Chapter III: Part 3

[48] A. SAWITSCH, "Les variations de la pesanteur dans les provinces occidentales de l'Empire russe," _Memoirs of the Royal Astronomical Society_ (1872), vol. 39, p. 19.

[49] J. J. BAEYER, _Ueber die Groesse und Figur der Erde_ (Berlin, 1861).

[50] _Comptes-rendus de la Conference Geodesique Internationale reunie a Berlin du 15-22 Octobre 1864_ (Neuchatel, 1865).

[51] Ibid., part III, subpart E.

[52] _Bericht ueber die Verhandlungen der vom 30 September bis 7 October 1867 zu Berlin abgehaltenen allgemeinen Conferenz der Europaeischen Gradmessung_ (Berlin, 1868). See report of fourth session, October 3, 1867.

[53] C. BRUHNS and ALBRECHT, "Bestimmung der Laenge des Secundenpendels in Bonn, Leiden und Mannheim," _Astronomisch-Geodaetische Arbeiten im Jahre 1870_ (Leipzig: Veroeffentlichungen des Koeniglichen Preussischen Geodaetischen Instituts, 1871).

[54] _Bericht ueber die Verhandlungen der vom 23 bis 28 September 1874 in Dresden abgehaltenen vierten allgemeinen Conferenz der Europaeischen Gradmessung_ (Berlin, 1875). See report of second session, September 24, 1874.

[55] CAROLYN EISELE, "Charles S. Peirce--Nineteenth-Century Man of Science," _Scripta Mathematica_ (1959), vol 24, p. 305. For the account of the work of Peirce, the authors are greatly indebted to this pioneer paper on Peirce's work on gravity. It is worth noting that the history of pendulum work in North America goes back to the celebrated Mason and Dixon, who made observations of "the going rate of a clock" at "the forks of the river Brandiwine in Pennsylvania," in 1766-67. These observations were published in _Phil. Trans._ (1768), vol. 58, pp. 329-335.

[56] The pendulums with conical bobs are described and illustrated in E. D. PRESTON, "Determinations of Gravity and the Magnetic Elements in Connection with the United States Scientific Expedition to the West Coast of Africa, 1889-90," _Report of the Superintendent of the Coast and Geodetic Survey for 1889-90_ (Washington, 1891), app. no. 12.

[57] EISELE, op. cit. (footnote 55), p. 311.

[58] The record of Peirce's observations in Europe during 1875-76 is given in C. S. PEIRCE, "Measurements of Gravity at Initial Stations in America and Europe," _Report of the Superintendent of the Coast Survey for 1875-76_ (Washington, 1879), pp. 202-337 and 410-416. Peirce's report is dated December 13, 1878, by which time the name of the Survey had been changed to U.S. Coast and Geodetic Survey.

[59] _Verhandlungen der vom 20 bis 29 September 1875 in Paris Vereinigten Permanenten Commission der Europaeischen Gradmessung_ (Berlin, 1876).

[60] Ibid. See report for fifth session, September 25, 1875.

[61] The experiments at the Stevens Institute, Hoboken, were reported by Peirce to the Permanent Commission which met in Hamburg, September 4-8, 1878, and his report was published in the general _Bericht_ for 1878 in the _Verhandlungen der vom 4 bis 8 September 1878 in Hamburg Vereinigten Permanenten Commission der Europaeischen Gradmessung_ (Berlin, 1879), pp. 116-120. Assistant J. E. Hilgard attended for the U.S. Coast and Geodetic Survey. The experiments are described in detail in C. S. PEIRCE, "On the Flexure of Pendulum Supports," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1880-81_ (Washington, 1883), app. no. 14, pp. 359-441.

[62] _Verhandlungen der vom 5 bis 10 Oktober 1876 in Brussels Vereinigten Permanenten Commission der Europaeischen Gradmessung_ (Berlin, 1877). See report of third session, October 7, 1876.

[63] _Verhandlungen der vom 27 September bis 2 Oktober 1877 zu Stuttgart abgehaltenen fuenften allgemeinen Conferenz der Europaeischen Gradmessung_ (Berlin, 1878).

[64] _Verhandlung der vom 16 bis 20 September 1879 in Genf Vereinigten Permanenten Commission der Europaeischen Gradmessung_ (Berlin, 1880).

