# geodesy

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## geodesy

(jēŏd`ĭsē) or## geodetic surveying,

theory and practice of determining the position of points on the earth's surface and the dimensions of areas so large that the curvature of the earth must be taken into account. It is distinguished from plane surveying**surveying,**

method of determining accurately points and lines of direction (bearings) on the earth's surface and preparing from them maps or plans. Boundaries, areas, elevations, construction lines, and geographical or artificial features are determined by the measurement of

**.....**Click the link for more information. , the operations of which are executed without regard to the earth's curvature. In geodetic surveying, two points, called stations, many miles apart are selected, and the latitude and longitude of each is determined by astronomical means. The line between these two points, the base line, is measured with a high degree of accuracy. The position of a third station is determined by the angle it makes with each end of the base line. This process, called triangulation, is continued until the whole area to be surveyed is mapped. For indicating a triangulation station the U.S. Coast and Geodetic Survey uses a bronze disk suitably marked and having a projection on the bottom for anchoring it in concrete. Where the curvature of the earth is great or where there are hills or high trees between stations, towers are built so that one station may be seen from another. In recent years, artificial earth satellites have come into wide use as geodetic instruments. Shifts in the orbits of the satellites Explorer I and Vanguard I provided data by which geodesists corrected the value for the oblateness of the earth. This led to a program of geodetic satellites specifically designed to measure variations in the earth's gravitational field, and to determine the exact geographic position of points on the earth's surface. A triangulation station in space, the geodetic satellite, is photographed against the background of stars in order to compare accurately the relative positions of points on the earth.

## geodesy

(gee-**od**-ĕ-see) The study and measurement of the external shape of the Earth, and hence of its gravitational field and internal construction, using both the measurements of the precise form of the geoid and observations of artificial Earth satellites.

## Geodesy

the science of determining the figure, dimensions, and gravitational field of the earth and of measurements on the earth’s surface for the purpose of representation on a plane and on maps and also for carrying out various activities of engineering and national economic significance. The name “geodesy” (“division of the earth”) indicates the initial practical tasks that gave rise to it, but does not reveal its current scientific problems and practical tasks, which are related to the varied needs of human activity.

** The primary tasks of geodesy.** In determining the figure and dimensions of the earth, geodesy proceeds from the concept of level earth surfaces, that is, surfaces such that the potential of the force of gravity on each surface always has an appropriate constant value and the surfaces intersect the directions of the plumb line at a right angle. In geodesy the direction of the plumb line is taken as one of the coordinate lines, since at any given point it may be drawn unambiguously with the assistance of the level or even of a simple plumb.

The water surface in the oceans and adjoining seas considered in a state of complete calm and equilibrium would be one of the level surfaces of the earth. This level surface, in an imaginary extension under the continents in such a way that it always intersects the direction of the plumb line at a right angle, is taken in geodesy as the primary level surface of the earth (Figure 1). In geodesy the smoothed out figure of the earth is considered a level surface and called the geoid.

The theory of the earth’s figure and the results of astronomical and geodetic measurements show that the geoid is generally close to an ellipsoid of revolution. The ellipsoid that by its dimensions and position in the body of the earth most correctly represents the geoid as a whole is called the general earth ellipsoid. Study of the earth’s figure involves determining the dimensions of the earth ellipsoid, its position in the body of the earth itself, and deviations of the geoid from this ellipsoid. If the elevations of points on the earth’s surface are determined relative to the geoid, that is, above sea level, then the figure of the earth’s physical surface will thereby also have been studied.

The dimensions of the earth ellipsoid and its position in the earth’s body are established by determining the directions of plumb lines at selected points on the earth’s surface and the positional relationships of these points in a certain system of coordinates. The direction of the plumb line at a given point is described by its astronomical latitude and longitude, which are derived from astronomical observations. The positional relationships of points on the earth’s surface are determined by their geodetic latitudes and longitudes, which describe the directions of the normals to the surface of the so-called reference ellipsoid at these points. The angle between the plumb line and the normal to the reference ellipsoid at the given point is the deflection of plumb and characterizes the slope of the level surface of the earth relative to the reference ellipsoid at this point. Both the dimensions of the earth ellipsoid and the elevation of the geoid are determined on the basis of observed deflections of plumb at selected points.

