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Talk:Phil Collins

Home in Norfolk ?
In the Mark Lawson interview mentioned, Collins says that he did not have a home in Norfolk, and that he didn't particularly like Norfolk. The Telegraph article cited also mentions him divorcing his second wife by fax which is something he has repeatedly denied, so it may be that the passing comments in that article were not fully researched. -- Beardo (talk) 10:57, 30 September 2023 (UTC)

Description of his relationships to his children and between his children among them in their articles.
Following an edit war on the articles of his children (specifically Joely, Simon and Lily), I'm starting this discussion in hopes of finding consensus on the correct way of describing how these three of his children are related to one another.

The situation is as follows: Phil adopted his first wife's daughter Joely and then had a bioligical song with that same first wife. This makes him Joely's adoptive father and Simon's father, while Joely and Simon are maternal half siblings. Then Phil had a second daughter, Lily, with his second wife. That makes here the adoptive sister of Joely and the paternal half sister of Simon.

And that is the way I tried to correctly describe them in their articles tonight, per our own article siblings. However, there is one user who just keeps reverting every user trying to change this information and whom I resultlessly tried to discuss with on their talk page.

So therefore I start this discussion in the hope of finding consensus with the input of other editors.

For courtesy I will ping the other users who I'm aware of who made edits on the subject (@Yours6700, @Untamed1910, @2601:580:c180:22d0:e801:13e8:f180:d2f, @2001:9b0:46::b4d5:2bcd). If I missed any please ping them here as well.

Note that due to partial blocks issued while the edit war was ensuing, the articles of Simon and Lily are now in the state in line with my above proposal, while Joely's isn't.Tvx1 00:37, 2 February 2024 (UTC) Tvx1 00:23, 2 February 2024 (UTC)

 * See original discussion at Geraldo Perez (talk) 01:13, 2 February 2024 (UTC)

 * The details of the relationships are in the articles in the "Personal life section". It is fully correct to drop the "adoptive-", "adopted-", "half-" and "step-" modifiers from the relationship descriptions and just refer to the people as they refer to each other. Some adopted people and adoptive parents find the labels offensive and demeaning and never think of their close family that way. It is also unnecessary to do so in a bio article particularly when the details are fully covered in the article with the proper context and explanations. The articles were correct and no information was missing before the changes. There is no compelling reason to add the somewhat demeaning labels. Adoption creates real legal and emotional family links. The links to the bio parent are legally broken with their permission so no longer exist. The bio info is basically trivia that does not need to be in the infobox or lead. Geraldo Perez (talk) 01:03, 2 February 2024 (UTC)
 * I don't think we should start making judgements of what is and what is not demeaning to someone. That's POV that we cannot quantify. Moreover, I struggle to see how just describing information accurately and neutrally could be construeer as demeaming. Also, I do not see how you can think that doing things like ignoring Joely Collins' biological father exists is any less demeaning. You need to understand that you are not writing and editing these articles for yourself, but for a general audience. So we need to write what is accurate and non-confusing for all readers, not only what is right in your eyes. Lastly you keep demonstrating a very poor every understanding of the subject do not. Your claim that adoptions always completely break any link with the biological parents is quite patently FALSE. There are various kinds of adoptions and some allow links with the original legal parent(s) to remain. I really don't know what it will take for you to finally accept and also to consider the posibility that you could be wrong here. Stop being so stubborn!
 * But I really want to see other people weigh in here now.Tvx1 01:54, 2 February 2024 (UTC)
 * Recommendation at WP:BRD should have been followed and this and the other articles returned to the state before the dispute started per WP:STATUSQUO and a discussion started when the initial edit was reverted. I see this as a WP:BLP issue that needs discussion and consensus before changes are made. The article was correct and complete before the changes were made.
 * Nothing is being ignored, the full details are in the article along with context. I object to adding the unnecessary modifiers in the infobox and lead - they are not used in normal adoptive relationships, and seldom used by most families when talking about each other. And yes some people find them demeaning as it implies a lesser level of relationship. See Language of adoption. The descriptions there are correct without them. Adoption changes who the legal guardian is, modern adoptions may permit some knowledge and acknowledgment of who the bio-parents are and give them some rights to interact with their bio-kids. It is not the same as fostering. Geraldo Perez (talk) 02:22, 2 February 2024 (UTC)
 * Please actually read what you are citing. WP:STATUSQUO is an essay and thuis does not override things WP:EW and WP:3RR. Hence why you were blocked from editing these pages as well. Your reverts were just as wrong. Also read THEWRONGVERSION
 * The article wasn't any less "correct" but certainly more complete with my edits. My edit didn't even all concern the adoptive relations in this family. What you personally consider to be straightforward and logical doesn't necessarily mean it is too for everyone possible reader of world. Your claim about what is the normal way to describe adoptive relationships is just a personal opinion and not the way how every person in the world sees that. Hence why it doesn't match at all what is explained in our sibling article. Almost all readers take terms like full and half sibling to mean a biological sibling. The way you insist the articles should be written thus created potential confusion. This is not an informal family gathering, but an encyclopedia and thus we should use non-confusing encylopedic language and remain consistent with other articles. Tvx1 02:52, 8 February 2024 (UTC)

title: Talk:Phil Collins


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Gene pool

The gene pool is the set of all genes, or genetic information, in any population, usually of a particular species.

Description
A large gene pool indicates extensive genetic diversity, which is associated with robust populations that can survive bouts of intense selection. Meanwhile, low genetic diversity (see inbreeding and population bottlenecks) can cause reduced biological fitness and an increased chance of extinction, although as explained by genetic drift new genetic variants, that may cause an increase in the fitness of organisms, are more likely to fix in the population if it is rather small.

When all individuals in a population are identical with regard to a particular phenotypic trait, the population is said to be 'monomorphic'. When the individuals show several variants of a particular trait they are said to be polymorphic.

History
The Russian geneticist Alexander Sergeevich Serebrovsky first formulated the concept in the 1920s as genofond (gene fund), a word that was imported to the United States from the Soviet Union by Theodosius Dobzhansky, who translated it into English as "gene pool."

Gene pool concept in crop breeding
Harlan and de Wet (1971) proposed classifying each crop and its related species by gene pools rather than by formal taxonomy.
 * 1) Primary gene pool (GP-1): Members of this gene pool are probably in the same "species" (in conventional biological usage) and can intermate freely. Harlan and de Wet wrote, "Among forms of this gene pool, crossing is easy; hybrids are generally fertile with good chromosome pairing; gene segregation is approximately normal and gene transfer is generally easy.". They also advised subdividing each crop gene pool in two:
 * 2) *Subspecies A: Cultivated races
 * 3) *Subspecies B: Spontaneous races (wild or weedy)
 * 4) Secondary gene pool (GP-2): Members of this pool are probably normally classified as different species than the crop species under consideration (the primary gene pool). However, these species are closely related and can cross and produce at least some fertile hybrids. As would be expected by members of different species, there are some reproductive barriers between members of the primary and secondary gene pools:
 * 5) *hybrids may be weak
 * 6) *hybrids may be partially sterile
 * 7) *chromosomes may pair poorly or not at all
 * 8) *recovery of desired phenotypes may be difficult in subsequent generations
 * 9) *However, "The gene pool is available to be utilized, however, if the plant breeder or geneticist is willing to put out the effort required."
 * 10) Tertiary gene pool (GP-3): Members of this gene pool are more distantly related to the members of the primary gene pool. The primary and tertiary gene pools can be intermated, but gene transfer between them is impossible without the use of "rather extreme or radical measures" such as:
 * 11) *embryo rescue (or embryo culture, a form of plant organ culture)
 * 12) *induced polyploidy (chromosome doubling)
 * 13) *bridging crosses (e.g., with members of the secondary gene pool).

Gene pool centres
Gene pool centres refers to areas on the earth where important crop plants and domestic animals originated. They have an extraordinary range of the wild counterparts of cultivated plant species and useful tropical plants. Gene pool centres also contain different sub tropical and temperate region species.

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

title: Gene pool


text:
D. Napier & Son

D. Napier & Son Limited was a British engineering company best known for its luxury motor cars in the Edwardian era and for its aero engines throughout the early to mid-20th century.

Napier was founded as a precision engineering company in 1808 and for nearly a century produced machinery for the financial, print, and munitions industries. In the early 20th century it moved for a time into internal combustion engines and road vehicles before turning to aero engines. Its powerful Lion dominated the UK market in the 1920s and the Second World War era Sabre produced 3500 hp in its later versions. Many world speed records on land and water, as well as the Hawker Typhoon and Tempest fighter planes, were powered by Napier engines. During the Second World War the company was taken over by English Electric, and engine manufacture eventually ceased. Today, Napier Turbochargers is a subsidiary of the American company Wabtec.

Early years and precision engineering
David Napier, second son of the blacksmith to the Duke of Argyll, was born in 1785. While cousins became shipbuilders, he took engineering training in Scotland before coming to London. There in 1808 he founded the firm that was to become D. Napier & Son in Lloyds Court, St Giles, London. He designed a steam-powered printing press, some of which went to Hansard (the printer and publisher of proceedings of the Houses of Parliament), as well as newspapers. The company moved to Lambeth, South London, in 1830.

Between 1840 and 1860, Napier was prosperous, with a well-outfitted factory and between 200 and 300 workers. Napier made a wide variety of products, including a centrifuge for sugar manufacturing, lathes and drills, ammunition-making equipment for the Royal Arsenal, Woolwich, and railway cranes. David's younger son James Murdoch Napier, born 1823, joined the firm in 1837 and became a partner in 1847, resulting in a change in the private company's name to D. Napier & Son.

