(2012): 150 Years of International Cooperation in Geodesy: Precursors and the Development of Baeyer’S Project to a Scientific Organisation

Total Page:16

File Type:pdf, Size:1020Kb

(2012): 150 Years of International Cooperation in Geodesy: Precursors and the Development of Baeyer’S Project to a Scientific Organisation Originally published as: Torge, W. (2012): 150 Years of International Cooperation in Geodesy: Precursors and the Development of Baeyer’s Project to a Scientific Organisation. ‐ Zeitschrift für Geodäsie, Geoinformation und Landmanagement (zfv), 137, 3/2012 Fachbeitra Torge, 150 Years of International Cooperation in Geodesy ... 150 Years of International Cooperation · in Geode.sy: Precursors and the Development of Baeyer's Project to a Scientific Organisation* Wolfgang Torge Summary ternationaler Kooperation wird ausführlicher eingegangen, Geodesy commemorates th is year the founda tion of the abschließend wird auf die spätere Erweiterung zur globalen "Mitteleuropäisc he Gradmessung", which started its activi­ Wissenschaftsorganisation und die immer stärker werdende ties 150 years ago. Originated from an initiative of the Prus­ Einbindung in die interdisziplinäre Geoforschung hingewiesen. sian General Baeyer, this regional geodetic project required international cooperation. Outstanding organization soon led Keywords: Are measurements, Earth figure, Genera l Baeyer, to a scientific body which continuously extended over the International Association of Geodesy, Mitteleuropäische globe and fin ally built a global network of geodetic scien ce, Gradmessu ng represented today by the "Internationa l Association of Geo­ desy" (lAG). The following paper first remembers the start of international The Origin of Modern Geodesy and Early cooperation at the beginning of modern geodesy, as real­ International Cooperation : 18th Century ized through the arc measurements of the 18th and the early 19th century. First attempts for arc measu rements covering Geodesy, by definition, requires in te rn ational collabora­ cen tral Europe then are fou nd in the firsthalf of the 19th cen­ tion on a global scale. Thi s becomes clearly visib le with tury - connected with the names of Zach, Schumacher, Gauß, the beginning of modern geoclesy, wh ich may be reck­ Müffl ing, Bessel and Struve, among others. Ba sed upon a onecl from the 171h century. The heli ocentric world system memorandum presented 1861, Baeyer proposed a coordinat­ with the annual revolution of the Earth araund the Sun ed proceeding and clearly defined the problemstobe solved. and the daily rotation of the Earth ha cl been accepted at This idea soo n led to a governmen tal supported project and an that time, and physics ancl astronomy postulate an Earth orga nization wh ich rapidly extended beyond the boundaries fi gure flattenecl at the poles (Perrier 1939, Bi alas 1982). of central Europe. Th is early phase of international coopera­ The corresponding Earth mo clel is basecl on the theory of tion is di scussed in more detail. Finally, the later extension of hycl rostatic equilibrium (Newton** 1687, Huygens 1690), this early structure to a global scientific organization and the the observecl polar flattening of Jupiter (Jean-Dominique increasing incorporation into interdiscipl inary geoscientific Cassini 1666). ancl the latitucle-clepenclence of gravity research is shortly described. found by pendulum measurements (Richer 1672/73, Hal­ ley 1677/78). This is a great challenge for geoclesy: to Zusammenfassung prove the polar flattening by geometric methocls and to in diesem Jahr gedenkt die Geodäsie der Entstehung ihrer in­ cl etermine the parameters of such an Earth moclel! For ternationalen wissenschaftlichen Vereinigung vor 150 Jahren. a rotational elli psoid, these parameters woulcl be the Auf Initiative des preußischen Generals Baeyer entstand die semi-major axis and the geometric flatteni ng. The arc 11Mitteleuropäische Gradmessung((, ein zunächst räumlich be­ measurement