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106-485: The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses . It was later expanded to include the output power of other power-generating machinery such as piston engines , turbines , and electric motors . The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With

212-450: A floating-point representation with a fixed number of significant digits . In a sequence of calculations, these rounding errors generally accumulate , and in certain ill-conditioned cases they may make the result meaningless. Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem

318-413: A ' brewery horse ' could produce 32,400 foot-pounds [43,929 J] per minute." James Watt and Matthew Boulton standardized that figure at 33,000 foot-pounds (44,742 J) per minute the next year. A common legend states that the unit was created when one of Watt's first customers, a brewer, specifically demanded an engine that would match a horse, and chose the strongest horse he had and driving it to

424-697: A European style of feudalism to Scotland along with an influx of people of French descent – by invitation, unlike England where it was by conquest. To this day, many of the common family names of Scotland can trace ancestry to Normans from this period, such as the Stewarts , the Bruces , the Hamiltons , the Wallaces and the Melvilles . The Northern Isles and some parts of Caithness were Norn -speaking (the west of Caithness

530-692: A centre for Scottish migration in the 1930s. In 1961 a third of residents were born in Scotland, and in 2011 the figure was 12.7%. Other European countries have had their share of Scots immigrants. The Scots have emigrated to mainland Europe for centuries as merchants and soldiers. Many emigrated to France, Poland, Italy , Germany, Scandinavia, and the Netherlands. Recently some scholars suggested that up to 250,000 Russian nationals may have Scottish ancestry. A number of Scottish people settled in South Africa in

636-568: A computed number, measurement, or estimate; for example, a quantity that was computed as 123456 but is known to be accurate only to within a few hundred units is usually better stated as "about 123500 ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic ; when computing mathematical functions such as square roots , logarithms , and sines ; or when using

742-520: A connection to Scotland. This connection may be active through cultural, linguistic, friendship, or professional links, or who may simply be interested Scotland’s heritage or culture). The majority of Scotch-Irish Americans originally came from Lowland Scotland and Northern England before migrating to the province of Ulster in Ireland (see Plantation of Ulster ) and thence, beginning about five generations later, to North America in large numbers during

848-428: A group of engineers modified a dynometer to be able to measure how much horsepower a horse can produce. This horse was measured to 5.7 hp (4.3 kW). When torque T is in pound-foot units, rotational speed N is in rpm , the resulting power in horsepower is The constant 5252 is the rounded value of (33,000 ft⋅lbf/min)/(2π rad/rev). When torque T is in inch-pounds, The constant 63,025

954-522: A healthy human can produce about 1.2 hp (0.89 kW) briefly (see orders of magnitude ) and sustain about 0.1 hp (0.075 kW) indefinitely; trained athletes can manage up to about 2.5 hp (1.9 kW) briefly and 0.35 hp (0.26 kW) for a period of several hours. The Jamaican sprinter Usain Bolt produced a maximum of 3.5 hp (2.6 kW) 0.89 seconds into his 9.58 second 100-metre (109.4 yd) sprint world record in 2009. In 2023

1060-475: A holding. Rounding Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ 23.4476 with $ 23.45 , the fraction 312/937 with 1/3, or the expression √2 with 1.414 . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of

1166-628: A museum, 'The Scots House' in the town of Veere was the only place outwith Scotland where Scots Law was practised. In Rotterdam, meanwhile, the doors of the Scots International Church have remained open since 1643. The first Scots to be mentioned in Russia's history were the Scottish soldiers in Muscovy referred to as early as the 14th century. Among the 'soldiers of fortune' was the ancestor of

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1272-479: A tie-breaking rule that is commonly taught and used, namely: If the fractional part of x is exactly 0.5, then y = x + 0.5 if x is positive, and y = x − 0.5 if x is negative. For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −24. This can be more efficient on computers that use sign-magnitude representation for the values to be rounded, because only the first omitted digit needs to be considered to determine if it rounds up or down. This

1378-640: A tie-breaking rule that is widely used in many disciplines. That is, half-way values of x are always rounded up. If the fractional part of x is exactly 0.5, then y = x + 0.5 For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −23. Some programming languages (such as Java and Python) use "half up" to refer to round half away from zero rather than round half toward positive infinity . This method only requires checking one digit to determine rounding direction in two's complement and similar representations. One may also round half down (or round half toward negative infinity ) as opposed to

1484-495: Is a coefficient of theoretical brake horsepower and cylinder pressures during combustion. Nominal horsepower (nhp) is an early 19th-century rule of thumb used to estimate the power of steam engines. It assumed a steam pressure of 7 psi (48 kPa). Scottish people Modern ethnicities The Scottish people or Scots ( Scots : Scots fowk ; Scottish Gaelic : Albannaich ) are an ethnic group and nation native to Scotland . Historically, they emerged in

