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]