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Trigonometrical Stations

Jottings for Cumbria about trig points, and the triangulation of Britain.

What's to See?

The Lakes Guide project is not the place for a detail study of triangulation, which is beyond my competence anyway. The Old Cumbria Gazetteer of the project is about what there is to see; not about processes of surveying, mapping, projections, and so on. So: What is there to see?
What you can see are the trig points, marked by pillars at the vertices of the triangulation network. The sides of the triangles, like the equator, are notional, invisible lines on the ground.

Trig Points

The triangulation stations were made permanent, marked by 4 foot high pillars of concrete or local stone, familar to any walker. They dot the tops of hills and are often far from a road or track. Think of the lorries, packhorses, and manual labour needed to get the materials on site for the more remote pillars.

Loughrigg Fell NY3469505141 altitide 335.2m.

The actual point is below ground, often fixed in the rock, protected and marked by the pillar. The pillar is a practical stand for a theodolite, whose three legs fit in the grooves on the bronze plate atop the pillar, and from which a plumb bob reaches to the point below: there is a fundamental mark even deeper down. The pillar often carries a bench mark, and some pillars have waymarks, topographs, and other additions.

Loughrigg Fell NY3469505141 altitide 335.2m.

Loughrigg Fell flush bracket benchmark.

Thornyslack, Skelsmergh SD5271298306 altitude 214.2m; spider:- 'ORDNANCE SURVEY / TRIANGULATION STATION'

The original survey stations we sometimes marked by cairns. When the new pillars were being made there was sometimes a local outcry about historic landmarks, these cairns, being destroyed. Which became quiet when all was explained.
Some marks are more basic:-

Selside Brow on Branstree, Longsleddale NY4780009970.

Selside Brow on Branstree, Longsleddale NY4780009970.

Early Sightings of Sappers at Work

Black Combe Jonathan Otley's guide book:-
    ... may be seen at a great distance; ... In 1808, it was made one of Colonel Mudge's stations, in the process of the Trigonometrical Survey. He calculated its height to be 1919 feet above the level of the sea. ... By the misprint of a single figure in the longitude of this mountain in the 3rd vol. of the Trigonometrical Survey, a great distortion has been caused in some maps lately constructed upon that basis.
Otley 1823 (5th edn 1834)
Black Combe William Wordsworth, 1813, wrote about a surveyor on Black Combe:-
    ... on the summit whither thou art bound,
    A geographic Labourer pitched his tent,
    With books supplied and instruments of art,
    To measure height and distance; lonely task,
    Week after week pursued! - To him was given
    Full many a glimpse (but sparingly bestowed
    On timid man) of Nature's processes
    Upon the exalted hills. He made report
    That once, while there he plied his studious work,
    Within that canvas Dwelling, colours, lines,
    And the whole surface of the out-spread map.
    Became invisible: for all around
    Had darkness fallen - unthreatened, unproclaimed -
    As if the golden day itself had been
    Extiguished in a moment; total gloom
    In which he sate alone, with unclosed eyes,
    Upon the blinded mountain's silent top!
Black Combe Harriet Martineau, 1855, comments about Colonel Mudge:-
    ... Col. Mudge's information that, when residing on Blackcombe for surveying purposes, he more than once saw Ireland before sunrise, would bring strangers to try their luck in seeing Scotland, Staffordshire, and Ireland, from the same point: but the mountain lies out of the ordinary track of tourists, and very few visit it. ...
Martineau 1855
Great Gable Jonathan Otley complained to Sir George Airy, Asronomer Royal, about the damage done by the Ordnance Survey engineers to the cistern on the top of Great Gable. The outcome is explained in the last letters of this correspondence:-
    Royal Observatory, Greenwich
    1854. October 5th.
    Dear Sir,-
    Your complaints about the cistern on Great Gable have not fallen to the ground.
    Since I last wrote to you, I have consulted with Dr. Leitch, who at my request, was so kind as to undertake the practical management of the matter, and we have fairly shifted the man ten feet to the Magnetic West. I have given notice of this to the Ordnance Survey Office, so that no confusion will be produced in their bearings. As you probably remember very well the former state of the cistern, perhaps you will have the goodness to compare notes with Dr. Leitch, or with Mr. John Jackson, the postmaster at Rosthwaite, who went up with Dr. Leitch and directed the wallers in the work. I should be glad to know that the cistern had not suffered under the operations of the Sappers of the Survey.
    I am, dear Sir,
    Yours truly,
    G. B. Airy.
and Jonathan Otley's reply:-
    October 10th, 1854
    Yours of the 5th came duly to hand. Dr. Leitch called on me yesterday to say that they had built a nice little man on the Gable, according to your directions. If you had not distinctly mentioned magnetic West, I should have thought it would have been true west, as I presume the Ordnance maps are laid down from the true meridian. He says that he cannot perceive any damage that has been done to it ...
    Although I shall never see it, I am glad that it has been restored to its original state, so that if ever it was worth looking at as a natural curiosity, it may still contimue the same. ...
Scawfell Pike Jonathan Otley's guide book:-
    ... Latterly however, it seems by common consent, the highest point is called Scawfell-Pikes; and since the erection of the large pile and staff upon it in 1826, there is no danger of mistaking the place.
    ... in towering majesty, the highest of the Pikes, rendered more conspicuous by an object lately erected in the prosecution of the Trigonometrical Survey. ...
Otley 1823 (5th edn 1834)
Scawfell Pike Harriet Martineau, 1855, notes that there is no longer any need to get lost:-
    ... The ascent of Scawfell ... ... The Ordnance surveyors set up a staff on a pile of stones on the highest peak; so that there need be no mistake henceforth. ...
Martineau 1855
Skiddaw Jonathan Otley's guide book, an account of a trip up Skiddaw in a a letter from a friend:-
    ... Proceeding along this ridge, we unexpectedly heard the sound of human voices, and presently descried some men engaged in building a large pile of stones around a structure of timber thirty feet high, upon the very summit. They proved to be a party of Royal Engineers and Artillerymen, who had been encamped here for several days, employed in erecting an object to be observed in the Trigonometrical Survey; as the Commanding Officer explained to us. Some philanthropic gentleman had caused a small cot to be constructed here for the accommodation of visitants, and on looking in we perceived that the men had spread their blankets on a little moss, and thus converted it into a temporary barrack. ...
Otley 1823 (3rd edn 1827)
Skiddaw Jonathan Otley's guide book:-
    ... the object of our journey, which is marked by a large pile of stones, with a central staff 30 feet high, erected in 1826 by a detachment of the ordnance surveyors. ...
Otley 1823 (5th edn 1834)
Old Man of Coniston Harriet Martineau, 1855, complains:-
    ... the summit of the Old Man is 2,632. On this rock, a "Man" formerly stood; but it was removed by the Ordnance Surveyors, who erected another, much inferior in convenience; for the first contained a chamber, welcome to shepherds and tourists overtaken by bad weather. ...
Martineau 1855