1590-504: Is also called convergent rounding , statistician's rounding , Dutch rounding , Gaussian rounding , odd–even rounding , or bankers' rounding . This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats. By eliminating bias, repeated addition or subtraction of independent numbers, as in a one-dimensional random walk , will give a rounded result with an error that tends to grow in proportion to

1696-420: Is also used in many places to symbolize brake horsepower. Drawbar power (dbp) is the power a railway locomotive has available to haul a train or an agricultural tractor to pull an implement. This is a measured figure rather than a calculated one. A special railway car called a dynamometer car coupled behind the locomotive keeps a continuous record of the drawbar pull exerted, and the speed. From these,

1802-460: Is equivalent to a boiler heat output of 33,469 Btu/h (9.809 kW). Present industrial practice is to define "boiler horsepower" as a boiler thermal output equal to 33,475 Btu/h (9.811 kW), which is very close to the original and revised definitions. Boiler horsepower is still used to measure boiler output in industrial boiler engineering in the US. Boiler horsepower is abbreviated BHP, which

1908-450: Is equivalent to a boiler heat output of 33,485 Btu/h (9.813 kW). A few years later in 1884, the ASME re-defined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" 212 °F (100 °C). This considerably simplified boiler testing, and provided more accurate comparisons of the boilers at that time. This revised definition

2014-480: Is in psi, and flow rate is in US gallons per minute. Drilling rigs are powered mechanically by rotating the drill pipe from above. Hydraulic power is still needed though, as 1 500 to 5 000 W are required to push mud through the drill bit to clear waste rock. Additional hydraulic power may also be used to drive a down-hole mud motor to power directional drilling . When using SI units, the equation becomes coherent and there

2120-449: Is known as " the table-maker's dilemma ". Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals . A wavy equals sign ( ≈ , approximately equal to ) is sometimes used to indicate rounding of exact numbers, e.g. 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892. Ideal characteristics of rounding methods include: Because it

2226-465: Is needed to pull a drawbar load of 2,025 pounds-force at 5 miles per hour? { P } h p = 2025 × 5 375 = 27. {\displaystyle \{P\}_{\mathrm {hp} }={\frac {2025\times 5}{375}}=27.} The constant 375 is because 1 hp = 375 lbf⋅mph. If other units are used, the constant is different. When using coherent SI units (watts, newtons, and metres per second), no constant

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2332-507: Is needed, and the formula becomes P = Fv . This formula may also be used to calculate the power of a jet engine, using the speed of the jet and the thrust required to maintain that speed. Example: how much power is generated with a thrust of 4000 pounds at 400 miles per hour? { P } h p = 4000 × 400 375 = 4266.7. {\displaystyle \{P\}_{\mathrm {hp} }={\frac {4000\times 400}{375}}=4266.7.} This measure

2438-433: Is no dividing constant. where pressure is in pascals (Pa), and flow rate is in cubic metres per second (m). Boiler horsepower is a boiler 's capacity to deliver steam to a steam engine and is not the same unit of power as the 550 ft lb/s definition. One boiler horsepower is equal to the thermal energy rate required to evaporate 34.5 pounds (15.6 kg) of fresh water at 212 °F (100 °C) in one hour. In

2544-411: Is not usually possible for a method to satisfy all ideal characteristics, many different rounding methods exist. As a general rule, rounding is idempotent ; i.e., once a number has been rounded, rounding it again to the same precision will not change its value. Rounding functions are also monotonic ; i.e., rounding two numbers to the same absolute precision will not exchange their order (but may give

2650-433: Is one method used when rounding to significant figures due to its simplicity. This method, also known as commercial rounding , treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias away from zero. It is often used for currency conversions and price roundings (when

2756-503: Is ordinarily stated in watts or kilowatts. In the United States, the power output is stated in horsepower which, for this purpose, is defined as exactly 746 W. Hydraulic horsepower can represent the power available within hydraulic machinery , power through the down-hole nozzle of a drilling rig , or can be used to estimate the mechanical power needed to generate a known hydraulic flow rate. It may be calculated as where pressure

2862-595: Is still spoken by a small number of residents. Cape Breton is the home of the Gaelic College of Celtic Arts and Crafts . Glengarry County in present-day Eastern Ontario is a historic county that was set up as a settlement for Highland Scots , where many from the Highlands settled to preserve their culture as a result of the Highland Clearances. Gaelic was the native language of the community since its settlement in

2968-737: Is the approximation of Assuming the third CGPM (1901, CR 70) definition of standard gravity , g n = 9.80665 m/s , is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one imperial horsepower is: Or given that 1 hp = 550 ft⋅lbf/s, 1 ft = 0.3048 m, 1 lbf ≈ 4.448 N, 1 J = 1 N⋅m, 1 W = 1 J/s: 1 hp ≈ 745.7 W The various units used to indicate this definition ( PS , KM , cv , hk , pk , k , ks and ch ) all translate to horse power in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on