The totality of astronomical and geodetic measurements that make possible determination of the figure and dimensions of the earth are called arc measurements and lead to geometric methods of solving this problem. There are also physical, or dynamic, methods of studying the earth’s figure and gravitational field. They are based on measurements of the acceleration of the force of gravity and observations of the movement of man-made earth satellites and spacecraft. The measured values of gravity are compared with corresponding theoretical values calculated for a certain ellipsoidal level surface. The differences between the particular values of gravity are called gravity anomalies and characterize the deviations of the earth’s level surfaces from the ellipsoid. They make it possible to determine flattening of the earth and deviations of the geoid from the earth ellipsoid. The deviations of the earth’s actual figure from a perfect spherical shape and the anomalies of the earth’s gravitational field cause perturbances in the orbits of man-made objects in space. Knowing the orbit perturbances of artificial earth-orbiting satellites, it is possible to determine the figure and external gravity field of the earth on the basis of observations and measurements. The modern use of geometric and dynamic methods makes it possible to determine simultaneously the figure, dimensions, and gravitational field of the earth as a planet.

Deflections of plumb and gravity anomalies reflect characteristics of the internal structure of the earth and are used to clarify questions of the distribution of mass within the earth and especially for studying the structure of the earth’s crust. Data on the figure, dimensions, and gravitational field of the earth are very important for establishing a scale of the relative distances and masses of celestial bodies. They are also used for computer calculations related to launching spacecraft and to studying space in general.

Other tasks of geodesy involve various measurements on the earth’s surface in order to represent it on a plane and on topographical maps, which are very important for military affairs and without which no national economic or engineering-technical activity can be pursued. Geodetic work is carried out to survey, plan, and build hydraulic structures and industrial enterprises, irrigation and navigation canals, surface and underground means of communication, and so on. Geodetic work and topographical maps serve as the basis for planning cities and population centers, conducting land and forest management activities, exploring for minerals, and exploiting natural wealth. At times consideration must be given to changes in the earth’s figure and gravitational field, as well as in the surface of the earth, these changes being caused by various external and internal factors. These are studied by repeated astronomical observations, geodetic measurements, and gravimetric determinations. The hypothesized horizontal motion of the continents is studied by repeated astronomical determinations of the position of specific points on the earth’s surface. Repeated geodetic determinations of the positional relationships and elevations of points on the earth’s surface at certain time intervals make it possible to determine the speed and direction of horizontal and vertical movements of the earth’s crust.

** Divisions of geodesy and types of geodetic work.** Geodetic knowledge is divided into higher geodesy and geodesy, and these, in turn, are subdivided into more or less independent branches.

The primary task of higher geodesy is to determine the figure, dimensions, and gravitational field of the earth and also to study the theories and methods of accomplishing this. The tasks of higher geodesy also include the study of theories and methods of primary geodetic work, which are used to construct a geodetic control network and provide the data required for accomplishing the scientific and practical tasks of geodesy. The geodetic network is a system of appropriately selected and fixed points on the earth’s surface, which are called geodetic control points. Their positional relationships and elevations are determined in an accepted system of coordinates and elevation calculation.

The positions of geodetic control points are determined primarily by the method of triangulation, which is based on the trigonometric principle of measuring distances. The triangulation method consists of constructing on the terrain chains and nets of triangles consecutively interconnected by common sides. Having measured one side, called the base or base side, of one of the triangles (see Figure 2) and at least two angles in each of them, one can determine the lengths of the sides of all triangles by means of trigonometric computations. Usually all three angles are measured in each triangle, and in any triangulation that covers a large territory, many bases located a definite distance from each other are measured. The method of survey traverse is also used to construct the geodetic network. It consists of measuring on the terrain the lengths of consecutively interconnected lines that form a polygonometric traverse and measuring the horizontal angles between them. Knowing the position of one point and the direction of one line of the polygonometric traverse connected to it, one can determine the position of all points on the traverse in the adopted system of coordinates by successive computations. Sometimes the position of geodetic control points is determined by the method of trilateration, measuring all three sides of all the triangles that form the geodetic network.

