text:
Alexisonfire

Alexisonfire (pronounced "Alexis on Fire") is a Canadian post-hardcore band formed in St. Catharines, Ontario in 2001. The band's members are George Pettit (vocals), Dallas Green (vocals, rhythm guitar, keyboards), Wade MacNeil  (lead guitar, backing vocals), Chris Steele (bass) and Jordan Hastings (drums, percussion). The band has won numerous awards, and in Canada their albums have all been certified either gold or platinum.

Alexisonfire (2001–2003)
Alexisonfire was formed in late 2001 in the aftermath of a three-band break up. Pettit was playing guitar in a metal band called Condemning Salem, Green was lead singer and guitar player in Helicon Blue, and MacNeil and Steele played in a punk band called Plan 9. These bands broke up at the same time, and Pettit, Steele, MacNeil and Green recruited drummer Jesse Ingelevics, and formed Alexisonfire. The band's name was derived from Alexis Fire, a pornographic actress. When Fire discovered that they were using her website name as their band name, she threatened to sue, but it was discovered that the moniker was not registered, and no further action took place.

In 2002, the band released its first EP, Math Sheets Demo, so named because the CD was wrapped in Jesse Ingelevics' math homework. This caught the attention of recording engineer Greg Below and Montreal journalist Mitch Joel, who were setting up the record label Distort Entertainment and were looking for artists. Below was also working with EMI, which allowed the band to record at the company's in-house studio, and land a co-publishing and distribution deal.

On October 31, 2002, Alexisonfire was released. Although there was a distribution deal with EMI, the album's success was mostly attributed to word-of-mouth. They had already been playing dates in Ontario and New York with bands like GWAR, Juliana Theory and Glassjaw; 2003 saw them touring in support of the album, crossing Canada twice, playing with Spitalfield and Billy Talent, appearing at Hellfest, and touring Europe with Rise Against.

In October 2005, Alexisonfire was certified gold in Canada, marking over 50,000 sales. (In 2014, Dine Alone Records released a remastered version of the album.)

At the 2004 Canadian Independent Music Awards, the video for the album's song "Pulmonary Archery" won Best Video. They were named Favourite Indie Band at the CASBY Awards, and the video for the song "Counterparts and Number Them" was nominated for Best Independent Video at the MuchMusic Video Awards.

Watch Out! (2004–2005)
Alexisonfire recorded their second album with Julius Butty at his Silo Studios near Hamilton, Ontario, Watch Out! and was released on June 29, 2004. It was released worldwide, mainly through Distort but through Equal Vision Records in the USA, and Sorepoint Records in the UK. It debuted at No. 6 on the Nielsen Soundscan Top 200, sold 6,000 copies in its first week, received gold certification in Canada in twelve weeks, and certified platinum in 2007. The critical reception came from the fact that the band was more focused from the eighteen months of touring, helping them harness more aggression, release more emotion, and fine-tune all the tracks. The album was noted as a real departure from their debut album, and was a critical success.

As soon as the album was released, the band went on tour, playing the Vans Warped Tour on several US dates, and then heading to the UK, playing the Reading and Leeds Festivals and other British gigs. (While playing Glasgow with Johnny Truant and The Blood Roses in, the members of all three bands had the word "Yeti" tattooed on themselves. On an episode of the MuchMusic program The New Music, Pettit and Green said that the idea for the tattoos came from the 1988 Gary Oldman film The Firm.) The band spent all of 2005 on the road, touring the UK, US, Canada and Europe. They also played the Summer Sonic Festival in Japan.

On June 14, 2005, Alexisonfire posted a statement on their website stating that founding drummer Jesse Ingelevics had left the band. He was replaced by Jordan Hastings, late of the band Jersey.

At the MuchMusic Video Awards, the video for the song "Accidents" won Best Independent Video, and the band was nominated for the Peoples' Choice Award – Favourite Canadian Group. At the Juno Awards of 2005, Alexisonfire won the award for New Group of the Year.

Crisis (2006–2007)
On August 22, 2006, the band released their third studio album, Crisis, which received rave reviews and continues to be deemed 'important'.

The album's release was marked with a party on a boat on the River Thames in London, England. This also launched a 10-month world tour that took them through the UK, Australia, Canada and the US. They were now playing to crowds of up to 80,000 people, at the Reading and Leeds Festivals, Festival d'été de Québec, and they headlined at the Brixton Academy in London. They played the Warped Tour, the Taste of Chaos tour, the Saints & Sinners Festival and Australia's Soundwave festival. At this point, they were one of the most popular bands in Canada.

The band toured with Anti-Flag, Saosin, The Bled, Norma Jean, Every Time I Die, Cancer Bats, Attack in Black, Moneen, Envy on the Coast, A Change of Pace, The Ghost of a Thousand and The Dear & Departed, among others.

The tour produced three live albums: Live At Brixton Academy (London, 11/13/07),  Live At Manchester Academy (11/14/07),  and Live At Birmingham Academy (now O2 Academy Birmingham) (11/16/07). At this time, Pettit told a reporter: "The next record, I think, is us pretty much wanting to put the knife in screamo. I don't want to be the band that saves it, I want to be the band that kills it." Pettit later regretted making the statement.

At the 2006 CASBY Awards, Crisis won Favorite New Indie Release. At the 2007 MuchMusic Video Awards, the video for "This Could Be Anywhere in the World" won the award for Best Cinematography and was nominated for Best Rock Video. The band was also nominated for the Peoples' Choice Award – Favourite Canadian Group. At the Juno Awards of 2007, Crisis garnered a nomination for CD/DVD Artwork Design of the Year, Julius Butty received a Producer of the Year nomination for "This Could Be Anywhere in the World", and Alexisonfire was nominated for Group of the Year.

Old Crows/Young Cardinals and Dog's Blood (2008–2010)
In 2008, MacNeil told a Bombshell Zine interviewer: "Alexis hasn't broken up, but we'll see what happens. We are at a crossroads now." As a result, by 2009, rumours that Alexisonfire was about to break up abounded, but the band announced the name of their new album on February 1. They began recording Old Crows/Young Cardinals on the same day. By March 1, the recording process was near completion and two songs were announced--"Midnight Regulations" and "Emerald St." On March 31, 2009, it was confirmed that Alexisonfire had signed to Dine Alone Records, whose founder, Joel Carriere, had once been the band's manager.

On April 20, Alexisonfire released the song "Young Cardinals" for radio airplay. The music video premiered on MuchOnDemand on May 15, 2009; the album was released on June 23, 2009, and was very well received.

The band then went on a 300-date tour through Europe, the US and Canada, which lasted through December 2010.

In 2008, Dallas Green told Canoe.ca that he had sketched out new songs that he hoped would take the band into "new, weird territories". These songs would become the four-track EP Dogs Blood, which was released in 2010. The band announced the release of Dogs Blood at the 2009 Verge Awards, hosted by The Verge (XM), where Old Crows/Young Cardinals was nominated for Album of the Year and the band was nominated as Artist of the Year. At the Juno Awards of 2010, Old Crows/Young Cardinals was nominated as Rock Album of the Year.

On February 16, 2010, the band was set to play a free all-ages show at the 2010 Winter Olympics venue Live City Yaletown when, seconds into the show, the rush of the audience broke a barrier and people were trampled; 20 were slightly injured. Alexisonfire returned to Vancouver later that year as headliners at the PNE Forum.

Also in 2010, the band released a collection of six songs available exclusively through iTunes as a digital download. The EP, iTunes Originals, contained previously-recorded material from the group's discography, versions of some of their previously released songs performed slightly differently, and interviews with the band. On November 22, 2010, a digital version of their Aussie Tour 7" was released on iTunes. It contains two cover songs, originally by Midnight Oil and The Saints.

Disbandment and farewell tour (2011–2012)
In 2005, Dallas Green had launched a solo folk/rock side project called City and Colour. The project had become very successful and between that and his commitments to Alexisonfire, he said that he suffered a nervous breakdown and that being in Alexisonfire was killing him. At the end of the Old Crows/Young Cardinals tour, Green told the band that he was leaving Alexisonfire, but that he would not announce his departure until the rest of the band decided on their future plans.

On February 14, 2011, Alexisonfire tweeted that they had been writing new music for their fifth studio album, describing it as "so heavy it's going to make Dog's Blood look like a ska record". Despite these statements, the album did not materialize and on August 5, 2011, Alexisonfire announced their break-up. In the statement, George Pettit cited the departures of both Green and MacNeil (who left to become the vocalist for Gallows), and personal issues among the remaining members as reasons for breaking up. Pettit also described the break-up as not being "amicable". Alexisonfire planned on celebrating their tenth anniversary with one last headlining Canadian tour and "a series of releases", although Green had specifically said that, for him, their December 19, 2010, show in their hometown was their last concert.

In July 2012, Green stated he had been in contact with other ex-Alexisonfire members, and that he and MacNeil had been "starting to talk about doing some final [Alexisonfire] shows, because when we did play our last show nobody knew it was our last show." In December 2012, Alexisonfire embarked on their farewell tour. It was initially nine dates, but it expanded to 30, with stops in Canada, the UK, Australia and Brazil. In December, the EP Death Letter was released, featuring new interpretations of songs spanning the band's previous four albums.

On December 25, 2013, the band released a limited-edition vinyl box set containing all the four albums as well as EPs, LPs, B-sides etc. One thousand copies were produced; they were sold out in 30 minutes. In August 2014, they released a slightly smaller second edition of the boxed set.

Reunion and Otherness (2015–present)

On March 9, 2015, the band announced a reunion tour, their first since their farewell tour in 2012, including dates at Reading and Leeds festivals, Sonic Boom, Heavy Montréal, X-Fest and Riot Fest. On September 19, 2015, at Riot Fest in Toronto, Wade MacNeil announced on stage that the band was officially back. The band later clarified this statement, reaffirming they had "no immediate plans" regarding new music or tours together, however they've played 100 concerts since 2015.

On February 12, 2016, the band released Live at Copps, a recording of their performance on December 30, 2012, at the Copps Coliseum in Hamilton, Ontario, which was the last show of their 2012 farewell tour. The album was released for download through iTunes, as well as in a special 4-record set, and as a Blu-ray video.

On June 22, 2016, Alexisonfire was announced as the main headliner for the 2017 Unify Gathering in Victoria, Australia, and announced a tour with The Dirty Nil, Behind Crimson Eyes and The Getaway Plan through Australia and New Zealand. The band was then announced as a headliner at the annual Quebec festival Montebello Rock and, on February 27, 2017, the band made a surprise three-song appearance at the Toronto stop of Billy Talent's Afraid of Heights Tour. They played Toronto's Danforth Music Hall in December 2017, and spent the following June touring Germany and the UK before heading back to Canada to play the Festival d'été de Québec.

On February 1, 2019, the band posted a black image on their Facebook page. Later in the day, the band posted a teaser video featuring a building with a green neon light spelling out the words "Familiar Drugs". Later, on February 12, 2019, the band posted 3 illusive black pictures on their Instagram page. Fans soon figured out that by changing the brightness and contrast on these black pictures, it revealed the numbers 2,15 and 19. On February 15, 2019, the band released a new song called "Familiar Drugs", their first new material in nearly nine years. On April 16, 2019, the band released the music video for "Familiar Drugs," which was shot completely on VHS and cellphones.

