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]
Figure 31.—Map showing the distribution of gravity stations throughout the United States as of December 1908.