# Helmert, Friedrich Robert

# Helmert, Friedrich Robert

(*b*. Freiberg, Saxony, Germany, 31 July 1843; *d*. Potsdam. Germany. 15 June 1917)

*geodesy, astronomy*.

The youngest child of Johann Friedrich Helmert, treasurer of the Johannishospitalgut of Freiberg, and of the former Christiana Friederika Linke, Helmert attended the secondary school in Freiberg and at the age of thirteen entered the Annenrealschule in Dresden, where an older brother was assistant headmaster. In 1859 he began to study engineering science at the Polytechnische Schule in Dresden. Since he was especially enthusiastic about geodesy, his teacher, August Nagel, Saxon commissioner for the Mitteleuropäische Gradmessung, hired him, while he was still a student, to work on the triangulation of the coalfield of the Erzgebirge and the drafting of the trigonometric network for Saxsony. In the summer of 1863 he became Nagel’s assistant on the measurement of degrees. Helmert’s work on this undertaking resulted in the *Studien über rationelle Vermessungen der höheren Geodäsie* (1868), with which he received his Ph.D. from the University of Leipzig in 1867, after a year’s study of mathematics and astronomy.

Helmert next worked on the establishment of a triangulation network around Leipzig under C. Bruhns and as a mathematics teacher at the *Realinstitut* run by Hölbe in Dresden; subsequently he participated in the discussion of exact standard weights conducted by the Commission on Standardization directed by Nagel. At the beginning of 1869, after declining a similar offer from the observatory at Leiden, he became an observer at the Hamburg astronomical observatory. A product of his stay in Hamburg was *Der Sternhaufen im Sternbilde des Sobieskischen Schildes* (1874).

In 1870 Helmert became geodesy instructor at the newly founded technical school in Aachen, where he was named professor in 1872. At Aachen he amassed a collection of instruments, met a busy teaching schedule, and wrote his masterpiece. *Die mathematischen und physikalischen Theorien der höheren Geodäsie*, which quickly made him known. He was an editor of *Zeitschrift für Vermessungswesen* from 1876 to 1883 and in 1877 became a member of the Scientific Advisory Council of the Prussian Geodetic Institute. He rejected offers from Córdoba, Argentina, in 1873 and from Karlsruhe in 1881.

Johann Jakob Baeyer died in 1885, and in 1886 Helmert was appointed provisional director of the Prussian Geodetic Institute in Berlin, which was connected with the central office of the Europäische Gradmessung. By the fall of 1886 he had secured the appointment of a permanent secretary for the central office, which thereby became freed for the scientific tasks of the Internationale Erdmessung. On 15 April 1887 Helmert was appointed professor of advanced geodesy at the University of Berlin and, a week later, director of the Geodetic Institute; also in 1887 he became a full member of the Prussian Commission on Standards. He suffered a stroke in 1916 and died of its effects the following year.

Helmert’s first wife was Jenny Oehme, who died in 1887; his second was his niece Marie Helmert. By his second marriage he had a son, Robert.

Helmert’s abilities were summed up in an obituary by O. Eggert:

Helmert possessed to a high degree the gift of a vivid and clear delivery, which was especially easy to understand because of his straightforward style. He was able to present mathematical developments in an extraordinarily clear manner.... That he could hold the interest of individual students... is evident from a series of dissertations which resulted from his influence. Those of his students who... had the good fortune to come into close contact with Helmert will always gratefully recall the friendly and sympathetic support that they found during their studies under him [

Zeitschrift für Vermessungswesen,46(1917), 294–295].

Helmert received many honors. In 1884 he became an honorary member of the Deutsche Geometerverein; in 1900 he became a full member of the Prussian Academy of Sciences in Berlin, and in 1903 honorary doctor of engineering of the Aachen Technische Hochschule. Besides some twenty-five German and foreign decorations, in 1912 he was awarded the Goldene Medaille für Wissenschaft.

