text:
Talk:Colm Meaney

Redundancy
"Colm Meaney (born ... in Dublin, Ireland) is an Irish-born actor, ..." is excessively redundant. Is he still Irish, or is he now Irish-American? --wwoods 01:37, 19 May 2004 (UTC)
 * Yes. Fixed. - Chairboy 22:51, 29 July 2005 (UTC)

 * LOL! There's redundant and then there's excessively redundant... PrometheusX303 19:06, 21 July 2006 (UTC)

Ok - he is Irish by birth. What is his citizenship? If he only works some in America (United States), does that alone make him Irish- American> if he became an American citizen by process, some where add a statement on that; and information on when. Wfoj3 (talk) 16:35, 10 September 2016 (UTC)

Star Trek Category
I added a breif overview of Meaney's time on Star Trek, since it is a pivotal point in his career, and I believe deserves more significant mentioning than it had. I apologize if I've made any errors, I have not edited many wikis before. CherryFlavoredAntacid 00:52, 20 June 2007 (UTC) I think that Star Trek should not be separate from Career. This makes less important roles come first on the page out of chronological order. I am fixing it. 66.41.66.213 18:55, 20 June 2007 (UTC)

 * Not directly related to that but related to his work on Star Trek, it mentions he was one of six people to be on the finales of two different Star Trek series. I know that Michael Dorn was another, but who were the other 4? Mr. College (talk) 22:21, 1 July 2008 (UTC)

 * Jonathan Frakes, Marina Sirtis, Brent Spiner and Jeffrey Combs. Frakes, Sirtis and Spiner were in the finales of The Next Generation and Enterprise while Combs was in the finales of Deep Space Nine and Enterprise GusF 00:24, 2 July 2008 (UTC)

 * What about Majel Barrett-Roddenberry? Wouldn't she have featured in a number of finales and pilots as the computer.

 * And as for the 2 actors in a pilot reference, I know strictly The Cage is the Star Trek pilot, but Where No Man Has Gone Before is considered the second pilot. So that would also include DeForest Kelley and possibly Leonard Nimoy. Ajmayhew (talk) 13:38, 6 August 2008 (UTC)

Republican Sinn Fein
The article says Republican Sinn Fein, the references refer to Sinn Fein. Membership of the former would have significantly different connotations and should be removed if not proven. —Preceding unsigned comment added by 220.233.38.35 (talk) 14:12, 15 September 2009 (UTC)
 * There appear to be 2 references to his opinions on Sinn Fein. However one is simply a blog. The other is from a newspaper interview, but it is not from the newspaper's own website. This information does need a secondary reference or the original interview. I'll see what I can find myself, but unless better documentation can be found I agree with the above comment, that is may have to be removed.BashBrannigan (talk) 18:53, 25 October 2009 (UTC)

Sinn Fein and Republican Sinn Fein are entirely different. The former is the well known party (Gerry Adams etc) the latter are a very small but extremist party. —Preceding unsigned comment added by 203.113.194.210 (talk) 04:04, 29 September 2010 (UTC)

Odd Behavior
For some reason when I go to the main article it says that it doesn't exist, however when I click edit everything is there, as it is in the history. I suppose one could go to edit and then save it without making any changes, that might fix it, but it might not, it might, in fact, just screw it up totally... StarkRG 03:10, 6 March 2006 (UTC)

 * That was odd. The article restored itself after a purge. All is well with the world again. -- Scjessey 03:57, 6 March 2006 (UTC)

[

Was he really in Family Guy?
"He is the voice of Peter Griffin's father, Francis Griffin, in one episode of the Fox animated television series Family Guy."
 * I'm pretty sure that's incorrect. In fact, in the Wiki link provided, it states that Francis Griffin is voiced by Charles Durning.  I'm not the expert on Family Guy, so maybe there's an early appearance by the character that I'm forgetting. Sir Lemming 20:13, 13 November 2006 (UTC)

 * Thanks for the note Sir Lemming. Here is colm's IMDB page  and here is Charles Durning's . As you can see there is no listing for Colm while there are three episodes listed for Charles. Now IMDb has been known to make mistakes so here   and here  are wikipedia's pages listing Mr Durning as the voice Francis. The FamilyGuy.com sebsite only lists the main characters. I did find this site  and yes it does list Colm stating that he will be the voice in an episode entitled Peter's Two Dads which has not aired yet. It is entirely possible that he will be replacing Mr Durning as the voice, or perhaps he will voice the second dad of the title, in any event Wikipedia is not a crystal ball so the entry should be removed until the episode in question airs and then all of this can be sorted out and entered properly. Thanks for your note which sent me off on this little research project. MarnetteD | Talk 21:01, 13 November 2006 (UTC)

 * I was using information on the article Holy Crap when adding that statement. Now that I've checked the DVD, Colm isn't in the episode's credits, so I guess that article is incorrect. Sorry for the mistake guys! ZJH 10:01, 14 November 2006 (UTC)

 * Other people are making the same mistake as I was, but it seems to be because TV Guide says that Meaney was in fact the voice of Francis Griffin. Now I'm conflicted. I could either trust iMDB (which isn't always 100% accurate) or trust TV guide (which isn't always accurate in their schedules but hasn't yet lied to me yet about other info). Meaney wasn't in the credits though. AGGHH DAMN YOU TV GUIDE!!!! :: ZJH (T C E) 21:59, 22 February 2007 (UTC)

 * Please check several websites Zachary. Most of the ones that I have found list Mr Durning. The TV guide site is just as likely to have incorrect info as IMDb. The final decider should be the credits as you stated in your message of Nov 14. A quick check of the My Two Dads ep shows that Mr Meaney was not a voice actor in it. Not being an avid watcher of the show I have only seen one ep with Pete's dad and it was definitly Mr Durning's voice I heard. It is lower and gruffer than Mr Meaney's. Short of contacting the makers of the show I think we have to go with the credits of the episodes over the conflicting info on the net. Thanks for keeping an eye on this situation. MarnetteD | Talk 22:17, 22 February 2007 (UTC)

 * Coming into this kind of late, but I just watched the Family Guy episode "Holy Crap" and Colm Meaney's name appears in the credits at the end. I wonder if the broadcast version's credits are different from the DVD? This could be the reason for the confusion as well. After watching the episode, I am almost certain it is not Colm Meaney voicing Francis Griffin, but I'm curious as to why his name is there in the first place. A7a09338 (talk) 18:34, 31 July 2009 (UTC)

Expand Article
Please help expand this article's biography section, most of article just seems to be a listing of credits. 74.204.40.46 13:02, 30 April 2007 (UTC)

 * What would you have to be added. He has not published his memoirs nor have any other cast members from his various shows. Publishing items from tabloids and interviews is always dicey as they can so easily be shaded and taken out of context. This pages bio section actually has more info on it than 100's of other actor bios here at wikipedia and I am afraid that your need to tag these actors articles without you doing any of the work to enhance them is a bit off-putting and I would vote that they be removed. MarnetteD | Talk 19:35, 30 April 2007 (UTC)

Assessment
I have added a quality assessment rating and importance rating to this article. Feel free to change them as the article improves! Also, feel free to add more issues to the list below, and strike them out ( strike ) when they're completed. — OranL (talk) 00:40, 6 August 2008 (UTC)

Notable issues

 * The article should cite sources in-line.
 * The filmography section doesn't include his work on television. I don't have any suggestion on what to do about this.
 * The infobox could have some more information in it.

Fan of
Until a reliable source can be provided IMO there should not be any info posted about what football teams he supports. At least one of the IPs trying to add this info has provided sources on other pages for team supporters so they should be able to perform that service here. MarnetteD | Talk 20:55, 9 December 2010 (UTC)

Edit request from, 14 November 2011
I submit that we should change line 4 of the code shown below to hyperlink to the Chief Miles O'Brien page.

Change:

 * 1993–1999
 * Star Trek: Deep Space Nine
 * Chief Miles O'Brien
 * Series regular
 * Series regular

To:

 * 1993–1999
 * Star Trek: Deep Space Nine
 * Chief Miles O'Brien
 * Series regular
 * Series regular

Ironsword782 (talk) 03:25, 14 November 2011 (UTC)
 * It's already linked 7 lines above. See WP:REPEATLINK C T J F 8 3  17:54, 14 November 2011 (UTC)

Quote from Meaney live broadcast in support of Provisional IRA - repeatedly deleted
All of the text in the bottom paragraph (except the first sentence) has been deleted by 3 different contributors on 3 occasions.

The full text and is fully relevant to the first sentence, and includes a link to the RTE Radio programme where the quotes were first transmitted.

Is there a good reason why this should be repeatedly deleted and is there a way of ensuring it remains on the Colm Meaney page, other than continually undoing the deletes of others?

He supported Sinn Féin candidate Martin McGuinness during the 2011 Irish Presidential Election. On the Irish radio station RTÉ Radio 1 program "Miriam Meets" on 14 Oct 2011, [8] when discussing the 2011 Irish Presidential elections Meaney confirmed his support for Martin McGuinness (Presidential candidate and former Provisional IRA leader). When asked by Mirriam if McGuinness's past (ie the thousands of deaths caused by the PIRA) did not concern him, he replied condemning those who criticised McGuinness for his past and suggested that "the peaceful way" had not worked. Meaney went on to say "... to stand up and defend your community in that context, I don't think is a crime" Program available as a podcast at podcaster.fm [9] — Preceding unsigned comment added by Ckxion (talk • contribs) 23:27, 10 December 2013 (UTC)
 * I don't see any sources we can use. Is there a newspaper, book, recording , web link etc which is publicly available? I have no idea what "podcaster.fm" is, but is there any direct link to the recording or circulating copy in a library? BashBrannigan (talk) 00:13, 11 December 2013 (UTC)

[9] Linked to the source podcaster.fm http://podcaster.fm/podcasts/viewEpisode.aspx?podcastitemid=1349885&title=Miriam+meets...actors+Colm+Meaney+and+Pat+Laffan

When you go to the link you will know what podcaster.fm is, and you can hear Meaney as quoted in deleted text. — Preceding unsigned comment added by Ckxion (talk • contribs) 17:15, 11 December 2013 (UTC)

I have only had 2 replies to this query. BashBrannigan above and a personal message from someone using a computer in Trinity College Dublin - message read "Ashole" sender decided to be anonymous.

I am still keen to know Is there a good reason why the information above should be repeatedly deleted and is there a way of ensuring it remains on the Colm Meaney page, other than continually undoing the deletes of others? — Preceding unsigned comment added by Ckxion (talk • contribs) 23:58, 31 December 2013 (UTC)

Semi-protected edit request on 19 June 2022
Under the section Filmography - Film, add the following information

79.154.48.188 (talk) 18:07, 19 June 2022 (UTC)
 * Semi-protection-unlocked.svg Not done: The page's protection level has changed since this request was placed. You should now be able to edit the page yourself. If you still seem to be unable to, please reopen the request with further details. MadGuy7023 (talk) 07:12, 21 June 2022 (UTC)

title: Talk:Colm Meaney


text:
Mentos

Mentos are a brand of packaged scotch mints or mint-flavored candies sold in many stores and vending machines. First produced in 1932, they are currently sold in more than 130 countries worldwide by the Italian-Dutch corporation Perfetti Van Melle. The mints are small oblate spheroids, with a slightly hard exterior and a soft, chewy interior.