James succeeded his father as head of the firm in 1867, and after his father's death in 1873, specialized in crafted precision machinery for making coins, and printing stamps and banknotes. James proved an excellent engineer, but a poor businessman, considering salesmanship undignified. His company's fortunes went so bad that there were as few as seven employees in 1895, and James attempted to sell the business, but failed.

Montague Napier and high-performance vehicles
James' son Montague, born 1870, inherited the business in 1895, along with his father's engineering talents. Montague was a hobby racing cyclist, and at the Bath Road Club, he met "ebullient Australian" S. F. Edge (then a manager at Dunlop Rubber and colleague of H. J. Lawson in London, and amateur racer of motor tricycles.) Edge persuaded Napier to improve his Panhard "Old Number 8" (which had won the 1896 Paris–Marseille–Paris), converting from a tiller to a steering wheel and improving the oiling.

Dissatisfied, Napier offered to fit an engine of his own design, an 8 hp vertical twin, with electric ignition, superior to the Panhard's hot tube type. Edge was sufficiently impressed to encourage Napier to make his own car and collaborated with Harvey du Cros, his former boss at Dunlop, to form the Motor Power Company, based in London, which agreed to buy Napier's entire output. The first of an initial order of six, three each two-cylinder 8 hp and four-cylinder 16 hp, all with aluminum bodies by Arthur Mulliner of Northampton and chain drive, was delivered 31 March 1900; Edge paid £400 and sold at £500.

In 1903 the manufacturing business moved from Lambeth to larger premises in Acton and in 1906 it became a limited liability company, D. Napier & Son Limited, although it remained in effect a private company for the next few years.

Outside the racing programme, Napier also gained fame in 1904 by being the first car to cross the Canadian Rockies: Mr and Mrs Charles Glidden, sponsors of the Glidden Tours, covered 3536 mi from Boston to Vancouver.

Racing

Recognizing the value of publicity gained from racing, which no other British marque did, in spring, Edge entered an 8 hp Napier in the Thousand Miles (1,600 km) Trial of the Automobile Club on behalf of Mary Eliza Kennard; driven by Edge, with Kennard along, on a circuit from Newbury to Edinburgh and back, it won its class, being one of only thirty-five finishers (of sixty-four starters ) and one of just twelve to average the requisite 12 mph in England and 10 mph in Scotland.

By June 1900, eight "16 hp"s had been ordered, and Edge entered one in the 837 mi Paris-Toulouse-Paris race, with Charles S. Rolls (co-founder of Rolls-Royce) as riding mechanic. The 301.6 cuin (101.6 x) sidevalve suffered problems with its ignition coils and cooling system, and failed to finish.

For 1901, Montague designed a car sure not to lack speed, having a 16.3 L (165.1 x) sidevalve four capable of 103 bhp at 800 rpm, on a wheelbase of 115 in with four-speed gearbox and chain drive. Called the "50 hp", only two or three were completed, including one for Rolls. Edge entered one in the 1901 Gordon Bennett Cup, only able to test it en route (it was completed 25 May, only four days before the event), Montague serving as his riding mechanic; it overpowered its Dunlops, and fitting new (French) tyres led to disqualification, since they were not of the same nation of origin. In the concurrent Paris-Bordeaux rally, it retired with clutch trouble.

For the 1902 Gordon Bennett, three entrants (the Charron-Girardot-Voigt, a Mors and a Panhard) contested for France, with Edge in a Napier and two Wolseleys. The Napier was a three-speed, shaft-drive 6.44-litre (392.7 cu in) four (127 x of 44.5 hp (though described as a 30 hp). Piloted by Edge and his cousin, Cecil, it wore what would become known as British racing green, and won at an average 31.8 mph; although by default, since all other entrants retired during the race. It was the first British victory in international motorsport, and would not be repeated until Henry Segrave took the French Grand Prix in 1923.

Napiers also inspired Charles J. Glidden to create the Glidden Tours in upstate New York, which in turn persuaded Napier to build a factory in Boston. It, along with the Genoa factory (managed by Arthur McDonald), which built Napiers under licence as San Giorgios from 1906 to 1909, was not a success.

Annual production reached 250 cars in 1903, overwhelming the Lambeth factory, so a move was made to a new 3.75 acre plant at Acton, in west London. On 16 October of that year, Napier announced a six-cylinder car for 1904 and became the first manufacturer to make a commercially successful six, a "remarkably smooth and flexible" vehicle 18 hp 301 cu in (4.9-litre) (101.6 x with a three-speed gearbox and chain drive. Within five years, there were 62 makers of six-cylinder cars in Britain alone, including the Ford Motor Company's 1906 Model K.

Napier's 1902 win brought the Gordon Bennett hosting duties to the United Kingdom, and the 1903 event was held south of Dublin, with three shaft-driven Napiers defending the British and Irish honour, all in the (later famous) racing green: two 470 cubic inch (7708 cc) 45 hp fours for Charles Jarrott and J. W. Stocks, with McDonald, the Genoa plant manager, his riding mechanic, and an 80-horsepower (838 cubic inch, 13,726 cc), the Type K5, for Edge. Jarrott and Stocks crashed, and Edge was disqualified. It was a bad year for Napier's racing programme; a 35 hp in the hands of Colonel Mark Mayhew in the Paris–Madrid rally lost its steering and hit a tree. Edge, again with McDonald, fared no better with the K5 in the 1904 Gordon Bennett in Germany, but a new 920 cubic inch (15-litre; 158.7 × 127 mm, 6.25 × 5-inch) six, the L48, with an external radiator reminiscent of the Cord 810, set the fastest time at the Velvet Strand speed trials at Portmarnock, Ireland, in September, piloted by McDonald.

In January 1905, the L48, again with McDonald in the seat, took the mile (1.6 km) record at Ormonde Beach at 104.65 mph; although this was shortly broken by Bowden's Mercedes, the run was disallowed. The versatile McDonald ran the L48 in the 1905 Gordon Bennett qualifying event at the Isle of Man, taken over for the race by works driver Clifford Earp, who placed ninth.

Edge's secretary, Dorothy Levitt, drove a 100 hp development of the K5 at the Blackpool and Brighton Speed Trials in 1905, and the next year ran the L48 at the Blackpool Speed Trials, showing talent by equalling Edge's speed and setting a women's record in the flying kilometre of 90.88 mph.

By 1907, 1200 people were employed by Napier and were making about a hundred cars a year, aided by continuing racing success. Brooklands opened that year, where Napier engineer H. C. Tryon won the first ever event in a 40 hp, and Edge made a famous 24-hour run in June, covering 1,581 mi at an average 65.905 mph in a 60-horsepower 589 cubic inch (9,652 cc) (127 × 127 mm, 5 × 5-inch) six, a record which stood for 18 years. The L48, nicknamed Samson, became famous there in the venue's first two years; in 1908, Napier's Frank Newton covered 1/2 mi at 119.34 mph in a stroked (178 mm, 7-inch) L48.

The company's last race win was with a four-cylinder at the 1908 Tourist Trophy, using an alias, Hutton, to preserve the reputation of the sixes, in the hands of Willy Watson. At the French Grand Prix, officials showed the perverse reasoning for which they later became notorious by claiming that removable wire wheels were an unfair advantage.

When Napier was no longer in racing, its Lion aero engine was used by several land speed record contestants: Malcolm Campbell's Napier-Campbell Blue Bird of 1927 and Campbell-Napier-Railton Blue Bird of 1931, Segrave's Golden Arrow of 1929, and John Cobb's Napier-Railton and Railton Mobil Special, which held the record from 1939 to 1964.

Motor yachting
Napier expanded into marine engines and launches. In 1903 a S. F. Edge's Napier launch won the inaugural British International Harmsworth Trophy for speedboats at Cork Harbour in Ireland, driven by Dorothy Levitt. She achieved 19.3 mi/h in a 40 ft steel-hulled, speedboat fitted with a 3-blade propeller. As both the owner and entrant of the boat, "S. F. Edge" is engraved on the trophy as the winner. The third crew member, Campbell Muir, may also have taken the controls.

On 8 August 1903 Levitt drove the Napier at Cowes and won the race. She was then commanded to the royal yacht by King Edward VII where he congratulated her on her pluck and skill, and they discussed the performance of the boat and its potential for British government despatch work.

Later in August Levitt won the Gaston Menier Cup at Trouville, France. This was described as the "five-mile world's championship of the sea" and the prize was $1,750.

In October 1903 Levitt won the Championship of the Seas at Trouville, and the French government bought the boat for £1,000.

The 1905 boat Napier II set the world water speed record for a mile at almost 30 knots (56 km/h).

Public limited company and WWI
In 1912, following a dispute with Edge, the business was restructured. D. Napier & Son Limited went public and bought out Edge's distribution and sales company, S.F. Edge (1907) Limited. The latter soon went into voluntary liquidation and thus the manufacture and marketing of Napier cars were united under a single organization. Production rose to around 700 cars a year with many supplied to the London taxi trade. That year, only six models were produced.

On the outbreak of war sales of private vehicles collapsed and Napier turned to military orders. Vehicle production continued for a time on this basis and 2,000 trucks and ambulances were supplied to the War Office. Montague Napier's health declined and in 1917 he moved to Cannes, France, but continued to take an active involvement in the company until his death in 1931.