On May 24, 2019, the band released another standalone single called "Complicit", followed by "Season of the Flood", on January 13, 2020.

Alexisonfire went out on a short tour in 2019, playing shows in London, New York City, Los Angeles and Toronto as well as a show at Ottawa Bluesfest. This was followed by 2020 performances in Winnipeg, Edmonton, Calgary, Vancouver and Seattle.

During the COVID-19 pandemic, the band hosted a special one-time watch party on YouTube, showing a filmed performance of the final show on their farewell tour in December 2012 in Hamilton, Canada. Starting before the livestream was the premiere of their music video for their song, "Season of the Flood", which is made up of footage shot exclusively by AOF concertgoers in Winnipeg, Edmonton, Calgary and Vancouver during the tour in January.

In an interview with the Toronto Star in 2019, George Pettit revealed that, in 2015, he had become a professional firefighter and that, even though the band had reunited, that new career would be his priority. He also remains the lead singer in his side project, Dead Tired. Wade MacNeil continues as the lead singer for Black Lungs and Gallows. On May 21, 2021, MacNeil presented his latest project, Doom’s Children with his first single and video, "Flower Moon". Jordan Hastings continues with his long-time side project, Cunter. Dallas Green has continued on with City and Colour, and with You+Me, his collaboration with Pink.

In a June 2021 interview, Green stated that Alexisonfire was "trying to get all these new songs together for the first time in like ten years" implying that more new music was in the works. On March 10, 2022, the band announced their fifth studio album Otherness, their first album of new studio recordings in thirteen years. It was released on June 24, 2022. The album won the Juno Award for Rock Album of the Year at the Juno Awards of 2023. The band are set to open for Blink-182 in Toronto on August 15, 2024.

Musical style and legacy
The band describes their music as "the sound of two Catholic high-school girls in mid-knife-fight"; in 2004, then-drummer Jesse Ingelevics described their sound as "Mogwai meets Sunny Day Real Estate". Others have described their music as post-hardcore, emo, melodic hardcore, and screamo. The band members originally bonded over the myriad punk rock styles that their hometown scene consisted of, including moshcore, screamo, youth crew, crust punk and emo. Their music is unique for its use of three main vocalists: one clean (Green), one unclean (Pettit) and one serving as a combination of the two (MacNeil). Their 2009 album Old Crows / Young Cardinals saw a more prominent overall use of clean vocals, with Pettit also providing further clean vocals, having occasionally done so on Crisis. The band's first two albums include occasional spoken word vocals, also performed by Pettit.

The band have cited influenced including Saetia, Refused, Fucked Up, Moneen, Quicksand, Planes Mistaken for Stars, the Misfits, Tears for Fears, Hot Water Music, Elliott, the Appleseed Cast, Iggy Pop, Nick Cave, Alice in Chains, Jeff Buckley, Leonard Cohen and Slint.

Alexisonfire has been cited as an influence by bands such as Cancer Bats, Silverstein, Four Year Strong and 36 Crazyfists. Revolver Magazine additionally cited them as influencing the majority of the mid-2000s post-hardcore scene. Liam Cormier, lead vocalist of Cancer Bats, stated "everyone will always remember Alexisonfire and Billy Talent as the two bands that brought heavy music to the forefront and broke that scene wide open in this country." The band has also been well-regarded for their live performances throughout the years. Ex-frontman of Grade, Kyle Bishop, credited them for this in an interview with The Grid TO. "Previous to them, Canadian content was pretty lame, palatable stuff," he said. "Then you had Alexis come in, George shredding his larynx and smashing his face against the wall. They destroyed everything. And a lot of people gravitated to that, and I've never seen that happen in Canada before. They opened up the door for a lot of bands to be appreciated, and brought a whole new group of people into punk rock." In an article for Exclaim!, Ian Gormely praised the band for "opening doors for like-minded artists steeped in Southern Ontario's potent punk and metal scenes," and as having an "enduring influence in Canadian rock, and aggressive music in general".

Band members
Current members
 * George Pettit – vocals (2001–2011, 2012, 2015–present), keyboards (2009–2011)
 * Dallas Green – vocals, guitar (2001–2011, 2012, 2015–present), keyboards (2005–2009)
 * Wade MacNeil – vocals, guitar (2001–2011, 2012, 2015–present)
 * Chris Steele – bass (2001–2011, 2012, 2015–present), backing vocals (2022–present)
 * Jordan Hastings – drums, percussion (2005–2011, 2012, 2015–present), backing vocals (2022–present)

Current touring musicians
 * Matt Kelly – keyboards, organ, synthesizers, pedal steel, backing vocals (2022–present)

Former members
 * Jesse Ingelevics – drums, percussion (2001–2005)

Former touring musicians
 * Kenny Bridges – bass (2008)

Official Member Timeline

Discography
Studio albums
 * Alexisonfire (2002)
 * Watch Out! (2004)
 * Crisis (2006)
 * Old Crows / Young Cardinals (2009)
 * Otherness (2022)

title: Alexisonfire


text:
Talk:Pine Grove, Schuylkill County, Pennsylvania

Multiple Pine Grove, Pennsylvanias
Because of the existence of multiple Pine Grove, Pennsylvanias, this article has been moved from Pine Grove, Pennsylvania to Pine Grove, Schuylkill County, Pennsylvania. Pine Grove, Pennsylvania is now a disambig page. Kevyn 09:03, 13 Aug 2004 (UTC)

External links modified
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text: Category:Cloning

title: Category:Cloning


text:
User:Dcljr/Sandbox

Summary of arguments in portal RFC
through DexDor's comment at 16:25
 * 8 April 2018
 * Arguments in support of deprecating and deleting portals
 * Lack of maintenance
 * Portals are not well maintained.
 * Portals contain out-of-date information for readers (including getting out of sync with the portal's topic article).
 * Portals contain out-of-date information for editors (e.g., things to do).
 * Many portal pages are badly formatted (e.g. on small screens).
 * Many portal pages have redlinks / broken links (e.g. to Wikispecies).
 * Editor-related stuff in portals often gets out of date.
 * Vandalism may last longer in portal space (since bots may not be checking the portal space for vandalism).
 * Lack of usefulness
 * Portals are "not useful" / "useless".
 * Most portals show randomly selected content.
 * Showing randomly-selected information in portals is useless to readers.
 * Although some portals have some "useful stuff worth salvaging", "99%" of them should be deleted.
 * "I" have never looked at / noticed / edited / ... portals.
 * Portals do not have a "net benefit" to the encyclopedia.
 * Lack of relevance
 * Portals have low readership / page views.
 * Readers "don't care" about portals.
 * Some portals have high readership only because they are linked to from the Main Page.
 * Page views of portals linked to from the Main Page are largely due to "random clicks".
 * Page views of portals linked to from the Main Page are not reflective of reader interest.
 * The Portal template should be removed from articles.
 * The "idea" of portals is "obsolete".
 * Lack of effectiveness
 * Portals try to be of use to both readers and editors, and "are terrible at both".
 * Portals do not encourage people to improve articles, unlike the Main Page.
 * Poor fit in the encyclopedia
 * Portals do not aid in navigation.
 * Portals "aren't really part of the encyclopedia".
 * Portals have inconsistent formats.
 * Portals often break the convention of separating reader-side stuff from editor-side stuff (e.g. when portals have things like a to-do list).
 * Redundancy / lack of purpose
 * Outlines can serve the navigational roles of portals.
 * Curation of featured content can be done by WikiProjects.
 * The function of portals is "duplicated (and done better) elsewhere".
 * Portals are sometimes confused with WikiProjects (e.g. editors asking for help at a portal talk page instead of at the corresponding WikiProject talk page).
 * Editor-related stuff (e.g. to-do lists) in portals often duplicate WikiProject stuff.
 * Waste of resources
 * Portals waste editor resources that could be better spent doing other things (time spent creating/editing/maintaining portals, watchlist and edit history noise on other pages as links to portals are added/removed, deletion discussions, etc.)
 * Links to portals cause clutter on other pages (including category pages).
 * Portals can lead to the creation of many templates and other supporting pages (infrastructure), requiring more maintenance activity.
 * Bots may not be checking the portal space for vandalism, so users have to do that manually.
 * Lack of coverage
 * The system of portals is incomplete and "strange and random" in its coverage of topics.
 * Target of bad behaviors
 * Portals attract POV edits.
 * Portals seem to attract bad edits.
 * Portals can be content forks.
 * Portals are prone to vandalism.
 * Other statements of (purported) fact cited in "Support" comments
 * Approximately "99%" of links to portals occur in WikiProject banners.
 * Some portals were created as a result of "the hype" surrounding them in the past.

 * 9 April 2018

Proposal
What I am proposing is the following: Many of our cleanup templates (and some other types of templates) tag articles for the kinds of attention that only editors familiar with the subject matter will be able to effectively provide (e.g., lead rewrite, context, expand section, missing information, confusing, disputed, undue weight, clarify, dubious, original research, more citations needed, citation needed, clarify, and several others). While the dating of templates (using ) has become almost universal, indicating the subject matter in a similar way has not (although expert needed does have a mechanism for associating the tag with a WikiProject). As far as I know, only stub templates are routinely marked with the subject area, allowing "sorting" into an appropriate stub category, but this is done by creating a separate template for each subject area. ...
 * 1) Certain cleanup templates that require subject-area knowledge to effectively respond to should accept a parameter marking the subject area of the article being tagged.
 * 2) This information should be used to categorize tagged articles into subcategories by subject area (as is currently done by month).
 * Background
 * The proposal

Record labels
(Information for eventual use on Template talk:Timeline of Major Record Labels, discussing Template:Timeline of Major Record Labels.)

"Majors"
North American Majors (according to User:78.26) in:
 * 1890: North American Phonograph Company
 * 1898: National Phonograph (Edison), Columbia, Berliner
 * 1905: Victor, Columbia, Edison
 * 1925: Victor, Columbia, Brunswick/Vocalion, possibly Pathe
 * 1930: Victor, American Record Corporation
 * 1935: Victor, Decca, American Record Corporation
 * 1940: Victor, Decca, Columbia
 * 1948: Victor, Decca, Columbia, Capitol, possibly Mercury

According to Record label, there were six major record labels in 1988.

 * Big Six (1988–1999)
 * Warner Music Group
 * EMI
 * Columbia Records / CBS Records (in 1988 it wasn't Sony Music yet)
 * BMG
 * Universal Music Group
 * PolyGram

PolyGram was merged into UMG in 1999.

 * Big Five (1999–2004)
 * Warner Music Group
 * EMI
 * Sony Music
 * BMG
 * Universal Music Group

In 2004, Sony and BMG agreed to a joint venture to create the Sony BMG label (which would be renamed Sony Music Entertainment after a 2008 merger).

 * Big Four (2004–2012)
 * Warner Music Group
 * EMI
 * Sony BMG / Sony Music
 * Universal Music Group

In 2012, the major divisions of EMI were sold off separately by owner Citigroup: most of EMI's recorded music division was absorbed into UMG; EMI Music Publishing was absorbed into Sony/ATV Music Publishing; finally, EMI's Parlophone and Virgin Classics labels were absorbed into Warner Music Group in July 2013.