They are typically sold in rolls which contain 14 mint discs, although the "Sour Mix" variety contains only 11 discs per roll. Smaller versions also exist, which typically contain 4 to 6 discs per roll. Certain flavors are sold in boxes in Australia, the United States, Malaysia, Indonesia, Brazil and the United Kingdom. The current slogan of Mentos is "Stay Fresh", while the line previously used extensively in the 1980s and 1990s was "The Freshmaker". Some Mentos packages describe the mints as "chewy dragées". The typical Mentos roll is approximately 2 cm in diameter and weighs 38 g. "Mentos" is the singular form.

Ingredients
Mint-flavored Mentos contain sugar, wheat glucose syrup, hydrogenated coconut oil, rice starch, natural flavors, gum arabic, sucrose esters of fatty acids, gellan gum, carnauba wax, and beeswax. Fruit-flavored Mentos contain sugar, wheat glucose syrup, hydrogenated coconut oil, citric acid, fruit juices from concentrate (strawberry, orange, lemon) (1%), rice starch, gum arabic, natural flavors, sucrose esters of fatty acids, gellan gum, carnauba wax, colors (beta-carotene, beetroot red), and beeswax. The formulation can vary based on country of manufacture.

Flavors
Mentos are available in several flavors including mint, mixed fruit, cola, bubble gum, and in an assortment of orange, strawberry, and lemon. Mentos first appeared as a liquorice-flavored sweet which can still be purchased in the Netherlands as "Drop Mentos". New flavors were initially test-marketed in the Netherlands and throughout Europe; however, most of the flavors have been available worldwide recently.

Other flavors include green apple, cinnamon, strawberry, mixed fruit (which contains a mix of cherry, strawberry, orange, and lemon flavors), grape, wintergreen, grapefruit, peach, plum, spearmint, strawberry yogurt, lemon yogurt, pineapple (pine fresh), red apple, currant and two versions of black licorice-flavored Mentos. Two varieties of the mint flavor, known as "Mentos Strong" and "Air action Mentos" are sold in the Netherlands. Also available in the Netherlands is the Special Mix 4 pack, containing the flavors mint, fruit, berry mix, strawberry, banana, cherry, and mango orange. Two varieties of the mint flavor are also sold in China, known as "Mint" and "Strong Mint". Grape and 'N Cream (presumably Apples and Cream), Strawberry 'N Cream, and Banana 'N Cream are also marketed in Asia. Chocolate Mentos were produced in 1989, but the flavor was discontinued. The chocolate variant is still available in some Asian countries. In 2006, the citrus mango flavor was introduced to the Japanese market. In the Philippines, a "Dalandan Fresh" variant is available. Other varieties of Mentos include: Mentos Sours, which recently became available in the United States, featuring Watermelon, Green Apple, and Lemon flavors; caffeinated "Energy" Mentos, sold mainly in Germany, where one roll equals the amount of caffeine in two cups of coffee; "Fresh Cola"-flavored Mentos released in New Zealand, Australia and parts of Europe and Asia; and "AIR Mentos" containing menthol, which are sold primarily in Belgium and the Netherlands. In India, the major flavors available are mint, lemon, strawberry, orange, watermelon and cola.

Mentos also make chewing gum, available in various flavors. It is available in Germany, Australia, Greece, China, Canada, Brazil, Turkey, the Netherlands, Poland, the Philippines, the United Kingdom and recently, the United States in blisters and bottles, both in three different flavors. In the Netherlands, Mentos Gum is sold in blisters and bottles in six different varieties: Pure (four flavors), Fruit (four flavors), Regular (five flavors), Bubblegum, Cubes (four flavors) and White (three flavors).

In August 2005, the variety of the mint which comes in "mixed berries" and "cool mint" flavors was changed to be sweetened with sucralose. In the Netherlands the flavors mint, licorice and fruit are also available in the sugar-free variety.

Australian varieties of Mentos are Fruit, Rainbow, Mint, Spearmint, Soft Drink and Smoothies.

The UK has five current flavors of rolls:
 * Fruit (Orange, Lemon and Strawberry)
 * Mint
 * Rainbow (with 2 dragees each of: Strawberry, Apple, Raspberry, Orange, Watermelon, Blueberry and Pink Grapefruit (the last two were new flavors for 2015, replacing Grape and Pineapple).
 * Spearmint
 * Tutti-Frutti - bubblegum flavored - new for 2012.

In the UK, Mentos Gum is also available in stick packs (peppermint, spearmint, pure white, air action (menthol) and fruit), Bottles (spearmint, peppermint and red fruit - which retails for approximately £0.99), as well as flip top boxes. Flavors include peppermint or spearmint with green tea extract, and a pure white with white tea extract. Sugar free versions are available, but these are rarer to find, usually only found in large supermarkets. Mentos gum holds a 4% market share of the UK gum market. A new Mentos 3 was launched in January 2011, in two flavors - mint and Strawberry/Apple/Raspberry, which are similar to Wrigleys' 5 in packaging. A new blackberry/kiwi/strawberry version was released into the UK market in January 2012.

In Greece, Mentos are very popular, and are available in the following flavors: Mini Mentos, somewhat smaller than ordinary Mentos, are available in the Netherlands in two varieties: Mini Mentos Fruitmix, which contains the flavors orange, lemon, strawberry and apple, and Mini Mentos Yoghurt, with the flavors strawberry yogurt, raspberry yogurt and blueberry yogurt. Also sold is Mentos KIDZ, a bag with 12 boxes containing 10 miniature candies, in the flavors strawberry, orange, lemon, apple and blueberry.
 * Mint
 * Strawberry
 * Melon
 * Watermelon
 * Fruit (Orange, lemon and strawberry)
 * Energy (each roll is equivalent to 2 cups of coffee)
 * Mentos gum in Bottles
 * Mentos Cube
 * Mentos in Boxes (mint and Fruit).

"Mentos Teens" is available in Brazil and the rest of Latin America. They come in a rectangular box. The mint is basically miniature Mentos roughly the size of Skittles, and they come in mixed flavors: white grape (green), lemon (yellow), strawberry (pink), orange (orange), raspberry (blue), and cherry (red).

During the 2014 FIFA World Cup, a Brazilian team Mentos was released in Brazil to support the national team. The mint was green apple and orange flavors.

In some countries, the Mentos Ice candy can be bought in flavors such as, cherry (red), green apple (green) and grape (purple).

Ume, Fuji apple, and Pine Fresh (pineapple) Mentos are sold exclusively in Japan.

Flavors only available in certain countries; Enigma (Czech Republic) Rainbow (UK and US) Ume (Japan) Fuji Apple (Japan) Pine Fresh (Japan) Ice (Canada)

Marketing
Part of Mentos's popularity in the US and Canada can be attributed to its campy TV commercials and catchy jingle, which debuted in late 1991 and were used well into 2001 on American and Canadian television. Individuals facing various day-to-day dilemmas consume Mentos and are subsequently inspired to solve their problems at hand in a creative, often-humorous fashion. For example, a job interviewee sits on a freshly painted bench, staining his suit, and then solves the problem by rolling around on the bench until his suit has pinstripes. Another features a woman whose parked car is boxed in; she calls a crew of construction workers over who lift her car onto the road for her. These unusual behaviors are typically witnessed by nearby, sometimes antagonistic characters, and a roll of Mentos is boisterously displayed by the commercial's respective protagonist to the observer as an explanation for their actions.

The ad campaign was parodied in multiple television shows and music videos, including the Foo Fighters' "Big Me".

Reaction with carbonated beverages

First publicly demonstrated by chemistry teacher Lee Marek on the Late Show with David Letterman on September 14, 1999, and later popularized in a June 2006 viral Internet video by Eepybird, a Mentos mint expedites a rapid release of carbon dioxide when dropped into a carbonated liquid, such as a soft drink. MythBusters concluded that the potassium benzoate, aspartame, and CO2 gas contained in the Diet Coke, in combination with the gelatin and gum arabic ingredients of the Mentos, all contribute to the formation of the foam. However, kinetic experiments with various candies have shown that the presence of gelatin and gum arabic in candies does not enhance the fountain. Rather, it is the physical structure of candies that conveys the fountain effect.

The structure of the Mentos is the most significant cause of the eruption due to nucleation. MythBusters reported that when fruit-flavored Mentos with a smooth waxy coating were tested in carbonated drink there was hardly a reaction, whereas mint-flavored Mentos (with no such coating) added to carbonated drink formed an energetic eruption, supporting the nucleation-site theory. According to MythBusters, the surface of the mint Mentos is covered with many small holes that increase the surface area available for reaction (and thus the quantity of reagents exposed to each other at any given time), thereby allowing CO2 bubbles to form with the rapidity and quantity necessary for the "jet"-, "geyser"-, or "eruption"-like nature of the effusion.

This hypothesis gained further support when rock salt was used as a "jump start" to the reaction. A paper by Tonya Coffey, a physicist at Appalachian State University in Boone, North Carolina, confirmed that the rough surface of the Mentos candy helps speed the reaction. Coffey also found that the aspartame in diet soda lowers the surface tension and causes a bigger reaction, but that caffeine does not accelerate the reaction. On the other hand, it has been shown that a wide variety of beverage additives such as sugars, citric acid, and natural flavors also enhance fountain heights. In some cases, dissolved solids that increase the surface tension of water (such as sugars) also increase fountain heights. These results suggest that additives serve to enhance geyser heights not by decreasing surface tension, but rather by decreasing bubble coalescence. Decreased bubble coalescence leads to smaller bubble sizes and greater foaming ability in water.

A Guinness World Record of 2,865 simultaneous geysers was set on 17 October 2010, in an event organized by Perfetti Van Melle (Philippines) at the SM Mall of Asia Complex, in Manila, Philippines. This record was afterwards beaten in November 2014 by another event organized by Perfetti Van Melle and Chupa Chups in Leon, Guanajuato, Mexico where 4,334 Mentos and soda fountains were set off simultaneously.

The resulting geyser can shoot as high as 6 m. The unofficial record, reached in MythBusters, was over 34 ft with the use of a nozzle.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Mentos


text:
Australian Stock Car Auto Racing

AUSCAR (Australian Stock Car Auto Racing) was an auto racing sanctioning body owned by Bob Jane, which ran American-style Superspeedway racing in Australia. The initial AUSCAR venue was the 1.801 km (1.119 mi), high-banked (24°) Calder Park Thunderdome Superspeedway in Melbourne, but over time the series expanded to include the Jane owned 1/2 mile (805 metre) Speedway Super Bowl at the eastern end of Adelaide International Raceway which first saw AUSCAR racing in 1990 (the Super Bowl was only other paved oval circuit in Australia with only 7° banking in the corners making it essentially a traditional flat track), the Surfers Paradise Street Circuit, and eventually several Australian road racing circuits including Calder Park's road course and the Oran Park Raceway in Sydney where racing was held under lights on the short version of the circuit. In the early 1990s, Jane and television station Channel 7 announced plans to turn the old Granville Showground trotting track which circled the Parramatta Speedway in Sydney into a paved, banked 1/2 mile track, but this did not happen.

Four categories of racing car were developed to run on the Australian circuits:

 * NASCAR: imported and locally developed versions of the American race cars. Engines were 6.0L V8s
 * AUSCAR: down spec-ed cars, closer to production specification with a control road tyre, The category comprised the Holden Commodore and Ford Falcon. After 1990/91, engines were restricted to 5.0L V8s.
 * Formula Falcon: Lasted the one season and was absorbed into Sportsman, ran the Ford Falcon.
 * Sportsman: lower specification again, cheaper to buy or build and older cars, and some former AUSCARs. Like AUSCAR, the category comprised the Commodore and Falcon. Engine restrictions saw Holdens use the 4.2L 253 V8 and Fords use de-tuned 5.0L 302 V8s.

