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99-523: Hardraw Force ( OS grid ref: SD869917 ) is a waterfall on Hardraw Beck in Hardraw Scar, a wooded ravine just outside the hamlet of Hardraw , 0.9 miles (1.5 km) north of the town of Hawes , Wensleydale , in the Yorkshire Dales . The Pennine Way long distance footpath passes close by. Comprising a single drop of 100 feet (30 m) from a rocky overhang, Hardraw Force

198-615: A {\displaystyle a} is the radius of the sphere, λ {\displaystyle \lambda } is the longitude from the central meridian of the projection (here taken as the Greenwich meridian at λ = 0 {\displaystyle \lambda =0} ) and φ {\displaystyle \varphi } is the latitude. Note that λ {\displaystyle \lambda } and φ {\displaystyle \varphi } are in radians (obtained by multiplying

297-546: A δ φ {\displaystyle a\,\delta \varphi } where a {\displaystyle a} is the radius of the sphere and φ {\displaystyle \varphi } is in radian measure. The lines PM and KQ are arcs of parallel circles of length ( a cos ⁡ φ ) δ λ {\displaystyle (a\cos \varphi )\delta \lambda } with λ {\displaystyle \lambda } in radian measure. In deriving

396-419: A meridian distance of about 10 km and over an east-west line of about 8 km. Thus a plan of New York City accurate to one metre or a building site plan accurate to one millimetre would both satisfy the above conditions for the neglect of curvature. They can be treated by plane surveying and mapped by scale drawings in which any two points at the same distance on the drawing are at the same distance on

495-400: A point property of the projection at P it suffices to take an infinitesimal element PMQK of the surface: in the limit of Q approaching P such an element tends to an infinitesimally small planar rectangle. Normal cylindrical projections of the sphere have x = a λ {\displaystyle x=a\lambda } and y {\displaystyle y} equal to

594-532: A clear distinction of the intrinsic projection scaling and the reduction scaling. From this point we ignore the RF and work with the projection map. Consider a small circle on the surface of the Earth centred at a point P at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } . Since the point scale varies with position and direction

693-656: A close, arranging mountain-top parties with enormous plum puddings . The British Geological Survey was founded in 1835 as the Ordnance Geological Survey under Henry De la Beche , and remained a branch of the Ordnance Survey until 1965. At the same time, the uneven quality of the English and Scottish maps was being improved by engravers under Benjamin Baker . By the time Colby retired in 1846,

792-428: A constant separation on the ground. While a map may display a graphical bar scale, the scale must be used with the understanding that it will be accurate on only some lines of the map. (This is discussed further in the examples in the following sections.) Let P be a point at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } on

891-531: A fire in the Tower of London , the headquarters of the survey was moved to Southampton taking over buildings previously occupied by a military orphanage (the Royal Military Asylum ) in 1841, and Yolland was put in charge, but Hall sent him off to Ireland so that when Hall left in 1854 Yolland was again passed over in favour of Major Henry James . Hall was enthusiastic about extending the survey of

990-471: A function of latitude only. Therefore, the infinitesimal element PMQK on the sphere projects to an infinitesimal element P'M'Q'K' which is an exact rectangle with a base δ x = a δ λ {\displaystyle \delta x=a\,\delta \lambda } and height  δ y {\displaystyle \delta y} . By comparing the elements on sphere and projection we can immediately deduce expressions for

1089-479: A large range of paper maps and digital mapping products. The Ordnance Survey's flagship digital product, launched in November 2001, is OS MasterMap , a database that records, in one continuous digital map, every fixed feature of Great Britain larger than a few metres. Every feature is given a unique TOID (TOpographical IDentifier), a simple identifier that includes no semantic information. Typically, each TOID

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1188-510: A nascent coordinate system for identifying locations were hinted by ancient Chinese astronomers that divided the sky into various sectors or lunar lodges. The Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period created a set of large-area maps that were drawn to scale. He produced a set of principles that stressed the importance of consistent scaling, directional measurements, and adjustments in land measurements in

1287-585: A new survey based on Airy 's spheroid in 1858, completing the Principal Triangulation . The following year, he completed an initial levelling of the country. After the Ordnance Survey published its first large-scale maps of Ireland in the mid-1830s, the Tithe Act 1836 led to calls for a similar six-inch to the mile survey in England and Wales . Official procrastination followed, but