methocl known since an tiqui ty is avail­ grenztes Projekt. Die hierzu notwendige internationale Zusam­ ab le for this purpose. Triangulation introcluced by Snel­ menarbeit wird effektiv organisiert und führt- bei laufender lius ( 1614/15) offers an efficient proceclure to determine Erweiterung der Aufgabenstellung - schließlich zur globalen geocletic (ell ipsoiclal) differences in length, wh ile the cle­ Vernetzung der geodä tischen Wissenschaft, heute repräsen• tennination of latitucle, longitucle and azim uth can be tiert durch die 11 /nternationa/ Association of Geodesy(( (lAG). basecl on well-known astronomical methods. A First at­ Der folgende Beitrag erinnert zunächst an die mit Beginn der tempt in this direction is carried out by J.-D. Cassini and modernen Geodäsie einsetzende länderübergreifende Zu­ his son Jacques carrying out a triangulation ( 1683 - 1718) sammenarbeit bei den Gradmessungen des 18. und des frü• along the meridian of Paris. Dividing this meridian arc of hen 19. Jahrhunderts. Erste Gradmessungen in Mitteleuropa a·2o' extension into a northern and a southern patt and oder Ansätze hierzu finden sich dann in der ersten Hälfte des 19. Jahrhunderts- verbunden u. a. mit den Namen Zach, * Modifizierte und ins Englische übersetzte Fassung eines Vor­ Schumacher. Gauß, Miiffling, Besse/ und Struve. Baeyers Idee trages im Ra hmen des Festkolloquiums ., 150 Jahre Mitteleuro­ eines koordinierten Vorgehens mit klarer Aufgabendefinition päische Gradmessung in Sachsen• am 1. Juni 20 12 in Dresden. führt schließlich - auf der Grundlage einer 1861 vorgelegten •• Names written in italics refer to historical persons, with rel­ Denkschrift - zu einer zwischenstaatlichen Zusammenarbeit, evant years of important publications or surveys, and not to Iist die bald über Europa hinausreicht. Auf diese frühe Phase in- of references. 166 zfv 3/2012 137.Jg. Torge, 150 Years of International Coope rati on in Geodesy ... Fachbeitrag separate evaluation led to an Earth model elongated at 2 Central Europe at the Turn of the 19th Century: th e poles, with a negative· fl attening of - 1/95. Thi s result Military Triangulations and the Beginning of was in agreement with a few older arc measurements, Are Measurements bu t contradicted the hypothesis of an Earth ll attened at th e poles. The poli tical situation in centrat Europe is less favour­ This is the .beginning of the well -known dispute be­ able for large-scale triangulations of high standard. This tween the fo llowers of Newton (llattening at the poles) is due to the strong separation into local territorial units, and the Cassi nis (elongation at the poles) which is solved which is especially pronounced in Germany; for the his­ by the famous arc measuret1lents in Lapland (Maupertuis, tOty of geodesy in Germany we refer to Torge (2009). Cla irnut et al. 1736/37) .and in the Spanish Vice-Kingdom Among the remarkable exceptions are the triangul a­ of Peru - today Ecuador (La Co11dami11e, Bouguer, Godi 11 tions carried out in the dukedo m of Oldenbu rg (Georg et al. 1735- 1744), ini tiated and organized by the French Christiall vo 11 Oeder, 1781- 1785) and in th e princi pali ty, Academy of Sciences. The early co mbination of the Lap­ and later kingdom, of Saxony (Friedrich Ludwig Aster, land arc with the Pa ri ~ ri1eridian arc revised by Cassi 11 i 1780-18 11), both fo llowing the example of the geodetic de Thu1y and La Caille ( 1739/40) already yields a polar sutvey of Denmark ( 1762 - 1779) un der Thomas Bugg e. fl attening of 1/304. This is co nfirmed by th e combina­ An important intermedi ate phase occurs at the turn of the tio n of further arc measurements, although the ll atten ing 19'" ce ntu ry, with the extension of French influence over values vaty between 1/1 44 and 1/352. These grea t French centrat Europe through the Napoleonic wars. The military arc measurements not only require political agreements sutveys carried out by th e well -trained French engi neer­ between the countries