Other categories, such as the HQs, a relatively cheap category based on the Holden HQ Kingswood powered by the 3.3L Holden red motor, were also popular at the Calder Park Thunderdome (as the HQs were Australian-made cars, like the AUSCARs they raced clockwise on the ovals). Another category was based on the American dirt track category known as Legends (similar in appearance, but unrelated to Aussie Racing Cars). Open-wheel cars such as Formula Vee also raced on occasion at the Thunderdome as a support to the NASCAR / AUSCAR races, as did the Dirt track racing Grand Nationals for a few meetings in 1990.

AUSCAR category
AUSCAR was also the name used for the second tier racing category that raced alongside the Australian NASCAR stock car racing series, starting in 1986 and continuing until 2001. The cars were not pure space frame chassis like NASCAR, but were built on Australian Holden Commodore and Ford Falcon road car chassis. As a result, AUSCARs are right-hand-drive and race clockwise on oval tracks, compared to the left-hand-drive, anticlockwise NASCAR vehicles - the theory being that the driver is located at the furthest point possible from the outside retaining walls. AUSCARs were also restricted to running 5.0 litre Holden and Ford V8 engines, though initially the Ford XF Falcons used the 5.8L 351 Cleveland V8 engines (despite the road going XFs not carrying the V8 as Ford Australia had stopped production of the engine in 1983), but subsequent Falcons (from the EB model which in 1991 re-introduced the Ford V8 to the Australian market for the first time in 8 years) would run the 5.0L V8. Commodore teams were also free to use the Group A size 4.9L Holden V8 engine, though unlike in Group A racing using the 4.9L engine did not come with an overall weight reduction for the car. As such most Holden competitors used the 5.0L engines.

The 5.0L AUSCAR engines were strictly controlled and developed around 390 bhp compared to the 700 bhp of the larger and more highly developed, 366 cubic inch (6.0L) engines used in NASCAR, and as a result AUSCARs were slower than their American counterparts (at the Thunderdome, NASCAR stock cars were capable of around 300 km/h while AUSCARs had a top speed of approximately 265 km/h). Like the NASCAR engines, the engines used in AUSCAR were carbureted rather than having fuel injection like the road going V8s used by Holden and Ford. AUSCARs also used a Goodyear Eagle control road tyre that was narrow unlike the slick racing tyres used in NASCAR. One thing in AUSCARs' favour was that they only weighed in at 2910 lb compared to the 3400 lb NASCAR stock cars. Although they weighed less, as a result of using smaller, less powerful engines and the road tyre, AUSCARs were generally around 15 mph, or around four seconds per lap, slower than the NASCAR stock cars around the Thunderdome.

Tony Kavich won the first ever AUSCAR championship in 1988. However, in a shock to the male dominated motor racing establishment, the first ever AUSCAR race at the Thunderdome (which was also the first race to exclusively use the track), the aptly named AUSCAR 200, was won by 18-year-old Melbourne based female driver Terri Sawyer driving a Holden VK Commodore. Sawyer had qualified her Commodore on the front row of the grid and ran at or near the front all day to win from Kim Jane (the nephew of Calder owner Bob Jane), Max de Jersey, Phil Brock and Graham Smith. The top five positions all going to those driving either a VK or VL Commodore. Greg East, also driving a VK Commodore, sat on pole for the AUSCAR 200 with a time of 33.2 seconds for an average speed of 121.34 mp/h.

While Sawyer would remain very competitive in the early years of the category, the early days were dominated by Jim Richards. Though it was Albury panel shop owner and Group E/Group A driver Brad Jones who would come to dominate the category, winning five consecutive titles during the peak of the series popularity, all in various model Commodores. Other notable drivers include: Greg East, Steve Harrington, Mark Seaton, Marshall J. Brewer, Gregg Hansford, Terry Wyhoon, Garry Rogers, Russell Ingall, John Faulkner, Steven Richards (the son of inaugural champion Jim), Tony Kavich, Nathan Pretty and his sister Nicole, Jason Whylie, Eddie Abelnecia and Leigh Watkins who was the only driver to win the championship driving a Falcon. Even Australian touring car legend Peter Brock briefly tried AUSCAR in 1988 driving an XF Falcon (after his 1987 split with Holden). Brock qualified 3rd for his first race, the 1988 Goodyear AUSCAR 200 and actually led for a number of laps until a split radiator saw him spin into retirement. To his credit, Brock later admitted that he wasn't comfortable racing on the high-speed ovals and his time in the category only lasted a couple of meetings. He did return however for his testimonial race meeting held on the Calder Park short (road) circuit in 1995 driving a VR Commodore.

Due to the returning popularity of the Australian Touring Car Championship, relaunched as V8 Supercars in 1997, as well as financial difficulties and other problems such as Bob Jane's long-running "feud" with the Confederation of Australian Motor Sport (CAMS), which saw CAMS ban its members from competing in the series, robbing it of a number of leading drivers, AUSCAR was quietly shut down and the drivers dispersed into other national racing series.

Several cars were converted to Future Tourers to race in that series from 1999 onwards, some AUSCARs that did not compete in Future Tourers were restored and now compete in Stock Cars Australia competition, such examples being the #6 Ford Falcon and the #22 Holden Commodore.

title: Australian Stock Car Auto Racing


text:
Ferrari F50

The Ferrari F50 (Type F130) is a mid-engine sports car manufactured by Italian automobile manufacturer Ferrari from 1995 until 1997. Introduced in 1995, the car is a two-door, two seat targa top. The F50 is powered by a 4.7 L naturally aspirated Tipo F130B 60-valve V12 engine that was developed from the 3.5 L V12 used in the 1990 Ferrari 641 Formula One car. The car's design is an evolution of the 1989 Ferrari Mythos concept car.

A total of 349 cars were made, with the last car rolling off the production line in July 1997. The F50's engine predated the car; it was used in the Ferrari 333 SP for the American IMSA GT Championship in 1994, allowing it to become eligible for the stock engine World Sports Car category.

Ferrari F50 GT

Ferrari developed the F50 based F50 GT in collaboration with its racing partners Dallara and Michelotto to compete in GT1-class racing, following the motorsport theme of the Ferrari F40 LM. Notable changes made to the car include a fixed roof, a large rear spoiler, new front spoiler, adjustable suspension system, Speedline racing alloy wheels with racing slicks and large rear diffusers. The 4.7-litre V12 engine in the F50 GT was tuned-up to generate a power output of around 551 kW at 10,500 rpm. A test was held in 1996 which proved the car to be quicker than even the 333SP, but this went unnoticed as Ferrari cancelled the F50 GT project due to entry of purpose built racing cars in competition such as the Porsche 911 GT1 and due to lack of funding, instead focusing on Formula One after the BPR Global GT Series folded. Only 3 examples were ever built, with the three remaining tubs reportedly destroyed.

General

 * Manufactured in: Maranello, Italy
 * Number produced: 349 (1995 until July 1997)
 * Inspiration: 1990 Ferrari 641 as driven by Alain Prost

Dimensions

 * Dry weight: 1230 kg for the F50 and 860 kg for the F50 GT
 * Distribution: 42%/58% (front/rear)
 * Length: 4,480 mm
 * Height: 1,120 mm
 * Width: 1,986 mm
 * Wheelbase: 2,581 mm
 * Front track: 1,621 mm
 * Rear track: 1,603 mm

Engine

 * Ferrari F130 B.jpg]]Ferrari F130 B side.jpgFerrari f50 interior (3427688771).jpgFerrari F50 4.7 1995 (30251319442).jpg: Tipo 036-derived, model SFE 4.7 VJGAEA, Tipo F130 B
 * Position: Rear mid-engine, rear-wheel-drive layout
 * Configuration: Longitudinally-mounted 65° V12
 * Aspiration: Naturally aspirated, with variable-length intake manifold via butterfly valve in intake manifold
 * Intake manifold: carbon fibre reinforced polymer
 * Block: Modular cast iron
 * Heads/Pistons: light-alloy aluminum heads/forged Mahle pistons
 * Oil sump: aluminium
 * Connecting rods: forged titanium
 * Crankshaft: forged steel
 * Cam covers/Oil and water pump housing: magnesium sand castings
 * Exhaust manifold: stainless steel
 * Engine weight: 198 kg
 * Valvetrain: 5 valves per cylinder (3 intake, 2 exhaust), 60-valves (total) DOHC per cylinder bank driven by low-noise Morse chain
 * Displacement: 4698.50 cc
 * Max. power: 382 kW at 8,000 rpm
 * Max. torque: 471 Nm at 6,500 rpm
 * Specific output.: 81.3 kW/litre
 * Weight/Power ratio: 2.69 kg/PS
 * Bore X Stroke: 85x69 mm
 * Bore:Stroke ratio: 1.23:1 (oversquare)
 * Compression ratio: 11.3:1
 * Redline: 8,500 rpm
 * Fuel cutoff: 8,640 rpm
 * Fuel feed: Bosch Motronic 2.7 sequential injection and Electronic control unit (controls the fuel feed, ignition timing, and variable length intake and exhaust systems)
 * Ignition system: Bosch static electronic distributor-less ignition
 * Lubrication: dry sump, tank incorporated within the final drive housing, 3 scavenger pumps
 * Variable intake: butterfly valve in carbon fibre intake manifold closed at low rpm, open at high rpm
 * Variable exhaust: butterfly valve in upper tailpipes closed at low rpm, open at high rpm
 * Fuel tank: foam filled, aeronautical-style Sekur rubber bladder, 105 L

Fuel consumption

 * EPA premium gasoline
 * Combined 8 mpgu.s.
 * City 7 mpgu.s.
 * Highway 10 mpgu.s.