1386-501: A proportion of its profits to the Treasury. In 2010, OS announced that printing and warehouse operations were to be outsourced, ending over 200 years of in-house printing. The Frome-based firm Butler, Tanner and Dennis (BT&D) secured its printing contract. As already stated, large-scale maps had not been printed at the Ordnance Survey since the common availability of geographical information systems (GISs), but, until late 2010,

1485-527: A ratio: if the scale is an inch to two miles and the map user can see two villages that are about two inches apart on the map, then it is easy to work out that the villages are about four miles apart on the ground. A lexical scale may cause problems if it expressed in a language that the user does not understand or in obsolete or ill-defined units. For example, a scale of one inch to a furlong (1:7920) will be understood by many older people in countries where Imperial units used to be taught in schools. But

1584-418: A scale of one pouce to one league may be about 1:144,000, depending on the cartographer 's choice of the many possible definitions for a league, and only a minority of modern users will be familiar with the units used. A small-scale map cover large regions, such as world maps , continents or large nations. In other words, they show large areas of land on a small space. They are called small scale because

1683-477: A second edition of the town plans: by 1909 only fourteen places had paid for updates. The review determined that revision of 1:2500 mapping should proceed apace. The most detailed mapping of London was the OS's 1:1056 survey between 1862 and 1872, which took 326 sheets to cover the capital; a second edition (which needed 759 sheets because of urban expansion) was completed and brought out between 1891 and 1895. London

1782-453: A separation along the line to the bar scale does not give a distance related to the true distance in any simple way. (But see addendum ). Even if a distance along this line of constant planar angle could be worked out, its relevance is questionable since such a line on the projection corresponds to a complicated curve on the sphere. For these reasons bar scales on small-scale maps must be used with extreme caution. The Mercator projection maps

1881-441: A separation from a parallel to the bar scale we must divide the bar scale distance by this factor to obtain the distance between the points when measured along the parallel (which is not the true distance along a great circle ). On a line at a bearing of say 45 degrees ( β = 45 ∘ {\displaystyle \beta =45^{\circ }} ) the scale is continuously varying with latitude and transferring

1980-431: A smaller area. Maps that show an extensive area are "small scale" maps. This can be a cause of confusion. Mapping large areas causes noticeable distortions because it significantly flattens the curved surface of the earth. How distortion gets distributed depends on the map projection . Scale varies across the map , and the stated map scale is only an approximation. This is discussed in detail below. The region over which

2079-407: A town plan, then a single value can be used as the scale without causing measurement errors. In maps covering larger areas, or the whole Earth, the map's scale may be less useful or even useless in measuring distances. The map projection becomes critical in understanding how scale varies throughout the map. When scale varies noticeably, it can be accounted for as the scale factor. Tissot's indicatrix

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2178-433: A traditional 1:1250 scale paper map. Scale (map) The first way is the ratio of the size of the generating globe to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected . The ratio of the Earth's size to the generating globe's size is called the nominal scale (also called principal scale or representative fraction ). Many maps state

2277-583: Is associated with a polygon that represents the area on the ground that the feature covers, in National Grid coordinates. OS MasterMap is offered in themed layers, each linked to a number of TOIDs. In September 2010, the layers were: Topography: Integrated transport network: Imagery Address: Address 2: ITN was withdrawn in April 2019 and replaced by OS MasterMap Highways Network The Address layers were withdrawn in about 2016 with

2376-435: Is claimed to be England's highest unbroken waterfall – at least discounting underground falls. The underground waterfall inside nearby Gaping Gill on the western flank of Ingleborough has an unbroken fall of more than 300 feet (91 m). Geologically the bed of the river and plunge pool is shale; on top of that is sandstone and the top layer is carboniferous limestone. It is on private land but public access to

2475-422: Is commonly illustrated by the impossibility of smoothing an orange peel onto a flat surface without tearing and deforming it. The only true representation of a sphere at constant scale is another sphere such as a globe . Given the limited practical size of globes, we must use maps for detailed mapping. Maps require projections. A projection implies distortion: A constant separation on the map does not correspond to

2574-488: Is conformal since it is constructed to preserve angles and its scale factor is isotropic, a function of latitude only: Mercator does preserve shape in small regions. Definition: on a conformal projection with an isotropic scale, points which have the same scale value may be joined to form the isoscale lines . These are not plotted on maps for end users but they feature in many of the standard texts. (See Snyder pages 203—206.) There are two conventions used in setting down