Early in the war, Napier was contracted to build engines from other companies' designs: initially the model RAF 3, a V-12 by Royal Aircraft Factory, and then the V-8 Sunbeam Arab. Both proved to be rather unreliable, and in 1916 Napier decided to design its own instead, an effort that led to the superb W-block 12-cylinder Lion. The Lion came into service shortly before the end of the war.

During the First World War the company was also contracted to build 600 aircraft at the Acton factory (50 Royal Aircraft Factory R.E.7, 400 Royal Aircraft Factory R.E.8 and 150 Sopwith Snipes). Together with the engine work, this required enormous expansion of the company.

Interwar period
By the end of the war, military production had tailed off and the Lion was still barely in use.

In 1919 civilian car production was recommenced. The T75 motor car would be Napier's last. Designed by A. J. Rowledge (who left for Rolls-Royce in 1921), its engine was a 40–50 hp 377 cuin (101.6 x) alloy six with detachable cylinder head, single overhead camshaft, seven-bearing crankshaft, dual magneto and coil ignition, dual plugs, and Napier-SU Carburettor. Coachwork was by Cunard, by then a subsidiary. 187 were built in all by 1924, and Napier quit car production with a total of 4,258 built. The car was very expensive, costing about the same as a Rolls-Royce Silver Ghost and in the early 1920s sales were slow. The last car was sold in 1924.

The Lion was by now becoming a best-seller for the company, which eventually dropped all the other aero-engines. The Lion went on to be adapted for land and water, to set the land speed record in Malcolm Campbell's Napier-Campbell Blue Bird of 1927 and Campbell-Napier-Railton Blue Bird of 1931 and Henry Segrave's Golden Arrow of 1931 and later in John Cobb's Napier-Railton and Railton Mobil Special, which held the record from 1939 to 1964.

In the 1930s the introduction of much larger and more powerful aero-engines from other companies ended sales of the Lion. Napier quickly started work on newer designs, building on experience gained on the X style 16-cylinder, 1,000 hp Cub, used in the Blackburn Cubaroo single-engined bomber of the 1920s, and the resulting later 16-cylinder Rapier and 24-cylinder Dagger were both air-cooled H-block designs. Neither the Rapier nor the Dagger proved very reliable, due to poor cooling of the rearmost cylinders, and even the Dagger's 1000 hp was less than its competitors' offerings when shipped.

As Lion sales faded, an attempt was also made to buy the bankrupt Bentley company in 1931 but Napier was outbid at the last minute by Rolls-Royce. The last vehicle project was a three-wheeled tractor-trailer goods vehicle, but rather than produce this itself, the design was sold to Scammell, which made several thousand.

Second World War
Starting from scratch, Napier decided to use the new sleeve valve design in a much larger H-block 24-cylinder engine, soon to be known as the Sabre. Designed under Frank Halford, the engine was very advanced and proved to be difficult to adapt to assembly line production. Therefore, although the engine was ready by 1940, it was not until 1944 that production versions were considered reliable. At that point efforts were made to improve it, leading eventually to the Sabre VII delivering 3,500 hp, making it the most powerful engine in the world, from an engine much smaller than its competition.

Napier also worked on diesel aircraft engines. In the 1930s it licensed the Junkers Jumo 204 for production in England, which it called the Culverin. It also planned to produce a smaller version of the same basic design as the Cutlass, but work on both was cancelled at the outbreak of war in 1939.

Napier developed a marine engine from the Lion aero engine, the petrol-driven Sea Lion, which could deliver 500 hp and was used in the "Whaleback" Air Sea Rescue Launches. During the war (1944) Napier was asked by the Royal Navy to supply a diesel engine for use in its patrol boats, but the Culverin's 720 hp was not nearly enough for its needs. Napier then designed under the leadership of Ernest Edward Chatterton, Chief Engineer, the Deltic, essentially three Culverins arranged in a large triangle. Considered one of the most complex engine designs of its day, the Deltic was nevertheless very reliable, and was taken into service after the war as a locomotive powerplant (in British Rail's Class 55) in addition to the torpedo boats, minesweepers and other small naval vessels for which it was designed.

Also during the Second World War a six-cylinder 300 cubic inch road-vehicle engine was commissioned by the government, but this design was sold to Leyland Motors by 1945.

English Electric
Napier had been taken over by English Electric on 23 November 1942.

Last of the great Napier internal combustion engines was the Nomad, a complex "turbo-compound" design that combined a diesel engine with a turbine to recover energy otherwise lost in the exhaust. The advantage of this complex design was fuel economy: it had the best specific fuel consumption of any aircraft engine, even to this day. However, even better fuel economy could be had by flying a normal jet engine at much higher altitudes, while existing designs filled the "low end" of the market fairly well. First run in 1949, the Nomad I underwent radical redesign for the Nomad II but was largely ignored by the market and was cancelled in 1955.

Along with every major aero engine company in the post-war era, Napier turned to the jet turbine. Seeing a niche not yet adopted up by the larger vendors, Napier developed a number of turboshaft designs which saw some use, notably in helicopters. Its first design, the Naiad and Double Naiad was developed for various Royal Navy Fleet Air Arm projects, but did not enter production. The smaller models developed later, the 3,000-hp-class Eland and 1,500-hp-class Gazelle did somewhat better, notably the Gazelle which powered several models of the popular Westland Wessex helicopter. Production ceased when a deal was struck with Rolls-Royce in 1961.

At the same time, the ramjet was showing promise for high-speed supersonic flight. From 1951 Napier developed a successful large-diameter experimental engine, the Napier Ram Jet (NRJ). Napier continued in ramjet development for several years, typically working alongside the English Electric aircraft design team.

Napier Aero Engines Limited
In 1961 a new company Napier Aero Engines Limited was formed by D. Napier & Son and Rolls-Royce, to take over the Napier aero-engine business and the Acton engine factory. It was to continue to market the Gazelle, while the completion of existing Gazelle contracts and the Eland remained the financial responsibility of the old company. But it closed only two years later, in 1963.

Following the move of the aero engine business, D. Napier & Son continued as a subsidiary of English Electric. With the ending of Deltic sales in the 1960s it had no new modern engine designs to offer. Today Napier is no longer in the engine business.

Napier Turbochargers
GEC bought English Electric in the late 1960s. The GEC operation, now part of Ruston Gas Turbines, later moved to GEC-Alsthom and then Alstom, before being sold to Siemens in March 2003.

Napier Turbochargers was bought from Siemens in June 2008 in a management buyout. The buyout was funded by the private equity company Primary Capital for around £100 million.

Early in 2013 Napier Turbochargers became part of Wabtec. Napier Turbochargers currently produces turbochargers for the marine, power, and rail industries, employing around 150 people.

List of Napier aero engines
These engines were all built, some in several variants.
 * Napier Cub
 * Napier Culverin
 * Napier Dagger
 * Napier Eland
 * Napier Gazelle
 * Napier Javelin
 * Napier Lion
 * Napier Lioness
 * Napier Naiad
 * Napier Nomad
 * Napier Oryx
 * Napier Rapier
 * Napier Sabre
 * Napier Scorpion

title: D. Napier & Son


text:
Dispersion (optics)

In optics and in wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium (plural dispersive media).

Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the pulses of light in optical fiber.

In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

All common transmission media also vary in attenuation (normalized to transmission length) as a function of frequency, leading to attenuation distortion; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth.

Examples
The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves.

Material and waveguide dispersion
Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal), whether or not the waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength, important for fast fiber-optic communication.

Material dispersion in optics

Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms is used to construct spectrometers and spectroradiometers. However, in lenses, dispersion causes chromatic aberration, an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives.

The phase velocity v of a wave in a given uniform medium is given by
 * $$v = \frac{c}{n},$$

where c is the speed of light in vacuum, and n is the refractive index of the medium.

In general, the refractive index is some function of the frequency f of the light, thus n = n(f), or alternatively, with respect to the wave's wavelength n = n(λ). The wavelength dependence of a material's refractive index is usually quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations.

Because of the Kramers–Kronig relations, the wavelength dependence of the real part of the refractive index is related to the material absorption, described by the imaginary part of the refractive index (also called the extinction coefficient). In particular, for non-magnetic materials (μ = μ0), the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χe = n2 − 1.

The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as angular dispersion.

For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease with increasing wavelength λ:
 * $$1 < n(\lambda_\text{red}) < n(\lambda_\text{yellow}) < n(\lambda_\text{blue}),$$

or generally,
 * $$\frac{dn}{d \lambda} < 0.$$

In this case, the medium is said to have normal dispersion. Whereas if the index increases with increasing wavelength (which is typically the case in the ultraviolet ), the medium is said to have anomalous dispersion.

At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin($sin θ⁄n$). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern.

Group-velocity dispersion

Beyond simply describing a change in the phase velocity over wavelength, a more serious consequence of dispersion in many applications is termed group-velocity dispersion (GVD). While phase velocity v is defined as v = c/n, this describes only one frequency component. When different frequency components are combined, as when considering a signal or a pulse, one is often more interested in the group velocity, which describes the speed at which a pulse or information superimposed on a wave (modulation) propagates. In the accompanying animation, it can be seen that the wave itself (orange-brown) travels at a phase velocity much faster than the speed of the envelope (black), which corresponds to the group velocity. This pulse might be a communications signal, for instance, and its information only travels at the group velocity rate, even though it consists of wavefronts advancing at a faster rate (the phase velocity).