3074-491: Is the fourth most commonly nominated ancestry and represents over 8.9% of the total population of Australia. Significant numbers of Scottish people also settled in New Zealand. Approximately 20 per cent of the original European settler population of New Zealand came from Scotland, and Scottish influence is still visible around the country. The South Island city of Dunedin , in particular, is known for its Scottish heritage and

3180-404: Is the integer that is closest to 0 (or equivalently, to x ) such that x is between 0 and y (included). For example, 23.2 gets rounded to 24, and −23.2 gets rounded to −24. These six methods are called rounding to the nearest integer . Rounding a number x to the nearest integer requires some tie-breaking rule for those cases when x is exactly half-way between two integers – that is, when

3286-437: Is the odd integer nearest to x . Thus, for example, 23.5 becomes 23, as does 22.5; while −23.5 becomes −23, as does −22.5. This method is also free from positive/negative bias and bias toward/away from zero, provided the numbers to be rounded are neither mostly even nor mostly odd. It also shares the round half to even property of distorting the original distribution, as it increases the probability of odds relative to evens. It

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3392-502: Is the smallest integer that is not less than x . For example, 23.2 gets rounded to 24, and −23.7 gets rounded to −23. One may also round toward zero (or truncate , or round away from infinity ): y is the integer that is closest to x such that it is between 0 and x (included); i.e. y is the integer part of x , without its fraction digits. For example, 23.7 gets rounded to 23, and −23.7 gets rounded to −23. One may also round away from zero (or round toward infinity ): y

3498-576: The Borders ( OE: Loðene ), a northern variety of Old English , also known as Early Scots , was spoken. As a result of David I, King of Scots' return from exile in England in 1113, ultimately to assume the throne in 1124 with the help of Anglo-Norman military force, David invited Anglo-Norman families from France and England to settle in lands he granted them to spread a ruling class loyal to him. This Davidian Revolution , as many historians call it, brought

3604-515: The Middle Ages . Craftsmen and tradesmen followed courtiers and in later centuries a brisk trade grew up between the two nations: Scotland's primary goods (wool, hides, salmon and then coal) in exchange for the luxuries obtainable in the Netherlands, one of the major hubs of European trade. By 1600, trading colonies had grown up on either side of the well-travelled shipping routes: the Dutch settled along

3710-549: The River Tweed to the south. They also occupied the southwest of Scotland up to and including the Plain of Kyle . Their language, Old English , was the earliest form of the language which eventually became known as Scots . Use of the Gaelic language spread through nearly the whole of Scotland by the 9th century, reaching a peak in the 11th to 13th centuries, but was never the language of

3816-766: The United States and Canada . Scots have travelled internationally for centuries, helping to build Scotland's international reputation and the promotion of Scottish culture , music , literature and art . The Scottish Government uses the term "Scottish connections" when described Scottish diaspora, and recognises Scottish connections as people of Scottish heritage (by ancestry, marriage or other family connection), lived diaspora (those who moved to Scotland to permanently reside at any time for any reason), educational diaspora (alumni of Scottish educational institutions, and Scots studying or working in international institutions) and affinity (individuals who associate themselves with

3922-589: The early Middle Ages from an amalgamation of two Celtic peoples , the Picts and Gaels , who founded the Kingdom of Scotland (or Alba ) in the 9th century. In the following two centuries, Celtic-speaking Cumbrians of Strathclyde and Germanic-speaking Angles of Northumbria became part of Scotland. In the High Middle Ages , during the 12th-century Davidian Revolution , small numbers of Norman nobles migrated to

4028-748: The kilowatt as the official power-measuring unit in EEC directives. Other names for the metric horsepower are the Italian cavallo vapore (cv) , Dutch paardenkracht (pk) , the French cheval-vapeur (ch) , the Spanish caballo de vapor and Portuguese cavalo-vapor (cv) , the Russian лошадиная сила (л. с.) , the Swedish hästkraft (hk) , the Finnish hevosvoima (hv) ,

4134-783: The plantation of Ulster , resulted in a Presbyterian and Scottish society, which formed the Ulster-Scots community. The Protestant Ascendancy did not however benefit them much, as the ascendancy was predominantly Anglican . The number of people of Scottish descent in England and Wales is difficult to quantify due to the many complex migrations on the island, and ancient migration patterns due to wars, famine and conquest. The 2011 Census recorded 708,872 people born in Scotland resident in England, 24,346 resident in Wales and 15,455 resident in Northern Ireland. Northamptonshire town Corby became

4240-634: The ' New World ' lands of North and South America, Australia and New Zealand . The highest concentrations of people of Scottish descent in the world outside of Scotland are in Nova Scotia and Prince Edward Island in Canada, Otago and Murihiku/Southland in New Zealand, the Falkland Islands , and Northern Ireland in the United Kingdom. Canada has the highest level of Scottish descendants per capita in

4346-561: The 1800s and were known for their road-building expertise, their farming experience, and architectural skills. The largest population of Scots in Latin America is found in Argentina , followed by Chile , , Colombia and Mexico . It is said that the first people from the Low Countries to settle in Scotland came in the wake of Maud's marriage to the Scottish king, David I , during