[65] _Assistants' Reports, U.S. Coast and Geodetic Survey, 1879-80._ Peirce's paper was published in the _American Journal of Science_ (1879), vol. 18, p. 112.

[66] _Comptes-rendus de l'Academie des Sciences_ (Paris, 1879), vol. 89, p. 462.

[67] _Verhandlungen der vom 13 bis 16 September 1880 zu Muenchen abgehaltenen sechsten allgemeinen Conferenz der Europaeischen Gradmessung_ (Berlin, 1881).

[68] Ibid., app. 2.

[69] Ibid., app. 2a.

[70] _Verhandlungen der vom 11 bis zum 15 September 1882 im Haag Vereinigten Permanenten Commission der Europaeischen Gradmessung_ (Berlin, 1883).

[71] _Verhandlungen der vom 15 bis 24 Oktober 1883 zu Rom abgehaltenen siebenten allgemeinen Conferenz der Europaeischen Gradmessung_ (Berlin, 1884). Gen. Cutts attended for the U.S. Coast and Geodetic Survey.

[72] Ibid., app. 6. See also, _Zeitschrift fuer Instrumentenkunde_ (1884), vol. 4, pp. 303 and 379.

[73] Op. cit. (footnote 67).

[74] _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1880-81_ (Washington, 1883), p. 26.

[75] _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1889-90_ (Washington, 1891), app. no. 12.

[76] _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1881-82_ (Washington, 1883).

[77] _Transactions of the Cambridge Philosophical Society_ (1856), vol. 9, part 2, p. 8. Also published in _Mathematical and Physical Papers_ (Cambridge, 1901), vol. 3, p. 1.

[78] Peirce's comparison of theory and experiment is discussed in a report on the Peirce memoir by WILLIAM FERREL, dated October 19, 1890, Martinsburg, West Virginia. _U.S. Coast and Geodetic Survey, Special Reports, 1887-1891_ (MS, National Archives, Washington).

[79] The stations at which observations were conducted with the Peirce pendulums are recorded in the reports of the Superintendent of the U.S. Coast and Geodetic Survey from 1881 to 1890.

[80] _Comptes-rendus de l'Academie des Sciences_ (Paris, 1880), vol. 90, p. 1401. HERVE FAYE's report, dated June 21, 1880, is in the same _Comptes-rendus_, p. 1463.

[81] COMMANDANT C. DEFFORGES, "Sur l'Intensite absolue de la pesanteur," _Journal de Physique_ (1888), vol. 17, pp. 239, 347, 455. See also, DEFFORGES, "Observations du pendule," _Memorial du Depot general de la Guerre_ (Paris, 1894), vol. 15. In the latter work, Defforges described a pendulum "reversible inversable," which he declared to be truly invariable and therefore appropriate for relative determinations. The knives remained fixed to the pendulums, and the effect of interchanging knives was obtained by interchanging weights within the pendulum tube.

[82] Papers by MAJ. VON STERNECK in _Mitteilungen des K. u. K. Militaer-geographischen Instituts, Wien_, 1882-87; see, in particular, vol. 7 (1887).

[83] T. C. MENDENHALL, "Determinations of Gravity with the New Half-Second Pendulum...," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1890-91_ (Washington, 1892), part 2, pp. 503-564.

[84] W. H. BURGER, "The Measurement of the Flexure of Pendulum Supports with the Interferometer," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1909-10_ (Washington, 1911), app. no. 6.

[85] E. J. BROWN, _A Determination of the Relative Values of Gravity at Potsdam and Washington_ (Special Publication No. 204, U.S. Coast and Geodetic Survey; Washington, 1936).

[86] M. HAID, "Neues Pendelstativ," _Zeitschrift fuer Instrumentenkunde_ (July 1896), vol. 16, p. 193.

[87] DR. R. SCHUMANN, "Ueber eine Methode, das Mitschwingen bei relativen Schweremessungen zu bestimmen," _Zeitschrift fuer Instrumentenkunde_ (January 1897), vol. 17, p. 7. The design for the stand is similar to that of Peirce's of 1879.

[88] DR. R. SCHUMANN, "Ueber die Verwendung zweier Pendel auf gemeinsamer Unterlage zur Bestimmung der Mitschwingung," _Zeitschrift fuer Mathematik und Physik_ (1899), vol. 44, p. 44.