 * Big Three (2012–present)
 * Universal Music Group
 * Sony Music Entertainment
 * Warner Music Group

Table
Large chunks of text from the relevant articles (sometimes verbatim, sometimes heavily edited) have been inserted when the history was too complicated to easily add to the table — although I am in the process of trying to do that.

To be added:
 * North American Phonograph Company
 * National Phonograph Company (Edison)
 * Berliner Gramophone
 * Decca Records
 * Capitol Records
 * Mercury Records
 * Epic Records

title: User:Dcljr/Sandbox


text:
Masters of Reality

Masters of Reality is an American rock band formed in 1981 by frontman Chris Goss and guitarist Tim Harrington in Syracuse, New York, United States. They took the name for the band from a misprinted label of the third Black Sabbath album. Goss has remained the only constant band member.

The band's music has touched on many styles, ranging from hard rock to blues, from progressive rock to Beatlesque pop music. The band is sometimes associated with the "Palm Desert Scene", which includes bands like Kyuss, Queens of the Stone Age and many other stoner rock and "desert rock" bands.

History
Frontman Chris Goss started out with a band covering heavy 1970s rock acts (New York Dolls, Aerosmith, David Bowie, Blue Öyster Cult, Alice Cooper, Led Zeppelin) and writing his own songs since circa 1975. After getting into punk rock for a while (performing at CBGB in 1978), he didn't play guitar for a few years, instead preferring electronic music like Kraftwerk and becoming a club DJ.

In 1981 Goss and Tim Harrington started to make experimental home recordings with lo-fi, cheap and/or borrowed equipment that included a Sanyo boombox Rhythm Ace drum machine, a Korg, synthesizers and a Fender Vibroverb amp. The rhythm tracks of synths and a beat recorded on cassette would be played back to "overdub" vocals, guitar, more synthesizers, et cetera. They considered Manson Family as a name for their act, but never actually used it for their performances. They played regularly at CBGB with a sound reminiscent of Suicide or somewhat like how Nine Inch Nails or Marilyn Manson would sound in the 1990s.

Early original songs included "Building the Kingdom", "Voodoo Doll", "Metal Entity", "Cash", "Anchor", "Stones in Every Field" and "Doraldina's Prophecies".

Masters of Reality grew into a four-piece with the addition of Googe (bass) and Vinnie Ludovico (drums) and developed a sound with less electronics and more heavy blues rock with influences like Black Sabbath, Cream, Led Zeppelin and King Crimson. A demo tape reached producer Rick Rubin who went to see a live show in late 1986 and then signed the band to Def Jam. Rubin brought out the blues rock character of the band Rubin quit Def Jam but took the band with him to his new Def American label, before their self-titled debut album was eventually released in 1989.

The band appears briefly in the 1990 film Marked for Death (starring Steven Seagal).

Goss got frustrated with the band while touring the debut album. He quit the tour after Matt Dike invited him to come to Los Angeles and to get signed to his Delicious Vinyl label. They bought the rights from Rubin and released a newly sequenced version of the album with Doraldina's Prophecies as an extra track.

In 1992 Goss and Googe resurfaced, now with Ginger Baker (formerly of Cream) on drums. The new album Sunrise on the Sufferbus spawned a Top 10 rock chart hit with the single "She Got Me (When She Got Her Dress On)". An album cut sometimes used by American radio shows when they have a British guest is "T.U.S.A.", a rap by Baker describing the inability of Americans to make a proper cup of tea. Baker left the band after a few years and was replaced by Victor Indrizzo (of Circus of Power and Samiam).

Masters of Reality recorded the song "Climb Inside My World" for a 1994 Ren & Stimpy episode entitled "Jerry the Bellybutton Elf". The song was written by Steve Mellor who also wrote the episode in which it appeared.

Masters of Reality recorded a full studio album entitled The Ballad of Jody Frosty for Epic that was scheduled to be released in 1995, but it was shelved. One song appeared on the live album How High the Moon (1997) and some of the studio recordings were released on Give Us Barabbas (2004). The full album was eventually leaked online in 2004.

Masters of Reality were quiet for several years as Goss was occupied producing music for other bands. However, the band did appear at Johnny Depp's Viper Room night club in 1997 for a two-night stand, and a resultant live album, How High the Moon featured Stone Temple Pilots vocalist Scott Weiland on "Jindalee Jindalie".

In 1999 the band released  Welcome to the Western Lodge. Goss' connection to Queens of the Stone Age resulted in the collaborative album Deep in the Hole in 2001, and two years later, in the release of the subsequent live album Flak 'n' Flight.

In 2003, the band covered the song "Devil's Radio" for the album Songs from the Material World: A Tribute to George Harrison.

The band released its fifth album, Give Us Barabbas, in 2004, a collection of lost tracks opening with the "Ballad of Jody Frosty".

On August 24, 2009, the band released Pine/Cross Dover.

Members
"Masters Of Reality will always be a project with alternating lineups. (...) I can't afford paying people to tell they're in the band." – Chris Goss in 2002

May 2024 European Tour:
 * Chris Goss (vocals, guitar)
 * Alain Johannes (guitar)
 * John Leamy (drums)
 * Paul Powell (bass guitar)

Spring 2015 European Tour:
 * Chris Goss (vocals, guitar)
 * John Leamy (drums)
 * Paul Powell (bass guitar)
 * Josh Urist (guitar, keyboards)

Summer 2013 European Tour:
 * Chris Goss (vocals, guitar, keyboard)
 * John Leamy (drums)
 * Mathias Schneeberger (keyboards)
 * Paul Powell (bass guitar)
 * Dave Catching (guitar)

late 2010 US/UK Pine/Cross Dover tour:
 * Chris Goss (vocals, guitar, keyboard)
 * John Leamy (drums)
 * Mathias Schneeberger (keyboards)
 * Abby Travis (bass guitar)
 * Dave Catching (guitar)

Previous line-ups included:
 * Tim Harrington (duo and first band lineup)
 * Googe (first band lineup) (appears on Masters of Reality, Sunrise on the Sufferbus, How High the Moon, Give Us Barabbas bass, keyboards and cannoli
 * Vinnie Ludovico (first band lineup) (appears on Masters of Reality
 * Mr. Owl [Al Dunn] (additional keyboards on Masters of Reality)
 * Ginger Baker (appears on Sunrise on the Sufferbus)
 * John Leamy (appears on Welcome to the Western Lodge, Deep in the Hole, Flak 'n' Flight, Pine/Cross Dover)
 * Josh Homme (appears on Deep in the Hole, Flak 'n' Flight)
 * Nick Oliveri (appears on Deep in the Hole, Flak 'n' Flight)
 * Mark Lanegan (appears on Deep in the Hole, Flak 'n' Flight)
 * Brendon McNichol
 * Liam O'Malley (bass guitar)
 * Paul Powell

Studio albums

 * 1989 – Masters of Reality
 * 1992 – Sunrise on the Sufferbus
 * 1999 – Welcome to the Western Lodge
 * 2001 – Deep in the Hole
 * 2004 – Give Us Barabbas
 * 2009 – Pine/Cross Dover

Live albums

 * 1997 – How High the Moon: Live at the Viper Room
 * 2003 – Flak 'n' Flight

title: Masters of Reality


text:
File:Alien Resurrection poster.jpg

A film poster for "Alien: Resurrection", contended as fair use. Source: IMP Awards

Fair use in Alien Resurrection
Though this image is subject to copyright, its use is covered by the U.S. fair use laws because: http://www.impawards.com/1997/posters/alien_resurrection_ver1.jpg
 * 1) It's a low resolution copy of a Film Poster / VHS or DVD Cover.
 * 2) It doesn't limit the copyright owner's rights to sell the film in any way, in fact, it may encourage sales.
 * 3) Because of the low resolution, copies could not be used to make illegal copies of the artwork/image.
 * 4) The image is itself a subject of discussion in the article or used in the infobox thereof.
 * 5) The image is significant because it was used to promoted a notable film.

title: File:Alien Resurrection poster.jpg


text:
User:Mathounette~enwiki

fr:Utilisateur:Mathounette

See my user page at fr:Utilisateur:Mathounette

title: User:Mathounette~enwiki


text:
Talk:King Leir

Comment
Is this really "Cordella"? If so, let's make it "Cordella [sic]". --Chinasaur

The Early English Books Online (EEBO) database attributes this play to Michael Drayton (1563-1631). Caliginous (talk) 03:58, 23 May 2010 (UTC)
 * Hello; the link directing to the comparison of both, Leir and Lear seems to be dead end? Could someone check out? Thx! —Preceding unsigned comment added by 89.204.137.250 (talk) 21:33, 26 September 2010 (UTC)

What happens to Cordelia in this?
Is she killed off like in Shakespeare's? Or does it imply she will become Queen following the account of Geophry of Monmouth?--JaredMithrandir (talk) 05:54, 10 December 2016 (UTC)

Logan and Smith
These sources are unnamed and cannot be found. Logan and Smith does not refer to On Reading Shakespeare by Logan Pearsall Smith, because that is only 177 pages in length.

Shakeeespeare (talk) 17:06, 18 February 2024 (UTC)

title: Talk:King Leir


text:
Palm Desert Scene

The Palm Desert Scene is a group of related bands and musicians from Palm Desert, California. Their hard rock sound – sometimes described as desert rock – contains elements of heavy metal, psychedelia, blues, punk, alternative, grunge, and other genres. It often features distinctive repetitive drum beats, a propensity for free-form jamming, and "trance-like" or "sludgy" grooves. The involved musicians often play in multiple bands simultaneously, and there is a high rate of collaboration between bands. The Palm Desert Scene is also notable for fostering stoner rock pioneers Kyuss. The term "stoner rock" is sometimes used interchangeably with the term "desert rock". However, not all Palm Desert scene bands are "stoner rock" and not all stoner rock bands sound exactly like those in Palm Desert. Palm Desert has been named by Blender magazine as "one of the top seven rock n' roll cities in America".

History
The scene evolved from various Palm Desert bands' (especially Yawning Man's) marijuana-driven instrumental jam sessions in the desert. It is largely known for its heavy, grinding riffs and association with the use of illicit substances, particularly marijuana, peyote, LSD, and magic mushrooms. These jam sessions inevitably contained some psychedelic rock influences. Possibly because of the scene's proximity to Mexico and Spanish speaking communities, there is a significant influence of Latin music on Palm Desert rock which is very evident with the El Miradors. Due in part to their roots as smalltime bar bands, many of the Palm Desert bands have strong blues elements in their music as well.

Palm Desert bands built a large local following by frequently performing at bars and parties in and around the isolated towns of Southern California's desert areas. The band Kyuss, specifically, performed shows at desert parties known as "generator parties". These shows consisted of small crowds of people partying in the desert, beer drinking, drugs, and the use of gasoline-powered generators to provide electricity for the musical equipment. Kyuss and Queens of the Stone Age member Josh Homme commented that playing in the desert "was the shaping factor for [Kyuss]", noting that "there's no clubs here, so you can only play for free. If people don't like you, they'll tell you. You can't suck."