Transmission

 * Configuration: longitudinal 6-speed manual + reverse, limited-slip differential, RWD
 * Gear ratios: 2.933:1 (1st), 2.157:1 (2nd), 1.681:1 (3rd), 1.360:1 (4th), 1.107:1 (5th), 0.903:1 (6th), 2.529:1 (reverse)
 * Final drive: 3.70:1
 * Final drive assembly: aluminum sand casting
 * Remaining gearset housing: magnesium sand casting
 * Support bracing: steel
 * Flywheel: steel
 * Clutch: dry, twin plate
 * Cooling: oil-water intercooler between gearbox lubricant and engine

Chassis

 * Type: central carbon fiber tub, light-alloy suspension and engine-gearbox assembly mounting points co-polymerised to the chassis
 * Materials: carbon fiber, epoxy resin, Nomex honeycomb structure core, sandwich construction
 * Torsional stiffness: 34,570 Nm per degree

Suspension

 * Front: Rose-jointed unequal-length wishbones, push-rods, coil springs, Bilstein gas-pressurised monotube dampers, electronic adaptive damping, electronic height adjustment (40 mm max)
 * Rear: Rose-jointed unequal-length wishbones, push-rods, coil springs, Bilstein gas-pressurised monotube dampers, electronic adaptive damping, mounting points on a spacer between the engine and gearbox
 * Travel: 55 mm bump, 60 mm rebound
 * Camber angle: -0.7 degrees front, -1.0 degrees rear
 * Anti-roll bars: front and rear
 * Max. roll angle: 1.5 degrees

 * Electronic adaptive damping (based on steering wheel angle and velocity, the body's vertical and longitudinal acceleration, brake line pressure, and vehicle speed)
 * Maximum reaction time (from minimum to maximum damping force or vice versa): 140 milliseconds (0.14 s)
 * Average reaction time (from minimum to maximum damping force or vice versa): 25 to 30 milliseconds (0.025 to 0.03 s)

Steering

 * Type: TRW rack and pinion, 3.3 turns lock-to-lock, unassisted
 * Caster angle: 5.5 to 5.7 degrees
 * Turning circle: 41 ft

Wheels/tires/brakes

 * Wheels: magnesium alloy, manufactured by Speedline
 * Hubs: titanium
 * Brake disc bells/suspension uprights/brake calipers: aluminum
 * Upper and lower wishbones: black powder-coated steel
 * Front wheels: 8.5 x
 * Front tires: 245/35ZR-18 Goodyear Eagle F1 GS Fiorano @ 35 psi
 * Front brakes: Brembo cross-drilled & ventilated cast iron discs, 4 piston aluminum Brembo calipers, Pagid brake pads, (without ABS)
 * Rear wheels: 13 x
 * Rear tires: 335/30ZR-18 Goodyear Eagle F1 GS Fiorano @ 30 psi
 * Rear brakes: Brembo cross-drilled & ventilated cast iron discs, 4 piston aluminum Brembo calipers, Pagid brake pads, (without ABS)
 * Unsprung mass: 99 lb/121 lb (front corners/rear corners)

Colour popularity

 * Rosso Corsa (red): 302
 * Giallo Modena (yellow): 31
 * Rosso Barchetta (dark red): 8
 * Argento Nurburgring (silver): 4
 * Nero Daytona (black): 4

Performance

 * 0–60 mi/h: 3.8 seconds
 * 0–100 mi/h: 8.5 seconds
 * 1/4 mile: 12.1 seconds at 198 km/h
 * Skidpad: 0.95 g
 * Braking 70-0 mph: 176 ft
 * Top speed: 325 km/h

Track tests
The F50 had the following track times:
 * Tsukuba Circuit: 1:05.81
 * Suzuka Circuit (2000): 2:25.525
 * Sugo: 1:38.573
 * Fiorano: 1:27.00

title: Ferrari F50


text:
Nova Scotia House of Assembly

The Nova Scotia House of Assembly (Assemblée législative de la Nouvelle-Écosse; Taigh Seanaidh Alba Nuadh), or Legislative Assembly, is the deliberative assembly of the General Assembly of Nova Scotia, and together with the Lieutenant Governor of Nova Scotia makes up the Nova Scotia Legislature.

The assembly is the oldest in Canada, having first sat in 1758; in 1848, it was the site of the first responsible government in the British Empire. Bills passed by the House of Assembly are given royal assent by the lieutenant governor in the name of the King of Canada.

Originally (in 1758), the Legislature consisted of the Crown represented by a governor (later a lieutenant governor), the appointed Nova Scotia Council holding both executive and legislative duties and an elected House of Assembly (lower chamber). In 1838, the council was replaced by an executive council with the executive function and a legislative council with the legislative functions based on the House of Lords. In 1928, the Legislative Council was abolished and the members pensioned off.

There are 55 Members of the Legislative Assembly (MLAs) representing 55 electoral districts. Members nearly always represent one of the three main political parties of the province: the Nova Scotia Liberal Party, Progressive Conservative Party of Nova Scotia, and Nova Scotia New Democratic Party.

The assembly meets in Province House. Located in Halifax, Province House is a National Historic Site and Canada's oldest and smallest legislative building. It opened on February 11, 1819. The building was also originally home to the Supreme Court of Nova Scotia, and the location of the "Freedom of the Press" trial of Joseph Howe. Its main entrance is found on Hollis Street in Halifax.

Officers
A number of officers of the house are appointed in accordance with legislation passed by the house. These officers fulfil numerous functions as prescribed in the relevant legislation. There are two categories of officers:

Officers under the authority of the speaker
The Speaker of the House has authority over the following offices and officers:

 * Clerk
 * Hansard
 * House Operations
 * Legislative Committees
 * Legislative Counsel
 * Legislative Library
 * Legislative Television Broadcasting Services
 * Sergeant-at-Arms
 * Speaker's Administration Office

Independent officers
These include the Auditor General, the Office of the Ombudsman and the Office of the Conflict of Interest Commissioner.

The Chief Electoral Officer of Nova Officer as head of Elections Nova Scotia is also appointed by a majority vote of the house and is considered an officer of the house.

Standing Committees

 * Assembly Matters
 * Community Services
 * Natural Resources and Economic Development
 * Health
 * Human Resources
 * Internal Affairs
 * Law Amendments
 * Private & Local Bills
 * Public Accounts
 * Veterans Affairs

Committees of the Whole House

 * Bills
 * Supply
 * Supply Subcommittee

Recent Former Select Committees
(final reports filed)
 * Electoral Boundaries
 * Fire Safety
 * National Unity
 * Petroleum Product Pricing
 * Workers' Compensation Act

Special Committee

 * to Review the Estimates of the Auditor General and the Chief Electoral Officer

Seating Plan
Current as of February 2024

title: Nova Scotia House of Assembly


text:
Talk:Falaise pocket

Lede too long
I know this is a featured article, but I estimate the lede to be about four times longer than it should be, relative to the length of the main article. Is it permissible to re-draft the lede in its entirety? Valetude (talk) 23:24, 17 December 2020 (UTC)

 * Me again. Looking closer, I see many points of reporting that could usefully be corrected. Let me propose this new version of the lede, and take your comments and critiques:

 * The Battle of the Falaise Pocket (German: Kessel von Falaise; 12–21 August 1944) was the final engagement in the Allied invasion of Normandy, Operation Overlord, in World War II, which drove the German defenders from the beachheads and opened the way to Paris.

 * After the initial landings on 6 June (D-Day), the British, Canadian and American armies had met heavy resistance which delayed by more than a month the liberation of their immediate objectives, Caen and St. Lô. But the enemy had expended manpower and supplies that could not be replaced, and there was dissension between their generals, especially after the attempt on Hitler’s life on 20 July.

 * The Allies had succeeded in establishing air superiority, and after extensive carpet-bombing, they started a pincer movement around Falaise, with the British and Canadians under Montgomery to the north and the American Third Army under Patton to the south. The local German commander, General Kluge, asked permission to retreat; Hitler’s refusal greatly improved the Allies’ chances of encircling the enemy.

 * On 19 August, the Allies linked up at Chambois, and the ‘pincer’ had effectively closed, though many Germans had been able to escape, cheating the Allies of the decisive victory they had hoped for. Patton insisted that he could have closed the gap earlier by taking Argentan, but Bradley claimed that this would have left his lines too thinly defended. It would also have put him on the wrong side of a line laid down by Montgomery, separating British and American operations.Valetude (talk) 16:41, 28 April 2021 (UTC)
 * Lurking while mobile... Mathglot (talk) 23:59, 28 April 2021 (UTC)
 * Concur on the length concern. On the principle of 'first define your terms', though, I'd like to retain both a mention of 'encirclement' in the opening para (to mitigate any possible 'pocket, wha'?' issue), and the Falaise Gap alt-title, and a very brief gloss of that.  Otherwise this seems to me to hit the key points and the (huge!) amount of other detail in the present lede can be refactored into later sections, which at the moment seem to work almost like footnotes to this vast monolith of text.  109.255.211.6 (talk) 03:17, 29 April 2021 (UTC)

 * I disagree with the proposed changes:
 * The proposed first paragraph is wrong; it was not the final engagement of the Allied invasion of Normandy, as the original correctly points out. Most of the proposed corrections are :errors.
 * Recommend keeping the first paragraph as it is, as it also provides additional names, and a description of the forces involved.
 * For the second paragraph, which provides background, I would suggest removing the details about the Eastern front and Bomb plot, but no more.
 * The proposed third paragraph is wrong, whereas the original is correct; Montgomery was in charge of both the forces to the north and those to the south. Also, von Kluge was :a field marshal.
 * The original third paragraph is better, but I would suggest moving the sentence about Goodwood into the Second paragraph; there is some repetition here.
 * The final two paragraphs could be merged.
 * Bottom line: The original lead could be trimmed a bit, but the proposal is too far short. Hawkeye7   (discuss)  04:08, 29 April 2021 (UTC)

 * Yes, 'decisive' but not 'final', fair point. I think the 'description of the forces involved' is a case in point of the problem.  We learn not just the name of the German formation involved (arguably already too specific and detailed at this point -- is this really one of the very first things we need to grasp about this topic?), but of all of its subordinate units (uh-huh...) and a former designation of one of those.  The second paragraph does indeed provide background -- an excessive quantity of it.  We do after all have a 'Background' section.  Certainly the original (lengthy) third paragraph contains no error about Montgomery's role...  because he's not even mentioned until the (not especially short) fifth.  If one were looking for a snappy summary of the command structure here, it'd be pretty much lost in the step-by-step chronological narrative we currently have (perhaps indeed leading that error on the part of the redrafter).  But hopefully this is iteratively approximatable to something that addresses both sets of concerns.  109.255.211.6 (talk) 05:13, 29 April 2021 (UTC)

 * Accuracy is the most important thing, but I agree the current lead is too long, lacking focus on the most important points in the article. (t · c)  buidhe  21:17, 29 April 2021 (UTC)
 * It also contains details that are not in the article at all (but should be). The lead is too long, and the article is too short. Hawkeye7   (discuss)  21:30, 29 April 2021 (UTC)
 * A very good summary (as it were), I think. There's information that appears only in the lede, but would better appear briefly there, and in more detail later.  On one such case, as I mentioned a little earlier, I think the force composition information is much too detailed, much too soon, and I'm very much inclined to trim it from the first paragraph.  I'm not 100% sure where it best should be, though.  Later in the lead section?  In the 'background' section timeline?  (Yes, I'm probably being excessively WP:TIMID here, but I don't want to antagonise editors by even temporarily 'losing' information from the article.)  109.255.211.6 (talk) 03:30, 30 April 2021 (UTC)