2673-468: Is no standard: The terms are sometimes used in the absolute sense of the table, but other times in a relative sense. For example, a map reader whose work refers solely to large-scale maps (as tabulated above) might refer to a map at 1:500,000 as small-scale. In the English language, the word large-scale is often used to mean "extensive". However, as explained above, cartographers use the term "large scale" to refer to less extensive maps – those that show

2772-505: Is often used to illustrate the variation of point scale across a map. The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was understood by the second century BC. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as counting rods , carpenter's square 's, plumb lines , compasses for drawing circles, and sighting tubes for measuring inclination. Reference frames postulating

2871-439: Is said to be conformal if the angle between a pair of lines intersecting at a point P is the same as the angle between the projected lines at the projected point P', for all pairs of lines intersecting at point P. A conformal map has an isotropic scale factor. Conversely isotropic scale factors across the map imply a conformal projection. Isotropy of scale implies that small elements are stretched equally in all directions, that

2970-459: Is the shape of a small element is preserved. This is the property of orthomorphism (from Greek 'right shape'). The qualification 'small' means that at some given accuracy of measurement no change can be detected in the scale factor over the element. Since conformal projections have an isotropic scale factor they have also been called orthomorphic projections . For example, the Mercator projection

3069-524: Is the site of an annual brass-band contest. The contest attracts bands from all over the North of England and is a popular event amongst players and audiences alike. The gorge is alongside the Pennine Way . Access to the gorge is via the nearby public house. In 1899 a great flood came racing over the waterfall and into Hardraw itself, ruining buildings and uprooting coffins from the graveyard. The lip of

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3168-452: Is useful to note that The following examples illustrate three normal cylindrical projections and in each case the variation of scale with position and direction is illustrated by the use of Tissot's indicatrix . The equirectangular projection , also known as the Plate Carrée (French for "flat square") or (somewhat misleadingly) the equidistant projection, is defined by where

3267-702: The British Library . Roy later had an illustrious career in the Royal Engineers (RE), rising to the rank of General, and he was largely responsible for the British share of the work in determining the relative positions of the French and British royal observatories. This work was the starting point of the Principal Triangulation of Great Britain (1783–1853), and led to the creation of the Ordnance Survey itself. Roy's technical skills and leadership set

3366-722: The Copyright Libraries hold complete or near-complete collections of pre-digital OS mapping. The origins of the Ordnance Survey lie in the aftermath of the Jacobite rising of 1745 . Prince William, Duke of Cumberland realised that the British Army did not have a good map of the Scottish Highlands to locate Jacobite dissenters such as Simon Fraser, 11th Lord Lovat so that they could be put on trial. In 1747, Lieutenant-Colonel David Watson proposed

3465-629: The Department for Business, Energy and Industrial Strategy (BEIS) appointed Steve Blair as the Chief Executive of the Ordnance Survey. The Ordnance Survey supported the launch of the Slow Ways initiative, which encourages users to walk on lesser used paths between UK towns. On 7 February 2023, ownership of Ordnance Survey Ltd passed to the newly formed Department for Science, Innovation and Technology . The Ordnance Survey produces

3564-619: The OS Explorer and OS Landranger series were printed in Maybush. In April 2009 building began of a new head office in Adanac Park on the outskirts of Southampton. By 10 February 2011 virtually all staff had relocated to the new "Explorer House" building and the old site had been sold off and redeveloped. Prince Philip officially opened the new headquarters building on 4 October 2011. On 22 January 2015 plans were announced for

3663-553: The Ordnance Survey National Grid 1:1250s, 1:2500s and 1:10,560s after the Second World War. During World War I, the Ordnance Survey was involved in preparing maps of France and Belgium . During World War II, many more maps were created, including: After the war, Colonel Charles Close , then Director General, developed a strategy using covers designed by Ellis Martin to increase sales in

3762-644: The Pilgrims' Way in the North Downs labelled the wrong route, but the name stuck. Similarly, the spelling of Scafell and Scafell Pike copied an error on an earlier map, and was retained as this was the name of a corner of one of the Principal Triangles , despite "Scawfell" being the almost universal form at the time. Colby believed in leading from the front, travelling with his men, helping to build camps and, as each survey session drew to

3861-476: The parallel scale is denoted by k ( λ , φ ) {\displaystyle k(\lambda ,\,\varphi )} . Definition: if the point scale depends only on position, not on direction, we say that it is isotropic and conventionally denote its value in any direction by the parallel scale factor k ( λ , φ ) {\displaystyle k(\lambda ,\varphi )} . Definition: A map projection

