Triangulation is a simple geometrically based process that makes accurate map-making possible. It works by determining the location and distance of a faraway object , by measuring angles to it from known points at either end of a fixed ,known ,baseline
It is based on a system devised over two thousand years ago by Euclid, the father of geometry . Trigonometry (the study of triangles) emerged about the third century BC . It stated that a triangle has six parts—three sides and three angles,and it postulated that given almost any three of them–three sides, two sides and one angle, or most importantly ,-one side and two angles –then the other three unknowns can be found.
Thus if we have a baseline and two angles, we can draw the triangle, and calculate not only the distance from the apex to the baseline but also the length of the other two sides.. This is the very simple basis of the trigonometrical /triangulation principle of distance measurement. The entire map can then be composed of a series of small triangles.

Triangulation was also originally used to calculate the distance of stars and planets by taking angular sight readings to a distant stellar object from both sides of the globe across the diameter of the earth (the known base line). This method was further improved in accuracy by taking angular sight readings across the diameter of the earth’s orbit at six month intervals ,thus extending the width of the baseline for greater precision.
In mapping a landscape ,if we have the distance between two trig points (the baseline) and two angular sightings from both ends of this baseline to a distant trig point on another summit ,then we can calculate the triangle and determine the various distances. Only one baseline ever needs to be manually measured, because all of the subsequent sides (i.e distances in km) of all the other triangles can be calculated. Hence ,incredible precision and a meticulous approach was needed when measuring the baseline many years ago . A single error in the baseline would be multiplied hundreds of times in all the subsequent calculated triangles.

The Triangulation Mapping Survey of Ireland 1824-1842
Europe, post the French Revolution was in turmoil, with Austria ,Russia ,Turkey and Napoleon’s France all flexing their collective muscles, and the Napoleonic wars were just over the horizon in towards 1803.Without good maps Britain felt vulnerable could not position its army strategically nor defensively
The Ordnance Survey (OS ) was established in Britain in 1791 to prepare a detailed map of the country and thereby to help defend Britain from external attack…. concern was rife about Napoleon’s ambitions at that time. The origins of Ordnance Survey in Britain go back to a triangulation survey carried out for King George III and The Royal Society between 1784 and 1790. The survey was determining the relative positions of the Greenwich Observatory and L’Observatoire de Paris, and measuring the distance between the two observatories. Major General William Roy carried out the survey under the authority of the Master General of the Board of Ordnance, and Roy’s first action was to measure a survey base-line across Hounslow Heath during the summer of 1784.
He used a baseline of approximately five miles long running through Hounslow Heath. The two terminals of this base-line are now marked by contemporary military cannon set in the ground muzzle upward. The north-western portion of the base-line is now occupied by Heathrow Airport. This baseline was used in the future mapping of Britain and became the the core liner measurement for the entire triangulation process for mapping Great Britain. By 1794 mapmakers had started the triangulation of the English coast from Sussex to Dorset. The coastal areas were initially of greater priority to the OS because of their strategic and defensive nature. It was also believed in London that Ireland required attention in this regard also, or broadly similar military reasons as well as for the purposes land taxation.
Accordingly, after 1800,many of the British OS staff were shipped across the sea to Ireland to instigate an Irish mapping project and to produce a detailed six inch map of Ireland for military and for land taxation purposes. The Ordnance Survey of Ireland (OSI) ,was established in 1824 as part of this British army ( post 1800 Act of Union) plan to create a detailed map of Ireland. This mapping project for Ireland had the objective of providing an accurate representation of lands ,landscape, town lands, villages and holdings. This would in turn facilitate the collection of local taxes ,identify boundaries, and also would be useful to Britain for other regulatory concerns and military planning. The failed insurrection of 1798 and Emmet’s 1803 abortive uprising were still fresh in British minds, and 1798 in particular had stressed the importance of knowing and policing the Irish landscape, all of which had led to Lord Cornwallis’s building of the Military Road
In the early 1820s, a consistent island -wide valuation of property was initiated by the British parliament as a basis for an effective taxation system, involving landlords and their large estates, as well as smaller town lands and parcels of land. The Irish map was intended to be much more detailed than the British one. At that time, the OSI office was located in Mountjoy House in the Phoenix park …a building that was originally constructed in 1728. It later housed the cavalry of the Lord Lieutenant who lived nearby in the Vice Regal Lodge in the park. The OSI continued to operate under the agency of the Dept Defence until 1924 when it was transferred to the fledgling Dept Defence.
The comprehensive mapping and triangulation of Ireland was commenced by the OSI in 1824 and was completed in 1842. Ireland was the first country in the world to be so extensively mapped in such detail and at a scale of six inches to one mile. The work was carried out by 2000 members of the Royal engineers. Major Thomas Colby was in charge of the survey which produced many innovations and introduced many novel scientific techniques. Some independent Irish engineers were also recruited and were involved in the survey .These engineers were under the control of Richard Griffith ..later to become famous for his national valuation.
Numerous triangulation stations (trig stations) and triangulation buildings were built and established at various high points in Ireland . These buildings were used for visual observations using light sources and reflectors

Triangulation building at Magilligan.