Why the capitals?
The pocket was lowercase for many years, and was capitalized (but only in the lead) in this 2009 copyedit on the leadup to FA; the article title followed about 6 years later. The text is still not case-consistent. You can see the effect of the over-capitalization in recent sources. It's still not close to the threshold suggested by MOS:CAPS though. We should fix this. To lowercase. Dicklyon (talk) 05:30, 29 April 2021 (UTC)
 * I might be a bit slow, but can you clarify which 'threshold' you're referring to specifically? Isn't this the 'accepted name of a battle' which is 'usually capitalized in sources'?  It's a fascinating ngram though -- the Title Case uptick really kicks in rather dramatically in the very early 1990s.  This article and Wikipedia as a whole have a pretty good alibi for being to blame for that.  I think one can perhaps overdo consistency on this:  'battle' and 'pocket' are still perfectly serviceable common nouns one might have cause to use in an article like this -- juxtaposed with 'Falaise' or otherwise.  But that doesn't mean that the Battle of Falaise Pocket -- battle of the Falaise Pocket!? -- Battle of the Falaise pocket?! -- isn't viable as a proper noun phrase.  If anything I think there might be a case (as it were) for retitling as tBotFP, but using Fp internally when referring to the geographical envelopment, rather than the engagement as a whole.  109.255.211.6 (talk) 06:22, 29 April 2021 (UTC)
 * From the MOS:CAPS lead: "Wikipedia relies on sources to determine what is conventionally capitalized; only words and phrases that are are capitalized in Wikipedia."  In my experience, "Battle of" is most often capped in sources, while many other terms are not.  So "Battle of Falais Pocket" would possibly make more sense as a proper name (though sources seem to more often say "battle of the Falais pocket", so maybe not), but "Falais pocket" is clearly not used that way in sources.  Dicklyon (talk) 17:16, 29 April 2021 (UTC)
 * There was indeed a big blip up of caps in the mid 1990s, but after that settled back, the next prominent steps up seem to be synchronized to our 2009 lead capitalization and 2015 title capitalization. See here.  Dicklyon (talk) 17:46, 29 April 2021 (UTC)
 * Ah, the eternal fuzziness of terms like 'accepted', 'substantial', 'consistent', 'usually' -- just throw in 'reasonable' and you have the full suite of lawyer's delights! (But their joy might be contingent on their fee for navigating them, it must be said.)  I'm not sure if we consistently applied 'consistent', we'd ever capitalise anything ever again, but I'll grant you that this isn't one of the...  consistenter ones.  (Battle of the) Falaise Gap seems similarly mixed, leaning capsed.  Yes, there's certainly another large uptick in 2016-8, but at that point it's merely 'running up the score' of an existing lead, by that graph.  The change in 2009 is much less dramatic.  As I say, I think it's somewhat inherent to the nature of the phrase, as it's doing double duty as a proper name, and a descriptive composition of common nouns.  It's a gap (and was a pocket) near Falaise and there was a battle there, so no law against juxtaposing those attributively and possessively on that basis!  109.255.211.6 (talk) 18:44, 29 April 2021 (UTC)
 * That runup in 2016–18 is exactly what I mean by the reaction to the 2015 title capitalization. Wikipedia is unreasonably effective at influencing such things.  And yes "consistently" is not a consistently interpreted threshold, but it as least means a sustained substantial super-majority.  If you correct the n-gram counts for the frequent appearance of capped terms in titles, references to titles, headings, captions, and such things that many styles cap a lot, you'll find that it's not close. Dicklyon (talk) 19:08, 29 April 2021 (UTC)

On my question of why?, the original capping in the lead was justified by edit summary "ce", which left the case in the article inconsistent to this day; not a good reason. The title move was justifed by edit summary "standardize title with lead", a bad reason to compound the error. I will work on a fix. Dicklyon (talk) 19:12, 29 April 2021 (UTC)
 * OK, fixed. If someone finds a consistently capped accepted name for this event, we can consider it. Dicklyon (talk) 20:01, 29 April 2021 (UTC)
 * 'ce' is the edit summary of last resort, I think. Covers anything from actual copy-editing -- a broad church at the best of times! -- to 'messing around with the format of infoboxes for no transparent reason'.  Not really insightful as to either 'what my edit did' much less 'why it did it'.  109.255.211.6 (talk) 22:48, 29 April 2021 (UTC)
 * Though on the subject of edit summaries: I think there very much is a 'suggestion of a source-based or guideline-based reason to cap these words here.'  I thought I'd already explicitly cited WP:MILTERMS, but apparently I only alluded to it.  "Accepted names of wars, battles, revolts, revolutions, rebellions, mutinies, skirmishes, fronts, raids, actions, operations and so forth are capitalized if they are usually capitalized in sources."  This is I think a (couple of different) accepted name(s) of a battle which is indeed usually capitalized in sources.  109.255.211.6 (talk) 23:42, 29 April 2021 (UTC)
 * I read "if they are usually capitalized in sources" as meaning usually, which is a lot more than we're seeing in sources, which I'd call "sometimes". Dicklyon (talk) 00:02, 30 April 2021 (UTC)

Sourcing + article organization
It's not typical for articles to have both a lead section and a subsection called "overview". The lead is only 1 paragraph, so I believe the "overview" section should be trimmed and incorporated into the lead. As it is, the article does not meet the FA criteria because of this weird organization and because every non-lead paragraph is required to have an inline citation. (t · c)  buidhe  09:24, 29 March 2023 (UTC)

title: Talk:Falaise pocket


text:
Reciprocal lattice

In physics, the reciprocal lattice emerges from the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, which is the dual of physical space considered as a vector space, and the reciprocal lattice is the sublattice of that space that is dual to the direct lattice.

In quantum physics, reciprocal space is closely related to momentum space according to the proportionality $$\mathbf{p} = \hbar \mathbf{k}$$, where $$\mathbf{p}$$ is the momentum vector and $$\hbar$$ is the reduced Planck constant. The reciprocal lattice of a reciprocal lattice is equivalent to the original direct lattice, because the defining equations are symmetrical with respect to the vectors in real and reciprocal space. Mathematically, direct and reciprocal lattice vectors represent covariant and contravariant vectors, respectively.

The reciprocal lattice is the set of all vectors $$\mathbf{G}_m$$, that are wavevectors of plane waves in the Fourier series of a spatial function whose periodicity is the same as that of a direct lattice $$\mathbf{R}_n$$. Each plane wave in this Fourier series has the same phase or phases that are differed by multiples of $$2\pi$$ at each direct lattice point (so essentially same phase at all the direct lattice points).

The reciprocal lattice plays a fundamental role in most analytic studies of periodic structures, particularly in the theory of diffraction. In neutron, helium and X-ray diffraction, due to the Laue conditions, the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector. The diffraction pattern of a crystal can be used to determine the reciprocal vectors of the lattice. Using this process, one can infer the atomic arrangement of a crystal.

The Brillouin zone is a Wigner–Seitz cell of the reciprocal lattice.

Reciprocal space
Reciprocal space (also called $k$-space) provides a way to visualize the results of the Fourier transform of a spatial function. It is similar in role to the frequency domain arising from the Fourier transform of a time dependent function; reciprocal space is a space over which the Fourier transform of a spatial function is represented at spatial frequencies or wavevectors of plane waves of the Fourier transform. The domain of the spatial function itself is often referred to as real space. In physical applications, such as crystallography, both real and reciprocal space will often each be two or three dimensional. Whereas the number of spatial dimensions of these two associated spaces will be the same, the spaces will differ in their quantity dimension, so that when the real space has the dimension length (L), its reciprocal space will of inverse length, so L−1 (the reciprocal of length).

Reciprocal space comes into play regarding waves, both classical and quantum mechanical. Because a sinusoidal plane wave with unit amplitude can be written as an oscillatory term $$\cos(kx - \omega t + \varphi_0)$$, with initial phase $$\varphi_0$$, angular wavenumber $$k$$ and angular frequency $$\omega$$, it can be regarded as a function of both $$k$$ and $$x$$ (and the time-varying part as a function of both $$\omega$$ and $$t$$). This complementary role of $$k$$ and $$x$$ leads to their visualization within complementary spaces (the real space and the reciprocal space). The spatial periodicity of this wave is defined by its wavelength $$\lambda$$, where $$k \lambda = 2\pi$$; hence the corresponding wavenumber in reciprocal space will be $$k = 2\pi / \lambda$$.

In three dimensions, the corresponding plane wave term becomes $$\cos(\mathbf{k} \cdot \mathbf{r} - \omega t + \varphi_0)$$, which simplifies to $$\cos(\mathbf{k} \cdot \mathbf{r} + \varphi)$$ at a fixed time $$t$$, where $$\mathbf{r}$$ is the position vector of a point in real space and now $$\mathbf{k}=2\pi \mathbf{e} / \lambda$$ is the wavevector in the three dimensional reciprocal space. (The magnitude of a wavevector is called wavenumber.) The constant $$\varphi$$ is the phase of the wavefront (a plane of a constant phase) through the origin $$\mathbf{r}=0$$ at time $$t$$, and $$\mathbf{e}$$ is a unit vector perpendicular to this wavefront. The wavefronts with phases $$\varphi + (2\pi)n$$, where $$n$$ represents any integer, comprise a set of parallel planes, equally spaced by the wavelength $$\lambda$$.

Reciprocal lattice
In general, a geometric lattice is an infinite, regular array of vertices (points) in space, which can be modelled vectorially as a Bravais lattice. Some lattices may be skew, which means that their primary lines may not necessarily be at right angles. In reciprocal space, a reciprocal lattice is defined as the set of wavevectors $$\mathbf{k}$$ of plane waves in the Fourier series of any function $$f(\mathbf{r})$$ whose periodicity is compatible with that of an initial direct lattice in real space. Equivalently, a wavevector is a vertex of the reciprocal lattice if it corresponds to a plane wave in real space whose phase at any given time is the same (actually differs by $$(2\pi)n$$ with an integer $$n$$) at every direct lattice vertex.

One heuristic approach to constructing the reciprocal lattice in three dimensions is to write the position vector of a vertex of the direct lattice as $$\mathbf{R} = n_1\mathbf{a}_1 + n_2\mathbf{a}_2 + n_3\mathbf{a}_3$$, where the $$n_i$$ are integers defining the vertex and the $$\mathbf{a}_i$$ are linearly independent primitive translation vectors (or shortly called primitive vectors) that are characteristic of the lattice. There is then a unique plane wave (up to a factor of negative one), whose wavefront through the origin $$\mathbf{R} = 0$$ contains the direct lattice points at $$\mathbf{a}_2$$ and $$\mathbf{a}_3$$, and with its adjacent wavefront (whose phase differs by $$2\pi$$ or $$-2\pi$$ from the former wavefront passing the origin) passing through $$\mathbf{a}_1$$. Its angular wavevector takes the form $$\mathbf{b}_1 = 2\pi \mathbf{e}_1 / \lambda_{1}$$, where $$\mathbf{e}_1$$ is the unit vector perpendicular to these two adjacent wavefronts and the wavelength $$\lambda_1$$ must satisfy $$\lambda_1 = \mathbf{a}_1 \cdot \mathbf{e}_1$$, means that $$\lambda_1$$ is equal to the distance between the two wavefronts. Hence by construction $$\mathbf{a}_1 \cdot \mathbf{b}_1 = 2\pi$$ and $$\mathbf{a}_2 \cdot \mathbf{b}_1 = \mathbf{a}_3 \cdot \mathbf{b}_1 = 0$$.

Cycling through the indices in turn, the same method yields three wavevectors $$\mathbf{b}_j$$ with $$\mathbf{a}_i \cdot \mathbf{b}_j = 2\pi \, \delta_{ij}$$, where the Kronecker delta $$\delta_{ij}$$ equals one when $$i=j$$ and is zero otherwise. The $$\mathbf{b}_j$$ comprise a set of three primitive wavevectors or three primitive translation vectors for the reciprocal lattice, each of whose vertices takes the form $$\mathbf{G} = m_1\mathbf{b}_1 + m_2\mathbf{b}_2 + m_3\mathbf{b}_3$$, where the $$m_j$$ are integers. The reciprocal lattice is also a Bravais lattice as it is formed by integer combinations of the primitive vectors, that are $$\mathbf{b}_1$$, $$\mathbf{b}_2$$, and $$\mathbf{b}_3$$ in this case. Simple algebra then shows that, for any plane wave with a wavevector $$\mathbf{G}$$ on the reciprocal lattice, the total phase shift $$\mathbf{G} \cdot \mathbf{R}$$ between the origin and any point $$\mathbf{R}$$ on the direct lattice is a multiple of $$2\pi$$ (that can be possibly zero if the multiplier is zero), so the phase of the plane wave with $$\mathbf{G}$$ will essentially be equal for every direct lattice vertex, in conformity with the reciprocal lattice definition above. (Although any wavevector $$\mathbf{G}$$ on the reciprocal lattice does always take this form, this derivation is motivational, rather than rigorous, because it has omitted the proof that no other possibilities exist.)