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4452-444: The 1840s, Scots-born immigrants constituted 12% of the non-Aboriginal population. Out of the 1.3 million migrants from Britain to Australia in the period from 1861 to 1914, 13.5% were Scots. Just 5.3% of the convicts transported to Eastern Australia between 1789 and 1852 were Scots. A steady rate of Scottish immigration continued into the 20th century and substantial numbers of Scots continued to arrive after 1945. From 1900 until

4558-484: The 18th century although the number of speakers decreased as a result of English migration . As of the modern 21st century, there are still a few Gaelic speakers in the community. John Kenneth Galbraith in his book The Scotch (Toronto: MacMillan, 1964) documents the descendants of 19th-century Scottish pioneers who settled in Southwestern Ontario and affectionately referred to themselves as 'Scotch'. He states

4664-638: The 18th century as " Erse ") and the Inglis -speaking " Lowlanders " (a language later to be called Scots ). However, movement between the two regions increased over the last few centuries. Highlanders moved to major cities (e.g. Glasgow and Edinburgh) and regions bordering the southern Highlands (e.g. Lowland Stirlingshire and Perthshire). This is evidenced by people with traditional Gaelic surnames (including anglicised varieties) currently living in these areas. Lowlanders also settled in Highland regions such as Moray , which

4770-499: The 1926 Iowa State Fair , they reported that the peak power over a few seconds has been measured to be as high as 14.88 hp (11.10 kW) and also observed that for sustained activity, a work rate of about 1 hp (0.75 kW) per horse is consistent with agricultural advice from both the 19th and 20th centuries and also consistent with a work rate of about four times the basal rate expended by other vertebrates for sustained activity. When considering human-powered equipment ,

4876-529: The 1950s, Scots favoured New South Wales, as well as Western Australia and Southern Australia. A strong cultural Scottish presence is evident in the Highland Games , dance, Tartan Day celebrations, clan and Gaelic-speaking societies found throughout modern Australia. According to the 2011 Australian census , 130,204 Australian residents were born in Scotland, while 1,792,600 claimed Scottish ancestry, either alone or in combination with another ancestry. This

4982-820: The Estonian hobujõud (hj) , the Norwegian and Danish hestekraft (hk) , the Hungarian lóerő (LE) , the Czech koňská síla and Slovak konská sila (k or ks ), the Serbo-Croatian konjska snaga (KS) , the Bulgarian конска сила , the Macedonian коњска сила (KC) , the Polish koń mechaniczny (KM) ( lit.   ' mechanical horse ' ), Slovenian konjska moč (KM) ,

5088-773: The Lowlands. In the 13th century, the Norse-Gaels of the Western Isles became part of Scotland, followed by the Norse of the Northern Isles in the 15th century. In modern usage, "Scottish people" or "Scots" refers to anyone whose linguistic, cultural, family ancestral or genetic origins are from Scotland. The Latin word Scoti originally referred to the Gaels, but came to describe all inhabitants of Scotland. Considered pejorative by some,

5194-670: The Scots. The Russian census lists do not distinguish Scots from other British people, so it is hard to establish reliable figures for the number of Scots living and working in modern Russia. From as far back as the mid-16th century there were Scots trading and settling in Poland . A "Scotch Pedlar's Pack in Poland" became a proverbial expression. It usually consisted of cloths, woollen goods and linen kerchiefs (head coverings). Itinerants also sold tin utensils and ironware such as scissors and knives. Along with

5300-473: The South Island. All over New Zealand, the Scots developed different means to bridge the old homeland and the new. Many Caledonian societies were formed, well over 100 by the early twentieth century, that helped maintain Scottish culture and traditions. From the 1860s, these societies organised annual Caledonian Games throughout New Zealand. The Games were sports meets that brought together Scottish settlers and

5406-647: The Ukrainian кінська сила (к. с.) , the Romanian cal-putere (CP) , and the German Pferdestärke (PS) . In the 19th century, revolutionary-era France had its own unit used to replace the cheval vapeur (horsepower); based on a 100 kgf ⋅m/s standard, it was called the poncelet and was abbreviated p . Tax or fiscal horsepower is a non-linear rating of a motor vehicle for tax purposes. Tax horsepower ratings were originally more or less directly related to

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5512-482: The amount is first converted into the smallest significant subdivision of the currency, such as cents of a euro) as it is easy to explain by just considering the first fractional digit, independently of supplementary precision digits or sign of the amount (for strict equivalence between the paying and recipient of the amount). One may also round half to even , a tie-breaking rule without positive/negative bias and without bias toward/away from zero. By this convention, if

