival of British reinforcements led by Stringer Lawrence and including Clive.  On 9 April Lawrence made a junction with troops sent out of Trichinopoly and made it inside the lines.  Two days later he led a sortie against the besiegers, prompting Law to lift the siege and retreat to the isle of Srirangam.

Aftermath
The British then seized the opportunity to act against an indecisive opponent, and besieged and the French on the island.  Chanda eventually negotiated a surrender to Tanjorean forces that had arrived to assist the British, believing this to be preferable to surrendering to the British.  The Tanjoreans violated their promises to assist in his escape and beheaded him on 14 June.  Law surrendered the French troops on the same day.

See also
 Fort St George
 Fort St David
 Tiruchirappalli Fort

References

Dodwell, Henry. Clive and Dupleix
Mehta, J. L. Advanced study in the history of modern India 1707-1813

Battles of the Second Carnatic War
French East India Company
Battles involving the French East India Company
Sieges involving the Indian kingdoms
Siege of Trichinopoly (1751-52)
Siege of Trichinopoly (1751-52)
Siege of Trichinopoly (1751-52)
1751 in India
1752 in India
Sieges involving the British East India Company
History of Tiruchirappalli

Siege of Trichinopoly (1751–1752)


Civilization III or Civ 3 is a turn based strategy computer game by Firaxis Games from 2001. It is the third part of the successful serial. The game become two expansion sets, Play the World and Conquests. In the game you control a nation from the stone age too the modern age. Civilization III has many new innovations in contrast with Civilization II. There are strategic resources, country borders and the military units will support by the nation, not by the cities.

Related pages
Civilization (series)
Civilization IV

Other websites
 official page

Civilization series
2001 video games

Civilization III


William Frederick Dahlen (January 5, 1870 – December 5, 1950), nicknamed "Bad Bill" for his ferocious temperament, was an American shortstop and manager in Major League Baseball who played for four National League teams from  to . After twice batting over .350 for the Chicago Colts, he starred on championship teams with the Brooklyn Superbas and the New York Giants.

At the end of his career, he held the major league record for career games played (2,443); he ranked second in walks (1,064, behind Billy Hamilton's 1,187) and fifth in at bats (9,033), and was among the top ten in runs batted in (1,234), doubles (414) and extra base hits (661). He was also among the NL's top seven players in hits (2,461; some sources list totals up to 2,471), runs (1,589), triples (163) and total bases (3,447). After leading the league in assists four times and double plays three times, he set major league records for career games (2,132), putouts (4,850), assists (7,500), total chances (13,325) and double plays (881) as a shortstop; he still holds the record for total chances, and is second in putouts and fourth in assists. His 42-game hitting streak in  was a record until , and remains the fourth longest in history and the longest by a right-handed NL hitter. In Defensive Wins above replacement (WAR), his 28.5 is eleventh best all-time, and he finished in the top five in the category in ten different seasons.

Early life

Dahlen was born in Nelliston, New York at the corner of Berthoud and Dahlen and East Main to a family of German descent. He attended Fort Plain High School and the Clinton Liberal Institute, where he began an amateur baseball career as a pitcher and second baseman. He played semi-professionally in 1889, and professionally in the New York State League in 1890.

Dahlen married his wife, Hattie, on January, 1, 1890, and the couple had a daughter, Corinne, the next year.

Professional career

Playing career
Dahlen was a very good hitter and had a good amount of power for the dead-ball era. He began his career with the Colts in , and during his eight years with the team finished among the NL's top ten players in home runs four times and in slugging average three times. He also scored over 100 runs with 10 or more triples in each of his first six seasons; in 1894 he posted the highest batting average to that time by a major league shortstop (various sources state .357 or .362), and he followed with a .352 average in . His 1894 season included a record 42-game hitting streak from June 20 to August 6, surpassing the 33-game streak by George Davis one year earlier. Amazingly, after going 0-for-6 in the next game, a 10-inning contest on August 7, Dahlen pulled off another 28-game streak, ending up having hit in 70 of 71 games. His mark was broken three years later by Willie Keeler, who hit in 44 straight; that NL record was eventually tied by Pete Rose. Only Joe DiMaggio, with his 56-game streak in , has bettered Dahlen's mark among right-handed batters. Dahlen also twice hit three triples in a game, and once he tripled twice in one inning (August 30, 1900).

Prior to the 1899 season, Dahlen was traded by Chicago, and ended up in Brooklyn after another deal. His new team won the NL title in each of his first two seasons, and although his batting average had dropped from that of earlier years, he compensated by continuing to accumulate numerous walks and stolen bases and by playing outstanding defense. In 1902, he finished fourth in the NL with 74 RBI. In  he set an NL record for fielding percentage with a .948 average, breaking George Wright's 1878 mark of .947; Tommy Corcoran broke his record in  with a .952 average.

After the 1903 season, Dahlen was traded to the Giants, the team he'd always strived to play for, in exchange for pitcher Jack Cronin and Charlie Babb. While Cronin and Babb contributed only three bad years to Brooklyn, Dahlen posted great numbers with the Giants, leading the league with 80 RBI in his first year, . In 1905 he was again among the RBI leaders, despite hitting only .242, as the Giants won their first World Series title. Although he was hitless in the five-game Series, he contributed with flawless defense and by drawing three walks and stealing three bases. He was often considered one of the quietest players in the game, keeping to himself most of the time. After the 1907 season, he was traded to the Boston Doves, for whom he played his last two full seasons. In  he broke Jake Beckley's record of 2,386 career games; his record was broken in turn by Honus Wagner in . He was named Brooklyn's manager for the 1910 season, but never finished above 6th place in four seasons. His last playing appearances were three games as a pinch-hitter in 1910, and one game at shortstop in .

In a 21-season career, Dahlen batted .272; his 84 home runs were then among the fifteen highest totals in history, and ranked behind only Herman Long (91) among shortstops. His 289 stolen bases after the statistic was redefined in 1898 were then among the ten highest totals, as were his 547 total steals since they were first recorded in 1887. His records for games and putouts at shortstop were broken by Rabbit Maranville, and his mark for assists was surpassed by Luis Aparicio, with his NL record standing until Ozzie Smith broke it in ; his record for double plays was broken by Roger Peckinpaugh. Dahlen's 14,566 total chances at all positions have been surpassed by only Maranville (16,091) and Wagner (15,536).

Managerial career
As early as 1908, Brooklyn owner Charles Ebbets sought to have Dahlen manage his club, though he was unable to achieve this until the 1910 season.

In four years as a manager, all for Brooklyn, he posted a 251–355 record for a .414 winning percentage; he earned his nickname with a ferocious arguing style which drew 65 ejections as a manager, still among the top ten in history.

Later years and death
Dahlen worked a number of jobs after his baseball career ended, including serving as an attendant at Yankee Stadium and working as a night clerk in a Brooklyn post office.

Dahlen died in Brooklyn after a long illness at age 80, and was buried in the Cemetery of the Evergreens, Brooklyn, New York City, New York. As of 2006, his grave remained unmarked.

Hall of Fame consideration
Dahlen initially received very little support for induction into the National Baseball Hall of Fame; he received just one vote from the Veterans Committee on the Hall's inaugural 1936 ballot and again received a single vote when he was included on the Baseball Writers' Association of America's 1938 ballot. Dahlen was not considered again by the Veterans Committee for several decades, however, in part due to the reputation of his advanced statistics, Dahlen's candidacy has received renewed interest in recent years. He was included on the committee's Pre-1943 ballot for 2009 but received three or fewer of the twelve member committee's votes. He was included again on the newly formed Pre-Integration Committee's ballot for 2013. Dahlen received ten out of sixteen votes, falling two votes short of election, the highest total of any person on the ballot who was not elected. Dahlen was included again on the Pre-Integration Committee's 2016 ballot but the committee selected no new Hall of Fame members as Dahlen tied for second place with eight of sixteen votes. Dahlen was considered again by the newly formed Early Baseball Era Committee for the 2022 ballot but received three or fewer of the committee's sixteen votes.