3960-534: The representative fraction is relatively small. Large-scale maps show smaller areas in more detail, such as county maps or town plans might. Such maps are called large scale because the representative fraction is relatively large. For instance a town plan, which is a large-scale map, might be on a scale of 1:10,000, whereas the world map, which is a small scale map, might be on a scale of 1:100,000,000. The following table describes typical ranges for these scales but should not be considered authoritative because there

4059-498: The 1:10,560 "six inches to the mile " scale in the 1950s.) These large scale maps are typically used in professional land-use contexts and were available as sheets until the 1980s, when they were digitised . Small-scale mapping for leisure use includes the 1:25,000 "Explorer" series, the 1:50,000 "Landranger" series and the 1:250,000 road maps. These are still available in traditional sheet form. Ordnance Survey maps remain in copyright for 50 years after their publication. Some of

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4158-454: The Board received the newer Ramsden theodolite (an improved successor to the one that Roy had used in 1784), and work began on mapping southern Great Britain using a 5 mi (8 km) baseline on Hounslow Heath that Roy himself had previously measured; it crosses the present Heathrow Airport . In 1991, Royal Mail marked the bicentenary by issuing a set of postage stamps featuring maps of

4257-428: The Earth's surface) and bearing (on the map) is not universally observed, many writers using the terms almost interchangeably. Definition: the point scale at P is the ratio of the two distances P'Q' and PQ in the limit that Q approaches P. We write this as where the notation indicates that the point scale is a function of the position of P and also the direction of the element PQ. Definition: if P and Q lie on

4356-518: The Kentish village of Hamstreet . In 1801, the first one-inch-to-the-mile (1:63,360 scale) map was published, detailing the county of Kent , with Essex following shortly afterwards. The Kent map was published privately and stopped at the county border, while the Essex maps were published by the Ordnance Survey and ignored the county border, setting the trend for future Ordnance Survey maps. During

4455-458: The RF (or principal scale) gives the actual circumference of the Earth. The bar scale on the map is also drawn at the true scale so that transferring a separation between two points on the equator to the bar scale will give the correct distance between those points. The same is true on the meridians. On a parallel other than the equator the scale is sec ⁡ φ {\displaystyle \sec \varphi } so when we transfer

4554-595: The Tissot diagram each infinitesimal circular element preserves its shape but is enlarged more and more as the latitude increases. Lambert's equal area projection maps the sphere to a finite rectangle by the equations where a, λ {\displaystyle \lambda } and φ {\displaystyle \varphi } are as in the previous example. Since y ′ ( φ ) = cos ⁡ φ {\displaystyle y'(\varphi )=\cos \varphi }

4653-483: The actual printed (or viewed) maps. If the definition of point scale in the previous section is in terms of the projection map then we can expect the scale factors to be close to unity. For normal tangent cylindrical projections the scale along the equator is k=1 and in general the scale changes as we move off the equator. Analysis of scale on the projection map is an investigation of the change of k away from its true value of unity. Actual printed maps are produced from

4752-522: The centre of Southampton (made worse by the bomb damage of the Second World War). The bombing during the Blitz devastated Southampton in November 1940 and destroyed most of the Ordnance Survey's city centre offices . Staff were dispersed to other buildings and to temporary accommodation at Chessington and Esher, Surrey, where they produced 1:25000 scale maps of France, Italy, Germany and most of

4851-481: The city's court complex. The new head office building was designed by the Ministry of Public Building and Works for 4000 staff, including many new recruits who were taken on in the late 1960s and early 1970s as draughtsmen and surveyors. The buildings originally contained factory-floor space for photographic processes such as heliozincography and map printing, as well as large buildings for storing flat maps. Above

4950-445: The company's annual revenue. It produces digital map data, online route planning and sharing services and mobile apps, plus many other location-based products for business, government and consumers. Ordnance Survey mapping is usually classified as either " large-scale " (in other words, more detailed) or "small-scale". The Survey's large-scale mapping comprises 1:2,500 maps for urban areas and 1:10,000 more generally. (The latter superseded

5049-563: The compilation of a map of the Highlands to help in pacifying the region. In response, King George II charged Watson with making a military survey of the Highlands under the command of the Duke of Cumberland. Among Watson's assistants were William Roy , Paul Sandby and John Manson. The survey was produced at a scale of 1 inch to 1,000 yards (1:36,000) and included " the Duke of Cumberland's Map " (primarily by Watson and Roy), now held in