It is possible to calculate the group velocity from the refractive-index curve n(ω) or more directly from the wavenumber k = ωn/c, where ω is the radian frequency ω = 2πf. Whereas one expression for the phase velocity is vp = ω/k, the group velocity can be expressed using the derivative: vg = dω/dk. Or in terms of the phase velocity vp,

 * $$v_\text{g} = \frac{v_\text{p}}{1 - \dfrac{\omega}{v_\text{p}} \dfrac{dv_\text{p}}{d\omega}}.$$

When dispersion is present, not only the group velocity is not equal to the phase velocity, but generally it itself varies with wavelength. This is known as group-velocity dispersion and causes a short pulse of light to be broadened, as the different-frequency components within the pulse travel at different velocities. Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d2k/dω2.

If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the longer-wavelength components. The pulse therefore becomes positively chirped, or up-chirped, increasing in frequency with time. On the other hand, if a pulse travels through a material with negative group-velocity dispersion, shorter-wavelength components travel faster than the longer ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time.

An everyday example of a negatively chirped signal in the acoustic domain is that of an approaching train hitting deformities on a welded track. The sound caused by the train itself is impulsive and travels much faster in the metal tracks than in air, so that the train can be heard well before it arrives. However, from afar it is not heard as causing impulses, but leads to a distinctive descending chirp, amidst reverberation caused by the complexity of the vibrational modes of the track. Group-velocity dispersion can be heard in that the volume of the sounds stays audible for a surprisingly long time, up to several seconds.

Dispersion control
The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion is too high, a group of pulses representing a bit-stream will spread in time and merge, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g., around 1.3–1.5 μm in silica fibres), so pulses at this wavelength suffer minimal spreading from dispersion. In practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as four-wave mixing). Another possible option is to use soliton pulses in the regime of negative dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape. Solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching the fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self-phase modulation, which interact with dispersion to make it very difficult to undo.

Dispersion control is also important in lasers that produce short pulses. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped mirrors. These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve a net negative dispersion.

In waveguides
Waveguides are highly dispersive due to their geometry (rather than just to their material composition). Optical fibers are a sort of waveguide for optical frequencies (light) widely used in modern telecommunications systems. The rate at which data can be transported on a single fiber is limited by pulse broadening due to chromatic dispersion among other phenomena.

In general, for a waveguide mode with an angular frequency ω(β) at a propagation constant β (so that the electromagnetic fields in the propagation direction z oscillate proportional to ei(βz−ωt)), the group-velocity dispersion parameter D is defined as
 * $$D = -\frac{2\pi c}{\lambda^2} \frac{d^2 \beta}{d\omega^2} = \frac{2\pi c}{v_g^2 \lambda^2} \frac{dv_g}{d\omega},$$

where λ = 2$\pi$c/ω is the vacuum wavelength, and vg = dω/dβ is the group velocity. This formula generalizes the one in the previous section for homogeneous media and includes both waveguide dispersion and material dispersion. The reason for defining the dispersion in this way is that |D| is the (asymptotic) temporal pulse spreading Δt per unit bandwidth Δλ per unit distance travelled, commonly reported in ps/(nm⋅km) for optical fibers.

In the case of multi-mode optical fibers, so-called modal dispersion will also lead to pulse broadening. Even in single-mode fibers, pulse broadening can occur as a result of polarization mode dispersion (since there are still two polarization modes). These are not examples of chromatic dispersion, as they are not dependent on the wavelength or bandwidth of the pulses propagated.

Higher-order dispersion over broad bandwidths
When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate the dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading.

In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion. These terms are simply a Taylor series expansion of the dispersion relation β(ω) of the medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations, by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation.

Generalized formulation of the high orders of dispersion – Lah-Laguerre optics
The description of the chromatic dispersion in a perturbative manner through Taylor coefficients is advantageous for optimization problems where the dispersion from several different systems needs to be balanced. For example, in chirp pulse laser amplifiers, the pulses are first stretched in time by a stretcher to avoid optical damage. Then in the amplification process, the pulses accumulate inevitably linear and nonlinear phase passing through materials. And lastly, the pulses are compressed in various types of compressors. To cancel any residual higher orders in the accumulated phase, usually individual orders are measured and balanced. However, for uniform systems, such perturbative description is often not needed (i.e., propagation in waveguides). The dispersion orders have been generalized in a computationally friendly manner, in the form of Lah-Laguerre type transforms.

The dispersion orders are defined by the Taylor expansion of the phase or the wavevector. $$ \varphi \mathrm{(}\omega\mathrm{)} = \varphi\left.\ \right|_{\omega_{0}} + \left. \ \frac{\partial\varphi}{\partial\omega} \right|_{\omega_{0}}\left(\omega - \omega_{0} \right) + \frac{1}{2}\left. \ \frac{\partial^\varphi}{\partial\omega^{2}} \right|_{\omega_{0}} \left(\omega - \omega_{0} \right)^{2}\ + \ldots + \frac{1}{p!}\left. \ \frac{\partial^\varphi}{\partial\omega^{p}} \right|_{\omega_{0}} \left(\omega - \omega_{0} \right)^{p} + \cdots $$ $$ k\mathrm{(}\omega\mathrm{)} = k\left.\ \right|_{\omega_{0}} + \left. \ \frac{\partial k}{\partial\omega} \right|_{\omega_{0}} \left(\omega - \omega_{0} \right) + \frac{1}{2}\left. \ \frac{\partial^k}{\partial\omega^{2}} \right|_{\omega_{0}} \left(\omega - \omega_{0} \right)^{2}\ + \ldots + \frac{1}{p!}\left. \ \frac{\partial^k}{\partial\omega^{p}} \right|_{\omega_{0}} \left(\omega - \omega_{0} \right)^{p} + \cdots$$

The dispersion relations for the wavector $$k \mathrm{(}\omega\mathrm{)} = \frac{\omega}{c}n \mathrm{(}\omega\mathrm{)}$$ and the phase $$\varphi \mathrm{(}\omega\mathrm{)} = \frac{\omega}{c}{\it OP} \mathrm{(}\omega\mathrm{)}$$ can be expressed as: $$ \begin{array}{c}\frac{ {\partial }^}{\partial {\omega }^p}k \mathrm{(}\omega \mathrm{)}=\frac{1}{c}\left(p\frac{ {\partial }^{p-1}}{\partial {\omega }^{p-1}}n  \mathrm{(}\omega \mathrm{)}+\omega \frac{ {\partial }^}{\partial {\omega }^p}n  \mathrm{(}\omega \mathrm{)}\right)\  \end{array}$$, $$\begin{array}{c}\frac{ {\partial }^}{\partial {\omega }^p}\varphi    \mathrm{(}\omega \mathrm{)} = \frac{1}{c}\left(p\frac{ {\partial }^{p-1}}{\partial {\omega }^{p-1}}{\it OP}   \mathrm{(}\omega \mathrm{)}+\omega \frac{ {\partial }^}{\partial {\omega }^p}{\it OP}   \mathrm{(}\omega \mathrm{)}\right)   \end{array} (1)$$ The derivatives of any differentiable function $$f\mathrm{(}\omega \mathrm{|}\lambda \mathrm{)}$$ in the wavelength or the frequency space is specified through a Lah transform as: $$,$$

The matrix elements of the transformation are the Lah coefficients: $$\mathcal{A}\mathrm{(}p,m\mathrm{)} = \frac{p\mathrm{!}}{\left(p\mathrm{-}m\right)\mathrm{!}m\mathrm{!}}\frac{\mathrm{(}p\mathrm{-}\mathrm{1)!}}{\mathrm{(}m\mathrm{-}\mathrm{1)!}}$$ Written for the GDD the above expression states that a constant with wavelength GGD, will have zero higher orders. The higher orders evaluated from the GDD are: $$\begin{array}{c} \frac{ {\partial }^}{\partial {\omega }^p}GDD  \mathrm{(}\omega \mathrm{)}={}{\left(\mathrm{-}\mathrm{1}\right)}^p{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^p\sum\limits^p_{m = {0}}{\mathcal{A}\mathrm{(}p,m\mathrm{)}{\lambda }^m\frac{ {\partial }^}{\partial {\lambda }^m}GDD  \mathrm{(}\lambda \mathrm{)}} \end{array}$$

Substituting equation (2) expressed for the refractive index $$n$$ or optical path $$OP$$ into equation (1) results in closed-form expressions for the dispersion orders. In general, the $$p^{th}$$ order dispersion POD is a Laguerre type transform of negative order two: $$POD = \frac{d^p \varphi(\omega) }{d\omega^p}=(-1)^p(\frac{\lambda}{2\pi c})^{(p-1)}\sum_{m=0}^{p}\mathcal{B(p,m)} (\lambda)^m\frac{d^m OP(\lambda) }{d\lambda^m} $$ $$,$$ $$POD = \frac{d^p k(\omega) }{d\omega^p}=(-1)^p(\frac{\lambda}{2\pi c})^{(p-1)}\sum_{m=0}^{p}\mathcal{B(p,m)} (\lambda)^m\frac{d^m n(\lambda) }{d\lambda^m} $$

The matrix elements of the transforms are the unsigned Laguerre coefficients of order minus 2, and are given as: $$ \mathcal{B}\mathrm{(}p,m\mathrm{)} = \frac{p\mathrm{!}}{\left(p\mathrm{-}m\right)\mathrm{!}m\mathrm{!}}\frac{\mathrm{(}p\mathrm{-}\mathrm{2)!}}{\mathrm{(}m\mathrm{-}\mathrm{2)!}}$$