In his dissertation Helmert developed the theory of the ellipse of error and of the middle points error; he also treated the most advantageous division of the work of measuring. In 1872 his *Die Ausgleichsrechnung nach der Methode der kleinsten Quadrate mit Anwendungen auf die Geadäsie und die Theorie der Messinstrumente* appeared. In this work Helmert introduced a new theory of equivalent observations and for the first time used the method of least squares in the examination of measuring instruments. His *Übergangskurven für Eisenbahngeleise* (1872) and *Günstige Wahl der Cardinalpunkte beim Abstecken einer Trace* (1875) resulted from his teaching at Aachen. A wealth of specialized papers served as preparation for his masterpiece, *Die mathematischen und physikalischen Theorien der höheren Geodäsie*, on which he worked from 1877.

In part 1 of that work. *Die mathematischen Theorien* (1880), Helmert demonstrated the validity of A. M. Legendre’s theorem for acute triangles and treated extensively the geodesy of the sphere and the slightly oblate ellipsoid of rotation; he linked geodesy to the actual surface of the earth by means of plumb-line deflection. He discussed for the first time calculation on the ellipsoid with chords, the differential formulas for geodetic lines, and the development of series for use in the computation of distances and azimuths from geographic positions. He also considered the geodetic lines between two nearly diametrical points, the maximum values of the higher terms of Legendre’s theorem, and the spherical computation of chains of triangulation. In addition he discussed the relationships between rectangular and geographical coordinates, the balancing of geodetic-astronomic measurements with regard to plumb-line deflections, and developments regarding the conclusiveness of measurements of degrees for representing the earth’s shape as that of an ellipsoid of rotation.

Part 2, *Die physikalischen Theorien* (1884), discusses the shape of the earth from the standpoint of potential theory, beginning with the analytical formulation of the concept of the acceleration of gravity and the introduction of its potential. There follows a treatment of the general properties of equipotential surfaces and of their discontinuities of curvature. After a presentation of Clairaut’s theorem Helmert derives the flattening of the sphere of the earth from 122 pendulum lengths. He finds it to be 1:299.26 ± 1.26, reduced to sea level, allowing for the condensation of the visible disturbing masses of the earth’s surface to a surface parallel to the surface of the sea, at a depth of three miles. He finds gravity at sea level to be 9.7800 (1 + 0.005310 ± 14 sin^{2}*B*). He also investigates the perturbation effect of the five continents, considered as blunted circular cones 4,000 meters thick, on the level planes near the surface and of other disturbing masses of various shapes.

Along with the temporal changes of the level planes, Helmert discusses the disturbances of the plumb line resulting from the moon and the sun, as well as from the small movements of the earth’s axis. Next he takes up the value of astronomical data for knowledge of the earth’s shape. In the section entitled “Das geometrische Nivellement” he insists on taking into account the variation of gravity with geographical latitude but deems the influence of gravity anomalies to be unimportant. In treating trigonometric altimetry he also considers lateral refraction and aberration. In opposition to the trigonometric method for determining the geoid, he holds that the method of plumb-line deflections in the preparation of meridian profiles by means of closely spaced stations of latitude, for which he proposes the term *astronomisches Nivellement*, is more advantageous.

In 1886, for the Prussian portion of the Mitteleuropäische Gradmessung, Helmert provided for the establishment of the plumb-line deflections of a net of seventy points centered on Point Rauenberg, near Berlin; for the astronomical measurements of latitudes and azimuths, telegraphic measurements of lengths were, in part, also executed. In October 1887 Helmert delivered to the commissioners of the Internationale Erdmessung, in “Lotabweichungen I,” the formulas and tables, with examples of their use, necessary for calculation of the plumb-line deflections. In 1890 he reported on the variations of geographical latitude in 1889, which, in 1891, he attributed to changes of position of the earth’s axis. In addition, he arranged for an expedition to Honolulu and inspired the establishment of the International Bureau of Latitudes to monitor the movements of the poles.

