Grade measurement
Encyclopedia
Grade measurement is the geodetic
determination of the local radius of curvature of the figure of the Earth
by determining the difference in astronomical latitude
between two locations on the same meridian
, the metric distance between which is known.
The first known grade measurement was performed by Eratosthenes
(240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The Dutch geodesist Snellius
(~1620) repeated the experiment between Alkmaar
and Bergen op Zoom
using more modern geodetic instrumentation.
Later grade measurements aimed at determining the flattening
of the Earth ellipsoid by measuring at different geographic latitudes. The first of these was the one commissioned by the French Academy of Sciences
in 1735-1738, involving measurement expeditions to Lapland (Maupertuis
et al.) and Peru (Pierre Bouguer
et al.).
Later, Struve
measured a geodetic triangle chain between the Arctic Sea and the Black Sea
, and Bessel
compiled several meridian arc
s to compute the famous Bessel ellipsoid
(1841). Nowadays, the method is replaced by worldwide geodetic network
s and by satellite geodesy
.
Also the imaginary grade measurement described by Jules Verne
in his book "Adventures of 3 Russians and 3 Englishmen in South Africa" of 1872 may be mentioned.
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
determination of the local radius of curvature of the figure of the Earth
Figure of the Earth
The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earth's size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and water areas. This is, in fact, the surface...
by determining the difference in astronomical latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
between two locations on the same meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...
, the metric distance between which is known.
The first known grade measurement was performed by Eratosthenes
Eratosthenes
Eratosthenes of Cyrene was a Greek mathematician, poet, athlete, geographer, astronomer, and music theorist.He was the first person to use the word "geography" and invented the discipline of geography as we understand it...
(240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The Dutch geodesist Snellius
Snellius
Snellius may refer to:*Rudolph Snellius , a Dutch linguist and mathematician at the Universities of Marburg and Leiden*Snellius , a lunar crater located near the southeast limb of the Moon...
(~1620) repeated the experiment between Alkmaar
Alkmaar
Alkmaar is a municipality and a city in the Netherlands, in the province of Noord Holland. Alkmaar is well known for its traditional cheese market. For tourists, it is a popular cultural destination.-History:...
and Bergen op Zoom
Bergen op Zoom
Bergen op Zoom is a municipality and a city located in the south of the Netherlands.-History:Bergen op Zoom was granted city status probably in 1266. In 1287 the city and its surroundings became a lordship as it was separated from the lordship of Breda. The lordship was elevated to a margraviate...
using more modern geodetic instrumentation.
Later grade measurements aimed at determining the flattening
Flattening
The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator...
of the Earth ellipsoid by measuring at different geographic latitudes. The first of these was the one commissioned by the French Academy of Sciences
French Geodesic Mission
The French Geodesic Mission was an 18th-century expedition to what is now Ecuador carried out for the purpose of measuring the roundness of the Earth and measuring the length of a degree of longitude at the Equator...
in 1735-1738, involving measurement expeditions to Lapland (Maupertuis
Pierre Louis Maupertuis
Pierre-Louis Moreau de Maupertuis was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great....
et al.) and Peru (Pierre Bouguer
Pierre Bouguer
Pierre Bouguer was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture"....
et al.).
Later, Struve
Friedrich Georg Wilhelm von Struve
Friedrich Georg Wilhelm von Struve was a Danish-Baltic German astronomer from a famous dynasty.-Life:...
measured a geodetic triangle chain between the Arctic Sea and the Black Sea
Black Sea
The Black Sea is bounded by Europe, Anatolia and the Caucasus and is ultimately connected to the Atlantic Ocean via the Mediterranean and the Aegean seas and various straits. The Bosphorus strait connects it to the Sea of Marmara, and the strait of the Dardanelles connects that sea to the Aegean...
, and Bessel
Friedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
compiled several meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
s to compute the famous Bessel ellipsoid
Bessel ellipsoid
The Bessel ellipsoid is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, in Europe and on other continents, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.The Bessel ellipsoid was derived...
(1841). Nowadays, the method is replaced by worldwide geodetic network
Geodetic network
A geodetic network is a network of triangles which are measured exactly by techniques of terrestrial surveying or by satellite geodesy.In "classical geodesy" this is done by triangulation, based on measurements of angles and of some spare distances; the precise orientation to the geographic north...
s and by satellite geodesy
Satellite geodesy
Satellite geodesy is the measurement of the form and dimensions of the Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques—geodesy by means of artificial satellites...
.
Also the imaginary grade measurement described by Jules Verne
Verne
-Surname:*Jules Verne , French early science-fiction writer*Adela Verne , English pianist and minor composer*Kaaren Verne , German actress*Larry Verne , American novelty song singer...
in his book "Adventures of 3 Russians and 3 Englishmen in South Africa" of 1872 may be mentioned.
See also
- Erdmessung
- Earth ellipsoidEarth ellipsoidAn Earth ellipsoid is a mathematical figure approximating the shape of the Earth, used as a reference frame for computations in geodesy, astronomy and the geosciences...
- Meridian arcMeridian arcIn geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
- Astrogeodesy
- Struve Geodetic ArcStruve Geodetic ArcThe Struve Geodetic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea, through ten countries and over 2,820 km, which yielded the first accurate measurement of a meridian....