The first ten dispersion orders, explicitly written for the wavevector, are: $$ \begin{array}{l}\boldsymbol = \frac{\partial }{\partial \omega }k \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(n  \mathrm{(}\omega \mathrm{)}+\omega \frac{\partial n  \mathrm{(}\omega \mathrm{)}}{\partial \omega }\right) = \frac{\mathrm{1}}{c}\left(n \mathrm{(}\lambda \mathrm{)}-\lambda \frac{\partial n \mathrm{(}\lambda \mathrm{)}}{\partial\lambda }\right) = v^{\mathrm{-}\mathrm{1}}_{gr}\end{array} $$

The group refractive index $$n_g$$ is defined as: $$n_g  =   cv^{\mathrm{-}\mathrm{1}}_{gr}$$.

$$ \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{2}}}k \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{2}\frac{\partial n\mathrm{(}\omega \mathrm{)}}{\partial \omega }+\omega \frac{ {\partial }^n\mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{2}}}\right)  =  \frac{\mathrm{1}}{c}\left(\frac{\lambda }{\mathrm{2}\pi c}\right)\left({\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}\right) \end{array} $$ $$ \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{3}}}k \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{3}\frac{ {\partial }^n\mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{2}}}+\omega \frac{ {\partial }^n\mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{3}}}\right)    = {-} \frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{2}}\Bigl(\mathrm{3}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}} +{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}\Bigr) \end{array} $$ $$ \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{4}}}k \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{4}\frac{ {\partial }^n\mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{3}}}+\omega \frac{ {\partial }^n\mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{4}}}\right)    = \frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{3}}\Bigl(\mathrm{12}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}    +\mathrm{8}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}\Bigr) \end{array} $$  $$ \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{5}}}k  \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{5}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{4}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{5}}}\right)=  {-}\frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{4}} \Bigl(\mathrm{60}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{60}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{15}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}\Bigr) \end{array} $$ $$ \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{6}}}k  \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{6}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{5}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{6}}}\right) =   \frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{5}}\Bigl(\mathrm{360}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}} +\mathrm{480}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{180}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{24}{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+{\lambda }^{\mathrm{6}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}\Bigr) \end{array} $$  $$    \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{7}}}k  \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{7}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{{\partial \omega }^{\mathrm{6}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{{\partial \omega }^{\mathrm{7}}}\right)    =   {-}\frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{6}} \Bigl(\mathrm{2520}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{4200}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{2100}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{420}{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+   \mathrm{35}{\lambda }^{\mathrm{6}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+{\lambda }^{\mathrm{7}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}\Bigr) \end{array} $$  $$    \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{8}}}k  \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{8}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{{\partial \omega }^{\mathrm{7}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{8}}}\right) =    \frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{7}}\Bigl(\mathrm{20160}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}} +\mathrm{40320}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{25200}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{6720}{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+ \mathrm{840}{\lambda }^{\mathrm{6}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}} +\\+\mathrm{48}{\lambda }^{\mathrm{7}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}+{\lambda }^{\mathrm{8}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{8}}}\Bigr) \end{array} $$ $$    \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{9}}}k \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{9}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{8}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{9}}}\right) =   {-}\frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{8}}\Bigl(\mathrm{181440}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{423360}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{317520}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{105840}{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+  \mathrm{17640}{\lambda }^{\mathrm{6}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+\\+\mathrm{1512}{\lambda }^{\mathrm{7}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}+\mathrm{63}{\lambda }^{\mathrm{8}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{8}}}+{\lambda }^{\mathrm{9}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{9}}}\Bigr) \end{array} $$       $$    \begin{array}{l}\boldsymbol = \frac{ {\partial }^}{\partial {\omega }^{\mathrm{10}}}k  \mathrm{(}\omega \mathrm{)} = \frac{\mathrm{1}}{c}\left(\mathrm{10}\frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{9}}}+\omega \frac{ {\partial }^n  \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{10}}}\right) =   \frac{\mathrm{1}}{c}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{9}}\Bigl(\mathrm{1814400}{\lambda }^{\mathrm{2}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{4838400}{\lambda }^{\mathrm{3}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{4233600}{\lambda }^{\mathrm{4}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+  {1693440}{\lambda }^{\mathrm{5}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+\\+\mathrm{352800}{\lambda }^{\mathrm{6}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+\mathrm{40320}{\lambda }^{\mathrm{7}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}+\mathrm{2520}{\lambda }^{\mathrm{8}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{8}}}+\mathrm{80}{\lambda }^{\mathrm{9}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{9}}}+  {\lambda }^{\mathrm{10}}\frac{ {\partial }^n \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{10}}}\Bigr) \end{array} $$

Explicitly, written for the phase $$\varphi$$, the first ten dispersion orders can be expressed as a function of wavelength using the Lah transforms (equation (2)) as:

$$,$$  $$	\begin{array}{c} \frac{ {\partial }^}{\partial {\lambda }^p}f \mathrm{(}\lambda \mathrm{)}={}{\left(\mathrm{-}\mathrm{1}\right)}^p{\left(\frac{\omega }{\mathrm{2}\pi c}\right)}^p\sum\limits^p_{m = {0}}{\mathcal{A}\mathrm{(}p,m\mathrm{)}{\omega }^m\frac{ {\partial }^}{\partial {\omega }^m}f   \mathrm{(}\omega \mathrm{)}}\end{array} $$

$$ \frac{\partial \varphi\mathrm{(}\omega \mathrm{)}}{\partial \omega }= {-}\left(\frac{\mathrm{2}\pi c}{{\omega }^{\mathrm{2}}}\right)\frac{\partial \varphi \mathrm{(}\omega \mathrm{)}}{\partial \lambda } = {-}\left(\frac{ {\lambda }^{\mathrm{2}}}{\mathrm{2}\pi c}\right)\frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda } $$

$$ \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{2}}} = \frac{\partial }{\partial \omega }\left(\frac{\partial \varphi  \mathrm{(}\omega \mathrm{)}}{\partial \omega }\right) = {\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{2}}\left(\mathrm{2}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}\right) $$

$$ \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{3}}}=  {-}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{3}}\left(\mathrm{6}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{6}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}\right) $$

$$ \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{4}}}=  {\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{4}}\Bigl(\mathrm{24}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{36}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{12}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}} +{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}\Bigr) $$ $$ \frac{ {\partial }^{\mathrm{5}}\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{5}}}= {-}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{5}}\Bigl(\mathrm{120}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{240}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}   +\mathrm{120}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{20}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}\Bigr) $$ $$ \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{6}}}= {\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{6}}\Bigl(\mathrm{720}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{1800}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{1200}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{300}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{30}{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}\mathrm{\ +}{\lambda }^{\mathrm{6}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}\Bigr) $$ $$ \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{7}}}= {-}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{7}} \Bigl(\mathrm{5040}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{15120}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+ \mathrm{12600}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{4200}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{630}{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+\mathrm{42}{\lambda }^{\mathrm{6}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+{\lambda }^{\mathrm{7}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}} \Bigr) $$ $$ \begin{array}{l} \displaystyle \frac{ {\partial }^{8}\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{8}}}=  {\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{8}}\Bigl(\mathrm{40320}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{141120}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+ \mathrm{141120}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{58800}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{11760}{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+\mathrm{1176}{\lambda }^{\mathrm{6}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+\mathrm{56}{\lambda }^{\mathrm{7}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}+\\ \displaystyle +{\lambda }^{\mathrm{8}}\frac{\partial^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial{\lambda }^{\mathrm{8}}}\Bigr) \end{array} $$ $$ \begin{array}{l} \displaystyle \frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{9}}}=  {-}{\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{9}}\Bigl(\mathrm{362880}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{1451520}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+ \mathrm{1693440}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{846720}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{211680}{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+\mathrm{28224}{\lambda }^{\mathrm{6}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+\\ \displaystyle +\mathrm{2016}{\lambda }^{\mathrm{7}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}}+\mathrm{72}{\lambda }^{\mathrm{8}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{8}}}+{\lambda }^{\mathrm{9}}\frac{\partial ^{\mathrm{9}}\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{9}}}\Bigr) \end{array} $$ $$ \begin{array}{l} \displaystyle\frac{ {\partial }^\varphi \mathrm{(}\omega \mathrm{)}}{\partial {\omega }^{\mathrm{10}}}=  {\left(\frac{\lambda }{\mathrm{2}\pi c}\right)}^{\mathrm{10}}\Bigl(\mathrm{3628800}\lambda \frac{\partial \varphi \mathrm{(}\lambda \mathrm{)}}{\partial \lambda }+\mathrm{16329600}{\lambda }^{\mathrm{2}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{2}}}+\mathrm{21772800}{\lambda }^{\mathrm{3}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{3}}}+\mathrm{12700800}{\lambda }^{\mathrm{4}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{4}}}+\mathrm{3810240}{\lambda }^{\mathrm{5}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{5}}}+\mathrm{635040}{\lambda }^{\mathrm{6}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{6}}}+\\ \displaystyle +\mathrm{60480}{\lambda }^{\mathrm{7}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{7}}} +\mathrm{3240}{\lambda }^{\mathrm{8}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{8}}}+\mathrm{90}{\lambda }^{\mathrm{9}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{9}}}+{\lambda }^{\mathrm{10}}\frac{ {\partial }^\varphi \mathrm{(}\lambda \mathrm{)}}{\partial {\lambda }^{\mathrm{10}}}\Bigr) \end{array} $$

Spatial dispersion
In electromagnetics and optics, the term dispersion generally refers to aforementioned temporal or frequency dispersion. Spatial dispersion refers to the non-local response of the medium to the space; this can be reworded as the wavevector dependence of the permittivity. For an exemplary anisotropic medium, the spatial relation between electric and electric displacement field can be expressed as a convolution:

 * $$D_i(t, r) = E_i(t, r) + \int_0^\infty \int f_{ik}(\tau; r, r') E_k(t - \tau, r') \,dV'\,d\tau,$$

where the kernel $$f_{ik}$$ is dielectric response (susceptibility); its indices make it in general a tensor to account for the anisotropy of the medium. Spatial dispersion is negligible in most macroscopic cases, where the scale of variation of $$E_k(t - \tau, r')$$ is much larger than atomic dimensions, because the dielectric kernel dies out at macroscopic distances. Nevertheless, it can result in non-negligible macroscopic effects, particularly in conducting media such as metals, electrolytes and plasmas. Spatial dispersion also plays role in optical activity and Doppler broadening, as well as in the theory of metamaterials.

