Chapter XVI: Introduction: 203 (6)

The best way to eliminate the effect of flexure is to use two
synchronized pendulums of the same length swinging on the same
apparatus in the same plane and with the same amplitudes but in
opposite phases; it is clear then the flexure is zero.[95]

In view of the fact that the symmetrical reversible pendulum is named for Bessel, who created the theory and a design for its application by Repsold, it appears appropriate to call the method of eliminating flexure by swinging two pendulums on the same support the Faye-Peirce method. Its successful application was made possible by Maj. von Sterneck's invention of the short, 1/4-meter pendulum.

Absolute Value of Gravity at Potsdam

The development of the reversible pendulum in the 19th century culminated in the absolute determination of the intensity of gravity at Potsdam by Kuehnen and Furtwaengler of the Royal Prussian Geodetic Institute, which then became the world base for gravity surveys.[96]

We have previously seen that in 1869 the Geodetic Institute--founded by Lt. Gen. Baeyer--had acquired a Repsold-Bessel reversible pendulum which was swung by Dr. Albrecht under the direction of Dr. Bruhns. Dissatisfaction with this instrument was expressed by Baeyer in 1875 to Charles S. Peirce, who then, by experiment and mathematical analysis of the flexure of the stand under oscillations of the pendulum, determined that previously reported results with the Repsold apparatus required correction. Dr. F. R. Helmert, who in 1887 succeeded Baeyer as director of the Institute, secured construction of a building for the Institute in Potsdam, and under his direction the scientific study of the intensity of gravity was pursued with vigor. In 1894, it was discovered in Potsdam that a pendulum constructed of very flexible material yielded results which differed markedly from those obtained with pendulums of greater stiffness. Dr. Kuehnen of the Institute discovered that the departure from expectations was the result of the flexure of the pendulum staff itself during oscillations.[97]

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 staff.[98] 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 authorization from the superintendent of the Coast and Geodetic Survey to arrange for the construction of such pendulums by Gautier 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 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, Kuehnen and Furtwaengler 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 Kuehnen and Furtwaengler published their monumental memoir, "Bestimmung der Absoluten Groesze 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/sec^{2}. 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 (T_{1})^{2}/(T_{2})^{2} = g_{2}/g_{1}. 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/sec^{2}.[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/sec^{2}.[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]

In 1939, J. S. Clark published the results of a determination of gravity with pendulums of a non-ferrous Y-alloy[105] at the National Physical Laboratory at Teddington, England, and, after recomputation of results by Jeffreys, the value was found to be 12.8 parts in 1 million less than the value obtained by transfer from Potsdam. Dr. Hugh L. Dryden of the National Bureau of Standards, and Dr. A. Berroth of the Geodetic Institute at Potsdam, have recomputed the Potsdam data by different methods of adjustment and concluded that the Potsdam value was too high by about 12 parts in a million.[106] Determination of gravity at Leningrad by Russian scientists likewise has indicated that the 1906 Potsdam value is too high. In the light of present information, it appears justifiable to reduce the Potsdam value of 981.274 by .013 cm/sec^{2} for purposes of comparison. If the Brown transfer from Potsdam in 1933 was taken as accurate, the value for the Washington base would be 980.105 cm/sec^{2}. In this connection, it is of interest to note that the value given by Charles S. Peirce for the comparable Smithsonian base in Washington, as determined by him from comparative methods in the 1880's and reported in the _Annual Report of the Superintendent of the Coast and Geodetic Survey for the year 1890-1891_, was 980.1017 cm/sec^{2}.[107] This value would appear to indicate that Peirce's pendulums, observations, and methods of reduction of data were not inferior to those of the scientists of the Royal Prussian Geodetic Institute at Potsdam.