Geodetic points are located on elevated points of the terrain and are selected by reconnaissance. Each point is fixed on the terrain by laying a concrete block at a certain depth with a mark on it that designates the apex of the triangle and constructing a wooden or metal tower that serves as a stand for the angle-measuring instrument and as a sighting target (geodetic signal) when measuring angles. Sometimes geodetic points are combined with prominent local objects, such as water towers and the steeples of tall buildings.

Geodetic networks are subdivided into classes, depending on the sequence of construction and precision of measurement. Thus, the state geodetic network of the USSR is divided into classes I, II, III, and IV. In the USSR class I state triangulation is constructed of a chain of approximately equilateral triangles with sides of 20-25 km located roughly in the direction of the earth’s meridians and parallels at intervals of 200-250 km. The area that is bordered by the class I triangulation chain is covered with solid nets of class II triangles with sides of about 10-20 km. The network of geodetic points can be made more dense by construction of class III and class IV triangles.

In places where class I triangulation chains intersect and in class II triangulation nets, bases at least 5-6 km long or base sides are measured. The bases are measured by measuring wires, which are laid out consecutively along the line of the base; error in measurement here is not greater than 1:1,000,000 of the length of the base. Base sides are measured directly by electrooptical range finders with an error of not more than 1:400,000. Radar is also used to measure the lines in polygonometric traverses and the sides of triangles in trilateration.

The angles of triangles and the angles of rotation of the polygonometric traverses are measured by means of geodetic instruments for measuring angles, which are complex optical-mechanical devices. In this case the angle between the directions to two observed objects at the specific point is understood to mean the angle between the planes passing through these objects and the plumb line at the specific point. The error in measurements of angles of the triangles in class I and class II triangulation is usually not more than 0.7”.

The results of observations of the movement of artificial earth-orbiting satellites are also used to construct the net of geodetic control points and determine their position. Satellite observations involve either photographing the satellite against a background of stars whose positions are known or measuring the distances to the satellite from stand points using radar; it is also possible to perform both operations simultaneously. If the laws of the satellite’s movement are well studied, it serves as a mobile geodetic point whose coordinates are known at each given moment of time. But if the laws of the satellite’s movement have not been studied, it serves as only an intermediate geodetic point; therefore, in order to determine an unknown point on the earth’s surface it is necessary to observe the satellite at exactly the same time at both this point and several known geodetic points. Consideration of the theories and methods of using satellites to accomplish the scientific and practical tasks of geodesy constitutes the content of satellite geodesy.

The latitude and longitude of points at the terminal points of the bases and base sides of class I and class II triangulation, as well as the azimuth of the direction to a selected object on earth, are determined by means of astronomical observations. The astronomical latitudes and longitudes are also determined for intermediate points of class I triangulation, selected at locations not farther than 70-100 km apart. Astronomical determinations at points of the geodetic control network transform it into an astronomical and geodetic network *that* provides the basic data for investigating the figure and dimensions of the earth and serves to spread a single system of coordinates to the entire territory of the country. The consideration of theories and methods of determining the geographic position of a place on the basis of astronomical observations belongs to geodetic astronomy.

The position on a plane of geodetic points is determined by geodetic coordinates, namely, the latitudes and longitudes of their projections on the surface of a certain ellipsoid—the reference ellipsoid. In addition to the coordinates, at each geodetic point the directions to adjacent points relative to a meridian are also determined. These directions are called geodetic azimuths and serve for orientation on the terrain.