The Nineteenth Century Committee of the Society for American Baseball Research named Dahlen the Overlooked 19th Century Baseball Legend for 2012—a 19th-century player, manager, executive or other baseball personality not yet inducted into the National Baseball Hall of Fame in Cooperstown, New York.

Dahlen was featured in David Pietrusza's 1995 television documentary Local Heroes in the segment "Knocking on Cooperstown's Door."

See also

 List of Major League Baseball career hits leaders
 List of Major League Baseball career doubles leaders
 List of Major League Baseball career triples leaders
 List of Major League Baseball career runs scored leaders
 List of Major League Baseball career runs batted in leaders
 List of Major League Baseball career stolen bases leaders
 List of Major League Baseball annual runs batted in leaders
 List of Major League Baseball player-managers

References

.

External links

Baseball Hall of Fame: Fierce Shortstop Dahlen Stands Test of Time
Bill Dahlen Baseballbiography.com
Baseball Evolution Hall of Fame – Player Profile

1870 births
1950 deaths
American people of German descent
Major League Baseball shortstops
Burials at the Cemetery of the Evergreens
Chicago Colts players
Chicago Orphans players
Brooklyn Superbas players
Brooklyn Dodgers players
New York Giants (NL) players
Boston Doves players
Baseball players from New York (state)
19th-century baseball players
National League RBI champions
Major League Baseball player-managers
Brooklyn Superbas managers
Brooklyn Dodgers managers
Cobleskill Giants players

Bill Dahlen


Wang Yun (, 1228–1304), was a writer of Chinese Sanqu poetry from Weizhou (卫州, in modern Henan province). He was born during the Jin dynasty, but became an official under the Yuan Dynasty. Initially a local official, he was given a series of appointments in Central Region, Henan Jiangbei and Jiangzhe provinces starting in 1268. Later he was summoned to the capital where he served in the Hanlin Academy. At twenty, he became the acquaintance of the renowned writer Yuan Haowen. He was a noted prose stylist in the Tang manner of unadorned directness. His poetry often depicted the downtrodden and the poor. His collected works in one-hundred fascicles is extant. A biography of Wang exists in the official history of the Yuan Dynasty (). Forty-one of his sanqu are extant.

Translations
(Yuediao: Pinghuyue)

Untitled

1.

Autumn green lotuses

And a calm lake stitched with clouds.

A cassia boat sews the moistness.

A song, a full cup of wine

Relieve the sorrow.

How can a man's life be as before?

When drunk I remember;

Then as now there were flowering branches,

Though now they blush above this old man's head.

(Yuediao: Pinghuyue)

On the Birthday of Mrs. Li

1.

The eyes enjoy a person at peace.

Your bracelets and ornaments are graced with fragrance.

The gem in the grotto shows its luster.

Eight thousand springs!

Mists announce this letter of long life,

I buy another cup of wine.

You, goddess by the vast sea,

Watch in peace

The stirrings of the world's dust.

See also
 Qu (poetry)

References
 Hu Qiaomu ed., The Great Encyclopedia of China, Chinese Literature, vol. 2, Beijing-Shanghai, 1986, p. 910.
 Lu Weifen and Wu Gengshun ed., Complete Yuan Period Sanqu Lyrics, Liaoning, 2000, vol. 1, pp. 144–51.
 Ma Liangchun and Li Futian ed., The Great Encyclopedia of Chinese Literature, Tianlu, 1991, vol. 2, p. 658.
 Carpenter, Bruce E. 'Chinese San-ch'ü Poetry of the Mongol Era: I', Tezukayama Daigaku kiyo (Journal of Tezukayama University), Nara, Japan, no. 22, pp. 34–5.

1228 births
1304 deaths
Yuan dynasty poets
Jin dynasty (1115–1234) people
Politicians from Xinxiang
Poets from Henan
Yuan dynasty government officials
Writers from Xinxiang

Wang Yun (Yuan dynasty)


Tamassos (Greek: Ταμασσός) or Tamasos (Greek: Τἀμασος) – names Latinized as Tamassus or Tamasus – was a city-kingdom in ancient Cyprus, one of the ten kingdoms of Cyprus. It was situated in the great central plain of the island, south-east of Soli, on the road from Soli to Tremithus. It is an archaeological site bordering the village of Politiko, about 21 kilometres southwest of Nicosia.

An Assyrian inscription from ca. 673 BC (Prism of Esarhaddon) refers to it as Tamesi, described as a city-state which paid tribute to the Neo-Assyrian Empire. As there were copper mines in the neighbourhood, it is very probably the Temese mentioned by Homer (Odyssey, I, 184), which was in his time the principal copper market of the island.

Today the villages of Psimolofou, Episkopeio, Pera Orinis, Ergates, Politiko, Kampia, Analyontas, and Kapedes occupy the site of the city.

History
The city-state prospered mainly because of its mines, from which metals (mostly copper, Cyprus's chief export in the ancient world) were extracted. However, it managed to survive despite exhaustion of its copper deposits.

Foundations, inhabitants, and economy
Unlike other city-states on the island, there is no precise information from either history or tradition concerning the establishment of the city as a human settlement and later as an important trade city.

The area itself was in fact home to a number of small farmer settlements, which the city replaced after the discovery and exploitation of the copper that became the heart of the economy in the succeeding centuries. Studies of the archaeological artefacts suggest that the region was inhabited since prehistoric times, more specifically since the Chalcolithic Age. Villages such as Kampia, Margi, Kotsiatis, and Mathiatis in the wider region were densely populated from the Early Bronze Age. The population increased significantly following exploitation of the copper mines. Tombs and copper-processing installations discovered in the area date back to the Late Bronze Age.

Writers such as Claudius Ptolemy and Stephanus of Byzantium mention the city. Stephanus describes the city as "mesogeia" (inland) with copper of excellent quality. Its inland location and lack of a port kept it from becoming a major trading post such as Salamis and Paphos. The city also lacked the cosmopolitan character of the island's coastal cities. It resembled an "industrial" city of mines and workshops, though it had without doubt also developed the agricultural and stock-breeding potentialities of the surrounding fertile land, enriched by one of the most important rivers of Cyprus, the Pediaios, and its tributaries.

Phoenician and Greek influence
The King of Tamassos, Pasikypros, is said to have sold his kingdom to the Phoenicians of Kition for a price of 50 talents. Having received this amount of money, the King went to spend his last days in Amathus

Athenaeus claims that Alexander the Great gave the same city to Pnytagoras, the King of Salamina, as he had assisted him with the invasion and capture of Tyros. The temple of Aphrodite and perhaps other public buildings were rebuilt at the beginning of the Hellenistic period. It is assumed that there was an alteration to the city character and political structure, and new public buildings built. During the same period, Greeks from various places of the empire came to live in Tamassos. One of these people was Aspendios from Asia Minor.

Decline
With the spread of Christianity throughout southern Europe, Tamasos became one of the first Greek Orthodox dioceses in Cyprus. The presence of its two first bishops, Saint Herakleidios and Saint Mnason, was prominent. The pseudepigraphical Acts of Barnabas mention Tamasus as the meeting point of Barnabas and Heraclide, made bishop by Barnabas.

Tamassos is referred to as a city of Cyprus until the 10th century AD, but by then it was already in decline. The mines were abandoned after their exhaustion, and the economy was destroyed. Much later on, the city was replaced by small settlements such as Politiko and Episkopeio. The name "Politiko" refers to the brilliant ancient city it has replaced, whereas the name "Episkopeio" is reminiscent of Tamassos's old diocese. "Ergates" has been thus named because it is the area where the mine workers lived, while "Pera Orinis" is named because it is opposite Politiko ("pera" being Greek for "yonder"), and because it is located in a hilly area ("oreinis" being Greek for "of the mountains" as opposed to the village "Pera Chorio Nisou" which is in the lowlands). It is believed that these settlements are a continuation of ancient Tamassos and that the inhabitation of this region has thus been continuous from the ancient Prehistoric times until present times.