in volved, but also are the begin­ geogra phers are based on triangulation, and shall extend ning of international participation at large-scale geodetic the French map of scale I : 86400 on the occup ied or al­ projects. The Lap land expedi tion, fo r instance, included lied countries. Triangul ation of the occupied German re­ the Swedish astronomer Celsius, and the Spanish navy gions left of the Rhine ( 1802- 1809) is connected with the officers Jorge Juan and A ntonio de Ulloa active ly co n­ name of Trc111c hot. The upper Rhine area is sutveyed by tributed to the measurements and the evalu ation of the He111y ( 1804), while Epailly performs a rapid triangul a­ Peruvian arc measurement. tion of Hannover ( 1805 - 1806), and Bo1111e establishes a The !arge differences found for th e tlattening (and nat­ first trigonometric network in the allied Bavaria ( 1801- ura lly also fo r the semi-major axis) of an Ea tt h ell ipsoid 1807). The Batavian Republic is triangulated by Krnye11 - led to first discussions on the figure of the Earth, starting l10jj ( 1802- 181 1) . All these triangulations are co nnected already in the 18'" century. ln the beginning it is tried to to the new arc measurement along the Pa ris mericlian keep the ellipsoidal Earth model, and to ex pl ain loca l and ( 1792 - 1798) carri ed out by Dela mbre and M echain in or­ later also large-scale deviati ons through the effects of der to defin e the metre as a natural unit of length, and topography, geology, and co ntinent-ocean distribution. thus refer to the geodeti c datum provid ed by the Paris Different strategies are proposed in order to solve this obsetvatoty. This is also va lid fo r the Prussian mi litary problem, including the red uction of loca l anomali es and triangulation of Westphalia ( 1795 - 1805) ca rried out un­ the introduction of a latitude- or longi tude-dependent der the direction of Colonel 110 11 Lecoq, in a period when tl attening parameter. Araund 1·800, the time is ri pe for Prussia had withd rawn from th e coalition against France. a new definition of the Ea rth fi gure, whi ch is introduced At the end of the Napoleo nic wa rs, Prussia reo rganized soo n after by Gauß, Besse/, ancl oth ers (see below).
Recommended publications
  • Stranger Than Fiction the Tale of the Epic Voyage Made to Establish the Metric System Is an Intriguing and Exciting One
    words Stranger than fiction The tale of the epic voyage made to establish the metric system is an intriguing and exciting one. Arago alone to complete the final readings Julyan Cartwright from Majorca. On Majorca, Arago chose ho thinks about science during a S’Eslop, a peak on the northwest coast, as vacation on the Balearic Islands? his viewpoint of Ibiza and Formentera. He WMajorca, Minorca, Ibiza and had a hut built on the summit and settled Formentera are holiday destinations par in with his instruments for the final series excellence, not places where famous scientists of measurements. But events didn’t go of the past lived and worked, or where great according to plan. experiments were carried out. But there was War broke out between France and Spain a moment in history when the Balearic in June 1808, while Arago was on the Islands were crucial for a major scientific summit of S’Eslop. Soon undertaking. Majorcans were com- It was 1806, and the French Bureau des menting that the nightly Longitudes had the task of determining the bonfires were signals Paris meridian — the line of longitude pass- and that Arago must be ing through Paris. At the time there was no a French spy, and a universally agreed prime meridian; it wasn’t detachment of soldiers until 1884 that an international congress was sent up the moun- decided it should be the one that passes tain to capture him. through Greenwich. The reason for deter- Arago got wind of this; Troubled trip: during François mining the meridian with precision wasn’t in his memoirs, he Arago’s year-long journey home map-making but the metric system.