The geodetic coordinates of the point that is the initial one in the geodetic control network and the geodetic azimuth of the direction between the initial point and one of the adjacent points are established by determining the initial point’s astronomical coordinates and the astronomical azimuth of the same direction by correcting the coordinates for the effect of the deflection of plumb. The data so obtained, as well as the elevation of the geoid above the reference ellipsoid at the initial point, characterize the position of the assumed ellipsoid in the earth’s body and are called the initial geodetic datums. The geodetic coordinates and azimuths of the other points are obtained by computation based on the results of geodetic measurements carried out relative to the reference ellipsoid.

The Krasovskii reference ellipsoid has been adopted for computing the coordinates of points in the USSR state geodetic network. This ellipsoid is characterized by the following data: semimajor axis *a* = 6,378,245 m and polar flattening *a* = 1:298.3. The Pulkovo Astronomical Observatory (the center of its Round Hall) is the initial point, with the following geodetic coordinates adopted for it: latitude *B* = 59° 46’18.55” and longitude *L* = 30° 19’42.09”. These coordinates were obtained by correcting the point’s astronomical latitude and longitude for the effect of the deflection of the plumb line from the normal to the surface of the Krasovskii ellipsoid. The elevation of the geoid above the surface of this ellipsoid at Pulkovo is taken as equal to zero.

One of the branches of higher geodesy considers the geometry of the earth ellipsoid and is called spheroidic geodesy. Its tasks include developing methods of reducing geodetic measurements to the surface of the reference ellipsoid and methods of solving triangles and computing the coordinates of control points on this surface. Spheroidic geodesy also provides the mathematical basis for methods of determining the figure and dimensions of the earth from arc measurements.

Reduction of geodetic measurements to the surface of the reference ellipsoid involves projecting the appropriate points on this surface by normals. This is achieved by correcting the results of geodetic measurements—for example, the lengths of lines and magnitudes of angles—for the elevation of the earth’s surface above the reference ellipsoid and for deflections of the plumb line at the points being determined.

The projections of the points being determined on the surface of the reference ellipsoid are connected by geodetic lines, and their coordinates are obtained by successive computations and summing of the differences of the coordinates of every two neighboring points by the length and direction of the geodetic lines that connect them. Because the geodetic coordinates are expressed in angle measure and are inconvenient for practical purposes, they are usually replaced by rectangular coordinates on a plane by representing the surface of the reference ellipsoid on the plane according to one or another mathematical law of point correspondence. Spheroidic geodesy considers the theories of representing only limited parts of the surface of the earth ellipsoid on a plane. Representation of the entire earth ellipsoid on a plane for the construction of geographic maps is considered in mathematical cartography.

The elevations of geodetic control points are determined by the methods of geometric leveling, which involves measuring and summing the differences of the elevations of every two successive points located at a distance (depending on the class) of 100-300 m from each other along a certain leveling line. Differences in elevations are determined by a leveling instrument as the difference of readings on rods having precise divisions when the rods are set by plumb and the sight line of the tube of the leveling instrument is strictly horizontal. Depending on the sequence and precision of work geometric leveling lines are subdivided into classes.

In the USSR class I leveling is done by specially marked lines that form closed polygons with a perimeter of about 1,600 km; it is done with the greatest precision, which is attained using modern instruments and work methods. Thus, for class I lines the random error of leveling is not greater than 0.5 mm, and the systematic error is only 0.03 mm per kilometer of the leveling line. The class II leveling network is constructed of lines laid along railroads, highways, unpaved roads, and large rivers; they form closed polygons with perimeters of about 600 km. Differences in elevation for class II leveling lines are determined with a mean random error of not more than 1 mm and a systematic error of not more than 0.2 mm per kilometer of the leveling line. Class I and class II leveling networks are made more dense by class III and class IV leveling lines.

Leveling lines of all classes are fixed on the terrain by datum points or markers that are set in the ground or in the walls of stone buildings every 3-5 km. So-called fundamental datum points, which are intended to last for a long time, are set every 50-80 km on class I, II, and III leveling lines and at their points of intersection. The elevations of the leveling datum points and markers are computed in a particular system of elevations above sea level at some initial point. In Soviet leveling work the system of normal elevations has been adopted and the Kronstadt depth gauge serves as the initial point. Its zero coincides with the long-term average level of the Baltic Sea.