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5148-634: The degree measure by a factor of π {\displaystyle \pi } /180). The longitude λ {\displaystyle \lambda } is in the range [ − π , π ] {\displaystyle [-\pi ,\pi ]} and the latitude φ {\displaystyle \varphi } is in the range [ − π / 2 , π / 2 ] {\displaystyle [-\pi /2,\pi /2]} . Since y ′ ( φ ) = 1 {\displaystyle y'(\varphi )=1}

5247-563: The development of the railways added to pressure that resulted in the Ordnance Survey Act 1841 ( 4 & 5 Vict. c. 30). This granted a right to enter property for the purpose of the survey. Following a fire at its headquarters at the Tower of London in 1841 the Ordnance Survey relocated to a site in Southampton and was in disarray for several years, with arguments about which scales to use. Major-General Sir Henry James

5346-522: The early 1940s, the OS produced many "restricted" versions of the County Series maps and other War Department sheets for War Office purposes, in a variety of large scales that included details of military significance such as dockyards, naval installations, fortifications and military camps. Apart from a brief period during the disarmament talks of the 1930s, these areas were left blank or incomplete on standard maps. The War Department 1:2500s, unlike

5445-407: The earth can be regarded as flat depends on the accuracy of the survey measurements. If measured only to the nearest metre, then curvature of the earth is undetectable over a meridian distance of about 100 kilometres (62 mi) and over an east-west line of about 80 km (at a latitude of 45 degrees). If surveyed to the nearest 1 millimetre (0.039 in), then curvature is undetectable over

5544-433: The equations of any given projection. For example, the equirectangular cylindrical projection may be written as Here we shall adopt the first of these conventions (following the usage in the surveys by Snyder). Clearly the above projection equations define positions on a huge cylinder wrapped around the Earth and then unrolled. We say that these coordinates define the projection map which must be distinguished logically from

5643-620: The falls is available through a turnstile behind the Green Dragon Inn. The current cost is £4 per adult, £2.50 per child. Access behind the falls is now prohibited. Hardraw Scar ( 54°18′58″N 2°12′18″W  /  54.316°N 2.205°W  / 54.316; -2.205 ) is a limestone gorge behind the Green Dragon inn at Hardraw near Hawes in the Yorkshire Dales . It is a natural amphitheatre and in September

5742-564: The falls: the Hawdraw Bash is a folk-rock concert in early July and the Hardraw Gathering is a three-day festival of traditional music at the end of July. Ordnance Survey The Ordnance Survey ( OS ) is the national mapping agency for Great Britain. The agency's name indicates its original military purpose (see ordnance and surveying ), which was to map Scotland in the wake of the Jacobite rising of 1745 . There

5841-403: The ground. True ground distances are calculated by measuring the distance on the map and then multiplying by the inverse of the scale fraction or, equivalently, simply using dividers to transfer the separation between the points on the map to a bar scale on the map. As proved by Gauss ’s Theorema Egregium , a sphere (or ellipsoid) cannot be projected onto a plane without distortion. This

5940-539: The high standard for which the Ordnance Survey became known. Work was begun in earnest in 1790 under Roy's supervision, when the Board of Ordnance (a predecessor of part of the modern Ministry of Defence ) began a national military survey starting with the south coast of England. Roy's birthplace near Carluke in South Lanarkshire is today marked by a memorial in the form of a large OS trig point . By 1791,

6039-483: The industrial areas were extensive office areas. The complex was notable for its concrete mural. Celestial , by sculptor Keith McCarter and the concrete elliptical paraboloid shell roof over the staff restaurant building. In 1995, the Ordnance Survey digitised the last of about 230,000 maps, making the United Kingdom the first country in the world to complete a programme of large-scale electronic mapping. By

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6138-516: The information now being available in the AddressBase products – so as of 2020, MasterMap consists of Topography and Imagery. Pricing of licenses to OS MasterMap data depends on the total area requested, the layers licensed, the number of TOIDs in the layers, and the period in years of the data usage. OS MasterMap can be used to generate maps for a vast array of purposes and maps can be printed from OS MasterMap data with detail equivalent to

6237-438: The late 1990s technological developments had eliminated the need for vast areas for storing maps and for making printing plates by hand. Although there was a small computer section at the Ordnance Survey in the 1960s, the digitising programme had replaced the need for printing large-scale maps, while computer-to-plate technology (in the form of a single machine) had also rendered the photographic platemaking areas obsolete. Part of