Principal Triangulation

Accurate surveying for mapping depends on triangulation, the application of theorems clearly expressed in the geometries of Euclid, and given numerical form in the equations of trigonometry.
The earliest description of triangulation for surveying - a measured base line, bearings measured from the ends of the base line - seems to have been given in Libellus de locorum by Gemma Frisius, 1533. He included the essay in the 2nd edn of Cosmographicus liber Petri Apiani. He describes a planimetrum, a circle with an alidade to take bearings, suggests the use of two tall towers, and a third to resolve difficult intersections of sight lines, and instructs on the measurement of the base line.
The triangulation of Great Britain was begun at the end of the 18th century, aimed at establishing a conistent framework for surveying the whole country. The first base line was measured by William Roy on Hounslow Heath, 1784. From the ends of this line bearings were taken to a third point to make a triangle, each of whose new sides was a new base line. The process is repeated until a network of triangles covers the land from north to south. As errors accumulate the network is checked by measuring the length of a line at the end of the network, and adjusting as necessary. The principal triangulation was a network of stations about 30 to 50Km apart. The shortest sides of triangles were about 8Km, the longest about 135Km, usually those linking Briain to Ireland, and to France.
Bearings were measured with Ramsden's 3 foot theodolite which could observe over 100Km and measure with errors less than 2 seconds of arc. Not all is straightforward; visibility is a problem, refraction is a problem, the curvature of the earth is a problem, ... Sadly this instrument was destroyed by bombing in World War II; but a second instrument made in 1791 is in the Science Museum collections, London.
The Principal Triangulation by the Ordnance Survey used some measurements taken in 1790s and many more in the 1840s-50s. The whole was recalculated and published in 1858.

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A Retriangulation was believed necessary by the 1930s, and was started in 1936. England and the south of Scotland had been covered by 1938, and the job finished after World War II, from 1948-52, published 1962.

Secondary and Teriary Stations

Between the primary stations was a network of secondary and stations 8 to 12Km apart, and tertiary stations as close a 1.5 to 2Km, particularly in built up areas.
button notes from 1858:- Principal Triangulation, 1858

Trig Point Data

Data about the position of Ordnance Survey trig points can be downloaded in a .csv (comma separated value) file, free, from:-
Data has been used to create Place Records to go in the Old Cumbria Gazetteer; place identifiers on the pattern:-
trig point, [10 figure grid reference]
trig point, NY0820745431


: 1967: History the Retriangulation of Great Britain: Ordnance Survey

Clarke, A R: 1858: Account of the Observations of the Principal Triangulation: Ordnance Survey

Close, Charles, Colonel Sir & Winterbotham, H StJ L, Colonel: 1925: Text Book of Topographical and Geographical Surveying: HMSO (London); how to do it all

Frisius, Gemma: 1533: Libellus de locorum describendorum ratione::: British Library C113c3 (1-2)

Harley, J B: 1975: Ordnance Survey: Ordnance Survey (Southampton, Hampshire)

James, Henry: 1875: Account of the Methods and Processes... Ordnance Survey: HMSO (London)

Keay, John: 2000: Great Arc, The: Harper Collins (London):: ISBN 0 00653123 7; describes what surveying can be like outside the comfort of Geat Britain.

Owen, Tim & Pilbeam, Elaine: 1992: Ordnance Survey, Map Makers to Britain since 1791: Ordnance Survey (Southampton, Hampshire):: ISBN 0 319 00498 8 (pbk); includes desriptions of building trig points.

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