Data on the distribution of the force of gravity on the earth’s surface are necessary to determine the coordinates and elevations of points of the geodetic control network. Questions of measuring gravity are dealt with in gravimetry, which is an independent branch of geodetic knowledge. The methods of using gravimetric data to accomplish the scientific and practical tasks of geodesy constitute the content of geodetic gravimetry, which was established by the works of the Soviet scientist M. S. Molodenskii.

Geodesy considers the methods, technique, and organization of work related to measurements on the earth’s surface for the purpose of representation on plans and maps. The sum total of this work constitutes topographic surveying of the terrain, and therefore the corresponding branch of geodesy is often called topography. In the past topographical surveying was done by the ground method, which is now used only for surveying small sectors of terrain. Topographical surveys of large areas of the earth’s surface are made by continuous photographing of the terrain from aircraft and by subsequent photogrammetric processing of aerial photographs. Topographical surveys result in topographical maps that serve as the raw material for making various maps on smaller scales. The methods of making and publishing all possible kinds of maps are considered in cartography.

The study of the methods, technique, and organization of geodetic work related to conducting various engineering activities (such as the construction of hydraulic structures, means of communication, large high-rise buildings, and industrial enterprises) constitutes the content of engineering geodesy. Study of analogous questions related to the construction of mines, tunnels, and subways is also a task of engineering geodesy and, at the same time, is a constituent part of underground surveying.

Because geodetic measurements are accompanied by inevitable errors of various kinds, it is customary in geodesy to measure each quantity a number of times and also to measure a larger number of quantities than are necessary to accomplish the given task. The measurement of each extra quantity creates one condition that links the quantity with other quantities and that is not fulfilled because of their errors. Methods of assessing the precision of geodetic measurements are studied by the theory of errors (for example, the least squares method); bringing geodetic measurements into correspondence with those mathematical conditions that they should satisfy constitutes the content of adjustment computation.

** Brief historical survey.** Geodesy arose in ancient times when it became necessary to measure land to make plans and maps for economic purposes. In the seventh century B.C. geographic maps that also contained economic information were drawn on clay tablets in Babylonia and Assyria. In the sixth through fourth centuries B.C. hypotheses concerning the sphericity of the earth were expressed, and some evidence for this was found. In the third century B.C. in Egypt, the Greek scientist Eratosthenes made the first determination of the radius of the globe on the basis of correct geometric principles, which became known as arc measurements. At this time the name “geodesy” as a branch of human knowledge related to astronomy, cartography, and geography appeared for the first time in the works of Aristotle. In the second century B.C. astronomers and mathematicians established the concepts of the geographic latitude and longitude of a place, developed the first cartographic projections, introduced the grid of meridians and parallels on maps, and proposed the first methods of determining the positional relationships of points on the earth’s surface by astronomical observations. At the beginning of the ninth century, Mamun, the caliph of Baghdad, commissioned one of the first arc measurements near Mosul, and the radius of the globe was determined quite exactly.

The start of geodetic work in Russia goes back to the tenth century. The collection of laws *Russkaia Pravda* (11 th— 12th centuries) contains decrees on determining land borders by measurement. One of the first maps of the Muscovite state, the so-called Great Drawing, which was made in the 16th century, was based on route surveys and information obtained by questioning people.

The development of modern geodesy and geodetic work began in the 17th century. The telescope was invented at the beginning of the 17th century. A major step in the development of geodesy was the invention, by the Dutch scientist W. Snell (Snellius) in 1615-17, of the method of triangulation. It continues to this day to be one of the basic methods of determining control points for topographical surveys. The appearance of the angle-measuring instrument, called the theodolite, and its combination with a telescope equipped with a grid of cross hairs increased the precision of angle measurements in triangulation. In the middle of the 17th century the barometer was invented, the first instrument for determining the elevation of points on the earth’s surface. Graphic methods of topographical survey, which simplified the making of topographical maps, were also developed.