    [Show full text]
  • So, What Is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations
    the International Journal Volume 7 on Marine Navigation Number 2 http://www.transnav.eu and Safety of Sea Transportation June 2013 DOI: 10.12716/1001.07.02.14 So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations A. Weintrit Gdynia Maritime University, Gdynia, Poland ABSTRACT: In the paper the author presents overview of the meridian distance approximations. He would like to find the answer for the question what is actually the distance from the equator to the pole ‐ the polar distance. In spite of appearances this is not such a simple question. The problem of determining the polar distance is a great opportunity to demonstrate the multitude of possible solutions in common use. At the beginning of the paper the author discusses some approximations and a few exact expressions (infinite sums) to calculate perimeter and quadrant of an ellipse, he presents convenient measurement units of the distance on the surface of the Earth, existing methods for the solution of the great circle and great elliptic sailing, and in the end he analyses and compares geodetic formulas for the meridian arc length. 1 INTRODUCTION navigational receivers and navigational systems (ECDIS and ECS [Weintrit, 2009]) suggest the Unfortunately, from the early days of the necessity of a thorough examination, modification, development of the basic navigational software built verification and unification of the issue of sailing into satellite navigational receivers and later into calculations for navigational systems and receivers. electronic chart systems, it has been noted that for the The problem of determining the distance from the sake of simplicity and a number of other, often equator to the pole is a great opportunity to incomprehensible reasons, this navigational software demonstrate the multitude of possible solutions in is often based on the simple methods of limited common use.
    [Show full text]
  • From Lacaille to Gill and the Start of the Arc of the 30 Meridian
    From LaCaille to Gill and the start of the Arc of the 30th Meridian Jim R. SMITH, United Kingdom Key words: LaCaille. Maclear. Gill. Meridian Arcs. 30th Arc. SUMMARY If one looks at a map of European arcs of meridian and parallel at the beginning of the 20th century there will be seen to be a plethora them. Turning to Africa there was the complete opposite. Other than the arcs of Eratosthenes (c 300 BC) and the short arcs by LaCaille (1752) and Maclear (1841-48) the continent was empty. It was in 1879 that David Gill had the idea for a Cape to Cairo meridian arc but 1954 before it was completed. This presentation summaries the work of LaCaille and Maclear and then concentrates on a description of the 30th Meridian Arc in East Africa. The only other comparable arcs at the time were that through the centre of India by Lambton and Everest observed between 1800 and 1843; the Struve arc of 1816 to 1852 and the various arcs in France during the 18th century. The usefulness of such arcs was highlighted in 2005 with the inscription by UNESCO of the Struve Geodetic Arc on the World Heritage Monument list. A practical extension to the Struve Arc Monument is the 30th Meridian Arc since there is a connection between the two. At an ICA Symposium in Cape Town, 2003, Lindsay Braun gave a presentation that detailed the political machinations of the history of the 30th Arc; here it is hoped to fill in other aspects of this work including some facts and figures since that is what surveyors thrive upon.
    [Show full text]
  • Geodesy Methods Over Time
    Geodesy methods over time GISC3325 - Lecture 4 Astronomic Latitude/Longitude • Given knowledge of the positions of an astronomic body e.g. Sun or Polaris and our time we can determine our location in terms of astronomic latitude and longitude. US Meridian Triangulation This map shows the first project undertaken by the founding Superintendent of the Survey of the Coast Ferdinand Hassler. Triangulation • Method of indirect measurement. • Angles measured at all nodes. • Scaled provided by one or more precisely measured base lines. • First attributed to Gemma Frisius in the 16th century in the Netherlands. Early surveying instruments Left is a Quadrant for angle measurements, below is how baseline lengths were measured. A non-spherical Earth • Willebrod Snell van Royen (Snellius) did the first triangulation project for the purpose of determining the radius of the earth from measurement of a meridian arc. • Snellius was also credited with the law of refraction and incidence in optics. • He also devised the solution of the resection problem. At point P observations are made to known points A, B and C. We solve for P. Jean Picard’s Meridian Arc • Measured meridian arc through Paris between Malvoisine and Amiens using triangulation network. • First to use a telescope with cross hairs as part of the quadrant. • Value obtained used by Newton to verify his law of gravitation. Ellipsoid Earth Model • On an expedition J.D. Cassini discovered that a one-second pendulum regulated at Paris needed to be shortened to regain a one-second oscillation. • Pendulum measurements are effected by gravity! Newton • Newton used measurements of Picard and Halley and the laws of gravitation to postulate a rotational ellipsoid as the equilibrium figure for a homogeneous, fluid, rotating Earth.