[89] P. FURTWAENGLER, "Ueber die Schwingungen zweier Pendel mit annaehernd gleicher Schwingungsdauer auf gemeinsamer Unterlage," _Sitzungsberichte der Koeniglicher Preussischen Akademie der Wissenschaften zu Berlin_ (Berlin, 1902) pp. 245-253. Peirce investigated the plan of swinging two pendulums on the same stand (_Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1880-81_, Washington, 1883, p. 26; also in CHARLES SANDERS PEIRCE, _Collected Papers_, 6.273). At a conference on gravity held in Washington during May 1882, Peirce again advanced the method of eliminating flexure by hanging two pendulums on one support and oscillating them in antiphase ("Report of a conference on gravity determinations held in Washington, D.C., in May, 1882," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1881-82_, Washington, 1883, app. no. 22, pp. 503-516).

[90] F. A. VENING MEINESZ, _Observations de pendule dans les Pays-Bas_ (Delft, 1923).

[91] A. BERROTH, "Schweremessungen mit zwei und vier gleichzeitig auf demselben Stativ schwingenden Pendeln," _Zeitschrift fuer Geophysik_, vol. 1 (1924-25), no. 3, p. 93.

[92] "Pendulum Apparatus for Gravity Determinations," _Engineering_ (1926), vol. 122, pp. 271-272.

[93] MALCOLM W. GAY, "Relative Gravity Measurements Using Precision Pendulum Equipment," _Geophysics_ (1940), vol. 5, pp. 176-191.

[94] L. G. D. THOMPSON, "An Improved Bronze Pendulum Apparatus for Relative Gravity Determinations," [published by] _Dominion Observatory_ (Ottawa, 1959), vol. 21, no. 3, pp. 145-176.

[95] W. A. HEISKANEN and F. A. VENING MEINESZ, _The Earth and its Gravity Field_ (McGraw: New York, 1958).

[96] F. KUEHNEN and P. FURTWAENGLER, _Bestimmung der Absoluten Groesze der Schwerkraft zu Potsdam mit Reversionspendeln_ (Berlin: Veroeffentlichungen des Koeniglichen Preussischen Geodaetischen Instituts, 1906), new ser., no. 27.

[97] Reported by Dr. F. Kuehnen to the fifth session, October 9, 1895, of the Eleventh General Conference, _Die Internationale Erdmessung_, held in Berlin from September 25 to October 12, 1895. A footnote states that Assistant O. H. 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 the Superintendent of the U.S. Coast and Geodetic Survey for 1883-84_, Washington, 1885, app. 16, pp. 483-485).

[98] _Assistants' Reports, U.S. Coast and Geodetic Survey, 1883-84_ (MS, National Archives, Washington).

[99] C. S. PEIRCE, "Effect of the Flexure of a Pendulum Upon its Period of Oscillation," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1883-84_ (Washington, 1885), app. no. 16.

[100] F. R. HELMERT, _Beitraege zur Theorie des Reversionspendels_ (Potsdam: Veroeffentlichungen des Koeniglichen Preussischen Geodaetischen Instituts, 1898).

[101] J. A. DUERKSEN, _Pendulum Gravity Data in the United States_ (Special Publication No. 244, U.S. Coast and Geodetic Survey; Washington, 1949).

[102] Ibid., p. 2. See also, E. J. BROWN, loc. cit. (footnote 85).

[103] PAUL R. HEYL and GUY S. COOK, "The Value of Gravity at Washington," _Journal of Research, National Bureau of Standards_ (1936), vol. 17, p. 805.

[104] SIR HAROLD JEFFREYS, "The Absolute Value of Gravity," _Monthly Notices of the Royal Astronomical Society, Geophysical Supplement_ (London, 1949), vol. 5, p. 398.

[105] J. S. CLARK, "The Acceleration Due to Gravity," _Phil. Trans._ (1939), vol. 238, p. 65.

[106] HUGH L. DRYDEN, "A Reexamination of the Potsdam Absolute Determination of Gravity," _Journal of Research, National Bureau of Standards_ (1942), vol. 29, p. 303; and A. BERROTH, "Das Fundamentalsystem der Schwere im Lichte neuer Reversionspendelmessungen," _Bulletin Geodesique_ (1949), no. 12, pp. 183-204.