The discovery of the law of universal gravitation by the English scientist I. Newton in the second half of the 17th century led to the appearance of the idea of the spheroidicity of the earth, that is, its oblateness in the direction of the poles. Proceeding from the law of gravitation and a hypothesis on the internal structure of the earth, I. Newton and the Dutch scientist C. Huygens determined in a purely theoretical manner that the earth spheroid is flattened. They obtained strongly contradictory results that aroused doubt as to the oblateness of the earth’s figure and even doubt concerning the soundness of the law of universal gravitation. In connection with this, in the first half of the 18th century the Paris Academy of Sciences sent geodetic expeditions to Peru and Lapland. There they made arc measurements that confirmed the correctness of the idea of the earth’s spheroidicity and proved the soundness of the law of universal gravitation. In the middle of the 18th century the French scientist A. Clairaut developed the fundamentals of the theory of the earth’s figure and substantiated the law of change in the force of gravity on the earth spheroid depending on geographical latitude. The age during which the law of gravitation was discovered and the above-mentioned geodetic expeditions were carried out was the age of the establishment of geodesy as the independent science of the earth’s figure and methods of studying it. At the end of the 18th century in France, P. Méchain and J. Delambre measured the arc of the meridian from Dunkerque to Barcelona in order to establish the length of the meter as 1:10,000,000 of the meridian quadrant and obtained one of the first reliable deductions on the dimensions of the earth ellipsoid.

The development of geodetic work in Russia intensified under Peter I who, in 1701, established the first astronomical observatory in Russia and founded the School of Mathematical and Navigational Sciences, which trained mathematicians, astronomers, geodesists, and geographers. Both were in Moscow. The first topographical surveys in Russia were begun at the turn of the 18th century. In 1720, Peter I placed topographical and cartographic work in Russia under the jurisdiction of the Senate, thus emphasizing its great state importance. In 1739 the Geographic Department was organized at the St. Petersburg Academy of Sciences. It directed all geodetic and cartographic work in Russia. On the basis of the manifesto on the general land survey, which was issued in 1765, geodetic work was done to make maps of landholdings. This work continued almost until the middle of the 19th century and provided extensive material for mapping the country. In 1779 a land surveying school was founded in Moscow, and in 1819 it became the Konstantin Land Surveying School; in 1835 it became the Konstantin Land Surveying Institute, and later it became a major higher educational institution for the training of geodesists and cartographers. In connection with the increased military demand for topographical maps, the Map Depot was organized at the General Staff in 1797. In 1812 it became the Military Topographical Depot, and in 1822 the Corps of Military Topographers was founded. All the main astronomical-geodetic and topographical work in prerevolutionary Russia was done by this institution; its work is a remarkable monument to the development of domestic geodetic and cartographic science. In 1816, under the leadership of the Russian military geodesist K. I. Tenner and the astronomer V. Ia. Struve, major astronomical-geodetic work was begun in the western border provinces of Russia; this project concluded in 1855 with the arc measurement of an enormous (more than 25° of latitude) meridian arc stretching along the 30° meridian from the mouth of the Danube to the shores of the Arctic Ocean.

Small arc measurements were made by the German scientists K. F. Gauss (1821-24 in Hanover) and F. W. Bessel (1831-34 in East Prussia). They also improved the methods and instruments of geodetic work and developed new procedures for solving geodetic problems on the surface of the earth ellipsoid. In 1828, Gauss proposed adopting the average level of the sea as the mathematical surface of the earth. In 1859 the Russian military geodesist F. F. Shubert was the first to express the idea that the earth possibly had three axes and to determine the dimensions of the triaxial earth ellipsoid. In 1873 the German physicist J. Listing introduced the concept of the geoid to signify the earth’s figure. In 1888 the Russian scientist F. A. Sludskii created an original theory of the earth’s figure and substantiated certain methods of studying it.

During the 19th century a number of determinations of the dimensions of the earth ellipsoid were obtained. In 1864 the European Geodetic Association was founded to solve the basic problem of geodesy. It later became the International Geodetic Association and was the ancestor of the International Geodetic and Geophysical Union. In the second half of the 19th century geodetic methods began to be used to study the internal structure of the earth and crustal movements.

