The Meridian Arc of Abbe de Lacaille

The pursuit of the figure of the earth has a long and interesting history in South Africa.  The year 2001 marks the 250^th anniversary since the prominent astronomer-geodesist Abbe de LaCaille who set foot on South African soil to catalogue the Southern stars by their celestial co-ordinates of right ascension and declination.  Shortly after his arrival at the Cape, LaCaille set out to measure a meridian of arc in the southern hemisphere as no such measurement existed. 

Abbe de LaCaille measured a triangulation arc (figure one) northwards from Cape Town, to determine the figure of the earth and obtained a result which indicated that the curvature of the earth was less at southern latitudes than at corresponding northern ones.  This perplexity was later to be verified by Sir Thomas Maclear, Her Majesty’s Astronomer at the Cape.   

Figure 1:  The Triangulation of Lacaille’s Arc of Meridian

The Verification of LaCailles Arc by Sir Thomas Maclear

Sir George Everest visited the Cape in 1820 and inspected the site of LaCailles meridian arc.  His experience in the Himalayas led him to believe that the presence of considerable mountain masses in the Cape could have caused some anomalous disturbance thus falsifying the astronomical latitude determinations made by LaCaille. 

Sir Thomas Maclear was tasked to verify LaCaille meridian arc and commenced such in 1840 completing the task in 1848.  The arc was extended southward beyond the possible gravitational effect of Table Mountain to Cape Town and northwards towards Namaqualand (figure two).  Indeed, it was confirmed that the predictions made by Everest of a large disturbance of gravity at LaCaille’s northern zenith sector station amounting to more than eight seconds of arc, accounted for the error in the observations made by LaCaille.

Figure 2:  Sir Thomas Maclear’s Meridian Arc

The Geodetic Survey of South Africa – ‘Creation of the Cape Datum’

The Cape coastal triangulation of Captain Bailey and Henry Fourcade was a  chain of triangles tied to the southern end of Maclear’s arc extending eastwards from Cape Town to the then Kei River frontier of the Cape Colony.  This chain is labelled ABC in figure (figure three).  Sir David Gill, Her Majesty’s Astronomer at the Cape in 1879 began to study the general question of the Geodetic Survey of South Africa.  Gill found Baileys field records to be erroneous and inconsistent.  However, the concept of the scheme of triangles was adopted by Gill.  It was Gill’s dream to commence an arc following the 30^th meridian and stretching from Cape to Cairo, through the Levant and terminating at Nordkapp.  A chain of triangles forming the backbone of the 30^th meridian was to provide the geodetic control for countries traversed by the arc. 

Gill being appointed the honorary scientific adviser of the Geodetic Survey set sail and landed in Durban in 1883 under the command of Captain William Morris.  The field party set out to measure the Pietermaritzburg base, labelled ‘2’ in (figure three), which was then extended by triangulation to the geodetic chain.  The geodetic chain later being extended northwards towards Newcastle.  The chain was carried south-west from Pietersmaritzburg to Port Elizabeth, then northwards from Port Elizabeth to Kimberly.  Thereafter, chain interconnections as depicted in (figure three).  These geodetic operations were completed before the Anglo-Boer War of 1899-1902, after which the work was extended over the Orange Free State and Transvaal up to the former Rhodesia where the 30^th meridian also commenced also under the instruction of Sir David Gill.  Astronomical observations of latitude and longitude were made at frequent intervals in order to position the geodetic chains on the earth, and azimuth observations to orient the work to the earth’s axis of rotation.  Sir David Gill had taken great care in choosing a datum point free of ‘considerable deviation of the plumb-line’ for the geodetic survey.  Differences between astronomic and geodetic measurements showed that his triangulation on the datum and the chosen Clarke 1880 ellipsoid was in good agreement with the figure of the earth in South Africa.

Figure 3:  The Geodetic Triangulation of South Africa

From the 1920’s onward the Trigonometrical Survey undertook extensive geodetic surveys.  In the mid 1930’s the Kaitob base numbered 10 and the Mtubatuba base numbered 11 in (figure three) were measured. Land Surveyor, H S K Simpson played a key role in these surveys.  These were the last of the taped baselines before- the advent of the EDM (electromagnetic distance measurement).  Recent additions to the geodetic framework include a looped chain of triangulation passing through the Mtubatuba baseline was attached to the northern Natal section of the 30^th meridian. The northern Transvaal section of the 30^th meridian arc was extended eastwards toward the Mozambiqeuan border; a loop of geodetic triangulation running parallel to the Botswana border was attached to the western side of the 30^th meridian arc.   