The Desert Sessions
One project within this scene are the Desert Sessions, in which Josh Homme invites a group of musicians, most of whom are from the Palm Desert scene, to Rancho De La Luna, a studio in the desert, where they write, rehearse and record some 10 songs in one week's time. The songs are recorded and then never played again by the same lineup, though a number of Desert Sessions songs have later been covered on albums by Queens of the Stone Age and become part of the QOTSA live repertoire. The Desert Sessions series has now yielded 12 volumes, which have been released in pairs on CD but individually in 10" vinyl EP format. Though the series is commonly associated with the Palm Desert Scene, not all artists in the scene have participated, and there have been other artists to contribute to the project who are clearly not from the scene, such as John McBain of Red Bank, New Jersey's Monster Magnet, Dean Ween of Pennsylvania's Ween and England's PJ Harvey.

title: Palm Desert Scene


text:
User talk:Nanson

Bill Nanson (DOB 14.10.1962) British Swiss Resident Married with a wife and one dog Research Chemist by training Currently Marketing by Profession Mainly wine articles for Wikipedia (predominantly Burgundy) It's all about communication... My websites

title: User talk:Nanson


text:
Pine Grove, West Virginia (disambiguation)

Pine Grove, West Virginia may refer to multiple places:

 * Pine Grove, Fayette County, West Virginia
 * Pine Grove, Marion County, West Virginia
 * Pine Grove, Pleasants County, West Virginia
 * Pine Grove, Wetzel County, West Virginia, a town


text:
Talk:Pine Grove, West Virginia

Multiple Pine Grove, West Virginias
Because of the existence of multiple Pine Grove, West Virginias, this page has been moved from Pine Grove, West Virginia to Pine Grove, Wetzel County, West Virginia. Pine Grove, West Virginia is now a disambiguation page. Kevyn 09:18, 13 Aug 2004 (UTC)

External links modified
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Wiki Education assignment: Urban Geography
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title: Talk:Pine Grove, West Virginia


text:
Lawrence Dundas, 1st Earl of Zetland

Lawrence Dundas, 1st Earl of Zetland (10 April 1766 – 19 February 1839) was a British politician and peer who sat in the House of Commons from 1790 to 1820 when he was raised to the peerage of the United Kingdom.

Early life
Dundas was the son of Thomas Dundas, 1st Baron Dundas and was born in Westminster on 10 April 1766. He was educated at Harrow and was admitted at Trinity College, Cambridge. He married Harriot Hale, one of the twenty-one children of General John Hale and his wife Mary Chaloner, by whom he had three sons and four daughters.

Political career
Dundas was elected Whig Member of Parliament for Richmond, North Yorkshire in 1790. Twelve years later he exchanged this seat for that of York, and in 1808 returned to Westminster as representative for his old Richmond seat. In 1811 he was again elected MP for York, and became Lord Mayor of the city that same year, having been an alderman since 1808. He was Lord Mayor a second time in 1821.

In 1820 Dundas succeeded his father as second Baron Dundas and as a baronet. He was appointed Lord Lieutenant of Orkney and Shetland in 1831, and in 1838, on the occasion of the coronation of Queen Victoria, he was created Earl of Zetland (i.e. Shetland) for having provided financial assistance to the new Queen's parents, the Duke & Duchess of Kent, in the years preceding her accession.

Slave holder
According to the Legacies of British Slave-Ownership at the University College London, Zetland was awarded compensation in the aftermath of the Slavery Abolition Act 1833 with the Slave Compensation Act 1837.

Zetland was associated with "T71/880 Grenada claim no. 604 (Dougalston Estate)" and "T71/881 Dominica claim no. 576A & B (Castle Bruce)", he owned 351 slaves in Grenada and Dominica and received a £8,135 payment at the time (worth £ in 2024).

Later life and legacy
Dundas's wife died in 1834. He died suddenly on 19 February 1839 at his home of Aske Hall, Yorkshire. He was succeeded by his eldest son Thomas Dundas, 2nd Earl of Zetland.

He is buried in the family vault at Trinity Church in central Falkirk.

title: Lawrence Dundas, 1st Earl of Zetland


text:
President of Benin

The president of Benin (Président de la République du Bénin) is both head of state and head of government in Benin. The Cabinet of Benin is under the authority of the President, and serves to advise and help formulate strategies. It also liaises with ministries and other government institutions.

A total of seven people have served as President (not counting two acting presidents, several interim military officeholders and a collective presidency). Additionally, one person, Mathieu Kérékou, has served on two non-consecutive occasions.

Election
The President of the Republic shall be elected by direct universal suffrage for a mandate of five years, renewable only one time.

In any case, no one shall be able to exercise more than two presidential mandates.

The election of the President of the Republic shall take place with a uninominal majority ballot in two rounds.

No one may be a candidate for the office of President of the Republic unless:

 * He is of Béninese nationality at birth or shall have acquired it for at least ten years;
 * He is of good morality and of great honesty;
 * He enjoys all his civil and political rights;
 * He is at least 40 years old but not more than 70 years old at the date of the filing of his candidacy;
 * He resides in the territory of the Republic of Bénin at the time of the elections;
 * He enjoys a satisfactory state of physical and mental well-being duly verified by a collegiate board of three doctors sworn and designated by the Constitutional Court.

The President of the Republic shall be elected by an absolute majority of votes cast. If that shall not be obtained in the first round of voting, it shall be followed, after a delay of fifteen days, by a second round.

The only ones who may be presented in the second round of balloting shall be the two candidates who shall have received the greatest number of votes in the first round. In case of the withdrawal of one or both of the two candidates, the next ones shall be presented in the order of their filing after the first balloting.

The candidate having received the relative majority of votes cast in the second round shall be declared elected.

The convocation of the electors shall be made by a decree issued in the Council of Ministers.

The first round of balloting for the election of the President of the Republic shall take place at least thirty days and at most forty days before the expiration date of the powers of the President in office.

The mandate of the new President of the Republic shall take effect by counting from the expiration date of the mandate of his predecessor.

Oath of office
Before taking his office, the President of the Republic shall take the following oath:

"Before God, the Manes [spirits] of the ancestors, the Nation and before the Béninese People, the only holder of sovereignty;

I, President of the Republic, elected in accordance with the laws of the Republic do solemnly swear

— To respect and defend the Constitution which the Béninese People have freely given to themselves;

— To fulfill loyally the high office that the Nation has entrusted to me;

— To allow myself to be guided only by the general interest and the respect for human rights to consecrate all my strength to the research and the promotion of the common good, of peace and of national unity;

— To preserve the integrity of the national territory;

— To conduct myself everywhere as a faithful and loyal servant of the people.

In case of perjury, that I shall submit to the severity of the law."

This oath shall be received by the President of the Constitutional Court before the National Assembly and the Supreme Court.

Vacancy
In case of vacancy of the Presidency of the Republic by death, resignation or permanent impediment, the National Assembly shall reconvene in order to rule on the case with an absolute majority of its members. The President of the National Assembly shall refer the matter to the Constitutional Court which shall certify it and declare the vacancy of the Presidency of the Republic. The duties of President of the Republic, with the exception of those mentioned in Articles 54 paragraph 3, 50, 60, 101, and 154 shall be temporarily exercised by the President of the National Assembly.

The election of a new President of the Republic shall take place thirty days at the least and forty days at most after the declaration of the permanent nature of the vacancy.

In case of bringing an accusation of the President of the Republic before the High Court of Justice, his interim shall be assumed by the President of the Constitutional Court who shall exercise all the duties of President of the Republic with the exception of those mentioned in Articles 54 paragraph 3, 58, 60, 101 and 154.

In case of absence from the territory, of illness and of vacation of the President of the Republic, his interim shall be assumed by a member of the Government whom he shall have designated and within the limitation of powers that he shall have delegated to him.

title: President of Benin


text:
Fermat curve

In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation:
 * $$X^n + Y^n = Z^n.\ $$

Therefore, in terms of the affine plane its equation is:
 * $$x^n + y^n = 1.\ $$

An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa. But by Fermat's Last Theorem it is now known that (for n > 2) there are no nontrivial integer solutions to the Fermat equation; therefore, the Fermat curve has no nontrivial rational points.

The Fermat curve is non-singular and has genus:

 * $$(n - 1)(n - 2)/2.\ $$

This means genus 0 for the case n = 2 (a conic) and genus 1 only for n = 3 (an elliptic curve). The Jacobian variety of the Fermat curve has been studied in depth. It is isogenous to a product of simple abelian varieties with complex multiplication.

The Fermat curve also has gonality:

 * $$n-1.\ $$

Fermat varieties
Fermat-style equations in more variables define as projective varieties the Fermat varieties.

title: Fermat curve


text:
File:Jubilee2000.png

Summary
Official logo for Great Jubilee of the year 2000. The five doves represent the five inhabited continents, Europe, Asia, Africa, the Americas and Oceania. The Latin text on the logo Christus Heri Hodie Semper means Christ, Yesterday, Today, Forever.

title: File:Jubilee2000.png


text:
Pine Grove, Wisconsin

Pine Grove, Wisconsin may refer to multiple places:
 * Pine Grove, Brown County, Wisconsin, unincorporated community
 * Pine Grove, Chippewa County, Wisconsin, unincorporated community
 * Pine Grove, Portage County, Wisconsin, town

title: Pine Grove, Wisconsin


text:
Ed Schieffelin

Edward Lawrence Schieffelin (1847–1897) was an Indian scout and prospector who discovered silver in the Arizona Territory, which led to the founding of Tombstone, Arizona. He entered into a partnership with his brother Al and mining engineer Richard Gird in a handshake deal that produced millions of dollars in wealth for all three men. During the course of Tombstone's mining history, about US $85,000,000 in silver was produced from its mines.

Early life
Ed Schieffelin was born in a coal-mining region of Wellsboro, Pennsylvania, the son of a prominent New York and Pennsylvania family, in 1847. His great-grandfather Jacob Schieffelin, Sr., born in 1757, joined the Loyalist army and served as Henry Hamilton's secretary during the Revolutionary War. Schieffelin was captured in 1779 and held prisoner in Williamsburg, Virginia. He escaped to Canada, where in 1780 he was appointed a lieutenant in the Queen's Rangers by Henry Clinton. He spent time in Montreal and Detroit, before returning to New York, where in 1794 he founded a drug company with his brother Lawrence. This firm still exists as a liquor import house, Schieffelin & Somerset. Jacob's wife, Hannah Lawrence, was a descendant of Quaker colonial religious pioneer John Bowne, Elizabeth Fones, and the Winthrop family of New England.

In January 1849, Jacob, Jr. traveled to California with his sons Alfred and Edward Girard on the ship Morrison. They arrived in September, but almost immediately booked passage home via Panama in November. Jacob Schieffelin, Jr. traveled overland and joined his brother and Ed. Schieffelin's father Clinton Emanuel Del Pela Schieffelin settled in the Rogue Valley, Oregon Territory, in the mid-1850s to raise cattle, grain and children. The family maintained an interest in the mining activities in the area.

Hunt for gold and silver
At age 17, Schieffelin set out on his own as a prospector and miner. He began looking for gold and silver in about 1865. From Oregon, he went east to Coeur d'Alene, then searched across Nevada into Death Valley, back into Colorado and then New Mexico.