[107] T. C. MENDENHALL, op. cit. (footnote 83), p. 522.

[108] A. H. COOK, "Recent Developments in the Absolute Measurement of Gravity," _Bulletin Geodesique_ (June 1, 1957), no. 44, pp. 34-59.

[109] See footnote 89.

[110] C. S. PEIRCE, "On the Deduction of the Ellipticity of the Earth, from Pendulum Experiments," _Report of the Superintendent of the U.S. Coast and Geodetic Survey for 1880-81_ (Washington, 1883), app. no. 15, pp. 442-456.

[111] HEISKANEN and VENING MEINESZ, op. cit. (footnote 95), p. 74.

[112] Ibid., p. 76.

[113] Ibid., p. 309.

[114] Ibid., p. 310.

[115] K. REICHENEDER, "Method of the New Measurements at Potsdam by Means of the Reversible Pendulum," _Bulletin Geodesique_ (March 1, 1959), no. 51, p.72.

U.S. GOVERNMENT PRINTING OFFICE: 1965

For sale by the Superintendent of Documents, U.S. Government Printing
Office Washington, D.C., 20402--Price 70 cents.

INDEX

Airy, G. B., 319, 324, 332

Albrecht, Karl Theodore, 322, 338

Al-Mamun, seventh calif of Bagdad, 306

Almansi, Emilio, 339

Aristotle, 306

Baeyer, J. J., 321, 322, 324, 338, 346

Baily, Francis, 317

Basevi, James Palladio, 345

Berroth, A., 342

Bessel, Friedrich Wilhelm, 313, 314, 319, 320, 324, 325, 338, 346

Biot, Jean Baptiste, 325, 329

Bohnenberger, Johann Gottlieb Friedrich, 315

Borda, J. C., 311, 312, 315, 325, 329, 346

Boscovitch, Pere R. J., 310, 311

Bouguer, Pierre, 307, 309, 327, 343, 345

Brahe, Tycho, 306

Brown, E. J., 334, 339

Browne, Henry, 304, 314

Bruhns, C., 322, 324, 338

Brunner Brothers (Paris), 329

Cassini, Giovanni-Domenico, 306, 307

Cassini, Jacques, 306

Cassini de Thury, J. D., 311, 312, 315, 325, 329, 346

Cellerier, Charles, 320, 321, 325, 326, 329, 336

Clairaut, Alexis Claude, 308, 309, 343, 345

Clark, J. S., 342

Clarke, A. R., 345

Colbert, Jean Baptiste, 306

Cook, A. H., 342

Cook, Guy S., 339, 342

Defforges, C., 314, 329, 346

De Freycinet, Louis Claude de Saulses, 317

De la Hire, Gabriel Philippe, 306

De Prony, M. G., 314

Dryden, Hugh L., 342

Du Buat, L. G., 314

Duperry, Capt. Louis Isidore, 317

Eratosthenes, 306, 308, 342

Eudoxus of Cnidus, 306

Faye, Herve, 325, 336, 346, 347

Fernel, Jean, 306

Furtwaengler, P., 337

Galilei, Galileo, 304, 305, 346

Gauss, C. F., 320

Gautier, P., 339

Godin, Louis, 307

Goldingham, John, 316, 345

Greely, A. W., 329

Gulf Oil and Development Company, 338

Haid, M., 335

Hall, Basil, 316

Heaviside, W. J., 321, 345

Heiskanen, W. A., 338, 345, 346

Helmert, F. R., 338, 339

Helmholtz, Hermann von, 326

Herschel, John, 319, 328, 345

Heyl, Paul R., 339, 342

Hirsch, Adolph, 322, 324

Huygens, Christiaan, 304, 305, 307, 314, 342, 346

Ibanez, Carlos, 325

Jeffreys, Sir Harold, 342

Jones, Thomas, 318

Kater, Henry, 304, 314, 325, 327, 329, 345, 346

Kuehnen, F., 338, 339

La Condamine, Charles Marie de, 307, 310, 311, 343

Laplace, Marquis Pierre Simon de, 309, 313, 320

Lorenzoni, Giuseppe, 336, 339

Luetke, Count Feodor Petrovich, 316, 345

Maupertius, P. L. Moreau de, 308, 343

Maxwell, James Clerk, 324

Medi, Enrico, 342

Mendenhall, Thomas Corwin, 319, 331, 332, 334, 347