In gemology
In the technical terminology of gemology, dispersion is the difference in the refractive index of a material at the B and G (686.7 nm and 430.8 nm) or C and F (656.3 nm and 486.1 nm) Fraunhofer wavelengths, and is meant to express the degree to which a prism cut from the gemstone demonstrates "fire". Fire is a colloquial term used by gemologists to describe a gemstone's dispersive nature or lack thereof. Dispersion is a material property. The amount of fire demonstrated by a given gemstone is a function of the gemstone's facet angles, the polish quality, the lighting environment, the material's refractive index, the saturation of color, and the orientation of the viewer relative to the gemstone.

In imaging
In photographic and microscopic lenses, dispersion causes chromatic aberration, which causes the different colors in the image not to overlap properly. Various techniques have been developed to counteract this, such as the use of achromats, multielement lenses with glasses of different dispersion. They are constructed in such a way that the chromatic aberrations of the different parts cancel out.

Pulsar emissions
Pulsars are spinning neutron stars that emit pulses at very regular intervals ranging from milliseconds to seconds. Astronomers believe that the pulses are emitted simultaneously over a wide range of frequencies. However, as observed on Earth, the components of each pulse emitted at higher radio frequencies arrive before those emitted at lower frequencies. This dispersion occurs because of the ionized component of the interstellar medium, mainly the free electrons, which make the group velocity frequency-dependent. The extra delay added at a frequency $n$ is
 * $$t = k_\text{DM} \cdot \left(\frac{\text{DM}}{\nu^2}\right),$$

where the dispersion constant kDM is given by
 * $$k_\text{DM} = \frac{e^2}{2 \pi m_\text{e} c} \approx 4.149~\text{GHz}^2\,\text{pc}^{-1}\,\text{cm}^3\,\text{ms},$$

and the dispersion measure (DM) is the column density of free electrons (total electron content) – i.e. the number density of electrons ne integrated along the path traveled by the photon from the pulsar to the Earth –  and is given by
 * $$\text{DM} = \int_0^d n_e\,dl$$

with units of parsecs per cubic centimetre (1 pc/cm3 = 30.857 m−2).

Typically for astronomical observations, this delay cannot be measured directly, since the emission time is unknown. What can be measured is the difference in arrival times at two different frequencies. The delay Δt between a high-frequency $undefined$hi and a low-frequency $n$lo component of a pulse will be
 * $$\Delta t = k_\text{DM} \cdot \text{DM} \cdot \left( \frac{1}{\nu_\text{lo}^2} - \frac{1}{\nu_\text{hi}^2} \right).$$

Rewriting the above equation in terms of Δt allows one to determine the DM by measuring pulse arrival times at multiple frequencies. This in turn can be used to study the interstellar medium, as well as allow observations of pulsars at different frequencies to be combined.

title: Dispersion (optics)


text:
Hannover 96

Hannoverscher Sportverein von 1896, commonly referred to as Hannover 96, is a German professional football club based in the city of Hanover, Lower Saxony. They played in the Bundesliga for a total of 30 years between 1964 and 2019 and currently play in the 2. Bundesliga, the second tier in the German football league system, having been relegated from the Bundesliga, Germany's first tier, after finishing 17th in the 2018–19 season.

Hannover 96 was founded in 1896. Hannover have won two German championships and one DFB-Pokal. Hannover's stadium is the HDI-Arena. Hannover 96 has a long-standing rivalry with Eintracht Braunschweig.

Foundation to the Second World War
The club was founded on 12 April 1896 as Hannoverscher Fußball-Club 1896, upon the suggestion of Ferdinand-Wilhelm Fricke, founder of the Deutscher FV 1878 Hannover. Their initial enthusiasm was for athletics and rugby; football did not become their primary interest until 1899. Most of the membership of Germania 1902 Hannover became part of 96 in 1902, while others of the club formed Hannoverscher Ballspielverein. In 1913, they merged with Ballverein 1898 Hannovera (formed in the 1905 merger of Fußballverein Hannovera, 1898 Hannover, and Hannoverscher BV) to become Hannoverscher Sportverein 1896. Hannoverscher FC's colours were black-white-green, but they played in blue, while BV played in red. The newly united team kept black-white-green as the club colours, but they chose to take to the field in red, giving the team the nickname Die Roten ("The Reds"). The team's third jersey is in the club's official colours. The club made regular appearances in the national playoffs through the early 1900s, but was unable to progress past Eintracht Braunschweig, planting the seeds of a rivalry that has survived to this day. HSV continued to field strong sides and make national level appearances on into the 1920s. During Nazi rule, German football was re-organized into 16 top-flight leagues in 1933 and Hannover became part of the Gauliga Niedersachsen. They appeared in the country's final rounds in 1935 and sent representatives to the national side the next year. They won their first national championship in 1938, in what was one of the biggest upsets in German football history, when they beat Schalke 04, the most dominant side in the country in the era. The two sides played to a 3–3 draw before Hannover prevailed 4–3 in a tension-filled re-match. In 1942, the team moved to the newly formed Gauliga Braunschweig-Südhannover.

Post-War era
In common with most other German organizations, the club was dissolved after the Second World War by occupying Allied authorities. A combined local side was assembled in August 1945 and the next month a mixed group of players from Hannover 96 and Arminia Hannover played their first post-war match against a British military team. HSV was later formally re-established as Hannoverscher SV on 11 November 1945, before re-adopting its traditional name on 27 April 1946. The club resumed league play in 1947 in the first division Oberliga Nord and was relegated, but quickly returned to the top-flight in 1949. Hannover 96's next appearance in a national final would not come until 1954 when they soundly defeated 1. FC Kaiserslautern 5–1. The beaten side included five of the same players who would go on later that year to win Germany's first World Cup in a surprise victory known as the Miracle of Bern. In 1963, the Bundesliga, Germany's new professional football league, began play with 16 of the nation's top teams. Hannover played in the Regionalliga Nord (II) that season, but earned promotion to the senior circuit in the following year. The club's advance to the Bundesliga in 1964 was well received, as they set a league attendance record in their first year, averaging 46,000 spectators a game. 96 played at the upper level for a decade, until they were relegated to the 2nd Bundesliga Nord for the 1974–75 season. They returned quickly, but again went down, this time to spend 17 of the next 20 years in the second tier.

Reunification to present
The club faced financial problems in the late 1970s and again in the early 1990s. Then, in 1992, Hannover's performance would lead them to earn their first DFB-Pokal and help to secure stable finances. That run included victories over Bundesliga sides Borussia Dortmund, VfL Bochum, Karlsruher SC, Werder Bremen and Borussia Mönchengladbach, as they became the first lower division side to win the competition. The team's low point came with demotion to Regionalliga Nord (III) for two years in 1996–98.

Hannover went on to acquire new players, many of whom went on to play for the national team – notably Gerald Asamoah, Sebastian Kehl and Fabian Ernst. 96 returned to tier II play in 1998, and to the Bundesliga in 2002 on the strength of a record-setting 75-point season. Since their promotion, the club have consolidated in the top flight, consistently earning mid-table finishes under several managers. Coach Dieter Hecking was brought in just weeks into the 2006–07 season after a poor start under Peter Neururer, in which the club lost the first three matches by a combined 11 goals. The 2007–08 season showed some early promise, with pre-season wins over Rangers and Real Madrid. However, they earned mixed results in their opening six Bundesliga matches. The team then put together a three match winning run, capped by a 2–0 win at champions VfB Stuttgart, to enter into the top six. Following the winter break, Hannover after some poor performances, which they turned around to be defeated only two times in their last 11 matches of the season. This secured a points record of 49 for Die Roten in the Bundesliga, thus ending them in eighth place.

The 2008–09 season started poorly for Hannover with losses. However, performance improved with a 5–1 victory of Borussia Mönchengladbach, a 1–0 win over Bayern Munich at home, which had not occurred for 20 years, and a 3–0 victory over Hamburger SV. Hannover settled in the lower-mid-table until the winter break. The second half of the season consisted of inconsistent results, relying almost entirely on home form to keep the club in the Bundesliga. The club finally achieved an away win with a few games remaining which stabilized them, leading to an 11th-place finish.

The 2009–10 season was launched, with a new kit being released which included traditional away and alternative kits. Hannover also signed a new technical director in Jörg Schmadtke. New signings were Karim Haggui and Constant Djakpa from Bayer Leverkusen, Valdet Rama from FC Ingolstadt. The season started with a late 1–0 loss to Hertha BSC and a home draw to Mainz 05, after which coach Dieter Hecking resigned voluntarily. He was succeeded by former assistant Andreas Bergmann. As the season continued, Hannover again had many key players injured, including the majority of attacking players and key defenders, alongside the suicide of Robert Enke, Hannover's German international goalkeeper. Andreas Bergmann was removed as coach and replaced by Mirko Slomka shortly after the winter break. Arouna Koné and Elson were signed to boost the squad. Hannover 96 spent the majority of the year in the relegation zone, and with a few wins in the last games of the season, Hannover had to win, and have results elsewhere be favorable to them. Hannover won 3–0, with Arnold Bruggink, Mike Hanke and Sérgio Pinto all scoring to keep them in the Bundesliga.