Archaeological site
The centre of the town, which is believed to have been the location of various public buildings and shrines, is thought to be under the village of Politiko and the nearby Greek Orthodox monastery of "Agios Herakleidios". This overlap of modern inhabited sites and ancient remains also means that large-scale archaeological excavations cannot be conducted.

Sporadic excavations between 1970 and 1990 in the outer area resulted in the discovery of many artifacts as well as parts of the original city dating from the Archaic, Classical, and Hellenistic eras. The visible sections of this large and important archaeological site also include the site of the temple of Aphrodite, the two majestic royal tombs, and other graves.

Fortifications which surrounded the city during the Archaic period have also been unearthed, as well as, copper-processing installations, clay and stone statuettes, and various oblation vessels, censers, and oil lamps. A limestone altar was found nearby Aphrodite's temple as well as a temple devoted to Kiveli (the Mother of Gods). The latter was discovered alongside an epigraphic testimony regarding the goddess' worship. In addition, there are various literary references proving the worshipping of Apollo, Aesculap, and Dionysus.

Necropolis
North-east of Aphrodite's temple lies the necropolis of Tamassos. In addition, three cemeteries are located in the region. One dates back to the Bronze Age / Copper, another to the Archaic period, whilst the third belongs to the Hellenistic era and the times of Roman rule.

Most of the Bronze Age cemetery is probably close to the Lambertes barrow (south-east of the Politiko village). South-west of the "Agios Herakleidios" monastery, a tomb belonging to the Middle Bronze era was dug up in 1963. Yet another tomb from the latter part of the Bronze Age was excavated south-east of the monastery, in the region between the present-day nunnery and the Lambertes barrow.

The Archaic era cemetery is located south-west of the village, between the region's two rivers, of which one is the torrential Pediaios, which waters most of Nicosia District and particularly the fertile area of Mesaoria (now part of North Cyprus).

The Hellenistic/Roman cemetery is found on a slope north-west of Politiko, where the "Agios Mnason" monastery once existed.

Many shrines also seem to have existed around the ancient city of Tamassos. This can be proven by the presence of the Archaic earthen statue and the famous bronze statue of Apollo found in the area.

Nowadays the two monasteries of St Herakleidios and St Mnason are believed to be important monuments of the region.

Royal tombs
The two royal tombs discovered are proof of the city's wealth during the Archaic era, due to their fine construction.

Recently, six unique life-size, limestone, undamaged sculptures were discovered in the royal necropolis, of which two represented sphinxes and four represented lions in a crouching position. The exquisite sculptures date from the 6th century BC.

Tamassos today
The area where Tamassos once stood now is home to the villages of Psimolofou, Episkopeio, Pera Orinis, Ergates, Politiko, Kampia, Analyontas, and Kapedes are located. For the past few centuries, they have developed from being poor agricultural villages housing some 10 families, to populations of 1000 inhabitants. Pera Orinis and Politiko retain much of the older buildings of the older settlements at the centre of the villages, which are deemed to be of high cultural significance. Highlights of these include the church of Panagia Odigitria, the Old Mill, the Parthenagogion and Arenagogion, as well as the recently restore chapel of St George of Pera Orinis, and the famous Tombs of the Kings of the village of Politiko.

See also

 Tamassos bilinguals

References

External links

Archeological Sites: Tamassos - Department of Antiquities of the Republic of Cyprus
Archeological findings of Tamassos at the British Museum
Rare Cypriot Sculptures found in Tamassos - archeology.org, a publication of the Archaeological Institute of America
tamassos.org - History and culture of the area; list of churches etc.
Weapons, Tools and Ritual Remains - Ashmolean Museum, Oxford
Information  and photos  of Tamassos

Cities in ancient Cyprus
Former populated places in Cyprus
Catholic titular sees in Europe
Phoenician colonies in Cyprus

Tamassos


Alexia "Ally" Ioannides (born January 1998) is an American actress, best known for playing Dylan Jones in the NBC drama series Parenthood from 2014 to 2015, and Tilda in the 2015-2019 AMC martial arts drama series Into the Badlands.

Early life
Ioannides was born in Atlanta, Georgia, and raised in Park City, Utah. She moved to Burbank, California at age 14. She started her career as a stage actor playing in musicals at the Egyptian Theatre in Park City, as well as the Pioneer Theatre Company and Hale Center Theater in Salt Lake City, Utah. These theaters were also established many years ago.

Ioannides began elementary school at Pace Academy in Atlanta, then Trailside in Park City, and finally the Madeleine Choir School, where she sang in over 300 services and concerts, notably at the Utah Opera.

Career
Ioannides gained her first professional acting role at age 11 as Ester in the stage adaptation of A Christmas Story. She continued with roles in plays such as White Christmas, Annie, and The Sound of Music.

By 2015, Ioannides was focusing mostly on film and television, notably as Dylan Jones on NBC's Parenthood. Her 2013 short film with Mark Moses, The Tsarevich, was shown at various film festivals and another short, Stray (2014), put her the top 200 for consideration in the final season of the series "Project Greenlight".

Filmography

Film

Television

Stage

References

External links

Living people
American people of Greek descent
Actresses from Atlanta
American film actresses
American television actresses
American stage actresses
American child actresses
21st-century American actresses
People from Park City, Utah
Actresses from Utah
1998 births

Ally Ioannides


Ned's Declassified School Survival Guide is a TV show on Nickelodeon.

From "A middle middle school full of bullies, insane teachers and gross school lunches" comes Ned's Declassified School Survival Guide, a show on Nickelodeon. The show stars Devon Werkheiser as Ned Bigby (that everyone hates), a 12-15-year-old student at James K. Polk Middle School. Every episode is a group of tips to surviving a school based activity. The show is part of Nick's Sunday lineup. It first aired on September 12, 2004.

The show is very successful, it has had a promising start. The show also stars Daniel Curtis Lee and Lindsey Shaw as Simon "Cookie" Cook and Jennifer "Moze/Mose" Mosley/Mozely.

It also comes on Family Channel.

Nickelodeon television series
English-language television programs
2004 television series debuts
2007 television series endings


Nathaniel Goss Pearlman (born October 7, 1965, in Manhattan, New York and raised in Boulder, Colorado) is an American political technology and information graphics entrepreneur aligned with the Democratic Party. In 1997, he founded NGP Software, Inc., a company which provides political software to a majority of federal and state level Democrats including most Democratic candidates for President (including Dean, Gephardt, Kerry, Graham, Edwards, Obama, Sanders and Clinton) in 2004, 2008, 2012, and 2016. He was chief technology officer for Hillary Clinton's 2008 presidential campaign and an early practitioner in the area of computers and politics. In 2010, NGP Software merged with the Voter Activation Network to become NGP VAN. Pearlman subsequently founded companies in the information graphics and data visualization space, Timeplots and Graphicacy. He now hosts a podcast called The Great Battlefield about progressive political entrepreneurs and the resistance to Trump.

Background

Nathaniel Goss Pearlman has a degree in Computer Science from Yale (1988). He worked for Election Data Services on legislative redistricting (1991). He attended the doctoral program in Political Science at the Massachusetts Institute of Technology from 1992 to 1996, finishing his exams, but he did not write a dissertation. Instead, he started NGP Software, Inc. in 1997, a fast-growing partisan political software firm. In 2004, Pearlman was named a Rising Star in American Politics by Campaigns and Elections Magazine. In 2008, Pearlman served as Chief Technology Officer for Hillary Clinton's presidential campaign. In 2009, he founded Timeplots, an information graphics product company. In 2012, he founded Graphicacy, a services company that helps enterprises tell complex stories in visual form. In 2014, he cofounded Leverfund, a nonprofit that provides grants to poverty fighting organizations in the DC metro area.