Thomas Drummond was the principal surveyor in this project. He had a problem in that some of the visual sightings from station to station extended over long distances , and thus Colby needed more powerful light than that provided by the Argand Lamps he was using
He invented a vapour called limelight which was bright enough to be seen at great distances, and he also invented the heliostat reflector which facilitated sighting of the limelight at distant trig stations in hazy and cloudy conditions. . These latter devices allowed visualisation and measurement from one trig station to another .
Colby and Drummond also invented “compensation bars” of iron and brass which allowed more precise measurement of linear distance used for the baseline. These allowed expansion and contraction of the metals, when temperatures varied, and Colby factored in the coefficient of expansion for greater accuracy in the eventual measurement of the linear distance.. Thus greater consistency and precision was guaranteed in his linear measurement.

Measuring the Baseline
The process of triangulation need a baseline to be accurately measured. This is the base of the triangle which, with two angles, allows the triangle to be drawn and the distance to be determined..
In order to complete the network of triangles, the length of one leg of one triangle had to be measured carefully. The longer the leg the greater the angular accuracy.
The OS in Britain had done all this years earlier in 1784 and calculated a baseline using a five mile stretch along Hounslow Heath. The leg chosen in Ireland as the core national triangulation baseline ,was along the shores of Lough Foyle and this was known as the Lough Foyle baseline. Once this was measured ,all the other smaller triangles and measurements fell into place. The accuracy of measurement of the Lough Foyle baseline was paramount .Errors due to inaccuracies in the baseline measurement would amplify as more triangles were calculated. Measurement of the Lough Foyle baseline began in 1827 and it lasted for 60 days. The distance of 7.89 miles was carefully measured by 70 men using tripods and compensation bars. The baseline started at Magilligan and extended to Ballykelly near Derry. Once the two end- angles were known, this single measurement alone was sufficient to calculate the lengths of all the other sides of all of the other triangles. The Lough Foyle base was re measured again, using modern techniques in 1960, and the result differed from the 1828 value by only 2,5 cm !!

Other persons were involved in the 1824 survey because the engineers of the British army and british OS staff could not undertake every single aspect of the work such as local gaelic place names, Irish language derivations,, archaeology, and local history. Musicologist and archaeologist George Petrie assembled a team for this purpose, including Irish scholars , John O’ Donovan ,Eugene O Curry, and James Larcom, and some painters and poets including James Clarence Mangan. These people supplied much of the corroborative detail and local colour into the mathematical detail of the large scale maps e.g… place names, gaelic derivations, populations,e conomy ,agriculture, etc.
Petrie , Larcom and John O Donovan, in particular , extensively researched the origins and history of local Irish place names and drew up translations . Petrie also headed the Survey Topographical department
Benchmarks were also a part of this first survey, and they were used to record the height of land features above sea level. The height of a point above sea level was marked with the shape of a crows foot cut into bricks, walls, corners and buildings. The reference point for sea level was set at the low watermark of spring tide at Poolbeg Lighthouse on April 8th 1837. This reference point remained until 1970 when it was superceded by a point at Malin Head. These cut arrows /crowsfeet were the commonest form of benchmarks and consisted of a horizontal bar cut into a wall or benchmark. This bar was the actual benchmark. A broad arrow was cut immediately below the centre of the horizontal bar. This gave the “crows” feet appearance.
By 1846 , the entire island of Ireland had been surveyed and a series of 2000 maps at a scale of six inches to the mile had been published. The total cost of the survey was £860,000. Ireland was the first country in the world to be mapped at this scale. By 1867 from Fair Head to Mizen head had been surveyed in great detail and Sir Richard Griffith and his team moved in to commence their valuations (Griffiths‘s Valuation)
The Re triangulation of Ireland 1959.
The OSI began their re triangulation mapping project of Ireland in 1959. This time instead of the buildings known as “triangulation stations” used in the 1824 survey, high measurement points were replaced by the construction of “triangulation pillars” or trig pillars.
In the UK in the early 20th century, map making was still based on the Principal Triangulation which was a piecemeal collection of observations taken between 1783 and 1853. The system was starting to collapse and couldn’t support the more accurate mapping needed to track the rapid socio economic development of Britain after the Great War. This led to Hotine’s development of the trig pillar and ,using it ,a much more more accurate mapping of the UK commenced in 1935
In the UK, the process of placing trig pillars on top of prominent hills and mountains began in 1935 to assist in the accurate re triangulation of Great Britain. Over 6500 trig pillars were constructed across the length and breadth of the UK to map the country more accurately and with greater precision. They continued being used until 1962.
The Irish trig pillars were essentially designed and constructed on the principle of the British Hotine trig pillar model which had been used in the UK from 1935 onwards into the 1940’s
These concrete trig pillars were constructed by the OSI in Ireland in 1959, often using donkey power to deliver the construction materials to the summits. All the pillars were made by hand and amazingly all the materials and equipment used to build these pillars were carried to the tops of the hills by the surveyors and their staff or assistants. Recording of data and sight lines was not always easy on account of problems of high winds or visibility at summits and often the surveyors had to camp on the summits.
In Ireland as in the UK ,these new trig pillars gave rise to more accurate triangulation techniques because they used precision theodolites on top of the pillar and were positioned over a centralised sunken brass bolt..
This very accurate process of triangulation measurement gave rise to the Ordnance Survey maps as we know them today. The coordinate system used on these trig pillar based OS maps is known as the National Grid