In 1876, David P. Lansing of Phoenix, Arizona, described Schieffelin as "about the strangest specimen of human flesh I ever saw. He was 6 ft tall and had black hair that hung several inches below his shoulder and a beard that had not been trimmed or combed for so long a time that it was a mass of unkempt knots and mats. He wore clothing pieced and patched from deerskins, corduroy and flannel, and his hat was originally a slouch hat that had been pieced with rabbit skin until very little of the original felt remained."

A year later as a 30-year-old, Schieffelin moved to California to find gold. He surveyed the Grand Canyon area as well. Unsuccessful, he heard that a group of Hualapai Indians had enlisted as scouts for the U.S. Army, which was establishing a camp to counter the Chiricahua Apache threat and to secure the nearby border with Mexico. The Army established Camp Huachuca at the foot of the Huachuca Mountains in Pima County, Arizona Territory on March 3, 1877. Silver had already been discovered in some northern areas of Arizona Territory, but the southern portion had been under continued Apache attack.

Schieffelin accompanied the scouts on a few trips into the back country while prospecting part-time. He finally decided to stay put and explore the hills east full-time. The hills east of the San Pedro River where he prospected could be dangerous. They were only about 12 mi from the hostile Chiricahua Apache Indians led by Cochise, Geronimo and Victorio that had established a stronghold in the Dragoon Mountains.

Ore discovery
Frederick Brunckow, a Prussian-born mining engineer, discovered silver in the hills of Cochise County in 1858. He built a cabin near the San Pedro River after finding a small silver deposit nearby. He hired three other white men and about a dozen Mexican miners. In September 1860, two of the white men were robbed and murdered at the cabin and Brunckow was found dead in the mine with a rock drill through him. The German cook blamed the Mexican workers for the murders. After Brunckow's death, ongoing conflict with native Indians prevented further development of the mines for several years. Brunckow's San Pedro mine influenced Ed Schieffelin to prospect the rocky outcropping northeast of the cabin. In 1876, Schieffelin and his party were attacked by Apaches, and a man named Lenox was killed. The cabin was the site of 22 murders during the frontier days.

When friend and fellow army scout Al Sieber learned what Schieffelin was up to, he is quoted as telling him, "The only rock you will find out there will be your own tombstone". Another account reported Schieffelin's friends told him, "Better take your coffin with you; you will find your tombstone there, and nothing else."

In 1877, Schieffelin used Brunckow's cabin as a base of operations to survey the country. After many months, Ed was working the hills east of the San Pedro River when he found pieces of silver ore in a dry wash on a high plateau called Goose Flats. It took him several more months to find the source. When he located the vein, he estimated the vein to be 50 ft long and 12 in wide. Schieffelin's claim was sited near Lenox's grave site, and when he filed his first mining claim on September 21, 1877, he fittingly named his stake "Tombstone".

Flat broke, Schieffelin persuaded William Griffith to pay for the legal paperwork required to file a mining claim on September 3, 1877. Tucson did not have an assay office, and when they showed the sample ore to some local men, they thought it was worthless.

With only 30 cents in his pocket, Schieffelin set out to find his brother Al, whom he had not seen in four years. He believed Al was working the Silver King mine, about 180 mi to the north in central Arizona Territory near present-day Globe. But Schieffelin learned that Al had moved on to the McCracken Mine in Signal City, Arizona, another 300 mi north. Schieffelin spent his 30 cents on tobacco and had to pause in his search for his brother to earn enough money to go on. He found a job as a hoist operator at the Champion silver mine, and for fourteen days hauled up a dozen tons of ore every night by cranking a hand windlass.

Partnership formed
When Ed finally located his brother in February 1878, Al asked the foreman at the McCracken mine to look at brother Ed's ore specimens. The foreman thought the samples were mostly lead. Unconvinced, Schieffelin showed the samples to 20 or 30 others who had some expertise, and they all thought the ore worthless. Frustrated, Schieffelin threw his ore specimens out his brother's cabin door, as far as he could throw, but at the last minute held on to three of them. For the next four weeks he worked in the McCracken Mine, wielding a pick and shovel.

Ed learned about the McCracken Mine's recently arrived assayer, Richard Gird, who had a reputation as an expert. Taking his last three ore samples, Ed Schieffelin asked Gird if he thought they were worth assaying. Gird took a look and said he'd get back to Ed. Three days later, Al shook Ed out of his bunk and said Gird wanted to see him now. When they met, Gird told Ed that he valued the best of the ore samples at $2,000 a ton. Ed, Al Schieffelin and Richard Gird formed a partnership on the spot. Gird offered his expertise, connections, and a grubstake. They shook hands on their three-way deal, a gentlemen's agreement that was never put down on paper but that resulted in millions of dollars of wealth for all three men. When Richard resigned, his employer offered to make him general superintendent of the mine, but he declined.

Gird bought a second-hand blue spring wagon and loaded it with supplies, his assay equipment, and also bought a second mule that with Ed's mule could haul the wagon. Gird wanted time to wind up his affairs and to wait for spring and better weather, but Ed insisted they depart immediately. Al hesitated to leave his well-paid, $4.00 a day job as a miner. Ed and Gird didn't wait for him, but left that day. Al reconsidered and joined them that night. Reaching Arizona Territory, and despite reports of continued Apache raids and the murder of miners and ranchers in the area, the three men returned to Cochise County and set up camp at the Brunckow cabin. The deaths of several locals at the hands of the Apache Indians were testified to by the fresh graves near the cabin.

The three partners formed the Tombstone Gold and Silver Mining Company to hold title to their claims. Gird built a crude assay furnace in the cabin's fireplace. He found that Schieffelin's initial find of silver ore was valuable, but within a few weeks of mining the vein, Ed discovered it ended in a pinch about three feet deep. His brother Al and Gird were despondent, but Ed was optimistic he could find more ore deposits. He continued his search for many more weeks until one day Al found Ed joyously exclaiming over another sample of float ore he had found. Indifferently, Al told Ed he was a "lucky cuss," and that became the name of one of the richest mining claims in the Tombstone District. The ore samples assayed at $15,000 a ton. Ed shortly afterward identified another claim, the "Tough Nut" lode, rich in horn silver.

On June 17, 1879, Schieffelin showed up in Tucson driving the blue spring wagon carrying the first load of silver bullion valued at $18,744 (about $0 today)

Tombstone founded

When the first claims were filed, the initial settlement of tents and cabins was located at Watervale near the Lucky Cuss mine. By March 1879, about 100 residents occupied tents and shacks at Watervale. Former Territorial Governor Anson P.K. Safford offered financial backing for a cut of the men's mining claims, and Ed Schieffelin, his brother Al, and their partner Richard Gird formed the Tombstone Mining and Milling Company and built a stamping mill. On March 5, 1879, U.S. Deputy Mineral Surveyor Solon M. Allis finished laying out a new town site on a mesa named Goose Flats at 4539 ft, to top of the Tough Nut mine, and large enough to hold a growing town. The town was named "Tombstone" after Schieffelin's initial mining claim. The shelters at Watervale were relocated to the new town site and a scattering of cabins and tents was quickly built for about 100 residents.

During the first few months of mining, the upper portion of the Tombstone mining district was accidentally discovered by Ed Williams and Jack Friday. Late one night, their mules broke loose and dragging their chain, left the miners' dry camp for water along an Indian trail. The men tracked the mules' chain trail all the way to the Schieffelin camp. Williams and Friday noticed a bright gleam where the iron had dragged across bare rock. They filed a claim for their find, but Al and Ed Schieffelin and Richard Gird contested their claim, asserting it violated their earlier claims. When the two parties finally resolved their arguments and counterclaims, they agreed to divide the ground. Williams and Friday took the higher end, which they called the Grand Central, and the Schieffelin company took the lower end, which they named the Contention in remembrance of the quarrel that led to its founding. Those two mines were eventually the most profitable mines in Tombstone. Some of the ore from the "Lucky Cuss", "Tough Nut", and the "Contention" mines assayed at around $15,000 to the ton.

Ed Schieffelin preferred prospecting to running a mine and he left Tombstone to find more ore. When he returned four months later, Gird had lined up buyers for their interest in the Contention, which they sold for $10,000 to J.H. White and S. Denson, who represented W.D. Dean of San Francisco. The sellers thought the $10,000 price was exorbitant. The Grand Central and Contention claims turned out to be the richest claims in the district, producing millions of dollars in bullion. The Schieffelin company also soon sold a half-interest in the Lucky Cuss, and the other half turned into a steady stream of money.

On March 13, 1879, Al and Ed Schieffelin sold their two-thirds interest in the Tombstone Mining and Milling Company, which owned the Tough Nut mine, for US$1 million each to the Corbin brothers, Hamilton Distin of Philadelphia, and Simmons Squire of Boston. Safford became president of the new Tombstone Gold and Silver Milling and Mining Company with Richard Gird as superintendent. Ed moved on, but Al remained in Tombstone for some time longer. Gird later sold off his one-third interest for US$1 million, doubling what the Schieffelins had been paid. Gird remained in the territory, but Ed Schieffelin left to pursue other interests.

When Cochise County was formed in February 1881, Tombstone became the county seat. In 1881, early in Tombstone's rapid growth, Ed's brother Al built Schieffelin Hall as a theater, recital hall, and a meeting place for Tombstone citizens. His great-niece Mary Schieffelin Brady reopened it in 1964 and it remains an attraction in Tombstone. It is the largest standing adobe structure in the southwest United States.

At its height in the mid-1880s, Tombstone's population was officially about 7,000 miners, but some estimates figure in an additional 5–7,000 women and children, Chinese, Mexicans, and prostitutes. In the late 1880s, the silver mines reached the water table and the mines eventually filled with water. Tombstone's population faded, until tourism became its main attraction.

Later life
Ed had accumulated more than $1 million in wealth as a result of the silver boom. While he had maintained a casual appearance, including long hair and beard, he cleaned himself up. He traveled to New York City, Chicago, Washington, D.C., and other cities. He met many distinguished people. Ever restless, over the next 20 years Ed showed up at nearly every boom town in the West.

Schieffelin had made a practice of studying maps and believed there was a great "continental belt" of mineral wealth that extended from South America through Mexico, the United States, and British Columbia. During 1882, Ed prepared for what he planned to be a three-year survey of mineral wealth. He began the expedition with his brother Al and three others on a trip up the Yukon River. They commissioned construction of and fitted out a small, shallow draft sternwheel steamer which they named the New Packet. Schieffelin prospected during the trip in Alaska and found some specks of gold. He was for a while convinced he had found the continental belt he had been searching for. But he was extremely discouraged by the Arctic cold he experienced, up to 50 F below zero (-46 C). He decided that mining in Alaska was a lost cause and he returned to the lower 48 states.

In 1883, he returned to San Francisco, where he met Mrs. Mary E. Brown. They married the same year in La Junta, Colorado, and they spent part of the winter in Salt Lake City, Utah. In the spring of 1884, they returned to California, where Ed built a mansion for his wife across the bay from San Francisco in Alameda. They bought a home in Los Angeles that they shared with Ed's brother Al until Al died of consumption in 1885.