5618-599: The area around Edinburgh. Their descendants gradually occupied all of the Lowlands." Knox College 's Stuart Macdonald, who specialises in early modern Scottish history, writes that during the 18th and 19th centuries, the people of Scotland remained grouped into multiple ethnicities: To speak of Scots as a single ethnic group is also somewhat problematic. It would be more accurate in the eighteenth and nineteenth centuries to talk of two distinct Scottish ethnic communities divided by language and culture, and, at times, mutual antagonisms – Highlanders and Lowlanders. With regard to

5724-482: The best-known being James Wylie . The next wave of migration established commercial links with Russia. The 19th century witnessed the immense literary cross-references between Scotland and Russia. A Russian scholar, Maria Koroleva, distinguishes between 'the Russian Scots' (properly assimilated) and 'Scots in Russia', who remained thoroughly Scottish. There are several societies in contemporary Russia to unite

5830-481: The book was meant to give a true picture of life in the community in the early decades of the 20th century. By 1830, 15.11% of the colonies' total non-Aboriginal population were Scots, which increased by the middle of the century to 25,000, or 20–25% of the non-Aboriginal population. The Australian Gold Rush of the 1850s provided a further impetus for Scottish migration: in the 1850s 90,000 Scots immigrated to Australia, far more than other British or Irish populations at

5936-566: The conventional round half away from zero . If the fractional part of x is exactly 0.5, then y = x − 0.5 if x is positive, and y = x + 0.5 if x is negative. For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −23. This method treats positive and negative values symmetrically, and therefore is free of overall positive/negative bias if the original numbers are positive or negative with equal probability. It does, however, still have bias toward zero. One may also round half away from zero (or round half toward infinity ),

6042-493: The descendants of emigrants, often Gaelic-speaking, from the Maritime Provinces of Canada , from the 1880s onward. Americans of Scottish descent outnumber the population of Scotland, where 4,459,071 or 88.09% of people identified as ethnic Scottish in the 2001 Census. In the 2013 American Community Survey 5,310,285 identified as Scottish and 2,976,878 as of Scots-Irish descent. Americans of Scottish descent outnumber

6148-401: The displacements from the original number x to the rounded value y are all directed toward or away from the same limiting value (0, +∞ , or −∞). Directed rounding is used in interval arithmetic and is often required in financial calculations. If x is positive, round-down is the same as round-toward-zero, and round-up is the same as round-away-from-zero. If x is negative, round-down is

6254-651: The early days of steam use, the boiler horsepower was roughly comparable to the horsepower of engines fed by the boiler. The term "boiler horsepower" was originally developed at the Philadelphia Centennial Exhibition in 1876, where the best steam engines of that period were tested. The average steam consumption of those engines (per output horsepower) was determined to be the evaporation of 30 pounds (14 kg) of water per hour, based on feed water at 100 °F (38 °C), and saturated steam generated at 70 psi (480 kPa). This original definition

6360-518: The eastern seaboard of Scotland; the Scots congregating first in Campvere —where they were allowed to land their goods duty-free and run their own affairs—and then in Rotterdam , where Scottish and Dutch Calvinism coexisted comfortably. Besides the thousands (or, according to one estimate, over 1 million) of local descendants with Scots ancestry, both ports still show signs of these early alliances. Now

6466-432: The eighteenth century. In the 2000 census, 4.8 million Americans self-reported Scottish ancestry, 1.7% of the total U.S. population. Over 4.3 million self-reported Scotch-Irish ancestry, for a total of 9.2 million Americans self-reporting some kind of Scottish descent. Self-reported numbers are regarded by demographers as massive under-counts, because Scottish ancestry is known to be disproportionately under-reported among

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6572-520: The engine's bore size, number of cylinders, and a (now archaic) presumption of engine efficiency. As new engines were designed with ever-increasing efficiency, it was no longer a useful measure, but was kept in use by UK regulations, which used the rating for tax purposes . The United Kingdom was not the only country that used the RAC rating; many states in Australia used RAC hp to determine taxation. The RAC formula

6678-498: The engine. The situation persisted for several generations of four- and six-cylinder British engines: For example, Jaguar's 3.4-litre XK engine of the 1950s had six cylinders with a bore of 83 mm (3.27 in) and a stroke of 106 mm (4.17 in), where most American automakers had long since moved to oversquare (large bore, short stroke) V8 engines . See, for example, the early Chrysler Hemi engine . The power of an engine may be measured or estimated at several points in

6784-399: The examples below, sgn( x ) refers to the sign function applied to the original number, x . One may round down (or take the floor , or round toward negative infinity ): y is the largest integer that does not exceed x . For example, 23.7 gets rounded to 23, and −23.2 gets rounded to −24. One may also round up (or take the ceiling , or round toward positive infinity ): y

6890-475: The famous Russian poet Mikhail Lermontov , called George Learmonth. A number of Scots gained wealth and fame in the times of Peter the Great and Catherine the Great . These include Admiral Thomas Gordon , Commander-in-Chief of Kronstadt , Patrick Gordon , Paul Menzies , Samuel Greig , Charles Baird , Charles Cameron , Adam Menelaws and William Hastie . Several doctors to the Russian court were from Scotland,