Publications
Margin of Victory: How Technologists Help Politicians Win Elections (New Trends and Ideas in American Politics)

Personal life

Pearlman resides in Washington, DC with his wife Connie KN Chang and their daughters Ella and Lola.

References

External links
 NGP VAN
 TIMEPLOTS
 GRAPHICACY
 LEVERFUND
 RESISTANCE DASHBOARD
 GREAT BATTLEFIELD
 https://www.inc.com/profile/ngp-van

1965 births
Living people
Politics and technology
American political consultants
People from Boulder, Colorado
Yale College alumni
American chief technology officers
MIT School of Humanities, Arts, and Social Sciences alumni

Nathaniel Pearlman


Carol's Daughter is an American multi-cultural beauty brand headquartered in New York City.

Its founder and president, Lisa Price, established the brand in 1993 in Brooklyn, New York City. The brand was named after Lisa Price's mother, Carol. The beauty brand offers a range of hair, body, and skincare products.

In October 2014, the brand was acquired by L'Oréal USA.

History
Price started the brand as a "side hustle" from her kitchen table in Brooklyn, New York City in the late 1980s. It initially started as a hobby while she was working full-time in television production, notably on "The Cosby Show" and its spin-off "Here and Now". She first began experimenting with fragrances and essential oils, which grew into an exploration of body care products. After gifting the homemade products to friends and family, her mother, Carol, implored her to start a business. Her mother died in 2003.

In 1993, Price began selling her products through word-of-mouth in her Bedford–Stuyvesant neighborhood of Brooklyn, and at local flea markets and craft fairs, building-up a loyal, devoted customer base.  The first Carol's Daughter boutique opened in Fort Greene, Brooklyn in 1999.  In 2000, the brand launched its e-commerce website. In 2002, Price was featured on the Oprah Winfrey Show, which gave her brand an enormous "Oprah Effect" boost. In 2005, Will Smith, Jada Pinkett Smith, and Jay-Z were among a group of movie and music stars who invested $10 million USD into Price's brand to help expand its nationwide reach. Other investors included record executive Steve Stoute, investor Andrew Farkas, Interscope Records chief Jimmy Iovine, and music executive Tommy Mottola and his wife, singer Thalía.

In 2008, Carol's Daughter launched on HSN. In 2010, HSN partnered with Mary J. Blige and Carol's Daughter for an exclusive, inaugural fragrance called "My Life", which rolled-out with an eau de parfum in a limited edition gold clutch, a shower cream, a body lotion, and an eau de parfum rollerpen.

In March 2014, Carol's Daughter launched an exclusive collection with Target.

In April 2014, the brand filed for Chapter 11 bankruptcy protection with the Manhattan bankruptcy court. The brand's chief financial officer, John D. Elmer, stated that most of Carol's Daughter stores had been unprofitable since 2010. Before filing papers, the company closed five of its seven retail stores, and terminated 29 of its 42 employees.

Six months later, in October 2014, Carol's Daughter was acquired by L'Oréal USA.

Price's story is frequently cited as an example of the entrepreneurial success story of a "minority-owned business that caters primarily to women of color".

References

External links

Cosmetics companies of the United States

Carol's Daughter


The Van der Waals radius is the radius of an atom that is seen as a hard sphere. It is named after someone who realized that atoms were not points, but actual objects. It can be found by the critical point and the physical properties of a gas. It also can be found by a molecular crystal.

Chemistry
Chemical bonding
Physics

Van der Waals radius


Shame is an emotion. Shame is rooted in a social or cultural environment. Some people feel shame when some of the rules (that are accepted by the respective society) have been broken. A person can feel ashamed because he or she has thought or done something no one else knows about. Children are often told to be ashamed of something, because they sometimes have trouble telling cause and effect apart. When they grow up, they can better tell the two apart. At that stage, the feeling of guilt becomes stronger.

Emotions

Shame


A spreadmart (spreadsheet data mart) is a business data analysis system running on spreadsheets or other desktop databases that is created and maintained by individuals or groups to perform tasks that can be done in a more structured way by a data mart or data warehouse. Typically a spreadmart is created by individuals at different times using different data sources and rules for defining metrics in an organization, creating a decentralized, fractured view of the enterprise.

The concept was coined in 2002 by Wayne Eckerson at TDWI in his article Taming Spreadsheet Jockeys, and intended pejoratively, as an undesirable system, which should be replaced by a data mart. However, critics such as Stephen Samild argue that spreadmarts have advantages over data marts and can be a desirable system.

Problems

Usually, spreadmarts grow where standard Business Intelligence (BI) reporting is too inflexible and too slow. A Business analyst uses the "export to Microsoft Excel" button in his BI software and creates his own report with the exported data table. By this, the number of independently generated spreadsheets dealing with a particular group of analyses grows inside the company, and the data inside each spreadsheet is uncoupled from its source.  When this happens, the data reflected in the spreadsheets is no longer verifiable and is not automatically kept up to date.
Usually these spreadsheet files are distributed via email to colleagues resulting in even more copies of the data roaming through the enterprise. With Microsoft Power Pivot for Microsoft SharePoint, Excel spreadsheets can be distributed as dashboards throughout the entire company, giving even more users the tools to create spreadmarts.

The growth of spreadmarts poses tangible risks for companies, since undefined and uncoupled data can be used to draw false conclusions that lead to wrong decisions, which will cost time and money to discover and correct. Although Business Intelligence 2.0 software vendors claim to have overcome this issue, locally installed spreadsheet and graphing software continues to be easier to access and use, giving the business analyst the freedom to create the needed analysis quickly, and choose to live with the risk of data inconsistency that goes with it.

Criticism of concept
Critics like Stephen Samild argue that the definition stems from a biased view that sees a data warehouse as desirable end-result, whereas One might more accurately define data marts and data warehouses as "scaled-up systems which perform some of the tasks normally done by a spreadmart". In the rest of the article Stephen Samild argues that a spreadmart fulfills a number of roles that a data warehouse cannot fulfill as easily or as cheaply due to the lack of integration with unstructured data, the lack of read-write capabilities, the long time span needed for integration of new sources in the data warehouse and the inherent 'free form' of many analytical presentations done in Word, PowerPoint or Excel.

Related technologies
 Microsoft Excel with PowerPivot as the standard
 LibreOffice Calc, the open source alternative to Excel

References

External links
 Can the Spreadmart Beast Be Tamed By Brian Moran at SQL Server Magazine (Archived at 2008-06-13)
 Excel is the most popular decision support tool for business users worldwide from Double-Tongued Dictionary
 Business Intelligence Can Stop The Spread of Spread-Mart By David Wallace from TIBCO Spotfire Blogging Team
 The Rise and Fall of Spreadmarts By Wayne Eckerson  from Information Management Magazine

Business intelligence
Data warehousing

Spreadmart


The Old Lyme Congregational Church is located in Old Lyme, Connecticut.   The church is noted as a favorite subject of Old Lyme Art Colony painters. It is affiliated with the United Church of Christ.

History

The first Meeting House was built in 1665 and the first minister was Moses Noyes.  New buildings were constructed in 1689 and 1738.  The present building was erected in 1816-7 by architect Samuel Belcher, Belcher also designed the John Sill and William Noyes houses on Lyme Street. The building was burnt down in a July 3, 1907 fire, then rebuilt with help from artists at the Old Lyme art colony in 1908-9.