The Brillouin zone is a primitive cell (more specifically a Wigner–Seitz cell) of the reciprocal lattice, which plays an important role in solid state physics due to Bloch's theorem. In pure mathematics, the dual space of linear forms and the dual lattice provide more abstract generalizations of reciprocal space and the reciprocal lattice.

Mathematical description

Assuming a three-dimensional Bravais lattice and labelling each lattice vector (a vector indicating a lattice point) by the subscript $$n = (n_1, n_2, n_3)$$ as 3-tuple of integers,

 * $$\mathbf{R}_n = n_1 \mathbf{a}_1 + n_2 \mathbf{a}_2 + n_3 \mathbf{a}_3$$ where $$n_1, n_2, n_3 \in \mathbb{Z}$$

where $$\mathbb{Z}$$ is the set of integers and $$\mathbf{a}_i$$ is a primitive translation vector or shortly primitive vector. Taking a function $$f(\mathbf{r})$$ where $$\mathbf{r}$$ is a position vector from the origin $$\mathbf{R}_n = 0$$ to any position, if $$f(\mathbf{r})$$ follows the periodicity of this lattice, e.g. the function describing the electronic density in an atomic crystal, it is useful to write $$f(\mathbf{r})$$ as a multi-dimensional Fourier series

 * $$\sum_m f_m e^{i \mathbf{G}_m \cdot \mathbf{r}} = f\left(\mathbf{r}\right) $$

where now the subscript $$m = (m_1, m_2, m_3)$$, so this is a triple sum.

As $$f(\mathbf{r})$$ follows the periodicity of the lattice, translating $$\mathbf{r}$$ by any lattice vector $$\mathbf{R}_n$$ we get the same value, hence

 * $$f(\mathbf{r} + \mathbf{R}_n) = f(\mathbf{r}).$$

Expressing the above instead in terms of their Fourier series we have $$\sum_m f_m e^{i \mathbf{G}_m \cdot \mathbf{r}} = \sum_m f_m e^{i \mathbf{G}_m \cdot (\mathbf{r} + \mathbf{R}_n)} = \sum_m f_m e^{i \mathbf{G}_m \cdot \mathbf{R}_n} \, e^{i \mathbf{G}_m \cdot \mathbf{r}}. $$

Because equality of two Fourier series implies equality of their coefficients, $$ e^{i \mathbf{G}_m \cdot \mathbf{R}_n} = 1$$, which only holds when

 * $$\mathbf{G}_m \cdot \mathbf{R}_n = 2\pi N$$ where $$N \in \mathbb{Z}.$$

Mathematically, the reciprocal lattice is the set of all vectors $$\mathbf{G}_m$$, that are wavevectors of plane waves in the Fourier series of a spatial function whose periodicity is the same as that of a direct lattice as the set of all direct lattice point position vectors $$\mathbf{R}_n$$, and $$\mathbf{G}_m$$ satisfy this equality for all $$\mathbf{R}_n$$. Each plane wave in the Fourier series has the same phase (actually can be differed by a multiple of $$2\pi$$) at all the lattice point $$\mathbf{R}_n$$.

As shown in the section multi-dimensional Fourier series, $$\mathbf{G}_m$$ can be chosen in the form of $$\mathbf{G}_m = m_1 \mathbf{b}_1 + m_2 \mathbf{b}_2 + m_3 \mathbf{b}_3$$ where $$\mathbf{a}_i \cdot \mathbf{b}_j = 2\pi \, \delta_{ij}$$. With this form, the reciprocal lattice as the set of all wavevectors $$\mathbf{G}_m$$ for the Fourier series of a spatial function which periodicity follows $$\mathbf{R}_n$$, is itself a Bravais lattice as it is formed by integer combinations of its own primitive translation vectors $$\left(\mathbf{b_{1}}, \mathbf{b}_2, \mathbf{b}_3\right)$$, and the reciprocal of the reciprocal lattice is the original lattice, which reveals the Pontryagin duality of their respective vector spaces. (There may be other form of $$\mathbf{G}_m$$. Any valid form of $$\mathbf{G}_m$$ results in the same reciprocal lattice.)

Two dimensions
For an infinite two-dimensional lattice, defined by its primitive vectors $$\left(\mathbf{a}_1, \mathbf{a}_2\right)$$, its reciprocal lattice can be determined by generating its two reciprocal primitive vectors, through the following formulae,

 * $$\mathbf{G}_m = m_1 \mathbf{b}_1 + m_2 \mathbf{b}_2$$

where $$m_i$$ is an integer and

 * $$\begin{align}

\mathbf{b}_1 &= 2\pi \frac{-\mathbf{Q} \, \mathbf{a}_2}{-\mathbf{a}_1 \cdot \mathbf{Q} \, \mathbf{a}_2} = 2\pi \frac{ \mathbf{Q} \, \mathbf{a}_2}{ \mathbf{a}_1 \cdot \mathbf{Q} \, \mathbf{a}_2} \\[8pt] \mathbf{b}_2 &= 2\pi \frac{ \mathbf{Q} \, \mathbf{a}_1}{ \mathbf{a}_2 \cdot \mathbf{Q} \, \mathbf{a}_1} \end{align}$$

Here $$\mathbf{Q}$$ represents a 90 degree rotation matrix, i.e. a quarter turn. The anti-clockwise rotation and the clockwise rotation can both be used to determine the reciprocal lattice: If $$\mathbf{Q}$$ is the anti-clockwise rotation and $$\mathbf{Q'}$$ is the clockwise rotation, $$\mathbf{Q}\,\mathbf{v}=-\mathbf{Q'}\,\mathbf{v}$$ for all vectors $$\mathbf{v}$$. Thus, using the permutation
 * $$\sigma = \begin{pmatrix}

1 & 2 \\ 2 & 1 \end{pmatrix}$$ we obtain

\mathbf{b}_n = 2\pi \frac{ \mathbf{Q} \, \mathbf{a}_{\sigma(n)}}{ \mathbf{a}_n \cdot \mathbf{Q} \, \mathbf{a}_{\sigma(n)}}=2\pi \frac{ \mathbf{Q}' \, \mathbf{a}_{\sigma(n)}}{ \mathbf{a}_n \cdot \mathbf{Q}' \, \mathbf{a}_{\sigma(n)}}. $$

Notably, in a 3D space this 2D reciprocal lattice is an infinitely extended set of Bragg rods—described by Sung et al.

Three dimensions
For an infinite three-dimensional lattice $$\mathbf{R}_n = n_1 \mathbf{a}_1 + n_2 \mathbf{a}_2 + n_3 \mathbf{a}_3$$, defined by its primitive vectors $$\left(\mathbf{a_{1}}, \mathbf{a}_2, \mathbf{a}_3\right)$$ and the subscript of integers $$n = \left( n_1, n_2, n_3 \right)$$, its reciprocal lattice $$\mathbf{G}_m = m_1 \mathbf{b}_1 + m_2 \mathbf{b}_2 + m_3 \mathbf{b}_3$$ with the integer subscript $$m = (m_1, m_2, m_3)$$ can be determined by generating its three reciprocal primitive vectors $$\left(\mathbf{b_{1}}, \mathbf{b}_2, \mathbf{b}_3\right)$$ $$\begin{align} \mathbf{b}_1 &= \frac{2\pi}{V} \ \mathbf{a}_2 \times \mathbf{a}_3 \\[8pt] \mathbf{b}_2 &= \frac{2\pi}{V} \ \mathbf{a}_3 \times \mathbf{a}_1 \\[8pt] \mathbf{b}_3 &= \frac{2\pi}{V} \ \mathbf{a}_1 \times \mathbf{a}_2 \end{align}$$ where $$V = \mathbf{a}_1 \cdot \left(\mathbf{a}_2 \times \mathbf{a}_3\right) = \mathbf{a}_2 \cdot \left(\mathbf{a}_3 \times \mathbf{a}_1\right) = \mathbf{a}_3 \cdot \left(\mathbf{a}_1 \times \mathbf{a}_2\right)$$ is the scalar triple product. The choice of these $$\left(\mathbf{b_{1}}, \mathbf{b}_2, \mathbf{b}_3\right)$$ is to satisfy $$\mathbf{a}_i \cdot \mathbf{b}_j = 2\pi \, \delta_{ij}$$ as the known condition (There may be other condition.) of primitive translation vectors for the reciprocal lattice derived in the heuristic approach above and the section multi-dimensional Fourier series. This choice also satisfies the requirement of the reciprocal lattice $$ e^{i \mathbf{G}_m \cdot \mathbf{R}_n} = 1$$ mathematically derived above. Using column vector representation of (reciprocal) primitive vectors, the formulae above can be rewritten using matrix inversion:

 * $$\left[\mathbf{b}_1\mathbf{b}_2\mathbf{b}_3\right]^\mathsf{T} = 2\pi\left[\mathbf{a}_1\mathbf{a}_2\mathbf{a}_3\right]^{-1}.$$

This method appeals to the definition, and allows generalization to arbitrary dimensions. The cross product formula dominates introductory materials on crystallography.

The above definition is called the "physics" definition, as the factor of $$2 \pi$$ comes naturally from the study of periodic structures. An essentially equivalent definition, the "crystallographer's" definition, comes from defining the reciprocal lattice $$\mathbf{K}_m = \mathbf{G}_m / 2\pi$$. which changes the reciprocal primitive vectors to be

\mathbf{b}_1 = \frac{\mathbf{a}_2 \times \mathbf{a}_3}{\mathbf{a}_1 \cdot \left(\mathbf{a}_2 \times \mathbf{a}_3\right)} $$ and so on for the other primitive vectors. The crystallographer's definition has the advantage that the definition of $$\mathbf{b}_1$$ is just the reciprocal magnitude of $$\mathbf{a}_1$$ in the direction of $$\mathbf{a}_2 \times \mathbf{a}_3$$, dropping the factor of $$2 \pi$$. This can simplify certain mathematical manipulations, and expresses reciprocal lattice dimensions in units of spatial frequency. It is a matter of taste which definition of the lattice is used, as long as the two are not mixed.

$$m = (m_1, m_2, m_3)$$ is conventionally written as $$(h, k, \ell)$$ or $$(hk\ell)$$, called Miller indices; $$m_1$$ is replaced with $$h$$, $$m_2$$ replaced with $$k$$, and $$m_3$$ replaced with $$\ell$$. Each lattice point $$(hk\ell)$$ in the reciprocal lattice corresponds to a set of lattice planes $$(hk\ell)$$ in the real space lattice. (A lattice plane is a plane crossing lattice points.) The direction of the reciprocal lattice vector corresponds to the normal to the real space planes. The magnitude of the reciprocal lattice vector $$\mathbf{K}_m$$ is given in reciprocal length and is equal to the reciprocal of the interplanar spacing of the real space planes.