6336-400: The latter was converted into a new conference centre in 2000, which was used for internal events and also made available for external organisations to hire. The Ordnance Survey became an Executive Agency in 1990, making the organisation independent of ministerial control. In 1999 the agency was designated a trading fund , required to cover its costs by charging for its products and to remit

6435-611: The leisure market. In 1920 O. G. S. Crawford was appointed Archaeology Officer and played a prominent role in developing the use of aerial photography to deepen understanding of archaeology. In 1922, devolution in Northern Ireland led to the creation of the Ordnance Survey of Northern Ireland (OSNI) and the independence of the Irish Free State led to the creation of the Ordnance Survey of Ireland , so

6534-402: The major axis to the minor axis is sec ⁡ φ {\displaystyle \sec \varphi } . Clearly the area of the ellipse increases by the same factor. It is instructive to consider the use of bar scales that might appear on a printed version of this projection. The scale is true (k=1) on the equator so that multiplying its length on a printed map by the inverse of

6633-550: The map. The distortion ellipse is known as Tissot's indicatrix . The example shown here is the Winkel tripel projection , the standard projection for world maps made by the National Geographic Society . The minimum distortion is on the central meridian at latitudes of 30 degrees (North and South). (Other examples ). The key to a quantitative understanding of scale is to consider an infinitesimal element on

6732-409: The mile) for Land Valuation and Inland Revenue purposes: the increased scale was to provide space for annotations. About a quarter of these 1:1250s were marked "Partially revised 1912/13". In areas where there were no further 1:2500s, these partially revised "fifty inch" sheets represent the last large-scale revision (larger than six-inch) of the County Series. The County Series mapping was superseded by

6831-486: The next 20 years, about a third of England and Wales was mapped at the same scale (see Principal Triangulation of Great Britain ) under the direction of William Mudge , as other military matters took precedence. It took until 1823 to re-establish the relationship with the French survey made by Roy in 1787. By 1810, one-inch-to-the-mile maps of most of the south of England were completed, but they were withdrawn from sale between 1811 and 1816 because of security fears. By 1840,

6930-438: The nominal scale and may even display a bar scale (sometimes merely called a "scale") to represent it. The second distinct concept of scale applies to the variation in scale across a map. It is the ratio of the mapped point's scale to the nominal scale. In this case 'scale' means the scale factor (also called point scale or particular scale ). If the region of the map is small enough to ignore Earth's curvature, such as in

7029-686: The north of England to a scale of 1:2,500. In 1855, the Board of Ordnance was abolished and the Ordnance Survey was placed under the War Office together with the Topographical Survey and the Depot of Military Knowledge. Eventually in 1870 it was transferred to the Office of Works . The primary triangulation of the United Kingdom of Roy, Mudge and Yolland was completed by 1841, but was greatly improved by Alexander Ross Clarke who completed

7128-456: The one-inch survey had covered all of Wales and all but the six northernmost counties of England. Surveying was hard work. For instance, Major Thomas Colby , the longest-serving Director General of the Ordnance Survey, walked 586 mi (943 km) in 22 days on a reconnaissance in 1819. In 1824, Colby and most of his staff moved to Ireland to work on a six-inches-to-the-mile (1:10,560) valuation survey. The survey of Ireland, county by county,

7227-476: The organisation to move from a trading fund model to a government-owned limited company , with the move completed in April 2015. The organisation remains fully owned by the UK government and retains many of the features of a public organisation. In September 2015 the history of the Ordnance Survey was the subject of a BBC Four TV documentary entitled A Very British Map: The Ordnance Survey Story . On 10 June 2019

7326-535: The original Ordnance Survey pulled its coverage back to Great Britain. In 1935, the Davidson Committee was established to review the Ordnance Survey's future. The new Director General, Major-General Malcolm MacLeod , started the retriangulation of Great Britain , an immense task involving the erection of concrete triangulation pillars ("trig points") on prominent hilltops as infallible positions for theodolites. Each measurement made by theodolite during

7425-486: The previous section gives For the calculation of the point scale in an arbitrary direction see addendum . The figure illustrates the Tissot indicatrix for this projection. On the equator h=k=1 and the circular elements are undistorted on projection. At higher latitudes the circles are distorted into an ellipse given by stretching in the parallel direction only: there is no distortion in the meridian direction. The ratio of