Five other Congregational churches were built on essentially the same design in the Connecticut towns of Milford (1823), Cheshire (the 1827 First Congregational Church of Cheshire), Litchfield (the 1829 First Congregational Church of Litchfield), Southington (1830), and Guilford (the 1830 First Congregational Church of Guilford). All six churches have front porticos with four fluted columns, the doors of all six have the same dimensions, all six steeples are of the same design and are surmounted by weathervanes that appear to have been cast from one mold, and all six churches have twenty-over-twenty double-hung windows. The similarities suggest that some of the building elements may have been prefabricated.

The building was restored circa 2001 by volunteers, including architect Stephen Lloyd.

Paintings

Impressionist Childe Hassam depicted the church in a series of three celebrated paintings from 1903 to 1906.  One hangs in the Parrish Art Museum in Southampton, New York.  Another is displayed in the Albright-Knox Art Gallery in Buffalo, New York. Hassam's paintings helped bring publicity to the Old Lyme art colony and helped tourism in the town. Other artists at the colony, including Charles Ebert and Everett Warner (in about 1911), also tried their hands at painting the church.

References

External links
 Official website of the First Congregational Church of Old Lyme
Childe Hassam: American Impressionist, a full-text exhibition catalog from The Metropolitan Museum of Art, which contains material on Old Lyme

United Church of Christ churches in Connecticut
Old Lyme, Connecticut
Churches in New London County, Connecticut
Churches completed in 1817
19th-century United Church of Christ church buildings
20th-century United Church of Christ church buildings
Churches completed in 1909

Old Lyme Congregational Church


Sayeeda Hussain Warsi, Baroness Warsi (surname pronounced VAR-SEY; born 28 March 1971 in Dewsbury, West Riding of Yorkshire, England) is a British politician and lawyer. She was born to Pakistani immigrants and is a member of the House of Lords. She has been the Chairman of the Conservative Party and Minister Without Portfolio in the Conservative-Liberal Democrat coalition government. She was the first Muslim woman to be a member of the British cabinet. She lives in Wakefield, West Yorkshire.

Personal life
In 1990 Warsi married her cousin Naeem in an arranged marriage. She and her first husband divorced in December 2007. On 20 August 2009, she married Iftikhar Azam.

References

1971 births
Living people
British lawyers
British Muslims
Politicians from Yorkshire
Members of the House of Lords

Sayeeda Warsi, Baroness Warsi


"Return to Plain Awful" is a Donald Duck story that was originally printed during the Gladstone Publishing run of Donald Duck Adventures, issue #12 in May 1989. It was written by Don Rosa as a sequel to "Lost in the Andes!" by Carl Barks, to commemorate that story's 40th anniversary.

Plot
Donald Duck and his nephews journey back to Plain Awful. This time, Scrooge McDuck goes with them. Scrooge plans to buy some square eggs from the natives, while Donald and the nephews plan to return the roosters they brought back from their first visit. Unfortunately, Flintheart Glomgold also wants the square eggs and again serves as Scrooge's unscrupulous rival.

In Plain Awful, the ducks discover that, since their last visit, the highly imitative residents have sculpted their entire culture around the appearance and personality of Donald Duck (just as they had previously built their entire culture around the personality of their previous visitor). One aspect of Plain Awful's culture that has remained constant, however, is the law forbidding round objects, which Scrooge inadvertently violates by showing the natives his Number One Dime. As a result, he is held prisoner in the stone quarries, finishing the square eggs deal for good. However, Plain Awful's "President" (The leader decided to imitate America's system after Donald and his nephews' first visit) offers Scrooge a full pardon and reconsideration of the square eggs deal, if they bring him a rare item called "Ice Cream Soda".

Donald and the nephews have to team up with Flintheart to deliver an Ice Cream Soda to the President of Plain Awful: Donald and his nephews need Flintheart to get the soda, while Flintheart needs guidance back to civilization since he arrived at Plain Awful just by a stroke of luck. Flintheart, of course, betrays them after getting the soda, forcing them to improvise making an ice cream soda on the spot, using dried milk, sugar, and chocolate from their ration packs, plus some snow and carbonated water from a fire extinguisher.

Scrooge and Glomgold race to the city with their sodas, but are surprised to see the natives now imitating them, instead of Donald.  The President (now the "Chairman of the Board") declares he is no longer interested in ice cream sodas, but instead asks for some money to store in Plain Awful's newly made money bin. Since Flintheart spent all his cash on the helicopter that brought them to Plain Awful (except for a coin, which he wouldn't show after what happened to Scrooge), Scrooge gives one billion dollars (in bills) for his freedom. Plain Awful's "chairman" happily accepts the money, but to Scrooge and Flintheart's horror, the bills are chopped in two (leaving perfect square halves) and put on public display inside the bin.

Scrooge and Flintheart are so disgusted by this that they want nothing more to do with Plain Awful, abandoning their aspirations of gaining export rights to the square eggs. The story ends with Huey, Dewey, and Louie leaving a copy of the Junior Woodchuck's Guidebook as a farewell gift to the natives, and Donald making fun of Scrooge and his famous motto, since the natives made their first billion "by being tougher than the toughies and smarter than the smarties! And they made it SQUARE!"

See also
 "Return to Plain Awful" served as the title story to Fantagraphics'' Uncle Scrooge and Donald Duck: The Don Rosa Library Vol. 2

External links

Disney comics stories
Donald Duck comics by Don Rosa
1989 in comics
Lost world comics

Return to Plain Awful


Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now be modeled to a very high degree of accuracy (see section Modern developments).

Lunar theory includes:
 the background of general theory; including mathematical techniques used to analyze the Moon's motion and to generate formulae and algorithms for predicting its movements; and also
 quantitative formulae, algorithms, and geometrical diagrams that may be used to compute the Moon's position for a given time; often by the help of tables based on the algorithms.

Lunar theory has a history of over 2000 years of investigation. Its more modern developments have been used over the last three centuries for fundamental scientific and technological purposes, and are still being used in that way.

Applications
Applications of lunar theory have included the following:
 In the eighteenth century, comparison between lunar theory and observation was used to test Newton's law of universal gravitation by the motion of the lunar apogee.
 In the eighteenth and nineteenth centuries, navigational tables based on lunar theory, initially in the Nautical Almanac, were much used for the determination of longitude at sea by the method of lunar distances.
 In the very early twentieth century, comparison between lunar theory and observation was used in another test of gravitational theory, to test (and rule out) Simon Newcomb's suggestion that a well-known discrepancy in the motion of the perihelion of Mercury might be explained by a fractional adjustment of the power -2 in Newton's inverse square law of gravitation (the discrepancy was later successfully explained by the general theory of relativity).
 In the mid-twentieth century, before the development of atomic clocks, lunar theory and observation were used in combination to implement an astronomical time scale (ephemeris time) free of the irregularities of mean solar time.
 In the late twentieth and early twenty-first centuries, modern developments of lunar theory are being used in the Jet Propulsion Laboratory Development Ephemeris series of models of the Solar System, in conjunction with high-precision observations, to test the exactness of physical relationships associated with the general theory of relativity, including the strong equivalence principle, relativistic gravitation, geodetic precession, and the constancy of the gravitational constant.

History
The Moon has been observed for millennia. Over these ages, various levels of care and precision have been possible, according to the techniques of observation available at any time. There is a correspondingly long history of lunar theories: it stretches from the times of the Babylonian and Greek astronomers, down to modern lunar laser ranging.

Among notable astronomers and mathematicians down the ages, whose names are associated with lunar theories, are:

 Babylonian/Chaldean
 Naburimannu
 Kidinnu
 Soudines
 Greek/Hellenistic
 Hipparchus
 Ptolemy
 Arab
 Ibn al-Shatir
 European, 16th to early 20th centuries
 Tycho Brahe
 Johannes Kepler
 Jeremiah Horrocks
 Ismaël Bullialdus
 John Flamsteed
 Isaac Newton
 Edmond Halley
 Leonhard Euler
 Alexis Clairaut
 Jean d'Alembert
 Tobias Mayer
 Johann Tobias Bürg
 Pierre-Simon Laplace
 Philippe le Doulcet
 Johann Karl Burckhardt
 Peter Andreas Hansen
 Charles-Eugène Delaunay
 John Couch Adams
 North American, 19th to early 20th centuries
 Simon Newcomb
 George William Hill
 Ernest William Brown
 Wallace John Eckert
Other notable mathematicians and mathematical astronomers also made significant contributions.

