page_title: Alexander Ross Clarke
section_title: Principal Triangulation, 1858
hierarchical_section_title: Alexander Ross Clarke / Major geodetic contributions / Principal Triangulation, 1858
caption_attribution_description: English: The triangulation mesh over Britain, 1860.
context_page_description: Col Alexander Ross Clarke FRS FRSE was a British geodesist, primarily remembered for his calculation of the Principal Triangulation of Britain, the calculation of the Figure of the Earth and one of the most important text books of Geodesy. He was an officer of the Royal Engineers employed on the Ordnance Survey.
context_section_description: The Principal Triangulation of Great Britain was initiated by the Board of Ordnance in 1791 and carried out under the direction of William Mudge and Thomas Frederick Colby. The field work was completed in 1853, just as Clark joined the Board. The methods of analysis had been planned in outline by William Yolland, his predecessor at the head of the Trigonometric Section, but it fell to Clarke to finalize the methods and carry them through to completion. This he achieved in the four years from 1854 to 1858: the report was published as Clarke & James (1858b) but it is entirely Clarke's work. The basic data was the collection of angle bearings taken from each of the 289 stations towards a number of other stations, typically from three to ten in number. The multiple observations were first subjected to a least squares error analysis to extract the most likely angles and then the triangles formed by the corrected bearings were adjusted simultaneously, again by least squares methods, to find the most likely geometry for the whole mesh. This was an immense undertaking which involved the solution of 920 equations without the aid of matrix methods or digital computers. The only available computers were the living personnel of the Trigonometric Section, twenty one of them. Once the triangles had been fixed it was then possible to calculate all the sides of the mesh in terms of the length of either of the bases, one by Lough Foyle in Ireland and the other on Salisbury plain. The accuracy of the survey was such that when the length of the Lough Foyle base was calculated through the triangulation mesh from the Salisbury base the error was only 5 inches when compared with its measured length (of 41,640.887 feet or about 8 miles). The final step was to use the distances and angles to work out the latitude and longitude of each triangulation point on the Airy ellipsoid.
  The natural course of events after a primary triangulation is to construct a secondary triangulation with sides of a few miles, and then a tertiary triangulation at a parish level to show all significant details. Unfortunately this did not happen because the infilling had been going on for fifty years of topographic surveying, with maps already published on a county basis. Some of those maps had origins that were connected to the primary triangulation, and some did not. As a result, the county maps were only loosely tied to the principal triangulation and no attempt was made to revise them.
caption: The principal triangulation mesh over Britain, 1860.
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