greater stiffness. Dr. Kiihnen of the Institute dis- 

 ci thai the departure from expectations was the 



result of the flexure of the pendulum staff itself during 

 oscillations. ' 7 



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 stall. " 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 authoriza- 

 tion from the superintendent of the Coast and Geo- 

 detic Survey to arrange for the construction of such 

 pendulums by Gauticr 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 pendu- 

 lum upon its period of oscillation," M Peirce deter- 

 mined anal) tii .illy the effect on the period of a pendu- 

 lum 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 it lie 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. 

 \iiei the independent discovery of the problem at 

 the Geodetic Institute, Dr. Helmert took up the prob- 

 lem and criticized the theories of Peirce and Loren- 

 zoni. He then presented his own theor) of flexure in 

 a comprehensive memoir. 100 In view of the previous 

 neglect of the flexure of the pendulum staff in the 



Reported by Dr. F. Kiihnen to the fifth session. October 9, 

 1895, of the Eleventh General Conference. Die Internationale 

 Erdmessung, held in Berlin from September 25 to October 1-. 

 1895. A footnote states that Assistant O. II. Tittmann, who 

 represented the United States, subsequently reported Peirce's 

 prior discovery of the influence of the flexure of the pendulum 

 itself upon the period (Report of tl luptrintci U.& 



Coast and Geodetic Survey J 01 1883 - I. Washington, 1885, app. 

 16, pp. 483-485). 



Hants' Reports, U.S. Coast and Geodetic Survey, 1S83-84 

 MS National Archives, Washington). 



" C S. I'i ii u i "Effect of the Flexure of a Pendulum Upon 

 its Period of Oscillation.'* Report of the Superintendent of • 

 Coast and Geodetic Survey for 1SS3-SJ (Washington, 1885), app. 

 no. 16. 



1(1(1 F. R. Hei.mert, Beitrage zur Theorie des Revcrsionspendels 

 (Potsdam: Veroflentlichungcn Konigliche Prcussischcn Gco- 

 d&tischen Instituts, 1898). 



reduction of observations, Helmert directed that the 

 Geodetic Institute make a new absolute determination 

 of the intensity of gravity at Potsdam, for this 

 purpose, Kiihnen and Furtwangler used the following 

 reversible pendulums which had been constru 

 by tin- lit in 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 < lb- 

 servatory, Padua. 



3. A heavy seconds pendulum from the Imperial and 

 Royal Military-Geographfcal Institute, Vienna. 



4. A li'_;lit, seconds pendulum from the Imperial and 

 Royal M ilil.it phical Institute. 



5. A ^-second, reversible pendulum or*the Geodetic 

 Institute procured in 1892. 



Work was begun in 1898, and in 1906'Kuhnen and 

 Furtwangler published their monumental memoir, 

 "Bestimmung der Absoluten Groszc dcr Schwerkrafl 

 zu Potsdam mit Reversionspendeln." 



The acceleration of gravity in the pendulum room 

 of the (Jeodetii Institute was determined to be 981.274 

 ±0.003 cm sec 2 . In \ iew 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 ol 

 gravity at some other station on the Potsdam system 

 was determined from the times of swing of an invari- 

 able pendulum at the station and at Potsdam by the 

 relation 



Tl ,,' 

 Thus, in 1900, Assistant G. R. Putnam of the Coast 

 and Geodetic Survey swung Mendenliall pendulums 

 at the Washington base and at Potsdam, and by trans- 

 fer from Potsdam determined the intensity oi gravity 

 at the Washington base to be 980.112 cm/sec 2 . 101 

 In L933, Lt. E. J. Brown made comparativi 

 urements with improved apparatus and raised the 

 value it the Washington base to 980.118 cm scc-."-' 

 In view of discrepancies between the results of 

 various relative determinations, the Coast and Geo- 

 detic Survey in 1928 requested the National Bureau 

 of Standards to make an absolute determination for 

 Washington. Ileyl and Cook used reversible pen- 

 dulums made of fused silica having a period of 



101 J. A. I)i i kksi n. Pendulum Gravity Data in the United States 

 (Special Publication No. 244. U.S. Coast and Geodetic Survey; 

 Washington, 1949). 



[bid . p. 2. See also, E.J. Brown, loc. cit. (footnote 85). 



PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN THE 1 ' * ill < 1 N'TLRV 



339 