The history can be considered to fall into three parts: from ancient times to Newton; the period of classical (Newtonian) physics; and modern developments.

Ancient times to Newton

Babylon
Of Babylonian astronomy, practically nothing was known to historians of science before the 1880s. Surviving ancient writings of Pliny had made bare mention of three astronomical schools in Mesopotamia – at Babylon, Uruk, and 'Hipparenum' (possibly 'Sippar'). But definite modern knowledge of any details only began when Joseph Epping deciphered cuneiform texts on clay tablets from a Babylonian archive: In these texts he identified an ephemeris of positions of the Moon. Since then, knowledge of the subject, still fragmentary, has had to be built up by painstaking analysis of deciphered texts, mainly in numerical form, on tablets from Babylon and Uruk (no trace has yet been found of anything from the third school mentioned by Pliny).

To the Babylonian astronomer Kidinnu (in Greek or Latin, Kidenas or Cidenas) has been attributed the invention (5th or 4th century BC) of what is now called "System  B" for predicting the position of the moon, taking account that the moon continually changes its speed along its path relative to the background of fixed stars. This system involved calculating daily stepwise changes of lunar speed, up or down, with a minimum and a maximum approximately each month. The basis of these systems appears to have been arithmetical rather than geometrical, but they did approximately account for the main lunar inequality now known as the equation of the center.

The Babylonians kept very accurate records for hundreds of years of new moons and eclipses. Some time between the years 500 BC and 400 BC they identified and began to use the 19 year cyclic relation between lunar months and solar years now known as the Metonic cycle.

This helped them build a numerical theory of the main irregularities in the Moon's motion, reaching remarkably good estimates for the (different) periods of the three most prominent features of the Moon's motion:
 The synodic month, i.e. the mean period for the phases of the Moon. Now called "System B", it reckons the synodic month as 29 days and (sexagesimally) 3,11;0,50 "time degrees", where each time degree is one degree of the apparent motion of the stars, or 4 minutes of time, and the sexagesimal values after the semicolon are fractions of a time degree. This converts to 29.530594 days = 29d 12h 44m 3.33s, to compare with a modern value (as at 1900 Jan 0) of 29.530589 days, or 29d 12h 44m 2.9s. This same value was used by Hipparchos and Ptolemy, was used throughout the Middle Ages, and still forms the basis of the Hebrew calendar.
 The mean lunar velocity relative to the stars they estimated at 13° 10′ 35″ per day, giving a corresponding month of 27.321598 days, to compare with modern values of 13° 10′ 35.0275″ and 27.321582 days.
 The anomalistic month, i.e. the mean period for the Moon's approximately monthly accelerations and decelerations in its rate of movement against the stars, had a Babylonian estimate of 27.5545833 days, to compare with a modern value 27.554551 days.
 The draconitic month, i.e. the mean period with which the path of the Moon against the stars deviates first north and then south in ecliptic latitude by comparison with the ecliptic path of the Sun, was indicated by a number of different parameters leading to various estimates, e.g. of 27.212204 days, to compare with a modern value of 27.212221, but the Babylonians also had a numerical relationship that 5458 synodic months were equal to 5923 draconitic months, which when compared with their accurate value for the synodic month leads to practically exactly the modern figure for the draconitic month.

The Babylonian estimate for the synodic month was adopted for the greater part of two millennia by Hipparchus, Ptolemy, and medieval writers (and it is still in use as part of the basis for the calculated Hebrew (Jewish) calendar).

Greece and Hellenistic Egypt
Thereafter, from Hipparchus and Ptolemy in the Bithynian and Ptolemaic epochs down to the time of Newton's work in the seventeenth century, lunar theories were composed mainly with the help of geometrical ideas, inspired more or less directly by long series of positional observations of the moon. Prominent in these geometrical lunar theories were combinations of circular motions – applications of the theory of epicycles.

Hipparchus

Hipparchus, whose works are mostly lost and known mainly from quotations by other authors, assumed that the Moon moved in a circle inclined at 5° to the ecliptic, rotating in a retrograde direction (i.e. opposite to the direction of annual and monthly apparent movements of the Sun and Moon relative to the fixed stars) once in 18 years. The circle acted as a deferent, carrying an epicycle along which the Moon was assumed to move in a retrograde direction. The center of the epicycle moved at a rate corresponding to the mean change in Moon's longitude, while the period of the Moon around the epicycle was an anomalistic month. This epicycle approximately provided for what was later recognized as the elliptical inequality, the equation of the center, and its size approximated to an equation of the center of about 5° 1'. This figure is much smaller than the modern value: but it is close to the difference between the modern coefficients of the equation of the center (1st term) and that of the evection: the difference is accounted for by the fact that the ancient measurements were taken at times of eclipses, and the effect of the evection (which subtracts under those conditions from the equation of the center) was at that time unknown and overlooked. For further information see also separate article Evection.

Ptolemy
Ptolemy's work the Almagest had wide and long-lasting acceptance and influence for over a millennium. He gave a geometrical lunar theory that improved on that of Hipparchus by providing for a second inequality of the Moon's motion, using a device that made the apparent apogee oscillate a little – prosneusis of the epicycle. This second inequality or second anomaly accounted rather approximately, not only for the equation of the center, but also for what became known (much later) as the evection. But this theory, applied to its logical conclusion, would make the distance (and apparent diameter) of the Moon appear to vary by a factor of about 2, which is clearly not seen in reality. (The apparent angular diameter of the Moon does vary monthly, but only over a much narrower range of about 0.49°–0.55°.) This defect of the Ptolemaic theory led to proposed replacements by Ibn al-Shatir in the 14th century and by Copernicus in the 16th century.

Ibn al-Shatir and Copernicus
Significant advances in lunar theory were made by the Arab astronomer, Ibn al-Shatir (1304–1375). Drawing on the observation that the distance to the Moon did not change as drastically as required by Ptolemy's lunar model, he produced a new lunar model that replaced Ptolemy's crank mechanism with a double epicycle model that reduced the computed range of distances of the Moon from the Earth. A similar lunar theory, developed some 150 years later by the Renaissance astronomer Nicolaus Copernicus, had the same advantage concerning the lunar distances.

Tycho Brahe, Johannes Kepler, and Jeremiah Horrocks

Tycho Brahe and Johannes Kepler refined the Ptolemaic lunar theory, but did not overcome its central defect of giving a poor account of the (mainly monthly) variations in the Moon's distance, apparent diameter and parallax. Their work added to the lunar theory three substantial further discoveries.
 The nodes and the inclination of the lunar orbital plane both appear to librate, with a monthly (according to Tycho) or semi-annual period (according to Kepler).
 The lunar longitude has a twice-monthly Variation, by which the Moon moves faster than expected at new and full moon, and slower than expected at the quarters.
 There is also an annual effect, by which the lunar motion slows down a little in January and speeds up a little in July: the annual equation.

The refinements of Brahe and Kepler were recognized by their immediate successors as improvements, but their seventeenth-century successors tried numerous alternative geometrical configurations for the lunar motions to improve matters further. A notable success was achieved by Jeremiah Horrocks, who proposed a scheme involving an approximate 6 monthly libration in the position of the lunar apogee and also in the size of the elliptical eccentricity. This scheme had the great merit of giving a more realistic description of the changes in distance, diameter and parallax of the Moon.

