Absolute Value of Gravity at Potsdam
The development of the reversible pendulum in the 19th century culminated in the absolute determination of the intensity of gravity at Potsdam by Kühnen and Furtwängler of the Royal Prussian Geodetic Institute, which then became the world base for gravity surveys.96
We have previously seen that in 1869 the Geodetic Institute—founded by Lt. Gen. Baeyer—had acquired a Repsold-Bessel reversible pendulum which was swung by Dr. Albrecht under the direction of Dr. Bruhns. Dissatisfaction with this instrument was expressed by Baeyer in 1875 to Charles S. Peirce, who then, by experiment and mathematical analysis of the flexure of the stand under oscillations of the pendulum, determined that previously reported results with the Repsold apparatus required correction. Dr. F. R. Helmert, who in 1887 succeeded Baeyer as director of the Institute, secured construction of a building for the Institute in Potsdam, and under his direction the scientific study of the intensity of gravity was pursued with vigor. In 1894, it was discovered in Potsdam that a pendulum constructed of very flexible material yielded results which differed markedly from those obtained with pendulums of greater stiffness. Dr. Kühnen of the Institute discovered that the departure from expectations was the result of the flexure of the pendulum staff itself during oscillations.97
Peirce, in 1883, had discovered that the recesses cut in his pendulums for the insertion of tongues that carried the knives had resulted in the flexure of the pendulum staff.98 By experiment, he also found an even greater flexure for the Repsold pendulum. In order to eliminate this source of error, Peirce designed a pendulum with knives that extended from each side of the cylindrical staff, and he received authorization from the superintendent of the Coast and Geodetic Survey to arrange for the construction of such pendulums by Gautier in Paris. Peirce, who had made his plans in consultation with Gautier, was called home before the pendulums were completed, and these new instruments remained undelivered.
In a memoir titled “Effect of the flexure of a pendulum upon its period of oscillation,”99 Peirce determined analytically the effect on the period of a pendulum with a single elastic connection between two rigid parts of the staff. Thus, Peirce discovered experimentally the flexure of the staff and derived for a simplified case the effect on the period. It is not known if he ever found the integrated effect of the continuum of elastic connections in the pendulum. Lorenzoni, in 1896, offered a solution to the problem, and Almansi, in 1899, gave an extended analysis. After the independent discovery of the problem at the Geodetic Institute, Dr. Helmert took up the problem and criticized the theories of Peirce and Lorenzoni. He then presented his own theory of flexure in a comprehensive memoir.100 In view of the previous neglect of the flexure of the pendulum staff in the reduction of observations, Helmert directed that the Geodetic Institute make a new absolute determination of the intensity of gravity at Potsdam. For this purpose, Kühnen and Furtwängler used the following reversible pendulums which had been constructed by the firm of A. Repsold and Sons in Hamburg:
1. The seconds pendulum of the Geodetic Institute procured in 1869.
2. A seconds pendulum from the Astronomical Observatory, Padua.
3. A heavy, seconds pendulum from the Imperial and Royal Military-Geographical Institute, Vienna.
4. A light, seconds pendulum from the Imperial and Royal Military-Geographical Institute.
5. A 1/2-second, reversible pendulum of the Geodetic Institute procured in 1892.
Work was begun in 1898, and in 1906 Kühnen and Furtwängler published their monumental memoir, “Bestimmung der Absoluten Grösze der Schwerkraft zu Potsdam mit Reversionspendeln.”
The acceleration of gravity in the pendulum room of the Geodetic Institute was determined to be 981.274 ± 0.003 cm/sec2. In view of the exceptionally careful and thorough determination at the Institute, Potsdam was accepted as the world base for the absolute value of the intensity of gravity. The absolute value of gravity at some other station on the Potsdam system was determined from the times of swing of an invariable pendulum at the station and at Potsdam by the relation T12/T22 = g2/g1. Thus, in 1900, Assistant G. R. Putnam of the Coast and Geodetic Survey swung Mendenhall pendulums at the Washington base and at Potsdam, and by transfer from Potsdam determined the intensity of gravity at the Washington base to be 980.112 cm/sec2.101 In 1933, Lt. E. J. Brown made comparative measurements with improved apparatus and raised the value at the Washington base to 980.118 cm/sec2.102
In view of discrepancies between the results of various relative determinations, the Coast and Geodetic Survey in 1928 requested the National Bureau of Standards to make an absolute determination for Washington. Heyl and Cook used reversible pendulums made of fused silica having a period of approximately 1 second. Their result, published in 1936, was interpreted to indicate that the value at Potsdam was too high by 20 parts in 1 million.103 This estimate was lowered slightly by Sir Harold Jeffreys of Cambridge, England, who recomputed the results of Heyl and Cook by different methods.104
In 1939, J. S. Clark published the results of a determination of gravity with pendulums of a non-ferrous Y-alloy105 at the National Physical Laboratory at Teddington, England, and, after recomputation of results by Jeffreys, the value was found to be 12.8 parts in 1 million less than the value obtained by transfer from Potsdam. Dr. Hugh L. Dryden of the National Bureau of Standards, and Dr. A. Berroth of the Geodetic Institute at Potsdam, have recomputed the Potsdam data by different methods of adjustment and concluded that the Potsdam value was too high by about 12 parts in a million.106 Determination of gravity at Leningrad by Russian scientists likewise has indicated that the 1906 Potsdam value is too high. In the light of present information, it appears justifiable to reduce the Potsdam value of 981.274 by.013 cm/sec2 for purposes of comparison. If the Brown transfer from Potsdam in 1933 was taken as accurate, the value for the Washington base would be 980.105 cm/sec2. In this connection, it is of interest to note that the value given by Charles S. Peirce for the comparable Smithsonian base in Washington, as determined by him from comparative methods in the 1880’s and reported in the Annual Report of the Superintendent of the Coast and Geodetic Survey for the year 1890-1891, was 980.1017 cm/sec2.107 This value would appear to indicate that Peirce’s pendulums, observations, and methods of reduction of data were not inferior to those of the scientists of the Royal Prussian Geodetic Institute at Potsdam.
Doubts concerning the accuracy of the Potsdam value of gravity have stimulated many new determinations of the intensity of gravity since the end of World War II. In a paper published in June 1957, A. H. Cook, Metrology Division, National Physical Laboratory, Teddington, England, stated:
At present about a dozen new absolute determinations are in progress or are being planned. Heyl and Cook’s reversible pendulum apparatus is in use in Buenos Aires and further reversible pendulum experiments have been made in the All Union Scientific Research Institute of Metrology, Leningrad (V N I I M) and are planned at Potsdam. A method using a very long pendulum was tried out in Russia about 1910 and again more recently and there are plans for similar work in Finland. The first experiment with a freely falling body was that carried out by Volet who photographed a graduated scale falling in an enclosure at low air pressure. Similar experiments have been completed in Leningrad and are in progress at the Physikalisch-Technische Bundesanstalt (Brunswick) and at the National Research Council (Ottawa), and analogous experiments are being prepared at the National Physical Laboratory and at the National Bureau of Standards. Finally, Professor Medi, Director of the Istituto Nazionale di Geofisica (Rome), is attempting to measure the focal length of the paraboloidal surface of a liquid in a rotating dish.108
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