7524-417: The production of six-inch maps of Ireland was complete. This had led to a demand for similar treatment in England, and work was proceeding on extending the six-inch map to northern England, but only a three-inch scale for most of Scotland. When Colby retired, he recommended William Yolland as his successor, but he was considered too young and the less experienced Lewis Alexander Hall was appointed. After

7623-452: The projection map by a constant scaling denoted by a ratio such as 1:100M (for whole world maps) or 1:10000 (for such as town plans). To avoid confusion in the use of the word 'scale' this constant scale fraction is called the representative fraction (RF) of the printed map and it is to be identified with the ratio printed on the map. The actual printed map coordinates for the equirectangular cylindrical projection are This convention allows

7722-400: The projection of the circle on the projection will be distorted. Tissot proved that, as long as the distortion is not too great, the circle will become an ellipse on the projection. In general the dimension, shape and orientation of the ellipse will change over the projection. Superimposing these distortion ellipses on the map projection conveys the way in which the point scale is changing over

7821-410: The rest of Europe in preparation for its invasion . Until 1969, the Ordnance Survey largely remained at its Southampton city centre HQ and at temporary buildings in the suburb of Maybush nearby, when a new purpose-built headquarters was opened in Maybush adjacent to the wartime temporary buildings there. Some of the remaining buildings of the original Southampton city-centre site are now used as part of

7920-498: The retriangulation was repeated no fewer than 32 times. The Davidson Committee's final report set the Ordnance Survey on course for the 20th century. The metric national grid reference system was launched and a 1:25000-scale series of maps was introduced. The one-inch maps continued to be produced until the 1970s, when they were superseded by the 1:50000-scale series – as proposed by William Roy more than two centuries earlier. The Ordnance Survey had outgrown its site in

8019-413: The same meridian ( α = 0 ) {\displaystyle (\alpha =0)} , the meridian scale is denoted by h ( λ , φ ) {\displaystyle h(\lambda ,\,\varphi )} . Definition: if P and Q lie on the same parallel ( α = π / 2 ) {\displaystyle (\alpha =\pi /2)} ,

8118-401: The scale factors are: In the mathematical addendum it is shown that the point scale in an arbitrary direction is also equal to sec ⁡ φ {\displaystyle \sec \varphi } so the scale is isotropic (same in all directions), its magnitude increasing with latitude as sec ⁡ φ {\displaystyle \sec \varphi } . In

8217-428: The scale factors on parallels and meridians. (The treatment of scale in a general direction may be found below .) Note that the parallel scale factor k = sec ⁡ φ {\displaystyle k=\sec \varphi } is independent of the definition of y ( φ ) {\displaystyle y(\varphi )} so it is the same for all normal cylindrical projections. It

8316-455: The scene where Maid Marian catches Robin Hood bathing under a waterfall. Hardraw Force is the setting for a brass-band competition held annually on the second Sunday in September. The competition was first held in the natural amphitheatre of the falls in 1884 when six bands took part; the competition lapsed in 1927 but was revived in 1976. In recent years two other musical events have started up at

8415-521: The six-inch standard was adopted in Great Britain for the un-surveyed northern counties and the 1:1056 scale also began to be adopted for urban surveys. Between 1842 and 1895, some 400 towns were mapped at 1:500 (126 inches), 1:528 (120 inches, "10 foot scale") or 1:1056 (60 inches), with the remaining towns mapped at 1:2500 (~25 inches). In 1855, the Treasury authorised funding for 1:2500 for rural areas and 1:500 for urban areas. The 1:500 scale

8514-607: The sphere (or ellipsoid ). Let Q be a neighbouring point and let α {\displaystyle \alpha } be the angle between the element PQ and the meridian at P: this angle is the azimuth angle of the element PQ. Let P' and Q' be corresponding points on the projection. The angle between the direction P'Q' and the projection of the meridian is the bearing β {\displaystyle \beta } . In general α ≠ β {\displaystyle \alpha \neq \beta } . Comment: this precise distinction between azimuth (on

8613-461: The sphere to a rectangle (of infinite extent in the y {\displaystyle y} -direction) by the equations where a, λ {\displaystyle \lambda \,} and φ {\displaystyle \varphi \,} are as in the previous example. Since y ′ ( φ ) = a sec ⁡ φ {\displaystyle y'(\varphi )=a\sec \varphi }