The Development of the Trig Pillar.
Martin Hotine & the Retriangulation of Britain in 1935
In the UK in 1935 the British Ordnance Survey, in a project led by Brigadier Martin Hotine, decided to implement a complete new mapping and grid network for the whole country and at the same time to unify the mapping from local county projections onto a single national grid , and reference system. This lead to the establishment of the OS GB 36 datum and the UK National Grid, both of which are still operational today. A key point of this measurement system was the trig pillar.
The man responsible for the trig pillar that we all recognise today on mountaintops all over Ireland was Brigadier Martin Hotine. Born in 1898 in, London, Hotine became head of the Trigonometrical and Levelling Division at OS in the UK. .
Hotine was responsible for the design, planning and implementation of the retriangulation process of mapping. In order to provide a solid base for the theodolites used by the survey teams and to improve the accuracy of the readings obtained he invented and designed the iconic trig pillar. As a result, they are sometimes referred to as ‘Hotine Pillars’. The pillars became a key feature of the accurate triangulation and mapping of Britain . In actuality it became rather difficult to locate and identify key sites for locating many of the trig pillars. They needed on the one hand to be located at high altitude ,but on the other hand , this of course necessitated carrying and transporting the heavy and cumbersome materials to remote sites and then building the trig pillars at the summit. In most parts of Ireland and the UK, trig points are truncated square concrete pyramids or obelisks tapering towards the top. On the top, a brass plate with three arms and a central depression is fixed: it is used to mount and centre a theodolite used to take angular measurements to neighbouring trig points. A benchmark is usually set on the side, marked with the letters “O S B M” (Ordnance Survey Bench Mark) and the reference number of the trig point. (Within and below the visible trig point, there may be concealed reference marks whose National Grid References are precisely known.)