In the 2010–11 season, Hannover finished in fourth place, qualifying for Europe for the first time in 19 years. In 2011–12, the team opened with a 2–1 win over 1899 Hoffenheim, followed by a 2–1 away win against 1. FC Nürnberg. In the play-offs to the Europa League, Hannover won against Sevilla 3–2 on aggregate to reach the group stage. Shortly before the end of the 2011–12 season, Hannover Technical Director Jörg Schmadtke resigned due to family issues.

Hannover finished bottom of the Bundesliga in the 2015–16 season and were relegated to the 2. Bundesliga. The club chose to keep the majority of their first-team squad together. However, after early in the 2016–17 season, poor performances prompted the club's board to sack manager Daniel Stendel, and appoint Andre Breitenreiter as their new manager. He led the team to seven wins in the final 11 games, helping the club secure second place behind VfB Stuttgart and return to the top flight.

Adverse publicity resulted for the club when a large contingent of ultras travelled to England for a 2017–18 pre-season game against Burnley. Supporters caused trouble in the town centre prior to the game. Once inside Turf Moor, they responded to a brief altercation on the pitch after 40 minutes by charging the home fans, tearing out seats and using them as missiles. On police advice the game was abandoned at half-time, with Hannover 96 trailing 1–0.

Death of Robert Enke
On 10 November 2009, at the age of 32, Hannover's first-choice goalkeeper Robert Enke died as a result of suicide after he stood in front of a regional express train at a level crossing in Eilvese, Neustadt am Rübenberge. Police confirmed a suicide note had been found, but did not publicise its details. His widow, Teresa, revealed that her husband had been suffering from depression for six years and was treated by a psychiatrist. After the death of his daughter Lara in 2006, he struggled to cope with the loss.

Upon news breaking of what had happened, many fans immediately gathered at Hannover 96's AWD-Arena home, where they laid flowers, lit candles and signed a book of condolence. His former club Barcelona held a minute's silence before their game that night, and several international matches the following weekend paid the same tribute. As a mark of respect, the German national team cancelled their friendly match against Chile, which had been scheduled for 14 November. A minute's silence was also held at all Bundesliga games on 21 and 22 November 2009, as well as at Benfica's game in the Taça de Portugal - Benfica was another former club of Enke's. Germany also cancelled a planned training session and all interviews after his death. Oliver Bierhoff, the national team's general manager, said, "We are all shocked. We are lost for words."

On 15 November 2009, nearly 40,000 attendees filled the AWD-Arena for his memorial service. Enke's coffin, covered in white roses, was carried by six of his Hannover 96 teammates. He was then buried in Neustadt, outside the city of Hanover, next to his daughter's grave. As a further mark of respect for their former teammate, Hannover 96 players displayed the number one in a circle on the breast of their jerseys, as approved by the German Football Association (DFL), as a subtle tribute for the rest of the 2009–10 season.

Stadium
Hannover 96 plays in the Heinz-von-Heiden-Arena, built in 1954 as the "Niedersachsenstadion", which now has a capacity of 49,000 spectators. Before the year 2013, the arena was called "AWD-Arena". But after changing the sponsor the stadium name was changed to "HDI-Arena". During the 2006 World Cup, the stadium was the site of four first round matches and one Round of 16 match. The stadium had also served as a site for matches in the 1974 World Cup and UEFA Euro 1988.

Honours
The club's honours:
 * German Championship
 * Champions: 1938, 1954
 * DFB-Pokal
 * Winners: 1991–92
 * 2. Bundesliga
 * Champions: 1975, 1986–87, 2001–02

Regional

 * Südkreisliga
 * Champions: 1921, 1927, 1928, 1930
 * Gauliga Niedersachsen
 * Champions: 1935, 1938
 * Oberliga Nord
 * Champions: 1954
 * Regionalliga Nord (Tier 3)
 * Champions: 1997, 1998
 * Lower Saxony Cup (Tiers 3–5)
 * Winners: 1982,1998, 1999

Youth

 * German Under 17 Championship
 * Runners-up: 1994, 1995
 * Under 19 Bundesliga North/Northeast
 * Champions: 2004

Records

 * Miscellaneous Records

Coach history

 * 🇩🇪 Robert Fuchs (football coach) (1 July 1931 – 30 June 1946)
 * 🇩🇪 Fritz Pölsterl (October 1946–47)
 * 🇩🇪 Otto Höxtermann (August 1947 – September 1947)
 * 🇩🇪 Robert Fuchs (football coach) (1 July 1947 – 30 June 1950)
 * 🇩🇪 Christian Bieritz (int.) (December 1950)
 * 🇩🇪 Paul Slopianka-Hoppe (January 1951–51)
 * 🇭🇺 Emil Izsó (1951–52)
 * 🇩🇪 Helmut Kronsbein (1 July 1952 – 30 June 1957)
 * 🇩🇪 Kuno Klötzer (1957–58)
 * 🇩🇪 Fritz Silken (1958–59)
 * 🇩🇪 Günter Grothkopp (1959 – Dec 61)
 * 🇩🇪 Hannes Kirk (31 December 1961 – 31 March 1962)
 * 🇩🇪 Heinz Lucas (1 July 1962 – 30 June 1963)
 * 🇩🇪 Helmut Kronsbein (1 July 1963 – 29 April 1966)
 * 🇩🇪 Hannes Kirk (int.) (29 April 1966 – 29 May 1966)
 * 🇩🇪 Horst Buhtz (1 July 1966 – 12 August 1968)
 * 🇩🇪 Karl-Heinz Mülhausen (int.) (13 February 1968 – 30 June 1968)
 * Zlatko Čajkovski (1 July 1968 – 8 December 1969)
 * 🇩🇪 Rolf Paetz (int.) (December 1969)
 * 🇩🇪 Hans Pilz (2 January 1970 – 30 June 1970)
 * 🇩🇪 Helmuth Johannsen (1 July 1970 – 13 November 1971)
 * 🇩🇪 Hans Hipp (18 November 1971 – 1 March 1973)
 * 🇩🇪 Hannes Baldauf (5 March 1973 – 12 March 1974)
 * 🇩🇪 Helmut Kronsbein (13 March 1974 – 14 January 1976)
 * 🇩🇪 Hannes Baldauf (15 January 1976 – 13 December 1976)
 * 🇩🇪 Helmut Kronsbein (1 January 1977 – 30 June 1978)
 * 🇩🇪 Anton Burghardt (1 July 1978 – 30 June 1979)
 * 🇩🇪 Diethelm Ferner (1 July 1979 – 14 December 1982)
 * 🇩🇪 Gerd Bohnsack (10 December 1982 – 24 October 1983)
 * 🇩🇪 Werner Biskup (25 October 1983 – 21 November 1985)
 * 🇩🇪 Jürgen Rynio (int.) (22 November 1985 – 12 January 1986)
 * 🇩🇪 Jörg Berger (13 January 1986 – 17 March 1986)
 * 🇩🇪 Helmut Kalthoff (18 March 1986 – 30 June 1986)
 * 🇩🇪 Jürgen Wähling (1 July 1986 – 19 September 1988)
 * 🇩🇪 Hans Siemensmeyer (19 September 1988 – 21 March 1989)
 * 🇩🇪 Reinhard Saftig (22 March 1989 – 30 June 1989)
 * Slobodan Čendić (1 July 1989 – 31 August 1989)
 * 🇩🇪 Michael Krüger (13 September 1989 – 30 September 1990)
 * 🇩🇪 Hans-Dieter Schmidt (int.) (1990)
 * 🇩🇪 Michael Lorkowski (17 October 1990 – 30 June 1992)
 * 🇩🇪 E. Vogel & 🇩🇪 H. Baldauf (1 July 1992 – 8 November 1993)
 * 🇩🇪 Rolf Schafstall (9 November 1993 – 30 October 1994)
 * 🇩🇪 Stefan Mertesacker (int.) (31 October 1994 – 6 November 1994)
 * 🇩🇪 Peter Neururer (7 November 1994 – 30 May 1995)
 * Miloš Đelmaš (int.) (31 May 1995 – 18 June 1995)
 * 🇩🇪 Egon Coordes (1 July 1995 – 25 March 1996)
 * 🇩🇪 Jürgen Stoffregen (26 March 1996 – 30 June 1996)
 * 🇩🇪 Reinhold Fanz (1 July 1996 – 21 December 1998)
 * 🇩🇪 Franz Gerber (1 January 1999 – 30 June 1999)
 * 🇭🇷 Branko Ivanković (1 July 1999 – 20 February 2000)
 * 🇩🇪 Horst Ehrmantraut (21 February 2000 – 23 April 2001)
 * 🇨🇿 Stanislav Levý (int.) (24 April 2001 – 30 June 2001)
 * 🇩🇪 R. Rangnick & 🇩🇪 M. Slomka (1 July 2001 – 7 March 2004)
 * 🇩🇪 E. Lienen & 🇩🇪 M. Frontzeck (9 March 2004 – 9 November 2005)
 * 🇩🇪 Peter Neururer (9 November 2005 – 30 August 2006)
 * 🇩🇰 Michael Schjønberg (int.) (1 September 2006 – 7 September 2006)
 * 🇩🇪 Dieter Hecking (8 September 2006 – 19 August 2009)
 * 🇩🇪 Andreas Bergmann (20 August 2009 – 19 January 2010)
 * 🇩🇪 Mirko Slomka (19 January 2010 – 27 December 2013)
 * 🇹🇷 Tayfun Korkut (31 December 2013 – 20 April 2015)
 * 🇩🇪 Michael Frontzeck (20 April 2015 – 21 December 2015)
 * 🇩🇪 Thomas Schaaf (4 January 2016 – 3 April 2016)
 * 🇩🇪 Daniel Stendel (3 April 2016 – 20 March 2017)
 * 🇩🇪 André Breitenreiter (20 March 2017 – 27 January 2019)
 * 🇩🇪 Thomas Doll (27 January 2019 – 30 June 2019)
 * 🇩🇪 Mirko Slomka (1 July 2019 – 3 November 2019)
 * 🇧🇦 Asif Šarić (int.) (4 November 2019 – 14 November 2019)
 * 🇹🇷 Kenan Koçak (14 November 2019 – 30 June 2021)
 * 🇩🇪 Jan Zimmermann (1 July 2021 – 29 November 2021)
 * 🇩🇪 Christoph Dabrowski (1 December 2021 – 30 June 2022)
 * 🇩🇪 Stefan Leitl (1 July 2022 – )