    [Show full text]
  • Geodetic Position Computations
    GEODETIC POSITION COMPUTATIONS E. J. KRAKIWSKY D. B. THOMSON February 1974 TECHNICALLECTURE NOTES REPORT NO.NO. 21739 PREFACE In order to make our extensive series of lecture notes more readily available, we have scanned the old master copies and produced electronic versions in Portable Document Format. The quality of the images varies depending on the quality of the originals. The images have not been converted to searchable text. GEODETIC POSITION COMPUTATIONS E.J. Krakiwsky D.B. Thomson Department of Geodesy and Geomatics Engineering University of New Brunswick P.O. Box 4400 Fredericton. N .B. Canada E3B5A3 February 197 4 Latest Reprinting December 1995 PREFACE The purpose of these notes is to give the theory and use of some methods of computing the geodetic positions of points on a reference ellipsoid and on the terrain. Justification for the first three sections o{ these lecture notes, which are concerned with the classical problem of "cCDputation of geodetic positions on the surface of an ellipsoid" is not easy to come by. It can onl.y be stated that the attempt has been to produce a self contained package , cont8.i.ning the complete development of same representative methods that exist in the literature. The last section is an introduction to three dimensional computation methods , and is offered as an alternative to the classical approach. Several problems, and their respective solutions, are presented. The approach t~en herein is to perform complete derivations, thus stqing awrq f'rcm the practice of giving a list of for11111lae to use in the solution of' a problem.
    [Show full text]
  • Models for Earth and Maps
    Earth Models and Maps James R. Clynch, Naval Postgraduate School, 2002 I. Earth Models Maps are just a model of the world, or a small part of it. This is true if the model is a globe of the entire world, a paper chart of a harbor or a digital database of streets in San Francisco. A model of the earth is needed to convert measurements made on the curved earth to maps or databases. Each model has advantages and disadvantages. Each is usually in error at some level of accuracy. Some of these error are due to the nature of the model, not the measurements used to make the model. Three are three common models of the earth, the spherical (or globe) model, the ellipsoidal model, and the real earth model. The spherical model is the form encountered in elementary discussions. It is quite good for some approximations. The world is approximately a sphere. The sphere is the shape that minimizes the potential energy of the gravitational attraction of all the little mass elements for each other. The direction of gravity is toward the center of the earth. This is how we define down. It is the direction that a string takes when a weight is at one end - that is a plumb bob. A spirit level will define the horizontal which is perpendicular to up-down. The ellipsoidal model is a better representation of the earth because the earth rotates. This generates other forces on the mass elements and distorts the shape. The minimum energy form is now an ellipse rotated about the polar axis.
    [Show full text]
  • World Geodetic System 1984
    World Geodetic System 1984 Responsible Organization: National Geospatial-Intelligence Agency Abbreviated Frame Name: WGS 84 Associated TRS: WGS 84 Coverage of Frame: Global Type of Frame: 3-Dimensional Last Version: WGS 84 (G1674) Reference Epoch: 2005.0 Brief Description: WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system and geodetic datum. WGS 84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields. WGS 84 is the standard U.S. Department of Defense definition of a global reference system for geospatial information and is the reference system for the Global Positioning System (GPS). It is compatible with the International Terrestrial Reference System (ITRS). Definition of Frame • Origin: Earth’s center of mass being defined for the whole Earth including oceans and atmosphere • Axes: o Z-Axis = The direction of the IERS Reference Pole (IRP). This direction corresponds to the direction of the BIH Conventional Terrestrial Pole (CTP) (epoch 1984.0) with an uncertainty of 0.005″ o X-Axis = Intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The IRM is coincident with the BIH Zero Meridian (epoch 1984.0) with an uncertainty of 0.005″ o Y-Axis = Completes a right-handed, Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system • Scale: Its scale is that of the local Earth frame, in the meaning of a relativistic theory of gravitation. Aligns with ITRS • Orientation: Given by the Bureau International de l’Heure (BIH) orientation of 1984.0 • Time Evolution: Its time evolution in orientation will create no residual global rotation with regards to the crust Coordinate System: Cartesian Coordinates (X, Y, Z).