Newton

A first gravitational period for lunar theory started with the work of Newton. He was the first to define the problem of the perturbed motion of the Moon in recognisably modern terms. His groundbreaking work is shown for example in the Principia in all versions including the first edition published in 1687.

Newton's biographer, David Brewster, reported that the complexity of Lunar Theory impacted Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692-3, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According to Brewster, Edmund Halley also told John Conduitt that when pressed to complete his analysis Newton "always replied that it made his head ache, and kept him awake so often, that he would think of it no more" [Emphasis in original].

Solar perturbation of lunar motion

Newton identified how to evaluate the perturbing effect on the relative motion of the Earth and Moon, arising from their gravity towards the Sun, in Book 1, Proposition 66, and in Book 3, Proposition 25. The starting-point for this approach is Corollary VI to the laws of motion. This shows that if the external accelerative forces from some massive body happens to act equally and in parallel on some different other bodies considered, then those bodies would be affected equally, and in that case their motions (relative to each other) would continue as if there were no such external accelerative forces at all. It is only in the case that the external forces (e.g. in Book 1, Prop. 66, and Book 3, Prop. 25, the gravitational attractions towards the Sun) are different in size or in direction in their accelerative effects on the different bodies considered (e.g. on the Earth and Moon), that consequent effects are appreciable on the relative motions of the latter bodies. (Newton referred to accelerative forces or accelerative gravity due to some external massive attractor such as the Sun. The measure he used was the acceleration that the force tends to produce (in modern terms, force per unit mass), rather than what we would now call the force itself.)

Thus Newton concluded that it is only the difference between the Sun's accelerative attraction on the Moon and the Sun's attraction on the Earth that perturbs the motion of the Moon relative to the Earth.

Newton then in effect used vector decomposition of forces, to carry out this analysis. In Book 1, Proposition 66 and in Book 3, Proposition 25, he showed by a geometrical construction, starting from the total gravitational attraction of the Sun on the Earth, and of the Sun on the Moon, the difference that represents the perturbing effect on the motion of the Moon relative to the Earth. In summary, line LS in Newton's diagram as shown below represents the size and direction of the perturbing acceleration acting on the Moon in the Moon's current position P (line LS does not pass through point P, but the text shows that this is not intended to be significant, it is a result of the scale factors and the way the diagram has been built up).

Shown here is Newton's diagram from the first (1687) Latin edition of the Principia (Book 3, Proposition 25, p. 434). Here he introduced his analysis of perturbing accelerations on the Moon in the Sun-Earth-Moon system. Q represents the Sun, S the Earth, and P the Moon.

Parts of this diagram represent distances, other parts gravitational accelerations (attractive forces per unit mass). In a dual significance, SQ represents the Earth-Sun distance, and then it also represents the size and direction of the Earth-Sun gravitational acceleration. Other distances in the diagram are then in proportion to distance SQ. Other attractions are in proportion to attraction SQ.

The Sun's attractions are SQ (on the Earth) and LQ (on the Moon). The size of LQ is drawn so that the ratio of attractions LQ:SQ is the inverse square of the ratio of distances PQ:SQ. (Newton constructs KQ=SQ, giving an easier view of the proportions.) The Earth's attraction on the Moon acts along direction PS. (But line PS signifies only distance and direction so far, nothing has been defined about the scale factor between solar and terrestrial attractions).

After showing solar attractions LQ on the Moon and SQ on the Earth, on the same scale, Newton then makes a vector decomposition of LQ into components LM and MQ. Then he identifies the perturbing acceleration on the Moon as the difference of this from SQ. SQ and MQ are parallel to each other, so SQ can be directly subtracted from MQ, leaving MS. The resulting difference, after subtracting SQ from LQ, is therefore the vector sum of LM and MS: these add up to a perturbing acceleration LS.

Later Newton identified another resolution of the perturbing acceleration LM+MS = LS, into orthogonal components: a transverse component parallel to LE, and a radial component, effectively ES.

Newton's diagrammatic scheme, since his time, has been re-presented in other and perhaps visually clearer ways. Shown here is a vector presentation indicating, for two different positions, P1 and P2, of the Moon in its orbit around the Earth, the respective vectors LS1 and LS2 for the perturbing acceleration due to the Sun. The Moon's position at P1 is fairly close to what it was at P in Newton's diagram; corresponding perturbation LS1 is like Newton's LS in size and direction. At another position P2, the Moon is farther away from the Sun than the Earth is, the Sun's attraction LQ2 on the Moon is weaker than the Sun's attraction SQ=SQ2 on the Earth, and then the resulting perturbation LS2 points obliquely away from the Sun.

Constructions like those in Newton's diagram can be repeated for many different positions of the Moon in its orbit. For each position, the result is a perturbation vector like LS1 or LS2 in the second diagram. Shown here is an often-presented form of the diagram that summarises sizes and directions of the perturbation vectors for many different positions of the Moon in its orbit. Each small arrow is a perturbation vector like LS, applicable to the Moon in the particular position around the orbit from which the arrow begins. The perturbations on the Moon when it is nearly in line along the Earth-Sun axis, i.e. near new or full moon, point outwards, away from the Earth. When the Moon-Earth line is 90° from the Earth-Sun axis they point inwards, towards the Earth, with a size that is only half the maximum size of the axial (outwards) perturbations. (Newton gave a rather good quantitative estimate for the size of the solar perturbing force: at quadrature where it adds to the Earth's attraction he put it at  of the mean terrestrial attraction, and twice as much as that at the new and full moons where it opposes and diminishes the Earth's attraction.)

Newton also showed that the same pattern of perturbation applies, not only to the Moon, in its relation to the Earth as disturbed by the Sun, but also to other particles more generally in their relation to the solid Earth as disturbed by the Sun (or by the Moon); for example different portions of the tidal waters at the Earth's surface. The study of the common pattern of these perturbing accelerations grew out of Newton's initial study of the perturbations of the Moon, which he also applied to the forces moving tidal waters. Nowadays this common pattern itself has become often known as a tidal force whether it is being applied to the disturbances of the motions of the Moon, or of the Earth's tidal waters – or of the motions of any other object that suffers perturbations of analogous pattern.

After introducing his diagram 'to find the force of the Sun to perturb the Moon' in Book 3, Proposition 25, Newton developed a first approximation to the solar perturbing force, showing in further detail how its components vary as the Moon follows its monthly path around the Earth. He also took the first steps in investigating how the perturbing force shows its effects by producing irregularities in the lunar motions.

For a selected few of the lunar inequalities, Newton showed in some quantitative detail how they arise from the solar perturbing force.

Much of this lunar work of Newton's was done in the 1680s, and the extent and accuracy of his first steps in the gravitational analysis was limited by several factors, including his own choice to develop and present the work in what was, on the whole, a difficult geometrical way, and by the limited accuracy and uncertainty of many astronomical measurements in his time.

Classical gravitational period after Newton

The main aim of Newton's successors, from Leonhard Euler, Alexis Clairaut and Jean d'Alembert in the mid-eighteenth century, down to Ernest William Brown in the late nineteenth and early twentieth century, was to account completely and much more precisely for the moon's motions on the basis of Newton's laws, i.e. the laws of motion and of universal gravitation by attractions inversely proportional to the squares of the distances between the attracting bodies. They also wished to put the inverse-square law of gravitation to the test, and for a time in the 1740s it was seriously doubted, on account of what was then thought to be a large discrepancy between the Newton-theoretical and the observed rates in the motion of the lunar apogee. However Clairaut showed shortly afterwards (1749–50) that at least the major cause of the discrepancy lay not in the lunar theory based on Newton's laws, but in excessive approximations that he and others had relied on to evaluate it.

Most of the improvements in theory after Newton were made in algebraic form: they involved voluminous and highly laborious amounts of infinitesimal calculus and trigonometry. It also remained necessary, for completing the theories of this period, to refer to observational measurements.

