pendulum has been a basic instrument for the determination of the
intensity of gravity, which is expressed as the acceleration of a freely
falling body. Basis of theory is the simple pendulum, whose time of
swing under gravity is proportional to the square root of the length
divided by the acceleration due to gravity. Since the length of a simple
pendulum divided by the square of its time of swing is equal to the
length of a pendulum that beats seconds, the intensity of gravity also
has been expressed in terms of the length of the seconds pendulum. The
reversible compound pendulum has served for the absolute determination
of gravity by means of a theory developed by Huygens. Invariable
compound pendulums with single axes also have been used to determine
relative values of gravity by comparative times of swing.
The history of gravity pendulums begins with the ball or "simple"
pendulum of Galileo as an approximation to the ideal simple pendulum.
Determinations of the length of the seconds pendulum by French
scientists culminated in a historic determination at Paris by Borda and
Cassini, from the corrected observations with a long ball pendulum. In
the 19th century, Bessel found the length of the seconds pendulum at
Koenigsberg and Berlin by observations with a ball pendulum and by
original theoretical considerations. During the century, however, the
compound pendulum came to be preferred for absolute and relative
determinations.
Capt. Henry Kater, at London, constructed the first convertible compound
for an absolute determination of gravity, and then he designed an
invariable compound pendulum, examples of which were used for relative
determinations at various stations in Europe and elsewhere. Bessel
demonstrated theoretically the advantages of a reversible compound
pendulum which is symmetrical in form and is hung by interchangeable
knives. The firm of A. Repsold and Sons in Hamburg constructed pendulums
from the specifications of Bessel for European gravity surveys.
Charles S. Peirce in 1875 received delivery in Hamburg of a
Repsold-Bessel pendulum for the U.S. Coast Survey and observed with it
in Geneva, Paris, Berlin, and London. Upon an initial stimulation from
Baeyer, founder of _Die Europaeische Gradmessung_, Peirce demonstrated by
experiment and theory that results previously obtained with the Repsold
apparatus required correction, because of the flexure of the stand under
oscillations of the pendulum. At the Stuttgart conference of the
geodetic association in 1877, Herve Faye proposed to solve the problem
of flexure by swinging two similar pendulums from the same support with
equal amplitudes and in opposite phases. Peirce, in 1879, demonstrated
theoretically the soundness of the method and presented a design for its
application, but the "double pendulum" was rejected at that time. Peirce
also designed and had constructed four examples of a new type of
invariable, reversible pendulum of cylindrical form which made possible
the experimental study of Stokes' theory of the resistance to motion of
a pendulum in a viscous fluid. Commandant Defforges, of France, also
designed and used cylindrical reversible pendulums, but of different
length so that the effect of flexure was eliminated in the reduction of
observations. Maj. Robert von Sterneck, of Austria-Hungary, initiated a
new era in gravity research by the invention of an apparatus with a
short pendulum for relative determinations of gravity. Stands were then
constructed in Europe on which two or four pendulums were hung at the
same time. Finally, early in the present century, Vening Meinesz found
that the Faye-Peirce method of swinging pendulums hung on a Stueckrath
four-pendulum stand solved the problem of instability due to the
mobility of the soil in Holland.
The 20th century has witnessed increasing activity in the determination
of absolute and relative values of gravity. Gravimeters have been
perfected and have been widely used for rapid relative determinations,
but the compound pendulums remain as indispensable instruments.
Mendenhall's replacement of knives by planes attached to nonreversible
pendulums has been used also for reversible ones. The Geodetic Institute
at Potsdam is presently applying the Faye-Peirce method to the
reversible pendulum.[115] Pendulums have been constructed of new
materials, such as invar, fused silica, and fused quartz. Minimum
pendulums for precise relative determinations have been constructed and
used. Reversible pendulums have been made with "I" cross sections for
better stiffness. With all these modifications, however, the foundations
of the present designs of compound pendulum apparatus were created in
the 19th century.
FOOTNOTES:
[1] The basic historical documents have been collected, with a
bibliography of works and memoirs published from 1629 to the end of
1885, in _Collection de memoires relatifs a la physique, publies par la
Societe francaise de Physique_ [hereinafter referred to as _Collection
de memoires_]: vol. 4, _Memoires sur le pendule, precedes d'une
bibliographie_ (Paris: Gauthier-Villars, 1889); and vol. 5, _Memoires
sur le pendule_, 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), 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.