Early death
In 1897 Schieffelin bought a ranch near his brothers Effingham (Eff) and Jacob (Jay) outside Woodville, now Rogue River, Oregon. He continued prospecting in the Canyonville area, where he searched for gold and silver. On May 12, 1897, after he had not shown up in town for supplies for several days, his neighbor checked on him and found him face down on the floor of his miner's cabin. The coroner ruled that he had died of a heart attack. The ore samples found in his cabin were later reported to have assayed at more than $2,000 to the ton. Other reports from his family said it was only valued at $7 per ton. Schieffelin did not leave a map or directions behind pointing to the origins of his discovery. He was initially buried near his cabin about 20 mi east of Canyonville.

It was shortly afterward learned that he had requested to be buried in Tombstone. "It is my wish, if convenient, to be buried in the dress of a prospector, my old pick and canteen with me, on top of the granite hills, about three miles westerly from the City of Tombstone, Arizona, and that a monument, such as prospectors build when locating a mining claim, be built over my grave." Schieffelin was interred about 3 mi northwest of Tombstone, Arizona, near the dry wash in which he originally found silver ore and the later location of the Grand Central Mine. He was buried as his will specified: in mining clothes, with pick, shovel, and his old canteen. He divided his estate between his wife and his brother Jay. "I give my wife, Mary E. Schieffelin, all interests, both real and personal properties—in Alameda and Santa Clara Counties, California—also fifteen $1,000 University of Arizona Bonds. All other properties, both real and personal, I give to my brother, Jay L. Schieffelin." Mary Schieffelin moved to New York City after her husband's death.

Legacy
A 25 ft tall monument representing the type of marker a miner makes in claiming a strike was erected near the spot of his original claim. The plaque on it reads, "Ed Shieffelin, died May 12, 1897, aged 49 years, 8 months. A dutiful son, a faithful husband, a kind brother, and a true friend." Years before, Schieffelin had written, "I never wanted to be rich, I just wanted to get close to the earth and see mother nature's gold." Schieffelin Gulch Road in the Rogue Valley, Oregon is named after the family who homesteaded there.

There are widely varying estimates of the value of gold and silver mined during the course of Tombstone's history. In 1883, writer Patrick Hamilton estimated that during the first four years of activity the mines produced about $25,000,000 (approximately $ today). Other estimates include $40 million to $85 million (about $ to $ today). Renewed mining is planned for the area.

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Hamilton–Jacobi equation

In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.

The Hamilton–Jacobi equation is a formulation of mechanics in which the motion of a particle can be represented as a wave. In this sense, it fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the eighteenth century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed by mechanical systems is similar to, but not identical with, Schrödinger's equation, as described below; for this reason, the Hamilton–Jacobi equation is considered the "closest approach" of classical mechanics to quantum mechanics. The qualitative form of this connection is called Hamilton's optico-mechanical analogy.

In mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations. It can be understood as a special case of the Hamilton–Jacobi–Bellman equation from dynamic programming.

Overview
The Hamilton–Jacobi equation is a first-order, non-linear partial differential equation

for a system of particles at coordinates $\mathbf{q}$. The function $$H$$ is the system's Hamiltonian giving the system's energy. The solution of the equation is the action functional, $S$, called Hamilton's principal function in older textbooks. The solution can be related to the system Lagrangian $$\ \mathcal{L}\ $$ by an indefinite integral of the form used in the principle of least action: $$\ S = \int \mathcal{L}\ \operatorname{d}t + ~\mathsf{ some\ constant}~$$ Geometrical surfaces of constant action are perpendicular to system trajectories, creating a wavefront-like view of the system dynamics. This property of the Hamilton–Jacobi equation connects classical mechanics to quantum mechanics.

Notation
Boldface variables such as $$\mathbf{q}$$ represent a list of $$N$$ generalized coordinates, $$\mathbf{q} = (q_1, q_2, \ldots, q_{N-1}, q_N)$$

A dot over a variable or list signifies the time derivative (see Newton's notation). For example, $$\dot{\mathbf{q}} = \frac{d\mathbf{q}}{dt}.$$

The dot product notation between two lists of the same number of coordinates is a shorthand for the sum of the products of corresponding components, such as $$\mathbf{p} \cdot \mathbf{q} = \sum_{k=1}^N p_k q_k.$$

Definition
Let the Hessian matrix $H_{\cal L}(\mathbf{q},\mathbf{\dot q},t) = \left\{\partial^2 {\cal L}/\partial {\dot q}^i\partial {\dot q}^j\right\}_{ij}$ be invertible. The relation $$ \frac{d}{dt}\frac{\partial {\cal L}}{\partial{\dot q}^i} = \sum^n_{j=1}\left(\frac{\partial^2 {\cal L}}{\partial{\dot q}^i\partial{\dot q}^j} {\ddot q}^j + \frac{\partial^2 {\cal L}}{\partial{\dot q}^i\partial{q}^j}{\dot q}^j \right) +\frac{\partial^2 {\cal L}}{\partial{\dot q}^i \partial t},\qquad i=1,\ldots,n, $$ shows that the Euler–Lagrange equations form a $$n \times n$$ system of second-order ordinary differential equations. Inverting the matrix $$H_{\cal L}$$ transforms this system into $$\ddot q^i = F_i(\mathbf{q},\mathbf{\dot q},t),\ i=1,\ldots, n.$$

Let a time instant $$t_0$$ and a point $$\mathbf{q}_0 \in M$$ in the configuration space be fixed. The existence and uniqueness theorems guarantee that, for every $$\mathbf{v}_0,$$ the initial value problem with the conditions $$\gamma|_{\tau=t_0} = \mathbf{q}_0$$ and $${\dot \gamma}|_{\tau=t_0} = \mathbf{v}_0$$ has a locally unique solution $$\gamma = \gamma(\tau; t_0,\mathbf{q}_0,\mathbf{v}_0).$$ Additionally, let there be a sufficiently small time interval $$ (t_0,t_1) $$ such that extremals with different initial velocities $$\mathbf{v}_0$$ would not intersect in $$M \times (t_0,t_1).$$ The latter means that, for any $$\mathbf{q} \in M$$ and any $$t \in (t_0,t_1),$$ there can be at most one extremal $$\gamma=\gamma(\tau;t,t_0,\mathbf{q},\mathbf{q}_0)$$ for which $$\gamma|_{\tau=t_0} = \mathbf{q}_0$$ and $$\gamma|_{\tau=t} = \mathbf{q}.$$ Substituting $$\gamma=\gamma(\tau;t,t_0,\mathbf{q},\mathbf{q}_0)$$ into the action functional results in the Hamilton's principal function (HPF)

where
 * $$\gamma=\gamma(\tau;t,t_0,\mathbf{q},\mathbf{q}_0),$$
 * $$\gamma|_{\tau=t_0} = \mathbf{q}_0,$$
 * $$\gamma|_{\tau=t} = \mathbf{q}.$$

Formula for the momenta
The momenta are defined as the quantities $ p_i(\mathbf{q},\mathbf{\dot q},t) = \partial {\cal L}/\partial \dot q^i.$ This section shows that the dependency of $$p_i$$ on $$\mathbf{\dot q}$$ disappears, once the HPF is known.

Indeed, let a time instant $$t_0$$ and a point $$\mathbf{q}_0$$ in the configuration space be fixed. For every time instant $$t$$ and a point $$\mathbf{q},$$ let $$\gamma=\gamma(\tau;t,t_0,\mathbf{q},\mathbf{q}_0)$$ be the (unique) extremal from the definition of the Hamilton's principal function $S$. Call $$\mathbf{v}\, \stackrel{\text{def}}{=}\, \dot \gamma(\tau;t,t_0,\mathbf{q},\mathbf{q}_0)|_{\tau=t}$$ the velocity at $\tau = t$. Then

$$

Formula
Given the Hamiltonian $$H(\mathbf{q},\mathbf{p},t)$$ of a mechanical system, the Hamilton–Jacobi equation is a first-order, non-linear partial differential equation for the Hamilton's principal function $$S$$,

$$

Alternatively, as described below, the Hamilton–Jacobi equation may be derived from Hamiltonian mechanics by treating $$ S$$ as the generating function for a canonical transformation of the classical Hamiltonian $$H = H(q_1,q_2,\ldots, q_N;p_1,p_2,\ldots, p_N;t).$$

The conjugate momenta correspond to the first derivatives of $$S$$ with respect to the generalized coordinates $$p_k = \frac{\partial S}{\partial q_k}.$$

As a solution to the Hamilton–Jacobi equation, the principal function contains $$N+1$$ undetermined constants, the first $$N$$ of them denoted as $$\alpha_1,\, \alpha_2, \dots, \alpha_N$$, and the last one coming from the integration of $$\frac{\partial S}{\partial t}$$.

The relationship between $$\mathbf{p}$$ and $$\mathbf{q}$$ then describes the orbit in phase space in terms of these constants of motion. Furthermore, the quantities $$\beta_k=\frac{\partial S}{\partial\alpha_k},\quad k=1,2, \ldots, N $$ are also constants of motion, and these equations can be inverted to find $$\mathbf{q}$$ as a function of all the $$\alpha$$ and $$\beta$$ constants and time.

Comparison with other formulations of mechanics
The Hamilton–Jacobi equation is a single, first-order partial differential equation for the function of the $$N$$ generalized coordinates $$q_1,\, q_2, \dots, q_N$$ and the time $$t$$. The generalized momenta do not appear, except as derivatives of $$S$$, the classical action.

For comparison, in the equivalent Euler–Lagrange equations of motion of Lagrangian mechanics, the conjugate momenta also do not appear; however, those equations are a system of $$N$$, generally second-order equations for the time evolution of the generalized coordinates. Similarly, Hamilton's equations of motion are another system of 2N first-order equations for the time evolution of the generalized coordinates and their conjugate momenta $$p_1,\, p_2, \dots, p_N$$.

Since the HJE is an equivalent expression of an integral minimization problem such as Hamilton's principle, the HJE can be useful in other problems of the calculus of variations and, more generally, in other branches of mathematics and physics, such as dynamical systems, symplectic geometry and quantum chaos. For example, the Hamilton–Jacobi equations can be used to determine the geodesics on a Riemannian manifold, an important variational problem in Riemannian geometry. However as a computational tool, the partial differential equations are notoriously complicated to solve except when is it possible to separate the independent variables; in this case the HJE become computationally useful.

Derivation using a canonical transformation
Any canonical transformation involving a type-2 generating function $$G_2 (\mathbf{q}, \mathbf{P}, t)$$ leads to the relations $$ \mathbf{p} = {\partial G_2 \over \partial \mathbf{q}}, \quad \mathbf{Q} = {\partial G_2 \over \partial \mathbf{P}}, \quad K(\mathbf{Q},\mathbf{P},t) = H(\mathbf{q},\mathbf{p},t) + {\partial G_2 \over \partial t} $$ and Hamilton's equations in terms of the new variables $$\mathbf{P}, \,\mathbf{Q}$$ and new Hamiltonian $$K$$ have the same form: $$ \dot{\mathbf{P}} = -{\partial K \over \partial \mathbf{Q}}, \quad \dot{\mathbf{Q}} = +{\partial K \over \partial \mathbf{P}}. $$

To derive the HJE, a generating function $$G_2 (\mathbf{q}, \mathbf{P}, t)$$ is chosen in such a way that, it will make the new Hamiltonian $$K=0$$. Hence, all its derivatives are also zero, and the transformed Hamilton's equations become trivial $$\dot{\mathbf{P}} = \dot{\mathbf{Q}} = 0$$ so the new generalized coordinates and momenta are constants of motion. As they are constants, in this context the new generalized momenta $$\mathbf{P}$$ are usually denoted $$\alpha_1,\, \alpha_2, \dots, \alpha_N$$, i.e. $$P_m =\alpha_m$$ and the new generalized coordinates $$\mathbf{Q}$$ are typically denoted as $$\beta_1,\, \beta_2, \dots , \beta_N$$, so $$Q_m =\beta_m$$.