8712-513: The sphere. The figure shows a point P at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } on the sphere. The point Q is at latitude φ + δ φ {\displaystyle \varphi +\delta \varphi } and longitude λ + δ λ {\displaystyle \lambda +\delta \lambda } . The lines PK and MQ are arcs of meridians of length

8811-477: The standard issue, were contoured . The de-classified sheets have now been deposited in some of the Copyright Libraries, helping to complete the map-picture of pre-Second World War Britain. From 1824, the OS began a 6-inch (1:10,560) survey of Ireland for taxation purposes but found this to be inadequate for urban areas and adopted the five-foot scale (1:1056) for Irish cities and towns. From 1840,

8910-524: The survey are to endeavour to obtain the correct orthography of the names of places by diligently consulting the best authorities within their reach. The name of each place is to be inserted as it is commonly spelt, in the first column of the name book and the various modes of spelling it used in books, writings &c. are to be inserted in the second column, with the authority placed in the third column opposite to each. Whilst these procedures generally produced excellent results, mistakes were made: for instance,

9009-416: The terrain that was being mapped. Map scales may be expressed in words (a lexical scale), as a ratio, or as a fraction. Examples are: In addition to the above many maps carry one or more (graphical) bar scales . For example, some modern British maps have three bar scales, one each for kilometres, miles and nautical miles. A lexical scale in a language known to the user may be easier to visualise than

9108-422: The two scales was completed by the 1890s, with a second edition completed in the 1890s and 1900s. From 1907 till the early 1940s, a third edition (or "second revision") was begun but never completed: only areas with significant changes on the ground were revised, many two or three times. Meanwhile, publication of the one-inch to the mile series for Great Britain was completed in 1891. From the late 19th century to

9207-464: The waterfall was demolished by the force of the water and the landowner at the time (Lord Wharncliffe) got his estate manager to repair the lip and it is now held together at the top by metal stakes. Both J. M. W. Turner and William Wordsworth visited the waterfall and both men stayed at the Green Dragon Inn. The falls were used as a location in the film Robin Hood: Prince of Thieves , in

9306-635: Was also a more general and nationwide need in light of the potential threat of invasion during the Napoleonic Wars . Since 1 April 2015, the Ordnance Survey has operated as Ordnance Survey Ltd, a government-owned company , 100% in public ownership. The Ordnance Survey Board remains accountable to the Secretary of State for Science, Innovation and Technology . It was also a member of the Public Data Group . Paper maps represent only 5% of

9405-527: Was by then Director General, and he saw how photography could be used to make maps of various scales cheaply and easily. He developed and exploited photozincography , not only to reduce the costs of map production but also to publish facsimiles of nationally important manuscripts. Between 1861 and 1864, a facsimile of the Domesday Book was issued, county by county; and a facsimile of the Gough Map

9504-543: Was completed in 1846. The suspicions and tensions it caused in rural Ireland are the subject of Brian Friel 's play Translations . Colby was not only involved in the design of specialist measuring equipment. He also established a systematic collection of place names, and reorganised the map-making process to produce clear, accurate plans. Place names were recorded in "Name Books", a system first used in Ireland. The instructions for their use were: The persons employed on

9603-457: Was considered more 'rational' than 1:528 and became known as the "sanitary scale" since its primary purpose was to support establishment of mains sewerage and water supply. However, a review of the Ordnance Survey in 1892 found that sales of the 1:500 series maps were very poor and the Treasury declined to fund their continuing maintenance, declaring that any revision or new mapping at this scale must be self-financing. Very few towns and cities saw

9702-449: Was issued in 1870. From the 1840s, the Ordnance Survey concentrated on the Great Britain " County Series ", modelled on the earlier Ireland survey. A start was made on mapping the whole country, county by county, at six inches to the mile (1:10,560). In 1854, "twenty-five inch" maps were introduced with a scale of 1:2500 (25.344 inches to the mile) and the six inch maps were then based on these twenty-five inch maps. The first edition of

9801-670: Was unusual in that land registration on transfer of title was made compulsory there in 1900. The 1:1056 sheets were partially revised to provide a basis for HM Land Registry index maps and the OS mapped the whole London County Council area (at 1:1056) at national expense. Placenames from the second edition were used in 2016 by the GB1900 project to crowd-source an open-licensed gazetteer of Great Britain. From 1911 onwards – and mainly between 1911 and 1913 – the Ordnance Survey photo-enlarged many 1:2500 sheets covering built-up areas to 1:1250 (50.688 inches to

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