Higher dimensions
The formula for $$n$$ dimensions can be derived assuming an $$n$$-dimensional real vector space $$V$$ with a basis $$(\mathbf{a}_1,\ldots,\mathbf{a}_n)$$ and an inner product $$g\colon V\times V\to\mathbf{R}$$. The reciprocal lattice vectors are uniquely determined by the formula $$g(\mathbf{a}_i,\mathbf{b}_j)=2\pi\delta_{ij}$$. Using the permutation
 * $$\sigma = \begin{pmatrix}

1 & 2 & \cdots &n\\ 2 & 3 & \cdots &1 \end{pmatrix},$$ they can be determined with the following formula:

\mathbf{b}_i = 2\pi\frac{\varepsilon_{\sigma^1i\ldots\sigma^ni}}{\omega(\mathbf{a}_1,\ldots,\mathbf{a}_n)}g^{-1}(\mathbf{a}_{\sigma^{n-1}i}\,\lrcorner\ldots\mathbf{a}_{\sigma^1i}\,\lrcorner\,\omega)\in V $$ Here, $$\omega\colon V^n \to \mathbf{R}$$ is the volume form, $$g^{-1}$$ is the inverse of the vector space isomorphism $$\hat{g}\colon V \to V^*$$ defined by $$\hat{g}(v)(w) = g(v,w)$$ and $$\lrcorner$$ denotes the inner multiplication.

One can verify that this formula is equivalent to the known formulas for the two- and three-dimensional case by using the following facts: In three dimensions, $$\omega(u,v,w) = g(u \times v, w)$$ and in two dimensions, $$\omega(v,w) = g(Rv,w)$$, where $$R \in \text{SO}(2) \subset L(V,V)$$ is the rotation by 90 degrees (just like the volume form, the angle assigned to a rotation depends on the choice of orientation ).

Reciprocal lattices of various crystals
Reciprocal lattices for the cubic crystal system are as follows.

Simple cubic lattice
The simple cubic Bravais lattice, with cubic primitive cell of side $$a$$, has for its reciprocal a simple cubic lattice with a cubic primitive cell of side $\frac{2\pi}{a}$ (or $ \frac{1}{a}$  in the crystallographer's definition). The cubic lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space.

Face-centered cubic (FCC) lattice
The reciprocal lattice to an FCC lattice is the body-centered cubic (BCC) lattice, with a cube side of $ \frac{4\pi}{a}$.

Consider an FCC compound unit cell. Locate a primitive unit cell of the FCC; i.e., a unit cell with one lattice point. Now take one of the vertices of the primitive unit cell as the origin. Give the basis vectors of the real lattice. Then from the known formulae, you can calculate the basis vectors of the reciprocal lattice. These reciprocal lattice vectors of the FCC represent the basis vectors of a BCC real lattice. The basis vectors of a real BCC lattice and the reciprocal lattice of an FCC resemble each other in direction but not in magnitude.

Body-centered cubic (BCC) lattice
The reciprocal lattice to a BCC lattice is the FCC lattice, with a cube side of $ 4\pi/a$.

It can be proven that only the Bravais lattices which have 90 degrees between $$\left(\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3\right)$$ (cubic, tetragonal, orthorhombic) have primitive translation vectors for the reciprocal lattice, $$\left(\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3\right)$$, parallel to their real-space vectors.

Simple hexagonal lattice
The reciprocal to a simple hexagonal Bravais lattice with lattice constants $ a$ and $ c$  is another simple hexagonal lattice with lattice constants $ 2\pi/c$  and $ 4\pi/(a\sqrt3)$  rotated through 90° about the c axis with respect to the direct lattice. The simple hexagonal lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space. Primitive translation vectors for this simple hexagonal Bravais lattice vectors are $$ \begin{align} a_1 & = \frac{\sqrt{3}}{2} a \hat{x} + \frac{1}{2} a \hat{y}, \\[8pt] a_2 & = - \frac{\sqrt{3}}{2} a \hat{x} + \frac{1}{2}a\hat{y}, \\[8pt] a_3 & = c \hat{z}. \end{align} $$

Arbitrary collection of atoms

One path to the reciprocal lattice of an arbitrary collection of atoms comes from the idea of scattered waves in the Fraunhofer (long-distance or lens back-focal-plane) limit as a Huygens-style sum of amplitudes from all points of scattering (in this case from each individual atom). This sum is denoted by the complex amplitude $$F$$ in the equation below, because it is also the Fourier transform (as a function of spatial frequency or reciprocal distance) of an effective scattering potential in direct space:

 * $$F[\vec{g}] = \sum_{j=1}^N f_j\!\left[\vec{g}\right] e^{2 \pi i \vec{g} \cdot \vec{r}_j}.$$

Here g = q/(2$\pi$) is the scattering vector q in crystallographer units, N is the number of atoms, fj[g] is the atomic scattering factor for atom j and scattering vector g, while rj is the vector position of atom j. The Fourier phase depends on one's choice of coordinate origin.

For the special case of an infinite periodic crystal, the scattered amplitude F = M Fh,k,ℓ from M unit cells (as in the cases above) turns out to be non-zero only for integer values of $$(h,k,\ell)$$, where

 * $$F_{h,k,\ell} = \sum_{j=1}^m f_j\left[g_{h,k,\ell}\right] e^{2\pi i \left(h u_j + k v_j + \ell w_j\right)}$$

when there are j = 1,m atoms inside the unit cell whose fractional lattice indices are respectively {uj, vj, wj}. To consider effects due to finite crystal size, of course, a shape convolution for each point or the equation above for a finite lattice must be used instead.

Whether the array of atoms is finite or infinite, one can also imagine an "intensity reciprocal lattice" I[g], which relates to the amplitude lattice F via the usual relation I = F*F where F* is the complex conjugate of F. Since Fourier transformation is reversible, of course, this act of conversion to intensity tosses out "all except 2nd moment" (i.e. the phase) information. For the case of an arbitrary collection of atoms, the intensity reciprocal lattice is therefore:

 * $$I[\vec{g}] = \sum_{j=1}^N \sum_{k=1}^N f_j \left[\vec{g}\right] f_k \left[\vec{g}\right] e^{2\pi i \vec{g} \cdot \vec{r}_{\!\!\;jk}}.$$

Here rjk is the vector separation between atom j and atom k. One can also use this to predict the effect of nano-crystallite shape, and subtle changes in beam orientation, on detected diffraction peaks even if in some directions the cluster is only one atom thick. On the down side, scattering calculations using the reciprocal lattice basically consider an incident plane wave. Thus after a first look at reciprocal lattice (kinematic scattering) effects, beam broadening and multiple scattering (i.e. dynamical) effects may be important to consider as well.

Generalization of a dual lattice
There are actually two versions in mathematics of the abstract dual lattice concept, for a given lattice L in a real vector space V, of finite dimension.

The first, which generalises directly the reciprocal lattice construction, uses Fourier analysis. It may be stated simply in terms of Pontryagin duality. The dual group V^ to V is again a real vector space, and its closed subgroup L^ dual to L turns out to be a lattice in V^. Therefore, L^ is the natural candidate for dual lattice, in a different vector space (of the same dimension).

The other aspect is seen in the presence of a quadratic form Q on V; if it is non-degenerate it allows an identification of the dual space V* of V with V. The relation of V* to V is not intrinsic; it depends on a choice of Haar measure (volume element) on V. But given an identification of the two, which is in any case well-defined up to a scalar, the presence of Q allows one to speak to the dual lattice to L while staying within V.

In mathematics, the dual lattice of a given lattice L in an abelian locally compact topological group G is the subgroup L∗ of the dual group of G consisting of all continuous characters that are equal to one at each point of L.

In discrete mathematics, a lattice is a locally discrete set of points described by all integral linear combinations of $dim = n$ linearly independent vectors in Rn. The dual lattice is then defined by all points in the linear span of the original lattice (typically all of Rn) with the property that an integer results from the inner product with all elements of the original lattice. It follows that the dual of the dual lattice is the original lattice.

Furthermore, if we allow the matrix B to have columns as the linearly independent vectors that describe the lattice, then the matrix $$A = B\left(B^\mathsf{T} B\right)^{-1}$$ has columns of vectors that describe the dual lattice.

title: Reciprocal lattice


text:
1912 Lawrence textile strike

The Lawrence Textile Strike, also known as the Bread and Roses Strike, was a strike of immigrant workers in Lawrence, Massachusetts, in 1912 led by the Industrial Workers of the World (IWW). Prompted by a two-hour pay cut corresponding to a new law shortening the workweek for women, the strike spread rapidly through the town, growing to more than twenty thousand workers and involving nearly every mill in Lawrence. On January 1, 1912, the Massachusetts government enforced a law that cut mill workers' hours in a single work week from 56 hours, to 54 hours. Ten days later, they found out that pay had been reduced along with the cut in hours. The strike united workers from more than 51 different nationalities many of whom knew little to no English. A large portion of the striking workers, including many of the leaders of the strike, were Italian immigrants. Carried on throughout a brutally cold winter, the strike lasted more than two months, from January to March, defying the assumptions of conservative trade unions within the American Federation of Labor (AFL) that immigrant, largely female and ethnically divided workers could not be organized. In late January, when a striker, Anna LoPizzo, was killed by police during a protest, IWW organizers Joseph Ettor and Arturo Giovannitti were framed and arrested on charges of being accessories to the murder. IWW leaders Bill Haywood and Elizabeth Gurley Flynn came to Lawrence to run the strike. Together they masterminded its signature move, sending hundreds of the strikers' hungry children to sympathetic families in New York, New Jersey, and Vermont. The move drew widespread sympathy, especially after police stopped a further exodus, leading to violence at the Lawrence train station. Congressional hearings followed, resulting in exposure of shocking conditions in the Lawrence mills and calls for investigation of the "wool trust." Mill owners soon decided to settle the strike, giving workers in Lawrence and throughout New England raises of up to 20 percent. Within a year, however, the IWW had largely collapsed in Lawrence.

The Lawrence strike is often referred to as the "Bread and Roses" strike. It has also been called the "strike for three loaves". The phrase "bread and roses" actually preceded the strike, appearing in a poem by James Oppenheim published in The American Magazine in December 1911. A 1915 labor anthology, The Cry for Justice: An Anthology of the Literature of Social Protest by Upton Sinclair, attributed the phrase to the Lawrence strike, and the association stuck. A popular rallying cry from the poem was interwoven with the memory of the strike: "Hearts starve as well as bodies; give us bread, but give us roses!"

Background
Founded in 1845, Lawrence was a flourishing but deeply-troubled textile city. By 1900, mechanization and the deskilling of labor in the textile industry enabled factory owners to eliminate skilled workers and to employ large numbers of unskilled immigrant workers, mostly women. Work in a textile mill took place at a grueling pace, and the labor was repetitive and dangerous. About one third of workers in the Lawrence textile mills died before the age of 25. In addition, a number of children under 14 worked in the mills. Half of the workers in the four Lawrence mills of the American Woolen Company, the leading employer in the industry and the town, were females between 14 and 18. Falsification of birth certificates, allowing for girls younger than 14 to work, was common practice at the time. Lawrence had the 5th highest child mortality rate of any city in the country at the time, behind four other mill towns in Massachusetts (Lowell, Fall River, Worcester, and Holyoke).

By 1912, the Lawrence mills at maximum capacity employed about 32,000 men, women, and children. Conditions had worsened even more in the decade before the strike. The introduction of the two-loom system in the woolen mills led to a dramatic increase in the pace of work. The greater production enabled the factory owners to lay off large numbers of workers. Those who kept their jobs earned, on average, $8.76 for 56 hours of work and $9.00 for 60 hours of work.

Some of the mills, worker housing and part of the town was owned by American Woolen Company president William Wood, who said he could not afford to pay his workers for the two hours per week  they were cut, even though the company had made a profit of $3,000,000 (~$ in ) in 1911.