After the October Revolution a new age in the development of geodesy and geodetic work in our country began. The decree of the Council of People’s Commissars of the RSFSR, dated Mar. 15, 1919, and signed by V. I. Lenin, founded the Higher Geodetic Administration, which later became the Main Administration of Geodesy and Cartography under the Council of Ministers of the USSR and is the center of the country’s state geodetic service. Later the geodetic institutes and secondary technical schools of the USSR, which graduate engineers and technicians in all types of geodetic and cartographic work, were established. At the end of 1928 the Central Scientific Research Institute of Geodesy, Aerial Photography, and Cartography was established in Moscow. It has become a major center in the development of scientific thought in the field of geodetic knowledge.

In 1928 the Soviet geodesist F. N. Krasovskii developed an orderly and scientifically substantiated diagram and program for constructing a geodetic control network that envisioned the creation of an astronomical and geodetic network over the entire territory of the USSR. During the course of building this network the theories, methods, and tools of astronomical determinations and geodetic measurements were improved. In the USSR the base instrument with suspended measuring wires made of invar was improved, the manufacture of invar measuring wires with any assigned coefficient of expansion was adopted, and original types of electrooptical range finders, radio range finders, and radio geodetic systems were developed, which made it possible to measure distances with great precision. An industry producing astronomical and geodetic instruments, aerial photography equipment, and photogrammetric instruments appeared.

In 1932, on the basis of the decree of the Council of Labor and Defense of the USSR, a general gravimetric survey of the country was begun. It later became very important for accomplishing the scientific and practical tasks of geodesy and geophysics. Geodetic gravimetry, which is now an important branch of geodetic knowledge, arose from the research of A. A. Mikhailov, M. S. Molodenskii, and others. While working on the difficulties in determining the figure of the geoid, M. S. Molodenskii justified the theory of studying the figure of the physical surface and external gravitational field of the earth. I. D. Zhongolovich developed methods of determining the figure, dimensions, and gravitational field of the earth on the basis of observations by artificial satellites.

In 1940, on the basis of arc measurements in the USSR and other countries, F. N. Krasovskii and A. A. Izotov determined the new dimensions of the earth ellipsoid, which are now used in the USSR and the other socialist countries. Later Izotov and Molodenskii determined the orientation of the Krasovskii ellipsoid in the earth’s body. In the years 1942–5, under the direction of D. A. Larin, a general adjustment of the vast astronomical and geodetic network of the USSR, which had been formed by that time, was carried out. Soviet geodesists developed methods of adjusting large astronomical and geodetic networks and continuous triangulation nets (F. N. Krasovskii, N. A. Urmaev, I. Iu. Pranis-Pranevich, and others).

Topographical surveys and cartographic work related to the needs of the national economy and the country’s defense have been extensively developed in the USSR. Since 1925 aerial photography and photogrammetric methods developed by Soviet scientists (such as F. V. Drobyshev, M. D. Konshin, and G. V. Romanovskii) have been used in topographical surveys. In 1945 work was completed on a multisheet state topographical map of the USSR on a scale of 1:1,000,000. Later a topographical map on the scale of 1:100,000 was made for the entire territory of the country, a significant part of which was covered by surveys on even larger scales.

Geodetic work has been done in connection with land management and the construction of cities, civil structures, industrial enterprises, and means of communication. The methods of geodesy have also been employed during the construction of atomic power stations, large charged-particle accelerators, and so on.

The development of geodesy in the USSR has been marked by the formulation and solution of large-scale scientific problems and practical tasks that have never been posed in other countries.

MANUALS AND MONOGRAPHS

Krasovskii, F. N., and V. V. Danilov. *Rukovodstvo po vysshei geodezii*, 2nd ed., part 1, fasc. 1-2. Moscow, 1938-39.

Krasovskii, F. N. *Rukovodstvo po vysshei geodezii*, part 2. Moscow, 1942.

Zakatov, P. S. *Kurs vysshei geodezii*, 3rd ed., Moscow, 1964.