Doubts concerning the accuracy of the Potsdam value of gravity have stimulated many new determinations of the intensity of gravity since the end of World War II. In a paper published in June 1957, A. H. Cook, Metrology Division, National Physical Laboratory, Teddington, England, stated:

At present about a dozen new absolute determinations are in
progress or are being planned. Heyl and Cook's reversible
pendulum apparatus is in use in Buenos Aires and further
reversible pendulum experiments have been made in the All Union
Scientific Research Institute of Metrology, Leningrad (V N I I M)
and are planned at Potsdam. A method using a very long pendulum
was tried out in Russia about 1910 and again more recently and
there are plans for similar work in Finland. The first
experiment with a freely falling body was that carried out by
Volet who photographed a graduated scale falling in an enclosure
at low air pressure. Similar experiments have been completed in
Leningrad and are in progress at the Physikalisch-Technische
Bundesanstalt (Brunswick) and at the National Research Council
(Ottawa), and analogous experiments are being prepared at the
National Physical Laboratory and at the National Bureau of
Standards. Finally, Professor Medi, Director of the Istituto
Nazionale di Geofisica (Rome), is attempting to measure the
focal length of the paraboloidal surface of a liquid in a
rotating dish.[108]

Application of Gravity Surveys

We have noted previously that in the ancient and early modern periods, the earth was presupposed to be spherical in form. Determination of the figure of the earth consisted in the measurement of the radius by the astronomical-geodetic method invented by Eratosthenes. Since the earth was assumed to be spherical, gravity was inferred to be constant over the surface of the earth. This conclusion appeared to be confirmed by the determination of the length of the seconds pendulum at various stations in Europe by Picard and others. The observations of Richer in South America, the theoretical discussions of Newton and Huygens, and the measurements of degrees of latitude in Peru and Sweden demonstrated that the earth is an oblate spheroid.

The theory of gravitation and the theory of central forces led to the result that the intensity of gravity is variable over the surface of the earth. Accordingly, determinations of the intensity of gravity became of value to the geodesist as a means of determining the figure of the earth. Newton, on the basis of the meager data available to him, calculated the ellipticity of the earth to be 1/230 (the ellipticity is defined by (a-b)/a, where a is the equatorial radius and b the polar radius). Observations of the intensity of gravity were made on the historic missions to Peru and Sweden. Bouguer and La Condamine found that at the equator at sea level the seconds pendulum was 1.26 Paris-lines shorter than at Paris. Maupertuis found that in northern Sweden a certain pendulum clock gained 59.1 seconds per day on its rate in Paris. Then Clairaut, from the assumption that the earth is a spheroid of equilibrium, derived a theorem from which the ellipticity of the earth can be derived from values of the intensity of gravity.

Early in the 19th century a systematic series of observations began to be conducted in order to determine the intensity of gravity at stations all over the world. Kater invariable pendulums, of which 13 examples have been mentioned in the literature, were used in surveys of gravity by Kater, Sabine, Goldingham, and other British pendulum swingers. As has been noted previously, a Kater invariable pendulum was used by Adm. Luetke of Russia on a trip around the world. The French also sent out expeditions to determine values of gravity. After several decades of relative inactivity, Capts. Basevi and Heaviside of the Indian Survey carried out an important series of observations from 1865 to 1873 with Kater invariable pendulums and the Russian Repsold-Bessel pendulums. In 1881-1882 Maj. J. Herschel swung Kater invariable pendulums nos. 4, 6 (1821), and 11 at stations in England and then brought them to the United States in order to make observations which would connect American and English base stations.[109]

The extensive sets of observations of gravity provided the basis of calculations of the ellipticity of the earth. Col. A. R. Clarke in his _Geodesy_ (London, 1880) calculated the ellipticity from the results of gravity surveys to be 1/(292.2 +- 1.5). Of interest is the calculation by Charles S. Peirce, who used only determinations made with Kater invariable pendulums and corrected for elevation, atmospheric effect, and expansion of the pendulum through temperature.[110] He calculated the ellipticity of the earth to be 1/(291.5 +- 0.9).