    [Show full text]
  • The Meridian Arc Measurement in Peru 1735 – 1745
    The Meridian Arc Measurement in Peru 1735 – 1745 Jim R. SMITH, United Kingdom Key words: Peru. Meridian. Arc. Triangulation. ABSTRACT: In the early 18th century the earth was recognised as having some ellipsoidal shape rather than a true sphere. Experts differed as to whether the ellipsoid was flattened at the Poles or the Equator. The French Academy of Sciences decided to settle the argument once and for all by sending one expedition to Lapland- as near to the Pole as possible; and another to Peru- as near to the Equator as possible. The result supported the view held by Newton in England rather than that of the Cassinis in Paris. CONTACT Jim R. Smith, Secretary to International Institution for History of Surveying & Measurement 24 Woodbury Ave, Petersfield Hants GU32 2EE UNITED KINGDOM Tel. & fax + 44 1730 262 619 E-mail: [email protected] Website: http://www.ddl.org/figtree/hsm/index.htm HS4 Surveying and Mapping the Americas – In the Andes of South America 1/12 Jim R. Smith The Meridian Arc Measurement in Peru 1735-1745 FIG XXII International Congress Washington, D.C. USA, April 19-26 2002 THE MERIDIAN ARC MEASUREMENT IN PERU 1735 – 1745 Jim R SMITH, United Kingdom 1. BACKGROUND The story might be said to begin just after the mid 17th century when Jean Richer was sent to Cayenne, S. America, to carry out a range of scientific experiments that included the determination of the length of a seconds pendulum. He returned to Paris convinced that in Cayenne the pendulum needed to be 11 lines (2.8 mm) shorter there than in Paris to keep the same time.
    [Show full text]
  • Geodetic Reference System 1980
    Geodetic Reference System 1980 by H. Moritz 1-!Definition meridian be parallel to the zero meridian of the BIH adopted longitudes". The Geodetic Reference System 1980 has been adopted at the XVII General Assembly of the IUGG in For the background of this resolution see the report of Canberra, December 1979, by means of the following!: IAG Special Study Group 5.39 (Moritz, 1979, sec.2). Also relevant is the following IAG resolution : "RESOLUTION N° 7 "RESOLUTION N° 1 The International Union of Geodesy and Geophysics, The International Association of Geodesy, recognizing that the Geodetic Reference System 1967 recognizing that the IUGG, at its XVII General adopted at the XIV General Assembly of IUGG, Lucerne, Assembly, has introduced a new Geodetic Reference System 1967, no longer represents the size, shape, and gravity field 1980, of the Earth to an accuracy adequate for many geodetic, geophysical, astronomical and hydrographic applications recommends that this system be used as an official and reference for geodetic work, and considering that more appropriate values are now encourages computations of the gravity field both on available, the Earth's surface and in outer space based on this system". recommends 2-!The Equipotential Ellipsoid a)!that the Geodetic Reference System 1967 be replaced According to the first resolution, the Geodetic Reference by a new Geodetic Reference System 1980, also System 1980 is based on the theory of the equipotential based on the theory of the geocentric equipotential ellipsoid. This theory has already been the basis of the ellipsoid, defined by the following conventional constants : Geodetic Reference System 1967; we shall summarize (partly quoting literally) some principal facts from the .!equatorial radius of the Earth : relevant publication (IAG, 1971, Publ.