Chebotarev, A. S. *Geodeziia*, 2nd ed., part 1. Moscow, 1955.

Chebotarev, A. S., V. G. Selikhanovich, and M. N. Sokolov. *Geodeziia*, part 2. Moscow, 1962.

Gerzhula, B. I. *Osnovy inzhenernoi geodezii*. Moscow, 1960.

*Topografiia*, parts 1-2. Edited by D. A. Slobodchikov. Moscow, 1954.

Mikhailov, A. A. *Kurs gravimetrii i teoriifigury Zemli*, 2nd ed. Moscow, 1939.

Brovar, V. V., V. A. Magnitskii, and B. P. Shimbirev. *Teoriiafigury Zemli*. Moscow, 1961.

Shokin, P. F. *Gravimetriia*. Moscow, 1960.

Molodenskii, M. S., M. I. Iurkina, and V. F. Eremeev. “Metody izucheniia vneshnego gravitatsionnogo polia i figury Zemli.” *Tr. Tsentral’nogo nauchno-issledovatel ’skogo in-ta geodezii, aeros”emki i kartografii*, 1960, issue 131.

Izotov, A. A. “Forma i razmery Zemli po sovremennym dannym.” *Ibid*., 1950, issue 73.

Eliseev, S. V. *Geodeziehe skie instrumenty i pribory*, 2nd ed. Moscow, 1959.

Chebotarev, A. S. *Sposob naimen’shikh kvadratov s osnovami teorii veroiatnostei*. Moscow, 1958.

Pranis-Pranevich, I. Iu. *Rukovodstvo po uravnitelnym vychisleniiam trianguliatsii*, 2nd ed. Moscow, 1956.

Veis, G. *Geodezicheskoe ispol’zovanie iskusstvennykh sputnikov Zemli*. Moscow, 1967. (Translated from English.)

Mueller, I. I. *Vvedenie v sputnikovuiu geodeziiu*. Moscow, 1967. (Translated from English.)

Berroth, A., and W. Hofmann. *Kosmicheskaia geodeziia*. Moscow, 1963. (Translated from German.)

Helmert, F. R. *Die mathematischen und physikalischen Theorien der höheren Geodäsie*, 2nd ed., vols. 1-2. Leipzig, 1962.

Jordan, W., O. Eggert, and M. Kneissl. *Handbuch der Vermessungskunde*, 10th ed., vols. 1-4. Stuttgart, 1955-61.

Rysavy, J. *Vyšši geodesie*. Prague, 1947.

HISTORY

Kotel’nikov, S. K. *Molodoi geodet, Hi pervye osnovaniia geodezii, soderzhashchie vse geodetskoe znanie, predlozhennoe vkratse, iz”iasnennoe pravilami i primerami*. St. Petersburg, 1766.

Bolotov, A. P. *Kurs vysshei i nizshei geodezii*, parts 1-2. St. Petersburg, 1845-49.

Struve, V. Ia. *Duga meridiana*, vols. 1-2. St. Petersburg, 1861.

Evteev, O. A. *Pervye russkie geodezisty na Tikhom okeane*. Moscow, 1950.

*50 let sovetskoi geodezii i kartografii*. Edited by A. N. Baranov and M. K. Kudriavtsev. Moscow, 1967.

Biruni. *Geodeziia: Izbr. proizv*, vol 3. Tashkent, 1966.

### REFERENCE WORKS

*Geodeziia: Spravochnoe rukovodstvo*. Edited by M. D. Bonch-Bruevich. Vols. 1-9. Moscow-Leningrad, 1939-49.

*Spravochnik geodezista*. Edited by V. D. Bol’shakov and G. P. Levchuk. Moscow, 1966.

*Bibliograficheskii ukazatel’ geodezicheskoi literatury s nachala knigopechataniia do 1917 g*. Compiled by E. F. Belikov and L. P. Solov’ev. Moscow, 1971.

A. A. IZOTOV

## geodesy

[jē′äd·ə·sē]## geodesy

## geodesy

,**geodetics**