Use of Trig Pillars
Trig points are the common name for “triangulation pillars”. These are concrete pillars, about 4′ tall, which were used by the Ordnance Survey in the UK and Ireland in order to assist in cartography and distance measurement.. They are generally constructed at the highest altitude possible in an area, so that there is a direct and unobstructed line of sight from one trig pillar to the next.. This process is called “triangulation”. Careful measurements of the angles between the lines-of-sight of other trig points then allowed the construction of a system of triangles which could then be referenced back to a single baseline to construct a highly accurate measurement system that covered the entire country. A theodolite is used as the key instrument in such calculations. A theodolite, in essence is a protractor (angle measurerer) set into a telescope. It can operate in the horizontal and vertical plane. By sitting the theodolite on the top of the flat concrete pillar,–the “spider” or “top plate”- accurate angles between other nearby trig points can be measured. In practice, a theodolite would have been secured to the top mounting plate and made level. It would then be directly over the brass bolt underneath the pillar. Angles were then measured from the pillar to other surrounding points. A theodolite is a precison instrument and before focussing and measuring angles through the eyepiece a number of preliminary procedures must be undertaken:-
– Setting up – fixing the theodolite onto a tripod or base along with approximate levelling and centering over the station mark. The theodolite had to be lined up directly with the brass bolt below and within the pillar.
– Centering – bringing the vertical axis of theodolite immediately over station mark using a centering plate also known as a tribrach.
– Levelling – levelling of the base of the instrument to make the vertical axis vertical usually with an in-built bubble-level.
Thus to facilitate the accuracy of the theodilite , a trig pillar must be accurately and precisely constructed ,in terms of the level spider or top plate, the central core and the brass bolt set into the base.
. With the advancement of modern scientific procedures and the arrival of better and more accurate technologies and digital techniques such as, satellite technology,and GPS and digital combinations, the original traditional trig pillar is now obsolete and redundant in its original guise.
Nonetheless, an interesting point however is that despite their rudimentary nature, the original measurements made via theodolites and trig pillars were incredibly accurate and when compared with GPS measurement years later, the distances calculated , if indeed they vary at all, do so by only millimetres or a few centimetres.!.
The pillars are about four feet high on a wide base and taper towards a flat top with a mounting-plate to hold a theodolite. Trigonometrical pillars are grouped together to form a triangulation network. Each pillar is in the clear sight line of several other trig pillars on distant summits so that their relative positions may be determined. Angles can be measured very precisely by taking theodolite sightings to distant peaks. In this way a network of triangles can be built up covering the entire country. Larger triangles can be subdivided into smaller ones, yielding a detailed mesh and interlocking network which facilitates fine-scale mapping.
If we know the length of one side of a triangle – the baseline – and the two angles at its ends, we can use trigonometry, the mathematics of triangles, to calculate the lengths of the other two sides. Thus distances between hills or to distant hills are easily measured.
The Ordnance Survey originally mapped Ireland in the 1820s. However a more accurate and detailed re-triangulation of the country began in 1959, and the familiar concrete pillars were erected on many hilltops at this time. The OSI took charge of the planning, overseeing and construction of these pillars, based on the British Hotine model. Thus the trig pillars we see on Irish hilltops today mostly date from sixty years ago.
Structure and Construction of Trig Pillars
Since angular measurement is such a precise visual science, the pillar on which the theodolite is placed must be of very solid and reliable design .In practice, a theodolite would have been secured to the top mounting plate and made level. It would then be directly over the brass bolt underneath the pillar.The pillar was of concrete built over a concrete box that just protrudes over soil level. The top of the pillar had a spider or top plate for the theodolite. A flush bracket was located on the side of the pillar displaying a bench march and OSI serial number .Originally this was an indentation holding a metal plate. Then it was made “flush” with the pillar (flush bracket) .It always displays the bench mark (BM) giving the height above sea level and the serial number of the trig pillar.
The trig pillar is usually a hand-cast concrete pillar, 4 feet high and 2 feet square at the base, tapering towards a flat top. Each pillar is in view of several others so that their position may be triangulated. TPs usually have a ‘spider’ or ‘top plate’ used to fix a theodolite or other ordnance surveying device to. Many have a Flush Bracket fixed to the side that has an identifying number on it.
The original Hottine design, consisted of a brass bolt set in concrete, ( The bolt over which the theodolite would be centred) inserted at a sufficient depth below ground level to be independant of the pillar foundations. The lower buried centre mark, consisting of a brass bolt set in concrete, is first inserted at a sufficient depth below ground level to be independent of the pillar foundations. This is a key central reference point. This depth naturally varies with the soil; on boggy ground, which was often encountered on hilltops, it was sometimes necessary to excavate as much as 15 feet before reaching rock or firm soil on which to emplace the lower mark. In such a case a correspondingly deep pillar foundation is necessary, whereas on out-cropping solid rock, a bolt is simply cemented in a hole drilled in the rock. Often times ,depending on the soil, the trig pillar could be compared to an iceberg with more below the surface than above it.
The lower centre mark and its concrete setting was covered with a small wooden box (which eventually distintegrates) to prevent adherance to the pillar base.
Concreting of the pillar base was commenced immediately over and around the box covering the lower mark, Concreting the pillar base was continued up to ground level where it was left rough to set. Four angle iron bars were then set in the base to project well up into the corners of the pillar, as a means of preventing fracture between the base and the pillar. The pillar bolt (upper centre mark) was also set in the base. The pillar bolt was next covered with a small wooden box, which was provided with side holes (to take the inner ends of the four sighting and drainage pipes) and a top hole (to take the lower end of the galvanized pipe running down the centre of the pillar).