Setting the generating function equal to Hamilton's principal function, plus an arbitrary constant $$A$$: $$G_2(\mathbf{q},\boldsymbol{\alpha},t)=S(\mathbf{q},t)+A, $$ the HJE automatically arises $$\mathbf{p}=\frac{\partial G_2}{\partial \mathbf{q}}=\frac{\partial S}{\partial \mathbf{q}} \, \rightarrow \, H(\mathbf{q},\mathbf{p},t) + {\partial G_2 \over \partial t}=0 \, \rightarrow \, H\left(\mathbf{q},\frac{\partial S}{\partial \mathbf{q}},t\right) + {\partial S \over \partial t}=0. $$

When solved for $$ S(\mathbf{q},\boldsymbol\alpha, t) $$, these also give us the useful equations $$\mathbf{Q} = \boldsymbol\beta = {\partial S \over \partial \boldsymbol\alpha},$$ or written in components for clarity $$ Q_{m} = \beta_{m} = \frac{\partial S(\mathbf{q},\boldsymbol\alpha, t)}{\partial \alpha_{m}}. $$

Ideally, these N equations can be inverted to find the original generalized coordinates $$ \mathbf{q} $$ as a function of the constants $$ \boldsymbol\alpha, \,\boldsymbol\beta, $$ and $$ t $$, thus solving the original problem.

Separation of variables
When the problem allows additive separation of variables, the HJE leads directly to constants of motion. For example, the time t can be separated if the Hamiltonian does not depend on time explicitly. In that case, the time derivative $$\frac{\partial S}{\partial t} $$ in the HJE must be a constant, usually denoted ($$-E $$), giving the separated solution $$ S = W(q_1,q_2, \ldots, q_N) - Et $$ where the time-independent function $$W(\mathbf{q}) $$ is sometimes called the abbreviated action or Hamilton's characteristic function and sometimes   written $$S_0$$ (see action principle names). The reduced Hamilton–Jacobi equation can then be written $$ H\left(\mathbf{q},\frac{\partial S}{\partial \mathbf{q}} \right) = E. $$

To illustrate separability for other variables, a certain generalized coordinate $$q_k $$ and its derivative $$\frac{\partial S}{\partial q_k} $$ are assumed to appear together as a single function $$\psi \left(q_k, \frac{\partial S}{\partial q_k} \right)$$ in the Hamiltonian $$ H = H(q_1,q_2,\ldots, q_{k-1}, q_{k+1},\ldots, q_N; p_1,p_2,\ldots, p_{k-1}, p_{k+1},\ldots, p_N; \psi; t). $$

In that case, the function S can be partitioned into two functions, one that depends only on qk and another that depends only on the remaining generalized coordinates $$S = S_k(q_k) + S_\text{rem}(q_1,\ldots, q_{k-1}, q_{k+1}, \ldots, q_N, t). $$

Substitution of these formulae into the Hamilton–Jacobi equation shows that the function ψ must be a constant (denoted here as $$\Gamma_k $$), yielding a first-order ordinary differential equation for $$S_k (q_k), $$

$$ \psi \left(q_k, \frac{ d S_k}{ d q_k} \right) = \Gamma_k. $$

In fortunate cases, the function $$S $$ can be separated completely into $$N $$ functions $$S_m (q_m), $$ $$ S=S_1(q_1)+S_2(q_2)+\cdots+S_N(q_N)-Et. $$

In such a case, the problem devolves to $$N $$ ordinary differential equations.

The separability of S depends both on the Hamiltonian and on the choice of generalized coordinates. For orthogonal coordinates and Hamiltonians that have no time dependence and are quadratic in the generalized momenta, $$S $$ will be completely separable if the potential energy is additively separable in each coordinate, where the potential energy term for each coordinate is multiplied by the coordinate-dependent factor in the corresponding momentum term of the Hamiltonian (the Staeckel conditions). For illustration, several examples in orthogonal coordinates are worked in the next sections.

Spherical coordinates
In spherical coordinates the Hamiltonian of a free particle moving in a conservative potential U can be written $$ H = \frac{1}{2m} \left[ p_{r}^{2} + \frac{p_{\theta}^{2}}{r^{2}} + \frac{p_{\phi}^{2}}{r^{2} \sin^{2} \theta} \right] + U(r, \theta, \phi). $$

The Hamilton–Jacobi equation is completely separable in these coordinates provided that there exist functions $$ U_{r}(r), U_{\theta}(\theta), U_{\phi}(\phi) $$ such that $$U$$ can be written in the analogous form $$ U(r, \theta, \phi) = U_{r}(r) + \frac{U_{\theta}(\theta)}{r^{2}} + \frac{U_{\phi}(\phi)}{r^{2}\sin^{2}\theta}. $$

Substitution of the completely separated solution $$S = S_{r}(r) + S_{\theta}(\theta) + S_{\phi}(\phi) - Et$$ into the HJE yields $$ \frac{1}{2m} \left( \frac{ dS_{r}}{ dr} \right)^{2} + U_{r}(r) + \frac{1}{2m r^{2}} \left[ \left( \frac{ dS_{\theta}}{ d\theta} \right)^{2} + 2m U_{\theta}(\theta) \right] + \frac{1}{2m r^{2}\sin^{2}\theta} \left[ \left( \frac{ dS_{\phi}}{ d\phi} \right)^{2} + 2m U_{\phi}(\phi) \right] = E. $$

This equation may be solved by successive integrations of ordinary differential equations, beginning with the equation for $$\phi$$ $$ \left( \frac{ dS_{\phi}}{ d\phi} \right)^{2} + 2m U_{\phi}(\phi) = \Gamma_{\phi} $$ where $$\Gamma_\phi$$ is a constant of the motion that eliminates the $$\phi$$ dependence from the Hamilton–Jacobi equation $$ \frac{1}{2m} \left( \frac{ dS_{r}}{ dr} \right)^{2} + U_{r}(r) + \frac{1}{2m r^{2}} \left[ \left( \frac{ dS_{\theta}}{ d\theta} \right)^{2} + 2m U_{\theta}(\theta) + \frac{\Gamma_{\phi}}{\sin^{2}\theta} \right] = E. $$

The next ordinary differential equation involves the $$\theta$$ generalized coordinate $$ \left( \frac{ dS_{\theta}}{ d\theta} \right)^{2} + 2m U_{\theta}(\theta) + \frac{\Gamma_{\phi}}{\sin^{2}\theta} = \Gamma_{\theta} $$ where $$\Gamma_\theta$$ is again a constant of the motion that eliminates the $$\theta$$ dependence and reduces the HJE to the final ordinary differential equation $$ \frac{1}{2m} \left( \frac{ dS_{r}}{ dr} \right)^{2} + U_{r}(r) + \frac{\Gamma_{\theta}}{2m r^{2}} = E $$ whose integration completes the solution for $$S$$.

Elliptic cylindrical coordinates
The Hamiltonian in elliptic cylindrical coordinates can be written $$ H = \frac{p_{\mu}^{2} + p_{\nu}^{2}}{2ma^{2} \left( \sinh^{2} \mu + \sin^{2} \nu\right)} + \frac{p_{z}^{2}}{2m}  + U(\mu, \nu, z) $$ where the foci of the ellipses are located at $$\pm a$$ on the $$x$$-axis. The Hamilton–Jacobi equation is completely separable in these coordinates provided that $$U$$ has an analogous form $$ U(\mu, \nu, z) = \frac{U_{\mu}(\mu) + U_{\nu}(\nu)}{\sinh^{2} \mu + \sin^{2} \nu} + U_{z}(z) $$ where $$ U_\mu(\mu)$$, $$U_\nu(\nu)$$ and $$U_z(z)$$ are arbitrary functions. Substitution of the completely separated solution $$S = S_{\mu}(\mu) + S_{\nu}(\nu) + S_{z}(z) - Et$$ into the HJE yields $$ \frac{1}{2m} \left( \frac{ dS_{z}}{ dz} \right)^{2} + U_{z}(z) + \frac{1}{2ma^{2} \left( \sinh^{2} \mu + \sin^{2} \nu\right)} \left[ \left( \frac{ dS_{\mu}}{ d\mu} \right)^{2} + \left( \frac{ dS_{\nu}}{ d\nu} \right)^{2} + 2m a^{2} U_{\mu}(\mu) + 2m a^{2} U_{\nu}(\nu)\right] = E. $$

Separating the first ordinary differential equation $$ \frac{1}{2m} \left( \frac{ dS_{z}}{ dz} \right)^{2} + U_{z}(z) = \Gamma_{z} $$ yields the reduced Hamilton–Jacobi equation (after re-arrangement and multiplication of both sides by the denominator) $$ \left( \frac{ dS_{\mu}}{ d\mu} \right)^{2} + \left( \frac{ dS_{\nu}}{ d\nu} \right)^{2} + 2m a^{2} U_{\mu}(\mu) + 2m a^{2} U_{\nu}(\nu) = 2ma^{2} \left( \sinh^{2} \mu + \sin^{2} \nu\right) \left( E - \Gamma_{z} \right) $$ which itself may be separated into two independent ordinary differential equations $$ \left( \frac{ dS_{\mu}}{ d\mu} \right)^{2} + 2m a^{2} U_{\mu}(\mu) + 2ma^{2} \left(\Gamma_{z} - E \right) \sinh^{2} \mu = \Gamma_{\mu} $$ $$ \left( \frac{ dS_{\nu}}{ d\nu} \right)^{2} + 2m a^{2} U_{\nu}(\nu) + 2ma^{2} \left(\Gamma_{z} - E \right) \sin^{2} \nu = \Gamma_{\nu} $$ that, when solved, provide a complete solution for $$S$$.