6996-734: The following: "The basic ethnic and cultural division in the British Isles has been that between the Anglo-Saxon peoples of England and the Scottish Lowlands and the Celtic peoples of Wales, Ireland and the Scottish Highlands. In 2014, historian Steven L. Danver, who specialises in indigenous ethnic research, wrote regarding Lowlands Scots and Gaelic Scots' unique ancestries: "The people of Scotland are divided into two groups - Lowland Scots in

7102-420: The fraction part of x is exactly 0.5. If it were not for the 0.5 fractional parts, the round-off errors introduced by the round to nearest method would be symmetric: for every fraction that gets rounded down (such as 0.268), there is a complementary fraction (namely, 0.732) that gets rounded up by the same amount. When rounding a large set of fixed-point numbers with uniformly distributed fractional parts,

7208-411: The fractional part of x is 0.5, then y is the even integer nearest to x . Thus, for example, 23.5 becomes 24, as does 24.5; however, −23.5 becomes −24, as does −24.5. This function minimizes the expected error when summing over rounded figures, even when the inputs are mostly positive or mostly negative, provided they are neither mostly even nor mostly odd. This variant of the round-to-nearest method

7314-482: The horse could pull with a force of 180 pounds-force (800 N). So: Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds (31,070 J) per minute. John Desaguliers had previously suggested 44,000 foot-pounds (59,656 J) per minute, and Thomas Tredgold suggested 27,500 foot-pounds (37,285 J) per minute. "Watt found by experiment in 1782 that

7420-635: The implementation of the EU Directive 80/181/EEC on 1 January 2010, the use of horsepower in the EU is permitted only as a supplementary unit. The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend : The idea was later used by James Watt to help market his improved steam engine. He had previously agreed to take royalties of one-third of

7526-448: The limit. In that legend, Watt accepted the challenge and built a machine that was actually even stronger than the figure achieved by the brewer, and the output of that machine became the horsepower. In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse. Citing measurements made at

7632-712: The majority of mixed ancestry, and because areas where people reported "American" ancestry were the places where, historically, Scottish and Scotch-Irish Protestants settled in North America (that is: along the North American coast, Appalachia , and the Southeastern United States ). Scottish Americans descended from nineteenth-century Scottish emigrants tend to be concentrated in the West, while many in New England are

7738-399: The market appeared to be rising. The problem was caused by the index being recalculated thousands of times daily, and always being truncated (rounded down) to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating the index for the same period using rounding to the nearest thousandth rather than truncation corrected the index value from 524.811 up to 1098.892. For

7844-426: The more common round half up . If the fractional part of x is exactly 0.5, then y = x − 0.5 For example, 23.5 gets rounded to 23, and −23.5 gets rounded to −24. Some programming languages (such as Java and Python) use "half down" to refer to round half toward zero rather than round half toward negative infinity . One may also round half toward zero (or round half away from infinity ) as opposed to

7950-502: The origin of the engine in question. DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one metre in one second: 75 kg × 9.80665 m/s × 1 m / 1 s = 75  kgf ⋅m/s = 1 PS. This is equivalent to 735.49875 W, or 98.6% of an imperial horsepower. In 1972, the PS was replaced by

8056-587: The people, also known as the Gaels , in the Kingdom of Dál Riata, in the western edge of Scotland. Bede used the word natio (nation) for the Scots, where he often refers to other peoples, such as the Picts, with the word gens (race). In the 10th-century Anglo-Saxon Chronicle , the word Scot is mentioned as a reference to the "Land of the Gaels". The word Scottorum was again used by an Irish king in 1005: Imperator Scottorum

8162-478: The period spanning the 16th century to the 18th century, sociologist Ian Carter's research into marriage patterns found little intermarrying between the groups. Today, Scotland has a population of just over five million people, the majority of whom consider themselves Scottish. It is estimated around 40 million people worldwide claim Scottish ancestry, particularly in Australia , New Zealand , continental Europe ,

8268-415: The political practicalities of nation building . Academics have explored how 15th and 16th-century Scottish poets and orators, such as Blind Harry , constructed terms such as 'trew Scottis' in an effort to diminish differences between the ethnic groups living within Scotland in the popular consciousness. A 1974 International Political Science Association report defined this ethnic plurality in Scotland as

8374-515: The population of Scotland, where 4,459,071 or 88.09% of people identified as ethnic Scottish in the 2001 Census. The number of Americans with a Scottish ancestor is estimated to be between 9 and 25 million (up to 8.3% of the total US population), and "Scotch-Irish", 27 to 30 million (up to 10% of the total US population), but these subgroups overlap and are often not distinguishable. The majority of Scotch-Irish originally came from Lowland Scotland and Northern England before migrating to