In the northern Cape, Surveyors Leipoldt and Heatlie connected the northern end of Maclear’s arc to the Port Elizabeth-Kimberly chain, while Surveyor Connan split this area in two with a north-south chain.  Meanwhile, Mr D P M Rosseau, took charge in the geodetic surveys in Namibia. 

The Trigonometrical Survey

The points of the geodetic survey were too far apart for a surveyor to connect to this system and therefore a densification of the Geodetic survey network was required.  The Natal Trigonometrical Survey established a secondary triangulation spreading throughout Natal emanating from the 30^th arc of meridian.  Many farm beacons were thus established in terms of a spheroidal rectangular or Cassini-Soldner projection co-ordinates.  This was the original co-ordinate system of the Geodetic survey which was later to be superseded by the Gauss Conform system thirty years later.  The Cassini-Soldner co-ordinate calculations were found to be awkward by Oscar Shreiber, who later influenced Van Der Sterr in using the Gauss Conform projection.

The work of Johannes Jacobus Bosman, Director of Secondary Triangulation in the Cape Colony is also worth mentioning.  Bosman, under the direction of Gill established a chain connecting the northern end of Maclear’s arc eastwards over the Kalahari Desert to connect with the geodetic chain near Kimberly.  Colonel Winterbotham  conducted a minor triangulation based on the geodetic survey of the Orange Free State. 

 By 1919 a considerable amount of trigonometrical control became available for cadastral and mapping purposes.  New concrete beacons were built over the old centre points, points were re-observed and co-ordinates were recomputed in the Gauss Conform system.  This revision was initiated in 1919 by the newly appointed Director of Trigonometrical Survey, Willem Cornelis van Der Sterr.  The present structure housing the Chief Directorate: Surveys and Mapping is named after him. 

 Later continued the Primary triangulation scheme under the direction of Van Der Sterr and computations carried out in Mowbray under watchful eyes of geodesist Oscar Shreiber.  Primary order triangulations of 40km sides were reconnoitred to fill the open spaces encircled by the loops of geodetic chains (figure four).  Then followed the interpolation into the primary points of the secondary order triangulation nets.  Thereafter followed the tertiary stations with these points being intersected by rays observed to and from the surrounding fixed secondary stations.  Sub-tertiary intersections were conducted in urban areas, often to church spires,  in order to provide control for street traverses which connect the underground reference marks placed at street intersections and upon which urban surveys are based.

This highlights the description of the unified trigonometrical system upon which all mapping, cadastral and engineering surveys are based.  Next we examine some of the more recent technological advances used in the science of measurement.

Figure 4:   Densification of Geodetic Network

A New Era in Surveying Technology:  Satellite Positioning Systems

• Impact of the Global Positioning System

The use of the US Doppler and Transit techniques for positioning was quickly superseded by the Navstar Global Positioning Systym (GPS), which was the next and perhaps most significant development in positioning technology. GPS was also developed by the US Department of Defense to meet its navigational, positioning and timing requirements for a wide range of applications. Signals from GPS satellites were deliberately dithered with to downgrade the position achievable by civilian users. Initially these users could achieve accuracy's around 100m but since May 2000 this has been improved and accuracy's of approximately 10m to 15 m are achievable using a single receiver.

 Various techniques were, however, developed to improve the relative accuracy between two points receiving data simultaneously from GPS satellites.  Positions with accuracy's of better than 0.05m are now achievable provided one of the points is located on a point of known position. In 1990 six GPS receivers were purchased by the Trigonometrical Survey Office and a project was set in motion to determine the position of 200 trigonometrical beacons of the national geodetic network in which the average distance between points was approximately 100km. The project took less than two years to complete which, if the traditional theodolites and EDM instruments had been used, would have taken at least five times longer and then only if adjacent points were intervisible. It was this project which became the foundation of the recomputation of the South African control survey network  on a modern reference frame.

 With the introduction of satellite based positioning techniques, and especially GPS, to the world of geodesy and surveying, the use of long range micro-wave EDM instruments and first order theodolites has become obsolete for geodetic purposes. The positions of well over 1000 points have been determined in recent years using GPS techniques exclusively and it is doubtful that young surveyors with less than 10 years experience even know how to use micro-wave instruments and first order theodolites let alone astronomic theodolites.