The workers in Lawrence lived in crowded and dangerous apartment buildings, often with many families sharing each apartment. Many families survived on bread, molasses, and beans; as one worker testified before the March 1912 congressional investigation of the Lawrence strike, "When we eat meat it seems like a holiday, especially for the children." Half of children died before they were six, and 36% of the adults who worked in the mill died before they were 25. The average life expectancy was 39.

The mills and the community were divided along ethnic lines: most of the skilled jobs were held by native-born workers of English, Irish, and German descent, whereas French-Canadian, Italian, Jewish, Slavic, Hungarian, Portuguese, and Syrian immigrants made up most of the unskilled workforce. Several thousand skilled workers belonged, in theory at least, to the American Federation of Labor-affiliated United Textile Workers, but only a few hundred paid dues. The Industrial Workers of the World (IWW) had also been organizing for five years among workers in Lawrence but also had only a few hundred actual members.

Strike
On January 1, 1912, a new labor law took effect in Massachusetts reducing the working week of 56 hours to 54 hours for women and children. Workers opposed the reduction if it reduced their weekly take-home pay. The first two weeks of 1912, the unions tried to learn how the owners of the mills would deal with the new law. On January 11, a group of Polish women textile workers in Lawrence discovered that their employer at the Everett Mill had reduced about $0.32 from their total wages and walked out.

On January 12, workers in the Washington Mill of the American Woolen Company also found that their wages had been cut. Prepared for the events by weeks of discussion, they walked out, calling "short pay, all out."

Joseph Ettor of the IWW had been organizing in Lawrence for some time before the strike; he and Arturo Giovannitti of the Italian Socialist Federation of the Socialist Party of America quickly assumed leadership of the strike by forming a strike committee of 56 people, four representatives of fourteen nationalities, which took responsibility for all major decisions. The committee, which arranged for its strike meetings to be translated into 25 different languages, put forward a set of demands: a 15% increase in wages for a 54-hour work week, double pay for overtime work, and no discrimination against workers for their strike activity. The city responded to the strike by ringing the city's alarm bell for the first time in its history; the mayor ordered a company of the local militia to patrol the streets. When mill owners turned fire hoses on the picketers gathered in front of the mills, they responded by throwing ice at the plants, breaking a number of windows. The court sentenced 24 workers to a year in jail for throwing ice; as the judge stated, "The only way we can teach them is to deal out the severest sentences." Governor Eugene Foss then ordered out the state militia and state police. Mass arrests followed.

At the same time, the United Textile Workers (UTW) attempted to break the strike by claiming to speak for the workers of Lawrence. The striking operatives ignored the UTW, as the IWW had successfully united the operatives behind ethnic-based leaders, who were members of the strike committee and able to communicate Ettor's message to avoid violence at demonstrations. Ettor did not consider intimidating operatives who were trying to enter the mills as breaking the peace.

The IWW was successful, even with AFL-affiliated operatives, as it defended the grievances of all operatives from all the mills. Conversely, the AFL and the mill owners preferred to keep negotiations between separate mills and their own operatives. However, in a move that frustrated the UTW, Oliver Christian, the national secretary of the Loomfixers Association and an AFL affiliate itself, said he believed John Golden, the Massachusetts-based UTW president, was a detriment to the cause of labor. That statement and missteps by William Madison Wood quickly shifted public sentiment to favor the strikers.

A local undertaker and a member of the Lawrence school board attempted to frame the strike leadership by planting dynamite in several locations in town a week after the strike began. He was fined $500 and released without jail time. Later, William M. Wood, the president of the American Woolen Company, was shown to have made an unexplained large payment to the defendant shortly before the dynamite was found.

The authorities later charged Ettor and Giovannitti as accomplices to murder for the death of striker Anna LoPizzo, who was likely shot by the police. Ettor and Giovannitti had been 3 mi away, where they spoke to another group of workers. They and a third defendant, who had not even heard of either Ettor or Giovannitti at the time of his arrest, were held in jail for the duration of the strike and several months thereafter. The authorities declared martial law, banned all public meetings, and called out 22 more militia companies to patrol the streets. Harvard students were even given exemptions from their final exams if they agreed to go and try to break up the strike. The IWW responded by sending Bill Haywood, Elizabeth Gurley Flynn, and a number of other organizers to Lawrence. Haywood participated little in the daily affairs of the strike. Instead, he set out for other New England textile towns in an effort to raise funds for the strikers in Lawrence, which proved very successful. Other tactics established were an efficient system of relief committees, soup kitchens, and food distribution stations, and volunteer doctors provided medical care. The IWW raised funds on a nationwide basis to provide weekly benefits for strikers and dramatized the strikers' needs by arranging for several hundred children to go to supporters' homes in New York City for the duration of the strike. When city authorities tried to prevent another 100 children from going to Philadelphia on February 24 by sending police and the militia to the station to detain the children and arrest their parents, the police began clubbing both the children and their mothers and dragged them off to be taken away by truck; one pregnant mother miscarried. The press, there to photograph the event, reported extensively on the attack. Moreover, when the women and children were taken to the Police Court, most of them refused to pay the fines levied and opted for a jail cell, some with babies in arms. The police action against the mothers and children of Lawrence attracted the attention of the nation, in particular that of first lady Helen Herron Taft, wife of President William Howard Taft. Soon, both the House and the Senate set out to investigate the strike. In the early days of March, a special House Committee heard testimony from some of the strikers' children, as well as various city, state and union officials. In the end, both chambers published reports detailing the conditions at Lawrence.

The children involved in the police riot were not only the children of striking workers, they were also striking workers themselves. Most of the workers at the mill were women and children. Families were suffering not only from the lost income of adult workers, but also the lost wages of children. Children were used several times during the strike to attract attention to the cause. On February 10, 119 children were sent to Manhattan to live with relatives, or strangers, who were able to feed them to alleviate the financial strain on the striking families. The children were welcomed in NY by cheering crowds that drew national attention. When another group of children were sent to NY, they were paraded down 5th Avenue, drawing even more attention. Embarrassed by the bad publicity, the city marshal tried to deter the next group of children that were being sent to Philadelphia on February 24, with disastrous results. Police attempted to stop the children from boarding the train and as mothers tried to force their children on board, police intervened with clubs and arrested parents and children, the latter being ferried out of the town to an orphanage. The next role that children played in the result of the strike was the testimony they gave about the working conditions in the factories. Most notable was that of Carmela Teoli, a 14-year-old mill worker who testified in front of a Congressional hearing. Teoli had been hospitalized for seven months after the cotton-twisting machine she operated had pulled her scalp off. The company paid her hospital bills, but did not provide her with sick pay. The national sympathy that children elicited changed the outcome of the strike. Children of the mill workers were brought to homes of supporters of the Lawrence textile strike. With the aid of Haywood and Flynn, these two individuals organized a way for donations for the children of strikers. In addition, the children began to form strike rallies to demonstrate the hardship and struggle occurring in the Lawrence mill factories. Strikes happened from Vermont all the way to New York City; those children fought to be seen and heard where they went.

The national attention had an effect: the owners offered a 5% pay raise on March 1, but the workers rejected it. American Woolen Company agreed to most of the strikers' demands on March 12, 1912. The strikers had demanded an end to the Premium System in which a portion of their earnings were subject to month-long production and attendance standards. The mill owners' concession was to change the award of the premium from once every four weeks to once every two weeks. The rest of the manufacturers followed by the end of the month; other textile companies throughout New England, anxious to avoid a similar confrontation, then followed suit.

The children who had been taken in by supporters in New York City came home on March 30.

Aftermath
Ettor and Giovanniti, both members of IWW, remained in prison for months after the strike was over. Haywood threatened a general strike to demand their freedom, with the cry "Open the jail gates or we will close the mill gates." The IWW raised $60,000 for their defense and held demonstrations and mass meetings throughout the country in their support; the Boston authorities arrested all of the members of the Ettor and Giovannitti Defense Committee. On March 10, 1912, an estimated 10,000 protestors gathered in Lawrence demanding the release of Ettor and Giovannitti. Then, 15,000 Lawrence workers went on strike for one day on September 30 to demand the release of Ettor and Giovannitti. Swedish and French workers proposed a boycott of woolen goods from the US and a refusal to load ships going there, and Italian supporters of the Giovannitti men rallied in front of the US consulate in Rome.

In the meantime, Ernest Pitman, a Lawrence building contractor who had done extensive work for the American Woolen Company, confessed to a district attorney that he had attended a meeting in the Boston offices of Lawrence textile companies, where the plan to frame the union by planting dynamite had been made. Pitman committed suicide shortly thereafter when he was subpoenaed to testify. Wood, the American Woolen Company owner, was formally exonerated. When the trial of Ettor and Giovannitti, as well as a third defendant, Giuseppe Caruso, accused of firing the shot that killed the picketer, began in September 1912 in Salem before Judge Joseph F. Quinn, the three defendants were kept in steel cages in the courtroom. All witnesses testified that Ettor and Giovannitti were miles away and that Caruso, the third defendant, was at home and eating supper at the time of the killing.

Ettor and Giovannitti both delivered closing statements at the end of the two-month trial. In Ettor's closing statement, he turned and faced the District Attorney:

"Does Mr. Ateill believe for a moment that... the cross or the gallows or the guillotine, the hangman's noose, ever settled an idea? It never did. If an idea can live, it lives because history adjudges it right. And what has been considered an idea constituting a social crime in one age has in the next age become the religion of humanity. Whatever my social views are, they are what they are. They cannot be tried in this courtroom."

All three defendants were acquitted on November 26, 1912.

The strikers, however, lost nearly all of the gains they had won in the next few years. The IWW, disdaining written contracts as encouraging workers to abandon the daily class struggle, thus left the mill owners to chisel away at the improvements in wages and working conditions, to fire union activists, and to install labor spies to keep an eye on workers. The more persistent owners laid off further employees during a depression in the industry.

By then, the IWW had turned its attention to supporting the silk industry workers in Paterson, New Jersey. The Paterson Silk Strike of 1913 was defeated.

Casualties
The strike had at least three casualties:
 * Anna LoPizzo, an Italian immigrant, who was shot in the chest during a clash between strikers and police
 * John Ramey, a Syrian youth who was bayoneted to death in the back by the militia
 * Jonas Smolskas, a Lithuanian immigrant who was beaten to death several months after the strike ended for wearing a pro-labor pin on his lapel

Conclusion and legacy
After the strike concluded, workers received a few of the demands established between mill workers and owners. Some workers went back to work at the mills and "others came and went, trying to find other jobs, failing, returning again to the music of the power loom". Even after the strike was finished, there were many other strikes that occurred in other states involving various mill factories. "On January 12, 1913, the IWW held anniversary celebration in Lawrence" which was one of the last celebrations for a couple of years.

Eugene Debs said of the strike, "The Victory at Lawrence was the most decisive and far-reaching ever won by organized labor." Author Peter Carlson saw this strike conducted by the militant Industrial Workers of the World (IWW) as a turning point. He wrote, "Wary of [a war with the anti-capitalist IWW], some mill owners swallowed their hatred of unions and actually invited the AFL to organize their workers.

On February 9, 2019, Senator Elizabeth Warren officially announced her candidacy for President of the United States at the site of the strike.

title: 1912 Lawrence textile strike


text:
Talk:South Australia

Adelade Meetups
People in SA are gorgeous and I’m doing a brochure about SA. 112.141.249.203 (talk) 06:17, 14 November 2023 (UTC)

title: Talk:South Australia