Results of the theories

The lunar theorists used (and invented) many different mathematical approaches to analyse the gravitational problem. Not surprisingly, their results tended to converge. From the time of the earliest gravitational analysts among Newton's successors, Euler, Clairaut and d'Alembert, it was recognized that nearly all of the main lunar perturbations could be expressed in terms of just a few angular arguments and coefficients. These can be represented by:
 the mean motions or positions of the Moon and the Sun, together with three coefficients and three angular positions, which together define the shape and location of their apparent orbits:
 the two eccentricities (, about 0.0549, and , about 0.01675) of the ellipses that approximate to the apparent orbits of the Moon and the Sun;
 the angular direction of the perigees ( and ) (or their opposite points the apogees) of the two orbits; and
 the angle of inclination (, mean value about 18523") between the planes of the two orbits, together with the direction () of the line of nodes in which those two planes intersect. The ascending node () is the node passed by the Moon when it is tending northwards relative to the ecliptic.

From these basic parameters, just four basic differential angular arguments are enough to express, in their different combinations, nearly all of the most significant perturbations of the lunar motions. They are given here with their conventional symbols due to Delaunay; they are sometimes known as the Delaunay arguments:
  the Moon's mean anomaly (angular distance of the mean longitude of the Moon from the mean longitude of its perigee );
  the Sun's mean anomaly (angular distance of the mean longitude of the Sun from the mean longitude of its perigee );
  the Moon's mean argument of latitude (angular distance of the mean longitude of the Moon from the mean longitude of its ascending (northward-bound) node );
  the Moon's mean (solar) elongation (angular distance of the mean longitude of the Moon from the mean longitude of the Sun).

This work culminated into Brown's lunar theory (1897–1908) and Tables of the Motion of the Moon (1919). These were used in the American Ephemeris and Nautical Almanac until 1968, and in a modified form until 1984.

Largest or named lunar inequalities
Several of the largest lunar perturbations in longitude (contributions to the difference in its true ecliptic longitude relative to its mean longitude) have been named. In terms of the differential arguments, they can be expressed in the following way, with coefficients rounded to the nearest second of arc ("):

Equation of the center

 The Moon's equation of the center, or elliptic inequality, was known at least in approximation, to the ancients from the Babylonians and Hipparchus onwards. Knowledge of more recent date is that it corresponds to the approximate application of Kepler's law of equal areas in an elliptical orbit, and represents the speeding-up of the Moon as its distance from the Earth decreases while it moves towards its perigee, and then its slowing down as its distance from the Earth increases while it moves towards its apogee. The effect on the Moon's longitude can be approximated by a series of terms, of which the first three are .

Evection

 The evection (or its approximation) was known to Ptolemy, but its name and knowledge of its cause dates from the 17th century. Its effect on the Moon's longitude has an odd-appearing period of about 31.8 days. This can be represented in a number of ways, for example as the result of an approximate 6-monthly libration in the position of perigee, with an accompanying 6-monthly pulsation in the size of the Moon's orbital eccentricity. Its principal term is .

Variation

 The Variation, discovered by Tycho Brahe, is a speeding-up of the Moon as it approaches new-moon and full-moon, and a slowing-down as it approaches first and last quarter. Its gravitational explanation with a quantitative estimate was first given by Newton. Its principal term is .

Annual equation
 The annual equation, also discovered by Brahe, was qualitatively explained by Newton in terms that the Moon's orbit becomes slightly expanded in size, and longer in period, when the Earth is at perihelion closest to the Sun at the beginning of January, and the Sun's perturbing effect is strongest, and then slightly contracted in size and shorter in period when the Sun is most distant in early July, so that its perturbing effect is weaker: the modern value for the principal term due to this effect is .

Parallactic inequality
 The parallactic inequality, first found by Newton, makes Brahe's Variation a little asymmetric as a result of the finite distance and non-zero parallax of the Sun. Its effect is that the Moon is a little behind at first quarter, and a little ahead at last quarter. Its principal term is .

Reduction to the ecliptic
 The reduction to the ecliptic represents the geometric effect of expressing the Moon's motion in terms of a longitude in the plane of the ecliptic, although its motion is really taking place in a plane that is inclined by about 5 degrees. Its principal term is .

The analysts of the mid-18th century expressed the perturbations of the Moon's position in longitude using about 25-30 trigonometrical terms.  However, work in the nineteenth and twentieth century led to very different formulations of the theory so these terms are no longer current. The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase.

Modern developments

Digital computers and lunar laser ranging

Since the Second World War and especially since the 1960s, lunar theory has been further developed in a somewhat different way. This has been stimulated in two ways: on the one hand, by the use of automatic digital computation, and on the other hand, by modern observational data-types, with greatly increased accuracy and precision.

Wallace John Eckert, a student of Ernest William Brown and employee at IBM, used the experimental digital computers developed there after the Second World War for computation of astronomical ephemerides. One of the projects was to put Brown's lunar theory into the machine and evaluate the expressions directly. Another project was something entirely new: a numerical integration of the equations of motion for the Sun and the four major planets. This became feasible only after electronic digital computers became available. Eventually this led to the Jet Propulsion Laboratory Development Ephemeris series.

In the meantime, Brown's theory was improved with better constants and the introduction of Ephemeris Time and the removal of some empirical corrections associated with this. This led to the Improved Lunar Ephemeris (ILE), which, with some minor successive improvements, was used in the astronomical almanacs from 1960 through 1983 and enabled lunar landing missions.

The most significant improvement of position observations of the Moon have been the Lunar Laser Ranging measurements, obtained using Earth-bound lasers and special retroreflectors placed on the surface of the Moon. The time-of-flight of a pulse of laser light to one of the retroreflectors and back gives a measure of the Moon's distance at that time. The first of five retroreflectors that are operational today was taken to the Moon in the Apollo 11 spacecraft in July 1969 and placed in a suitable position on the Moon's surface by Buzz Aldrin. Range precision has been extended further by the Apache Point Observatory Lunar Laser-ranging Operation, established in 2005.

Numerical integrations, relativity, tides, librations
The lunar theory, as developed numerically to fine precision using these modern measures, is based on a larger range of considerations than the classical theories: It takes account not only of gravitational forces (with relativistic corrections) but also of many tidal and geophysical effects and a greatly extended theory of lunar libration. Like many other scientific fields this one has now developed so as to be based on the work of large teams and institutions. An institution notably taking one of the leading parts in these developments has been the Jet Propulsion Laboratory (JPL) at California Institute of Technology; and names particularly associated with the transition, from the early 1970s onwards, from classical lunar theories and ephemerides towards the modern state of the science include those of J. Derral Mulholland and J.G. Williams, and for the linked development of solar system (planetary) ephemerides E. Myles Standish.

Since the 1970s, JPL has produced a series of numerically integrated Development Ephemerides (numbered DExxx), incorporating Lunar Ephemerides (LExxx). Planetary and lunar ephemerides DE200/LE200 were used in the official Astronomical Almanac ephemerides for 1984–2002, and ephemerides DE405/LE405, of further improved accuracy and precision, have been in use as from the issue for 2003. The current ephemeris is DE440.

Analytical developments
In parallel with these developments, a new class of analytical lunar theory has also been developed in recent years, notably the Ephemeride Lunaire Parisienne by Jean Chapront and Michelle Chapront-Touzé from the Bureau des Longitudes. Using computer-assisted algebra, the analytical developments have been taken further than previously could be done by the classical analysts working manually. Also, some of these new analytical theories (like ELP) have been fitted to the numerical ephemerides previously developed at JPL as mentioned above. The main aims of these recent analytical theories, in contrast to the aims of the classical theories of past centuries, have not been to generate improved positional data for current dates; rather, their aims have included the study of further aspects of the motion, such as long-term properties, which may not so easily be apparent from the modern numerical theories themselves.

Notes

References

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External links

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