part 2 (Paris: Gauthier-Villars, 1891). Important secondary

sources are: C. WOLF, "Introduction historique," pp. 1-42 in vol. 4, above; and GEORGE BIDDELL AIRY, "Figure of the Earth," pp. 165-240 in vol. 5 of _Encyclopaedia metropolitana_ (London, 1845).

[2] Galileo Galilei's principal statements concerning the pendulum occur in his _Discourses Concerning Two New Sciences_, transl. from Italian and Latin into English by Henry Crew and Alfonso de Salvio (Evanston: Northwestern University Press, 1939), pp. 95-97, 170-172.

[3] P. MARIN MERSENNE, _Cogitata physico-mathematica_ (Paris, 1644), p. 44.

[4] CHRISTIAAN HUYGENS, _Horologium oscillatorium, sive de motu pendulorum ad horologia adaptato demonstrationes geometricae_ (Paris, 1673), proposition 20.

[5] The historical events reported in the present section are from AIRY, "Figure of the Earth."

[6] ABBE JEAN PICARD, _La Mesure de la terre_ (Paris, 1671). JOHN W. OLMSTED, "The 'Application' of Telescopes to Astronomical Instruments, 1667-1669," _Isis_ (1949), vol. 40, p. 213.

[7] The toise as a unit of length was 6 Paris feet or about 1,949 millimeters.

[8] JEAN RICHER, _Observations astronomiques et physiques faites en l'isle de Caienne_ (Paris, 1679). JOHN W. OLMSTED, "The Expedition of Jean Richer to Cayenne 1672-1673," _Isis_ (1942), vol. 34, pp. 117-128.

[9] The Paris foot was 1.066 English feet, and there were 12 lines to the inch.

[10] CHRISTIAAN HUYGENS, "De la cause de la pesanteur," _Divers ouvrages de mathematiques[mathematiques] et de physique par MM. de l'Academie Royale[Royal] des Sciences_ (Paris, 1693), p. 305.

[11] ISAAC NEWTON, _Philosophiae naturalis principia mathematica_ (London, 1687), vol. 3, propositions 18-20.

[12] PIERRE BOUGUER, _La figure de la terre, determinee par les observations de Messieurs Bouguer et de La Condamine, envoyes par ordre du Roy au Perou, pour observer aux environs de l'equateur_ (Paris, 1749).

[13] P. L. MOREAU DE MAUPERTUIS, _La figure de la terre determinee par les observations de Messieurs de Maupertuis, Clairaut, Camus, Le Monnier, l'Abbe Outhier et Celsius, faites par ordre du Roy au cercle polaire_ (Paris, 1738).

[14] Paris, 1743.

[15] GEORGE GABRIEL STOKES, "On Attraction and on Clairaut's Theorem," _Cambridge and Dublin Mathematical Journal_ (1849), vol. 4, p. 194.

[16] See _Collection de memoires_, vol. 4, p. B-34, and J. H. POYNTING and SIR J. J. THOMSON, _Properties of Matter_ (London, 1927), p. 24.

[17] POYNTING and THOMSON, ibid., p. 22.

[18] CHARLES M. DE LA CONDAMINE, "De la mesure du pendule a Saint Domingue," _Collection de memoires_, vol. 4, pp. 3-16.

[19] PERE R. J. BOSCOVICH, _Opera pertinentia ad Opticam et Astronomiam_ (Bassani, 1785), vol. 5, no. 3.

[20] J. C. BORDA and J. D. CASSINI DE THURY, "Experiences pour connaitre la longueur du pendule qui bat les secondes a Paris," _Collection de memoires_, vol. 4, pp. 17-64.

[21] F. W. BESSEL, "Untersuchungen ueber die Laenge des einfachen Secundenpendels," _Abhandlungen der Koeniglichen Akademie der Wissenschaften zu Berlin, 1826_ (Berlin, 1828).

[22] Bessel used as a standard of length a toise which had been made by Fortin in Paris and had been compared with the original of the "toise de Peru" by Arago.

[23] L. G. DU BUAT, _Principes d'hydraulique_ (Paris, 1786). See excerpts in _Collection de memoires_, pp. B-64 to B-67.