Mersenne, P. Marin, 305

Newton, Sir Isaac, 303, 307, 308, 342, 343

Norwood, Richard, 306

Oppolzer, Theodor von, 322, 324

Patterson, Carlile Pollock, 325, 326

Peirce, Charles Sanders, 314, 322, 332, 336, 342, 345

Peters, C. A. F., 322, 324

Picard, Abbe Jean, 306, 308, 342

Plantamour, E., 319, 324

Posidonius, 306

Preston, E. D., 328, 329

Putnam, G. R., 339

Pythagoras, 306

Repsold, A., and Sons (Hamburg), 320, 322, 338, 339, 346

Richer, Jean, 307, 342

Sabine, Capt. Edward, 315, 325, 329, 345

Sawitsch, A., 321, 322

Schumacher, H. C., 320

Schumann, R., 335, 336

Snell, Willebrord, 306

Sterneck, Robert von, 331, 332, 335, 338, 346

Stokes, George Gabriel, 324, 328, 329, 345, 346

Ulloa, Antonio de, 308

Vening Meinesz, F. A., 337, 338, 345

Volet, Charles, 342

Wilkes, Charles, 317, 318

* * * * *

Transcriber's note:

Footnotes have been moved to the end of the paper. Illustrations and the GLOSSARY OF GRAVITY TERMINOLOGY section have been moved to avoid breaks in paragraphs. Minor punctuation errors have been corrected without note. Typographical errors and inconsistencies have been corrected as follows:

P. 320 'difference T_{1} - T_{2} is sufficiently'--had 'sufficlently.'
P. 321 'faites a Geneve avec le pendule a reversion'--had 'reversion.'
P. 326 'Schwere mit Hilfe verschiedener Apparate'--had 'verschiedene.'
P. 328 'between the yard and the meter.'--closing quote mark deleted.
P. 334 'Mendenhall apparatus were part of'--'was' changed to 'were.'
P. 342 'of the Geodetic Institute at Potsdam'--had 'Postdam.'
P. 345 'The gravimetric methods of physical'--had 'mtehods.'
Footnote 1 'Societe francaise de Physique'--had 'Francaise.'
Footnote 3 'Cogitata physico-mathematica'--had 'physica.'
Footnote 10 'mathematiques et de physique par MM. de l'Academie
Royale'--had 'mathematiques,' 'Royal.'
Footnote 12 'par ordre du Roy au Perou, pour observer'--had 'Perou,
pour observir.'
Footnote 19 'Opticam et Astronomiam'--had 'Astronomian.'
Footnote 20 'connaitre la longueur du pendule qui'--had 'connaitre la
longuer.'
Footnote 21 'Abhandlungen der Koeniglichen Akademie'--had 'Koenigliche.'
Footnote 25 'pour determiner la longueur du pendule'--had 'longeur.'
Footnote 41 'Survey of India (Calcutta, 1879)'-- had 'Surey.'
Footnotes 45 and 47 'Societe de Physique et d'histoire'--had
'd'historire.'
Footnote 49 'Ueber die Groesse und Figur der Erde'--had 'Grosse.'
Footnote 53 'Bestimmung der Laenge'--had 'Lange';
'Astronomisch-Geodaetische Arbeiten'--had 'Astronomische';
'Veroeffentlichungen des Koeniglichen'--had 'Koenigliche.'
Footnote 55 '(1768), vol. 58, pp. 329-335.'--had '329-235.'
Footnote 66 'Comptes-rendus de l'Academie'--had 'L'Academie.'
Footnote 81 'Sur l'Intensite absolue'--had 'l'Intensite.'
Footnote 89 'Sitzungsberichte der Koeniglicher'--had 'Koenigliche.'
Footnote 100 'Veroeffentlichungen des Koeniglichen' had
'Veroeffentlichungen Koenigliche.'

Capitalisation of 'Von'/'von' has been regulaized to 'von' for all personal names, except at the beginning of a sentence, and when referring to the Von Sterneck pendulum.

<pre id="pg-footer">