South African Geodetic foot

In South Africa, an unintentionally created unit of length, about 0.304 797 265 54 meter. Abbr., “S.A.G. feet”. The feet which appear in the Report on the Geodetic Survey of South Africa, vols. 1-6, are S.A.G. feet.

The first real standards for geodetic work in South Africa were two 10-foot wrought iron bars made by Troughton and Simms in London, compared with the Astronomical Society's standard, and delivered in 1839. One of the bars, Cape Standard Bar A, is still in existence at Surveys and Mapping, Mowbray. Cape Standard Bar A was first used by T. Maclear in 1840 – 1848 to refine and extend an earlier survey, and then stored at the Cape Observatory.

This particular style of 10-foot iron bar was the usual standard of length in the British Empire for geodetic surveys. In a geodetic survey, an area of hundreds of square miles (or kilometers) is covered by a network of triangles whose angles are measured. The distances can then be calculated if one knows the length of the side of one of the triangles—the baseline. The accuracy of the survey is limited by the precision with which the length of the baseline is known. In the 19th century, baselines were more than a mile long, and sometimes more than 10 miles.

In the 1880's an ambitious new geodetic survey was undertaken advised by His Majesty's Astronomer at the Cape, David Gill. They dreamed of ultimately reaching the Mediterranean.

Length on the 10-foot standards is indicated on two inlaid gold pins, one on either end of the bar. On each pin is stamped a dot. The distance between the dots is 10 feet.

In Gill's opinion, the dots were too ambiguous, and he returned the Cape Standard Bar A to Troughton and Simms with instructions to engrave fine lines beside the dots, and then forward the bar to the BIPM at Breteuil, France. There, in 1886, Benoit compared the distance between the lines now ruled on Cape Standard Bar A with the International Metre. The bar was then returned to South Africa and used to calibrate new instrumentation, also made by Troughton and Simms. The new survey, in other words, was actually done in international meters.

For publication, Gill wished to express results in English feet, which required a conversion from meters to feet. Unfortunately, he chose to use the conversion factor arrived at by Clarke, “for reasons which are rather obscure,” according to Hendrickz and Smuts. But perhaps they are not so obscure. Clarke was arguably the most prominent English geodicist, the man who wrote the book (and even the articles on the subject in the Encyclopedia Britannica). Moreover, Clarke's factor was especially developed for geodetic use. He had been careful to develop his conversion factor by comparing standards actually used for geodetic surveys in Europe, to assure that the Ordnance Survey in Britain could be connected with the European grid. For the meter, he used Borda's Bar #1, not the 1799 Mètre des Archives, which he ignored (and, of course, the International Prototype of the Meter did not even exist in 1866). As it turned out, Clarke's version of the meter was 8 microns longer than the international meter.

Clarke's conversion factor is not valid for converting measurements in International Meters to English measure. Applying it created the S.A.G. foot.

Compare the United States survey foot, which also arose from an improvement in the definition of a unit of length.

Tomasz Zakiewicz.
The Cape Geodetic Standards and Their Impact on Africa.
FIG Working Week 2005, From Pharoahs to Geoinformatics, Cairo, April 2005.

Available on the web at www.fig.net/pub/cairo/papers/wshs_03/wshs03_02_zakiewich.pdf

sources

1

This name ["South African Geodetic foot"] is preferred to the term Cape Geodetic Foot sometimes used, since the latter is likely to be confused with the Cape Foot or legal measure employed in the Union of South Africa.

D. R. Hendrikz and P. M. Smuts.
The Cape Bar 'A' and the Metre-Foot Relation.
Empire Survey Review, vol. 10, no. 75 (January 1950).
Page 206, footnote.
This article contains a useful bibliography on the subject (page 203, footnote), mostly articles by G. T. McCaw in the Empire Survey Review, but also Special Publication no. 2, Trigonometrical Survey of Union of South Africa.

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