[24] CAPT. HENRY KATER, "An Account of Experiments for Determining the Length of the Pendulum Vibrating Seconds in the Latitude of London," _Philosophical Transactions of the Royal Society of London_ (1818), vol. 108, p. 33. [Hereinafter abbreviated _Phil. Trans._]

[25] M. G. DE PRONY, "Methode pour determiner la longueur du pendule simple qui bat les secondes," _Collection de memoires_, vol. 4, pp. 65-76.

[26] _Collection de memoires_, vol. 4, p. B-74.

[27] _Phil. Trans._ (1819), vol. 109, p. 337.

[28] JOHN HERSCHEL, "Notes for a History of the Use of Invariable Pendulums," _The Great Trigonometrical Survey of India_ (Calcutta, 1879), vol. 5.

[29] CAPT. EDWARD SABINE, "An Account of Experiments to Determine the Figure of the Earth," _Phil. Trans._ (1828), vol. 118, p. 76.

[30] JOHN GOLDINGHAM, "Observations for Ascertaining the Length of the Pendulum at Madras in the East Indies," _Phil. Trans._ (1822), vol. 112, p. 127.

[31] BASIL HALL, "Letter to Captain Kater Communicating the Details of Experiments made by him and Mr. Henry Foster with an Invariable Pendulum," _Phil. Trans._ (1823), vol. 113, p. 211.

[32] See _Collection de memoires_, vol. 4, p. B-103.

[33] Ibid., p. B-88.

[34] Ibid., p. B-94.

[35] FRANCIS BAILY, "On the Correction of a Pendulum for the Reduction to a Vacuum, Together with Remarks on Some Anomalies Observed in Pendulum Experiments," _Phil. Trans._ (1832), vol. 122, pp. 399-492. See also _Collection de memoires_, vol. 4, pp. B-105, B-112, B-115, B-116, and B-117.

[36] One was of case brass and the other of rolled iron, 68 in. long, 2 in. wide, and 1/2 in. thick. Triangular knife edges 2 in. long were inserted through triangular apertures 19.7 in. from the center towards each end. These pendulums seem not to have survived. There is, however, in the collection of the U.S. National Museum, a similar brass pendulum, 37-5/8 in. long (fig. 15) stamped with the name of Edward Kuebel (1820-96), who maintained an instrument business in Washington, D.C., from about 1849. The history of this instrument is unknown.

[37] See Baily's remarks in the _Monthly Notices of the Royal Astronomical Society_ (1839), vol. 4, pp. 141-143. See also letters mentioned in footnote 38.

[38] This document, together with certain manuscript notes on the pendulum experiments and six letters between Wilkes and Baily, is in the U.S. National Archives, Navy Records Gp. 37. These were the source materials for the information presented here on the Expedition. We are indebted to Miss Doris Ann Esch and Mr. Joseph Rudmann of the staff of the U.S. National Museum for calling our attention to this early American pendulum work.

[39] G. B. AIRY, "Account of Experiments Undertaken in the Harton Colliery, for the Purpose of Determining the Mean Density of the Earth," _Phil. Trans._ (1856), vol. 146, p. 297.

[40] T. C. MENDENHALL, "Measurements of the Force of Gravity at Tokyo, and on the Summit of Fujiyama," _Memoirs of the Science Department, University of Tokyo_ (1881), no. 5.

[41] J. T. WALKER, _Account of Operations of The Great Trigonometrical Survey of India_ (Calcutta, 1879), vol. 5, app. no. 2.

[42] BESSEL, op. cit. (footnote 21), article 31.

[43] C. A. F. PETERS, _Briefwechsel zwischen C. F. Gauss und H. C. Schumacher_ (Altona, Germany, 1860), _Band_ 2, p. 3. The correction required if the times of swing are not exactly the same is said to have been given also by Bohnenberger.

[44] F. W. BESSEL, "Construction eines symmetrisch geformten Pendels mit reciproken Axen, von Bessel," _Astronomische Nachrichten_ (1849), vol. 30, p. 1.

[45] E. PLANTAMOUR, "Experiences faites a Geneve avec le pendule a reversion," _Memoires de la Societe de Physique et d'histoire naturelle de Geneve, 1865_ (Geneva, 1866), vol. 18, p. 309.

[46] Ibid., pp. 309-416.

[47] C. CELLERIER, "Note sur la Mesure de la Pesanteur par le Pendule," _Memoires de la Societe de Physique et d'histoire naturelle de Geneve, 1865_ (Geneva, 1866), vol. 18, pp. 197-218.

[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),