Hannover 96 Amateure (II)
Hannover fields a successful amateur side that has three German amateur championships to its credit (1960, 1964, 1965) as well as losing appearances in the 1966 and 1967 finals. The second team has also taken part in the German Cup tournament and currently plays in the 3. Liga.

Honours
The team's honours:
 * Amateurliga Niedersachsen-West
 * Champions: 1960
 * Amateurliga Niedersachsen-Ost
 * Champions: 1964
 * Amateurliga Niedersachsen
 * Champions: 1965, 1966, 1967
 * German amateur championship
 * Champions: 1960, 1964, 1965
 * Lower Saxony Cup
 * Winners: 1982

title: Hannover 96


text:
Dispersion (materials science)

In materials science, dispersion is the fraction of atoms of a material exposed to the surface. In general, D = NS/N, where D is the dispersion, NS is the number of surface atoms and NT is the total number of atoms of the material. It is an important concept in heterogeneous catalysis, since only atoms exposed to the surface can affect catalytic surface reactions. Dispersion increases with decreasing crystallite size and approaches unity at a crystallite diameter of about 0.1 nm.

title: Dispersion (materials science)


text:
Mohair

Mohair (pronounced ) is a fabric or yarn made from the hair of the Angora goat (not Angora wool from the fur of the Angora rabbit). Both durable and resilient, mohair is lustrous with high sheen, and is often blended to add these qualities to a textile. Mohair takes dye exceptionally well. It feels warm in winter due to excellent insulating properties, while moisture-wicking keeps it cool in summer. It is durable, naturally elastic, flame-resistant and crease-resistant. It is considered a luxury fiber, like cashmere, alpaca, angora, and silk, but is more expensive than most sheep's wool.

Mohair is composed mostly of keratin, a protein in the hair, wool, horns and skin of all mammals, but mohair's special properties are unique to the Angora goat. While it has scales like wool, they are not fully developed, thus, mohair feels different from common or standard wool.

Mohair fiber is approximately 25–45 micrometres in diameter. It expands in diameter with the age of the goat, growing along with the animal. Finer, softer hair from younger animals is used (for example) in scarves and shawls; the thicker, coarser hair from older animals is more often used for carpets and in heavy fabrics intended for outerwear.

The term mohair is sometimes used to describe the material in the folding roof on convertible cars. In this case mohair refers to a denim-like canvas.

Production

Shearing is done twice a year, in the spring and in the fall. One goat will produce 11 to(-) of mohair a year. Shearing is done on a cleanly-swept floor and extra care is taken to keep the hair clean and free of debris. The hair is then processed to remove natural grease, dirt and vegetable matter. Mohair grows in uniform locks. The Angora goat is a single-coat breed, and unlike pygora or cashmere, there is no need to dehair a mohair fleece to separate the coarse hair from the down hair.

South Africa is the world's largest mohair producer as of 2013, supplying around 50% of the total world production. Due to animal cruelty in the South African farms, Zara, H&M, Gap, Topshop, Lacoste, and many more will no longer sell mohair clothing.

History
Mohair is one of the oldest textile fibers in use. The Angora goat is thought to originate from the mountains of Tibet, reaching Turkey in the 16th century. Fabric made of mohair was known in England by the early 18th century. The word "mohair" was adopted into English sometime before 1570 from the Arabic: mukhayyar, a type of haircloth, literally "choice", from khayyara, "he chose".

In about 1820, raw mohair was first exported from Turkey to England, which then became the leading manufacturer of mohair products. The Yorkshire mills spun yarn that was exported to Russia, Germany, Austria, etc., as well as woven directly in Yorkshire.

Until 1849, the Turkish province of Ankara was the sole producer of Angora goats. Charles V is believed to be the first to bring Angora goats to Europe. Due to the great demand for mohair fiber, throughout the 1800s there was a great deal of crossbreeding between Angora goats and common goats. The growing demand for mohair further resulted in attempts on a commercial scale to introduce the goat into South Africa (where it was crossed with the native goat) in 1838, the United States in 1849, Australia from 1856 to 1875, and later still New Zealand. In 1849, Angora goats made their way to America as a gift from Turkey.

During the 1960s, a blend of mohair and wool suiting fabric known as Tonik or Tonic was developed in England. This had a shiny, color-changing appearance and was popular among rude boys and the mod subculture. Similar suits were worn by mod revivalists, skinheads, and fans of ska punk and two tone music during the early to mid-1980s.

Today, South Africa is the largest mohair producer in the world, with the majority of South African mohair being produced in the Eastern Cape. The United States is the second-largest producer, with the majority of American mohair being produced in Texas. Turkey also produces good-quality mohair. Because the goats are sheared once a year (different from South Africa), Turkey produces the longest mohair of the world.

In December 2006, the General Assembly of the United Nations proclaimed 2009 to be the International Year of Natural Fibres, so as to raise the profile of mohair and other natural fibers.

Uses
Mohair is used in scarves, winter hats, suits, sweaters, coats, socks and home furnishing. Mohair fiber is also found in carpets, wall fabrics, craft yarns, and many other fabrics, and may be used as a substitute for fur. Because its texture resembles fine human hair, mohair is often used in making high-grade doll wigs or in rooting customized dolls.

Mohair is a very soft yarn when compared with other natural and synthetic fibers. Due to mohair's lacking prominent, protruding scales along the hair's surface, it is often blended with wool or alpaca. Blending the heavily scaled wool helps the smooth mohair fibers hold their shape and stick together when spun into yarn. Mohair is also valued for certain other unique characteristics: it is warmer than other fibers, even when used to make a light-weight garment, and is often blended with wool for this reason; and mohair fibers have a distinctive luster created by the way they reflect light. Combined with mohair's ability to absorb dyes exceptionally well, pure mohair yarns are usually recognizable for their vivid, saturated colours.

Fibers from young goats are softest and are used to manufacture yarn for clothing. Fibers from mature goats are used to produce such things as rugs and carpets. Mohair is also used in 'climbing skins' for randonnée skiing and ski touring. The mohair is used in a carpet allowing the skier an appropriate ascension method without sliding downhill.

Mohair industry worldwide
As of 2009, world output of mohair was estimated at around 5,000 tonnes a year, down from a high of 25,000 tonnes in the 1990s. South Africa accounts for 60% of total production. South African mohair is generally exported raw or semi-processed to textile makers in Europe, the UK and the Far East. Prices for adult mohair declined in 2010 while prices for kid mohair remained the same. An emerging market for mohair producers has been China.

U.S. subsidies for mohair production
During World War II, U.S. soldiers wore uniforms made of wool. Worried that domestic producers could not supply enough for future wars, Congress enacted loan and price support programs for wool and mohair in the National Wool Act of 1954 as part of the 1954 Farm Bill. Despite these subsidies, wool and mohair production declined. The strategic importance declined as well; the US military adopted uniforms made of synthetic fibers, such as dacron, and officially removed wool from the list of strategic materials in 1960. Nevertheless, the U.S. government continued to provide subsidies to mohair producers until 1995, when the subsidies were "eliminated effective with the marketing year ending December 31, 1995". In The Future of Freedom: Illiberal Democracy at Home and Abroad, Fareed Zakaria points out that the subsidies were reinstated a few years later, due in large part to the lobbying on behalf of the special interests of the subsidy recipients. By 2000, Congress had appropriated US$20 million for goat and sheep producers. As of 2002, mohair producers were still able to receive special assistance loans from the U.S. government, after an amendment to eliminate the subsidy was defeated. The U.S. currently subsidizes mohair production under the Marketing Assistance Loan Program of the 2014 Farm Act.

In popular culture
In the Elton John song "Bennie and the Jets," Bennie is said to wear a suit made of mohair.

In the Song "The Boy from New York City," first recorded by The Ad Libs, and made popular by The Manhattan Transfer, the lines "And he's cute In his mohair suit" appear.

In the Tom Waits song Jockey Full of Bourbon, the jockey claims to have, "two pair of pants and a mohair vest."

In the Seinfeld episode The Sniffing Accountant, Jerry's mohair sweater figures prominently into the plot.

title: Mohair