8480-670: The power generated can be calculated. To determine the maximum power available, a controllable load is required; it is normally a second locomotive with its brakes applied, in addition to a static load. If the drawbar force ( F ) is measured in pounds-force (lbf) and speed ( v ) is measured in miles per hour (mph), then the drawbar power ( P ) in horsepower (hp) is { P } h p = { F } l b f { v } m p h 375 . {\displaystyle \{P\}_{\mathrm {hp} }={\frac {\{F\}_{\mathrm {lbf} }\{v\}_{\mathrm {mph} }}{375}}.} Example: How much power

8586-567: The preferred term is Scots . Many Scottish people find the term Scotch to be offensive when applied to people. The Oxford Dictionary describes Scotch as an old-fashioned term for "Scottish". In the Early Middle Ages , Scotland saw several ethnic or cultural groups mentioned in contemporary sources, namely the Picts , the Gaels , the Britons , and the Angles , with the last of these settling in

8692-501: The protection offered by King Stephen in the Royal Grant of 1576, a district in Kraków was assigned to Scottish immigrants. Records from 1592 mention Scots settlers who were granted citizenship of Kraków give their employment as traders or merchants. Fees for citizenship ranged from 12 Polish florins to a musket and gunpowder, or an undertaking to marry within a year and a day of acquiring

8798-671: The province of Ulster in Ireland (see Plantation of Ulster ) and thence, beginning about five generations later, to North America in large numbers during the 18th century. Several Presidents of the United States have claimed Scottish ancestry or Scotch-Irish ancestry, including James Monroe through his great-great-grandfather Patrick Andrew Monroe emigrated to America, Andrew Jackson , Theodore Roosevelt , Franklin D. Roosevelt , Harry S. Truman , Lyndon B. Johnson , Richard Nixon , Ronald Reagan , Bill Clinton , George W. Bush and Donald Trump , whose mother, Mary Anne MacLeod Trump ,

8904-538: The question and the numerous responses for "Canadian" do not give an accurate figure for numerous groups, particularly those of British Isles origins. Scottish-Canadians are the 3rd biggest ethnic group in Canada. Scottish culture has particularly thrived in the Canadian province of Nova Scotia ( Latin for "New Scotland"). There, in Cape Breton , where both lowland and highland Scots settled in large numbers, Canadian Gaelic

9010-531: The rounding errors by all values, with the omission of those having 0.5 fractional part, would statistically compensate each other. This means that the expected (average) value of the rounded numbers is equal to the expected value of the original numbers when numbers with fractional part 0.5 from the set are removed. In practice, floating-point numbers are typically used, which have even more computational nuances because they are not equally spaced. One may round half up (or round half toward positive infinity ),

9116-540: The same as round-away-from-zero, and round-up is the same as round-toward-zero. In any case, if x is an integer, y is just x . Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in 1982. It was initially set at 1000.000 (three decimal places of accuracy), and after 22 months had fallen to about 520, although

9222-478: The same value). In the general case of a discrete range, they are piecewise constant functions . Typical rounding problems include: The most basic form of rounding is to replace an arbitrary number by an integer. All the following rounding modes are concrete implementations of an abstract single-argument "round()" procedure. These are true functions (with the exception of those that use randomness). These four methods are called directed rounding to an integer , as

9328-406: The savings in coal from the older Newcomen steam engines . This royalty scheme did not work with customers who did not have existing steam engines but used horses instead. Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet (3.7 m) in radius; therefore, the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that

9434-421: The size of the engine; but as of 2000, many countries changed over to systems based on CO 2 emissions, so are not directly comparable to older ratings. The Citroën 2CV is named for its French fiscal horsepower rating, "deux chevaux" (2CV). Nameplates on electrical motors show their power output, not the power input (the power delivered at the shaft, not the power consumed to drive the motor). This power output

9540-569: The south-east of the country. King Edgar divided the Kingdom of Northumbria between Scotland and England; at least, most medieval historians now accept the 'gift' by Edgar. In any case, after the later Battle of Carham the Scottish kingdom encompassed many English people, with even more quite possibly arriving after the Norman invasion of England in 1066. South-east of the Firth of Forth , then in Lothian and

9646-456: The southeast of the country. Culturally, these peoples are grouped according to language. Most of Scotland until the 13th century spoke Celtic languages , and these included, at least initially, the Britons , as well as the Gaels and the Picts . Germanic peoples included the Angles of Northumbria , who settled in south-eastern Scotland in the region between the Firth of Forth to the north and

9752-468: The southern part of the country and Highland Scots in the north - that differ from one another ethnically, culturally, and linguistically ... Lowlanders differ from Highlanders in their ethnic origin. While Highland Scots are of Celtic (Gaelic) descent, Lowland Scots are descended from people of Germanic stock. During the seventh century C.E., settlers of Germanic tribes of Angles moved from Northumbria in present-day northern England and southeastern Scotland to

9858-406: The square root of the number of operations rather than linearly. However, this rule distorts the distribution by increasing the probability of evens relative to odds. Typically this is less important than the biases that are eliminated by this method. One may also round half to odd , a similar tie-breaking rule to round half to even. In this approach, if the fractional part of x is 0.5, then y