When Sterneck measured gravity with his pendulum apparatus (constructed in 1887), Helmert made a critical evaluation of Sterneck’s methods of measurement and investigated the cause of the gravitational disturbances (“Die Schwerkraft im Hochgebirge,” 1890); in addition, he carried out his own measurements with this device beginning in 1892. In 1893–1894 he made test measurements with the reversible pendulum supplied by J. A. Repsold in Hamburg; in 1898 he collected the results in *Beiträige zur Theorie des Reversionspendels*. They constituted the basis for the determination of absolute gravity by Friedrich Kühnen and Philipp Furtwängler between 1900 and 1906 at the Potsdam Geodetic Institute. The value ascertained in 1906, 981.274 ± 0.003 gal was accepted in 1909 by the Internationale Erdmessung

Helmert was always concerned with improvements in the gravitational formula and in the reduction of determinations of gravity (1901–1904, 1915). In 1909 he calculated the value of the flattening of the earth as 1:298.3 ±t 0.7 (as opposed to J. F. Hayford and William Bowie, whose figure [1912] was 1:298.4 ± 1.5). He investigated the state of equilibrium of the masses of the earth’s crust (1908, 1912), the depth of the isostatic surface according to J. H. Pratt’s isostasy hypothesis (1909), and the accuracy of the dimensions of Hayford’s ellipsoidal earth (1911). In 1915 he made the ellipticity of the equator probable, although he was unable to complete these studies.

## BIBLIOGRAPHY

I. Original Works. Helmert’s publications are listed in Poggendorff, III, 610–611; IV, 611–612; V, 516–517; VI, 1076. His articles appeared chiefly in *Zeitschrift für Vermessungswesen, Astronomische Nachrichten, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, and Verhandlungen der Internationalen Erdmessung*. Important works not mentioned in the text are *Instrumente für hoühere Geodäsie* (Brunswick. 1878): *Übersicht der Arbeiten des Geodätischen Instituts unter Generallieutnant Baeyer* (Berlin, 1886); *Das kgl. Preussische Geodätische Institut* (Berlin, 1890); *Die europäische Längengradmessung in* 52° *Breite von Greenwich bis Warschau. I Hauptdreiecke und Grundlinienanschlüsse von England bis Polen* (Berlin, 1893); *Zenitdislanz und Bestimmung der Höhenlage der Nordsee-Inseln Helgoland*... (Berlin, 1895); “Geodäsie und Geophysik.” in *Enzyklopädie der mathematischen Wissenschaften*, VI, 1, supp. 2 (Leipzig, 1910); and “Die internationale Erdmessung in den ersten 50 Jahren ihres Bestehens,” in *International Monatssehrift für Wissenschaft, Kunst und Technik* (1913).

II. Secondary Literature. Obituaries include O. Eggert, in *Zeitschrifi für Vermessungswesen*, 46 (1917), 281–295; O. Hecker, in *Beiträgen zur Geophysik*, **14** , no. 4 (1918); L. Krüger, in *Astronomische Nachrichten*, 204 (1917); M. Schmidt, in *Jahrbuch der Bayerischen Akademie der Wissenschaften* (1917), 53–58; and R. Schumann, in *Oüsterreichische Zeitschrift für Vermessungswesen* 15 (1917), 97–100. See also W. Fischer, “Helmert,” in *Gedenktage des mitteldeutschen Raumes 1967* (Bonn, 1967), pp. 32–34, 63–64; Paul Gast, “Der Lehrstuhl für Vermessungskunde (Lehrstuhl Helmert),” in his *Die Technische Hochschule zu Aachen 1870–1920* (Aachen, 1920), pp. 247–250; H. Peschel, “Gendenkrede zu Helmerts 50. Todestag am 15. Juni 1967 in Freiberg,” in *Vermessungstechnik*, 15 (1967), 334–340; and Rudolf Sigl, in *Neue deutsche Biographie,* VIII (1969), 497–498.

Walther Fischer

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