Parabolic cylindrical coordinates
The Hamiltonian in parabolic cylindrical coordinates can be written $$ H = \frac{p_{\sigma}^{2} + p_{\tau}^{2}}{2m \left( \sigma^{2} + \tau^{2}\right)} + \frac{p_{z}^{2}}{2m} + U(\sigma, \tau, z). $$

The Hamilton–Jacobi equation is completely separable in these coordinates provided that $$U$$ has an analogous form $$ U(\sigma, \tau, z) = \frac{U_{\sigma}(\sigma) + U_{\tau}(\tau)}{\sigma^{2} + \tau^{2}} + U_{z}(z) $$ where $$U_\sigma (\sigma)$$, $$U_\tau (\tau)$$, and $$U_z(z)$$ are arbitrary functions. Substitution of the completely separated solution $$S = S_{\sigma}(\sigma) + S_{\tau}(\tau) + S_{z}(z) - Et + \text{constant}$$ into the HJE yields $$ \frac{1}{2m} \left( \frac{ dS_{z}}{ dz} \right)^{2} + U_{z}(z) + \frac{1}{2m \left( \sigma^{2} + \tau^{2} \right)} \left[ \left( \frac{ dS_{\sigma}}{ d\sigma} \right)^{2} + \left( \frac{ dS_{\tau}}{ d\tau} \right)^{2} + 2m U_{\sigma}(\sigma) + 2m U_{\tau}(\tau)\right] = E. $$

Separating the first ordinary differential equation $$\frac{1}{2m} \left( \frac{ dS_{z}}{ dz} \right)^{2} + U_{z}(z) = \Gamma_{z}$$ yields the reduced Hamilton–Jacobi equation (after re-arrangement and multiplication of both sides by the denominator) $$\left( \frac{ dS_{\sigma}}{ d\sigma} \right)^{2} + \left( \frac{ dS_{\tau}}{ d\tau} \right)^{2} + 2m U_{\sigma}(\sigma) + 2m U_{\tau}(\tau) = 2m \left( \sigma^{2} + \tau^{2} \right) \left( E - \Gamma_{z} \right)$$ which itself may be separated into two independent ordinary differential equations $$\left( \frac{ dS_{\sigma}}{ d\sigma} \right)^{2} + 2m U_{\sigma}(\sigma) + 2m\sigma^{2} \left(\Gamma_{z} - E \right) = \Gamma_{\sigma}$$ $$\left( \frac{ dS_{\tau}}{ d\tau} \right)^{2} + 2m U_{\tau}(\tau) + 2m \tau^{2} \left(\Gamma_{z} - E \right) = \Gamma_{\tau}$$ that, when solved, provide a complete solution for $$S$$.

Optical wave fronts and trajectories
The HJE establishes a duality between trajectories and wavefronts. For example, in geometrical optics, light can be considered either as “rays” or waves. The wave front can be defined as the surface ${\cal C}_{t}$ that the light emitted at time $t=0$  has reached at time $t$. Light rays and wave fronts are dual: if one is known, the other can be deduced.

More precisely, geometrical optics is a variational problem where the “action” is the travel time $T$ along a path,$$T = \frac{1}{c}\int_{A}^{B} n \, ds$$ where $n$  is the medium's index of refraction and $ds$  is an infinitesimal arc length. From the above formulation, one can compute the ray paths using the Euler–Lagrange formulation; alternatively, one can compute the wave fronts by solving the Hamilton–Jacobi equation. Knowing one leads to knowing the other.

The above duality is very general and applies to all systems that derive from a variational principle: either compute the trajectories using Euler–Lagrange equations or the wave fronts by using Hamilton–Jacobi equation.

The wave front at time $t$, for a system initially at $\mathbf{q}_{0}$ at time $t_{0}$ , is defined as the collection of points $\mathbf{q}$  such that $S(\mathbf{q},t)=\text{const}$. If $S(\mathbf{q},t)$ is known, the momentum is immediately deduced.$$\mathbf{p}=\frac{\partial S}{\partial\mathbf{q}}.$$

Once $\mathbf{p}$ is known, tangents to the trajectories $\dot{\mathbf{q}}$  are computed by solving the equation$$\frac{\partial{\cal L}}{\partial\dot{ \mathbf{q}}}=\boldsymbol{p}$$for $\dot{\mathbf{q}}$, where ${\cal L}$  is the Lagrangian. The trajectories are then recovered from the knowledge of $\dot{\mathbf{q}}$.

Relationship to the Schrödinger equation
The isosurfaces of the function $$S(\mathbf{q}, t)$$ can be determined at any time t. The motion of an $$S$$-isosurface as a function of time is defined by the motions of the particles beginning at the points $$\mathbf{q}$$ on the isosurface. The motion of such an isosurface can be thought of as a wave moving through $$\mathbf{q}$$-space, although it does not obey the wave equation exactly. To show this, let S represent the phase of a wave $$ \psi = \psi_{0} e^{iS/\hbar} $$ where $$\hbar$$ is a constant (the Planck constant) introduced to make the exponential argument dimensionless; changes in the amplitude of the wave can be represented by having $$S$$ be a complex number. The Hamilton–Jacobi equation is then rewritten as $$ \frac{\hbar^{2}}{2m} \nabla^2 \psi - U\psi = \frac{\hbar}{i} \frac{\partial \psi}{\partial t} $$ which is the Schrödinger equation.

Conversely, starting with the Schrödinger equation and our ansatz for $$\psi$$, it can be deduced that $$ \frac{1}{2m} \left( \nabla S \right)^{2} + U + \frac{\partial S}{\partial t} = \frac{i\hbar}{2m} \nabla^{2} S. $$

The classical limit ($$\hbar \rightarrow 0$$) of the Schrödinger equation above becomes identical to the following variant of the Hamilton–Jacobi equation, $$ \frac{1}{2m} \left( \nabla S \right)^{2} + U + \frac{\partial S}{\partial t} = 0. $$

HJE in a gravitational field
Using the energy–momentum relation in the form $$g^{\alpha\beta}P_\alpha P_\beta - (mc)^2 = 0 $$ for a particle of rest mass $$m $$ travelling in curved space, where $$g^{\alpha \beta}$$ are the contravariant coordinates of the metric tensor (i.e., the inverse metric) solved from the Einstein field equations, and $$c$$ is the speed of light. Setting the four-momentum $$P_\alpha$$ equal to the four-gradient of the action $$S $$, $$P_\alpha =-\frac{\partial S}{\partial x^\alpha}$$ gives the Hamilton–Jacobi equation in the geometry determined by the metric $$g $$: $$g^{\alpha\beta}\frac{\partial S}{\partial x^\alpha}\frac{\partial S}{\partial x^\beta} -(mc)^2 = 0,$$ in other words, in a gravitational field.

HJE in electromagnetic fields
For a particle of rest mass $$m$$ and electric charge $$e$$ moving in electromagnetic field with four-potential  $$A_i  =  (\phi,\Alpha)$$ in vacuum, the Hamilton–Jacobi equation in geometry determined by the metric tensor $$g^{ik} = g_{ik}$$ has a form $$g^{ik}\left ( \frac{\partial S}{\partial x^i} + \frac {e}{c}A_i \right ) \left ( \frac{\partial S}{\partial x^k} + \frac {e}{c}A_k \right ) = m^2 c^2$$ and can be solved for the Hamilton principal action function $$S$$ to obtain further solution for the particle trajectory and momentum: $$x = - \frac {e}{c \gamma}\int A_z \,d\xi,$$ $$y = - \frac {e}{c \gamma} \int A_y \,d\xi,$$ $$z = - \frac {e^2}{2c^2 \gamma^2}\int (\Alpha^2 - \overline {\Alpha^2 }) \, d \xi,$$ $$\xi = ct - \frac{e^2}{2 \gamma^2 c^2}\int (\Alpha^2 - \overline {\Alpha^2}) \, d \xi, $$ $$p_x = - \frac{e}{c}A_x, \quad p_y = - \frac{e}{c}A_y,$$ $$p_z = \frac{e^2}{2\gamma c}(\Alpha^2 - \overline {\Alpha^2}),$$ $$\mathcal{E} = c\gamma + \frac{e^2}{2 \gamma c}(\Alpha^2 - \overline {\Alpha^2}),$$ where $$\xi = ct - z$$ and $$\gamma^2 = m^2 c^2 + \frac{e^2}{c^2} \overline{A}^2 $$ with $$\overline{\mathbf{A}}$$ the cycle average of the vector potential.

A circularly polarized wave
In the case of circular polarization, $$E_x = E_0 \sin \omega \xi_1, \quad E_y = E_0 \cos \omega \xi_1, $$ $$A_x = \frac{ cE_0 }{\omega} \cos \omega \xi_1, \quad A_y = - \frac{ cE_0 }{\omega} \sin \omega \xi_1. $$

Hence $$x = - \frac{ecE_0} \omega \sin \omega \xi_1, $$ $$y = - \frac{ecE_0} \omega \cos \omega \xi_1, $$ $$p_x = - \frac{eE_0} \omega \cos \omega \xi_1, $$ $$p_y = \frac{eE_0}{\omega} \sin \omega \xi_1, $$ where $$\xi_1 = \xi /c $$, implying the particle moving along a circular trajectory with a permanent radius $$e cE_0 / \gamma \omega^2 $$ and an invariable value of momentum $$e E_0 / \omega^2 $$ directed along a magnetic field vector.

A monochromatic linearly polarized plane wave
For the flat, monochromatic, linearly polarized wave with a field $$E$$ directed along the axis $$y$$ $$E_y = E_0 \cos \omega \xi_1,$$ $$A_y = - \frac {cE_0}{\omega} \sin \omega \xi_1,$$ hence $$x = \text{const},$$ $$y_0 = -\frac{ecE_0}{\gamma \omega^2},$$ $$y = y_0 \cos \omega \xi_1, \quad z = C_z y_0 \sin 2\omega \xi_1,$$ $$C_z = \frac{eE_0}{8\gamma \omega}, \quad \gamma^2 = m^2 c^2 + \frac{e^2 E_0^2}{2 \omega^2}, $$ $$p_x = 0,$$ $$p_{y,0} = \frac{eE_0}{\omega},$$ $$p_y = p_{y,0} \sin \omega \xi_1, $$ $$p_z = - 2C_z p_{y,0} \cos 2\omega \xi_1 $$ implying the particle figure-8 trajectory with a long its axis oriented along the electric field $$E$$ vector.

An electromagnetic wave with a solenoidal magnetic field
For the electromagnetic wave with axial (solenoidal) magnetic field: $$E = E_\phi = \frac{\omega \rho_0}{c} B_0 \cos \omega \xi_1, $$ $$A_\phi = - \rho_0 B_0 \sin \omega \xi_1 = - \frac{L_s}{\pi \rho_0 N_s} I_0 \sin \omega \xi_1,$$ hence $$x = \text{constant},$$ $$y_0 = -\frac{e \rho_0 B_0}{\gamma \omega},$$ $$y = y_0 \cos \omega \xi_1,$$ $$z = C_z y_0 \sin 2\omega \xi_1,$$ $$C_z = \frac{e \rho_0 B_0}{8c \gamma},$$ $$\gamma^2 = m^2 c^2 + \frac{e^2 \rho_0^2 B_0^2}{2c^2},$$ $$p_x = 0,$$ $$p_{y,0} = \frac{e \rho_0 B_0}{c},$$ $$p_y = p_{y,0} \sin \omega \xi_1,$$ $$p_z = - 2C_z p_{y,0} \cos 2 \omega \xi_1,$$ where $$B_0$$ is the magnetic field magnitude in a solenoid with the effective radius $$\rho_0$$, inductivity $$L_s$$, number of windings $$N_s$$, and an electric current magnitude $$I_0$$ through the solenoid windings. The particle motion occurs along the figure-8 trajectory in $$yz$$ plane set perpendicular to the solenoid axis with arbitrary azimuth angle $$\varphi$$ due to axial symmetry of the solenoidal magnetic field.

title: Hamilton–Jacobi equation