    [Show full text]
  • The Solar System Questions KEY.Pdf
    THE SOLAR SYSTEM 1. The atmosphere of Venus is composed primarily of A hydrogen and helium B carbon dioxide C methane D ammonia Base your answers to questions 2 through 6 on the diagram below, which shows a portion of the solar system. 2. Which graph best represents the relationship between a planet's average distance from the Sun and the time the planet takes to revolve around the Sun? A B C D 3. Which of the following planets has the lowest average density? A Mercury B Venus C Earth D Mars 4. The actual orbits of the planets are A elliptical, with Earth at one of the foci B elliptical, with the Sun at one of the foci C circular, with Earth at the center D circular, with the Sun at the center 5. Which scale diagram best compares the size of Earth with the size of Venus? A B C D 6. Mercury and Venus are the only planets that show phases when viewed from Earth because both Mercury and Venus A revolve around the Sun inside Earth's orbit B rotate more slowly than Earth does C are eclipsed by Earth's shadow D pass behind the Sun in their orbit 7. Which event takes the most time? A one revolution of Earth around the Sun B one revolution of Venus around the Sun C one rotation of the Moon on its axis D one rotation of Venus on its axis 8. When the distance between the foci of an ellipse is increased, the eccentricity of the ellipse will A decrease B increase C remain the same 9.
    [Show full text]
  • The International Association of Geodesy 1862 to 1922: from a Regional Project to an International Organization W
    Journal of Geodesy (2005) 78: 558–568 DOI 10.1007/s00190-004-0423-0 The International Association of Geodesy 1862 to 1922: from a regional project to an international organization W. Torge Institut fu¨ r Erdmessung, Universita¨ t Hannover, Schneiderberg 50, 30167 Hannover, Germany; e-mail: [email protected]; Tel: +49-511-762-2794; Fax: +49-511-762-4006 Received: 1 December 2003 / Accepted: 6 October 2004 / Published Online: 25 March 2005 Abstract. Geodesy, by definition, requires international mitment of two scientists from neutral countries, the collaboration on a global scale. An organized coopera- International Latitude Service continued to observe tion started in 1862, and has become today’s Interna- polar motion and to deliver the data to the Berlin tional Association of Geodesy (IAG). The roots of Central Bureau for evaluation. After the First World modern geodesy in the 18th century, with arc measure- War, geodesy became one of the founding members of ments in several parts of the world, and national geodetic the International Union for Geodesy and Geophysics surveys in France and Great Britain, are explained. The (IUGG), and formed one of its Sections (respectively manifold local enterprises in central Europe, which Associations). It has been officially named the Interna- happened in the first half of the 19th century, are tional Association of Geodesy (IAG) since 1932. described in some detail as they prepare the foundation for the following regional project. Simultaneously, Gauss, Bessel and others developed a more sophisticated Key words: Arc measurements – Baeyer – Helmert – definition of the Earth’s figure, which includes the effect Figure of the Earth – History of geodesy – of the gravity field.
    [Show full text]
  • A General Formula for Calculating Meridian Arc Length and Its Application to Coordinate Conversion in the Gauss-Krüger Projection 1
    A General Formula for Calculating Meridian Arc Length and its Application to Coordinate Conversion in the Gauss-Krüger Projection 1 A General Formula for Calculating Meridian Arc Length and its Application to Coordinate Conversion in the Gauss-Krüger Projection Kazushige KAWASE Abstract The meridian arc length from the equator to arbitrary latitude is of utmost importance in map projection, particularly in the Gauss-Krüger projection. In Japan, the previously used formula for the meridian arc length was a power series with respect to the first eccentricity squared of the earth ellipsoid, despite the fact that a more concise expansion using the third flattening of the earth ellipsoid has been derived. One of the reasons that this more concise formula has rarely been recognized in Japan is that its derivation is difficult to understand. This paper shows an explicit derivation of a general formula in the form of a power series with respect to the third flattening of the earth ellipsoid. Since the derived formula is suitable for implementation as a computer program, it has been applied to the calculation of coordinate conversion in the Gauss-Krüger projection for trial. 1. Introduction cannot be expressed explicitly using a combination of As is well known in geodesy, the meridian arc elementary functions. As a rule, we evaluate this elliptic length S on the earth ellipsoid from the equator to integral as an approximate expression by first expanding the geographic latitude is given by the integrand in a binomial series with respect to e2 , regarding e as a small quantity, then readjusting with a a1 e2 trigonometric function, and finally carrying out termwise S d , (1) 2 2 3 2 0 1 e sin integration.
    [Show full text]