9964-567: The term Scotch has also been used for Scottish people, now primarily outwith Scotland. People of Scottish descent live in many countries. Emigration, influenced by factors such as the Highland and Lowland Clearances , Scottish emigration to various locales throughout the British Empire , and latterly industrial decline and unemployment, have resulted in the spread of Scottish languages and culture . Large populations of Scottish people settled

10070-709: The time. Literacy rates of the Scottish immigrants ran at 90–95%. By 1860, Scots made up 50% of the ethnic composition of Western Victoria , Adelaide , Penola and Naracoorte . Other settlements in New South Wales included New England , the Hunter Valley and the Illawarra . Much settlement followed the Highland Potato Famine , Highland Clearances and the Lowland Clearances of the mid-19th century. In

10176-502: The transmission of the power from its generation to its application. A number of names are used for the power developed at various stages in this process, but none is a clear indicator of either the measurement system or definition used. In general: All the above assumes that no power inflation factors have been applied to any of the readings. Engine designers use expressions other than horsepower to denote objective targets or performance, such as brake mean effective pressure (BMEP). This

10282-472: The wider New Zealand public. In so doing, the Games gave Scots a path to cultural integration as Scottish New Zealanders. In the 1961 census there were 47,078 people living in New Zealand who were born in Scotland; in the 2013 census there were 25,953 in this category. Many people of Scottish descent live in other parts of the United Kingdom. In Ulster particularly the colonial policies of James VI , known as

10388-452: The words Scot and Scottish are applied mainly to inhabitants of Scotland. The possible ancient Irish connotations are largely forgotten. The language known as Ulster Scots , spoken in parts of northeastern Ireland, is the result of 17th- and 18th-century immigration to Ireland from Scotland. In the English language, the word Scotch is a term to describe a thing from Scotland, such as Scotch whisky . However, when referring to people,

10494-555: The world and the second-largest population of Scottish descendants, after the United States. Originally the Romans used Scotia to refer to Ireland. The Venerable Bede ( c.  672 or 673 – 27 May, 735) uses the word Scottorum for the nation from Ireland who settled part of the Pictish lands: " Scottorum nationem in Pictorum parte recipit ." This can be inferred to mean the arrival of

10600-713: Was Gaelic-speaking into the 20th century, as were some small communities in parts of the Central Highlands). From 1200 to 1500, the Early Scots language spread across the lowland parts of Scotland between Galloway and the Highland line, being used by Barbour in his historical epic The Brus in the late 14th century in Aberdeen. From 1500 on, Scotland was commonly divided by language into two groups of people, Gaelic-speaking " Highlanders " (the language formerly called Scottis by English speakers and known by many Lowlanders in

10706-535: Was born in Tong on the Isle of Lewis . As the third-largest ethnic group in Canada and amongst the first Europeans to settle in the country, Scottish people have made a large impact on Canadian culture since colonial times. According to the 2011 Census of Canada , the number of Canadians claiming full or partial Scottish descent is 4,714,970, or 15.10% of the nation's total population. Many respondents may have misunderstood

10812-531: Was instituted by the Royal Automobile Club and was used to denote the power of early 20th-century British cars. Many cars took their names from this figure (hence the Austin Seven and Riley Nine), while others had names such as "40/50 hp", which indicated the RAC figure followed by the true measured power. Taxable horsepower does not reflect developed horsepower; rather, it is a calculated figure based on

10918-475: Was named as a tribute to Edinburgh by the city's Scottish founders. Scottish migration to New Zealand dates back to the earliest period of European colonisation, with a large proportion of Pākehā New Zealanders being of Scottish descent. However, identification as "British" or "European" New Zealanders can sometimes obscure their origin. Many Scottish New Zealanders also have Māori or other non-European ancestry. The majority of Scottish immigrants settled on

11024-469: Was sometimes applied in British colonies as well, such as Kenya (British East Africa) . where Since taxable horsepower was computed based on bore and number of cylinders, not based on actual displacement, it gave rise to engines with "undersquare" dimensions (bore smaller than stroke), which tended to impose an artificially low limit on rotational speed , hampering the potential power output and efficiency of

11130-450: Was the title given to Brian Bóruma by his notary, Mael Suthain, in the Book of Armagh . This style was subsequently copied by the Scottish kings. Basileus Scottorum appears on the great seal of King Edgar (1074–1107). Alexander I ( c.  1078 –1124) used the words Rex Scottorum on his great seal, as did many of his successors up to and including James VI . In modern times,

11236-408: Was traditionally Gaelic-speaking but replaced with Doric in the 19th century. Today, immigrants have brought other languages, such as Polish , Punjabi and Urdu , but almost every adult throughout Scotland is fluent in the English language. Historian Susan Reynolds has put forward how, since the Middle Ages , there have been attempts to obfuscate the ethnic plurality of Scottish people due to

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