Wooden shuttering, was then erected on the pillar base. This shuttering had four side holes to take the outer ends of the four sighting pipes, which are then inserted, and a wedge fillet to which the level flush bracket in one side of the pillar may be wired in a vertical position. It also carries wooden corner fillets to provide an automatic chamfering to the edges of the pillar.
The centre pipe, which serves as further reinforcement, was set in position and plumbed, the plumbing being continually being checked during concreting. Before the concrete set, the brass spider, complete with holding down bolts, was set over the centre pipe and was carefully plumbed over the pillar bolt from a special temporary fitting to the spider Concreting was then carried up to the top of the spider .
On the top of every trig point is a brass plate with three arms which was used to mount the theodolite from which accurate measurements and angles to neighbouring trig points could be made.
Top Plate or “spider” for theodolite

On one side there is an indentation with a metal plate and here is found the benchmark

Trig point built on boggy soil ,now eroded, showing the large fraction of the pillar that lies underground

Benchmarks on the side of Trig Pillars.
A benchmark (BM) forms the reference frame for heights above mean sea level. If the exact height of one BM is known, the exact height of the next can be found by measuring the difference in heights, through a process of spirit levelling. Benchmarks are on the sides of all Trig Pillars in the form of a flush bracket.
The term benchmark, derives from the chiseled horizontal indented line that the surveyors made in stone structures, into which an angle-iron could be placed to form a “bench” for a leveling rod (graduated measuring rod). A surveyors “bench” is a type of bracket, onto which measuring equipment is mounted. These lines were usually indicated with a chiseled arrow below the horizontal line.
The term is generally applied to any item used to mark a point as an elevation reference when compared to sea level. In 1837 the reference sea level point was set as the low watermark of spring tide at Poolbeg Lighthouse on April 8th 1837 Dublin Bay for the primary sea level comparative standard. The network of bench marks from the first levelling left a mark on the landscape in the form of the crows foot cut into walls buildings and bridges all over Ireland. , This Poolbeg reference point remained in use until it was superceded by Mean Sea Level at Malin Head in 1970..

Flush bracket showing bench mark on side of trig pillar.The BM number ,the recess for the “bench” (bracket ),and the arrow (crow’s foot” )are clearly visible.

Bench marks were historically used to record the height above sea level of a location as surveyed against the Mean Sea Level data . Thousands of bench marks were sited all around the UK & Ireland from the mid 19th to late 20th centuries. The recorded altitude refers to the small horizontal platform at the point of the broad arrow marked on the plate face
Bench marks can also be seen not only on trig pillars but also on stone buildings near the corner and not very high.
A cut bench mark is the commonest form of bench mark. It consists of a horizontal bar cut into vertical brickwork or similar surfaces. A broad arrow is cut immediately below the centre of the horizontal bar.

And Finally :
Although trig pillars are now obsolete and generally in some disrepair, their role having been overtaken by satellite technology and GPS, many hill walkers now like to bag trig pillars (trigpointing) and add to their collection.!
Trig pointing is now becoming quite a popular hobby, perhaps more so in GB (there’s a lot more pillars there).
(In 2016 a UK hillwalker, Rob Woodall , bagged and visited all of the 6000 plus trig pillars in the UK for which he received an award.).
With the advance of satellite mapping, the Ordnance Survey in Britain has decided to retire 5,000 of its 6,000 trig pillars because they are no longer needed to pinpoint accurately the positions of landmarks. The Ordnance Survey (UK) has decided to stop inspecting and maintaining these pillars and is looking for people who will volunteer to do it for them. In the UK thousands of people all over Britain are volunteering to adopt abandoned ‘trig pillars’, those familiar concrete monuments used by the Ordnance Survey to map the country. About 2,000 of the 5,000 redundant pillars have already been assigned on a first come, first served basis. The person adopting must inspect the pillar twice yearly and paint it when necessary.
This clearly gives another meaning to the term “pillars of the community”!! Maybe this might also happen in Ireland !!
In Ireland, although trig stations and trig pillars are now redundant, being unnecessary for modern surveying purposes, they are greatly loved by hikers and mountaineers as navigational aids and as a type of comfort blanket and a visual objective . It is always a pleasure for most hill walkers and hikers to reach a summit, no matter how big or small ,have a photo taken at the trig pillar, or to take time out and sit in the sunshine and unwrap one’s sandwiches, while resting against these historical small monoliths.!!
And of course ,while you are there, read your OSI map and check your grid reference, and don’t forget as you lean against the pillar ,that this is where it all started !!