 Surveying techniques and the design of instruments changed little from the time of Sir Thomas Maclear up until about the late 1950's when electronics started to have a major impact on instrument design. The launching of the Russian Sputnik satellite heralded the dawn of a new era in positioning to the extent where GPS is the primary positioning tool of many surveyors. GPS has also resulted in a radical change in philosophy with respect to the establishment of national control survey networks. During all these changes and advances in technology the Trigonometrical Survey Office adopted the new technologies and adapted its measuring procedures accordingly and has led the way in which surveyors go about their work in South Africa. In spite of the modern technology and the ease with which the position of points can be determined, the application of sound basic principals of surveying and geodesy remain at the core of the office's procedures to produce high quality co-ordinates and heights thus satisfying the needs of surveyors, engineers, planners, geographers and so on.

 GPS has changed the manner in geodesists and surveyors carry out their work. It has also changed the philosophy surrounding national control survey networks not only in South Africa but in many other countries around the world. The network of trigonometrical beacons on tops of mountain and tall structures and buildings is known as a passive network since the beacon merely represents the position of the co-ordinate assigned to it and plays no role in updating or monitoring its position.

 In contrast to passive networks, the current thinking lies in the establishment of active control survey networks which utilise GPS as the primary positioning tool. A network of GPS base stations is established which record GPS data continuously. The data from each station is fed back to a central control station where the data is processed and quality checked before being made available to users via an internet facility. Users add the data to that collected by themselves and in so doing are able to determine the position of surveyed points to within .05m or better depending on number of factors. The network of base stations established in South Africa is known as TrigNet (figure five) and will consist of approximately 40 stations when completely installed. The stations have been set up on Municipal and Provincial offices, manned weather stations, airports and other such facilities.

The New South African Datum is referred to as the Hartebeesthoek 94 Datum and uses the World Geodetic System 1984 (WGS84) ellipsoid as a reference.  The datum was implemented nationally on 1 January 1999.  The Hartebeesthoek94 Datum enables South Africa to retain its status of possessing one of the most up to date and advanced integrated survey reference systems in the world, which affords its users the freedom to integrate their geo-spatial data in the world arena.  The new datum provides South Africa with the opportunity to assist its southern African neighbours with technical and technological expertise in upgrading their geodetic network.  Since its implementation on 1 January 1999, the Chief Directorate has conducted workshops (to educate users and producers of spatial data).  The Hartebeesthoek94 Datum brochure’s initial print run of 5 000 copies was exhausted by mid 1999, requiring subsequent print runs.  The brochure is available as a power point presentation on this website . . . .

Feedback from users has been overwhelmingly positive.  Users have achieved accuracy's better than 5 cm in surveys conducted over distances exceeding 50 km.  In general, however the positive impact of the new datum will only be felt after users have used it for a few more years.

• The South African Network of Active Base Stations - TrigNet

The worldwide trend for the provision of national control survey networks is moving away from the passive networks represented by highly visible trigonometrical beacons and easily accessible town survey marks.  To take advantage of the benefits of GPS and GLONASS (the Russian equivalent of GPS) as highly efficient positioning tools, national survey organisations are establishing active control survey networks consisting of a number of well distributed  continuously operating GPS/GLONASS base stations.  These provide data to surveyors, GIS data gatherers, navigators and other users, enabling them to correct the positions measured with their own satellite positioning equipment. 

In terms of the Land Survey Act of 1997, the Chief Directorate of Surveys and Mapping is mandated to establish and maintain a national control survey network.  In keeping with the change in modern technology, the Chief Directorate is in the process of installing a network of approximately 40 active GPS base stations, to be known as TrigNet (figure five), which will provide both post process and real time GPS correction data.  The stations will be approximately 200 km apart and are being connected via Telkom land lines to a central control centre at the offices of the Chief Directorate in Mowbray, Cape Town.  At the beginning of December 2001, 25 stations TrigNet (figure six) were fully operational and a further 12 sites identified.  The data provided by the network will enable users to achieve accuracy's between 5 cm and 2 m, thereby reducing capital costs to surveyors and GIS data collectors, which in turn will reduce the cost of geo-referencing services to the public. 

In establishing this network the Chief Directorate has the full co-operation of the Weather Bureau, ESKOM, Telkom, Mikomtek, Hermanus Magnetic Observatory, the Council for Geoscience, the Hartebeesthoek Radio Astronomy Observatory and numerous local authorities.  A major contribution has come from the National Land Survey of Sweden which, with funding from SIDA, has provided extensive training and consultancy.  Without this assistance, the project would not yet have reached its present advanced stage.  

Figure 5:  TrigNet:  The South African Network of GPS Base Stations

Figure 6: Trignet Base Station

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