The 19th century witnessed the culmination of the ellipsoidal era of geodesy, but the rapid accumulation of data made possible a better approximation to the figure of the earth by the geoid. The geoid is defined as the average level of the sea, which is thought of as extended through the continents. The basis of geodetic calculations, however, is an ellipsoid of reference for which a gravity formula expresses the value of normal gravity at a point on the ellipsoid as a function of gravity at sea level at the equator, and of latitude. The general assembly of the International Union of Geodesy and Geophysics, which was founded after World War I to continue the work of _Die Internationale Erdmessung_, adopted in 1924 an international reference ellipsoid,[111] of which the ellipticity, or flattening, is Hayford's value 1/297. In 1930, the general assembly adopted a correlated International Gravity Formula of the form

[gamma] = [gamma]_{E}(1 + [beta]sin^{2} [phi] + [epsilon]sin^{2} 2[phi])

where [gamma] is normal gravity at latitude [phi], [gamma]_{E} is the value of gravity at sea level at the equator, [beta] is a parameter which is computed on the basis of Clairaut's theorem from the flattening value of the meridian, and [epsilon] is a constant which is derived theoretically. The plumb line is perpendicular to the geoid, and the components of angle between the perpendiculars to geoid and reference ellipsoid are deflections of the vertical. The geoid is above the ellipsoid of reference under mountains and it is below the ellipsoid on the oceans, where the geoid coincides with mean sea level. In physical geodesy, gravimetric data are used for the determination of the geoid and components of deflections of the vertical. For this purpose, one must reduce observed values of gravity to sea level by various reductions, such as free-air, Bouguer, isostatic reductions. If g_{0} is observed gravity reduced to sea level and [gamma] is normal gravity obtained from the International Gravity Formula, then

[Delta]g = g_{0} - [gamma]

is the gravity anomaly.[112]

In 1849, Stokes derived a theorem whereby the distance N of the geoid from the ellipsoid of reference can be obtained from an integration of gravity anomalies over the surface of the earth. Vening Meinesz further derived formulae for the calculation of components of the deflection of the vertical.

Geometrical geodesy, which was based on astronomical-geodetic methods, could give information only concerning the external form of the figure of the earth. The gravimetric methods of physical geodesy, in conjunction with methods such as those of seismology, enable scientists to test hypotheses concerning the internal structure of the earth. Heiskanen and Vening Meinesz summarize the present-day achievements of the gravimetric method of physical geodesy by stating[113] that it alone can give:

1. The flattening of the reference ellipsoid.

2. The undulations N of the geoid.

3. The components of the deflection of the vertical [xi] and
[eta] at any point, oceans and islands included.

4. The conversion of existing geodetic systems to the same world
geodetic system.

5. The reduction of triangulation base lines from the geoid to
the reference ellipsoid.

6. The correction of errors in triangulation in mountainous
regions due to the effect of the deflections of the vertical.

7. Geophysical applications of gravity measurements, e.g., the
isostatic study of the earth's interior and the exploration of
oil fields and ore deposits.

With astronomical observations or with existing triangulations, the gravimetric method can accomplish further results. Heiskanen and Vening Meinesz state:

It is the firm conviction of the authors that the gravimetric
method is by far the best of the existing methods for solving
the main problems of geodesy, i.e., to determine the shape of
the geoid on the continents as well as at sea and to convert the
existing geodetic systems to the world geodetic system. It can
also give invaluable help in the computation of the reference
ellipsoid.[114]

Summary

Since the creation of classical mechanics in the 17th century, the 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.

[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.

* * * * *

Paper 44 - Transcriber's Note

Formatting of equations has been altered from the original: variables are shown without italics; to display them 'in line'; and brackets have been added to clarify expressions where necessary.

Typographical errors and inconsistencies have been corrected as follows:

Page 320: 'difference T_{1} - T_{2} is sufficiently' had 'sufficlently.'

Page 321: 'faites à Genève avec le pendule à réversion' had 'reversion.'

Page 326: 'Schwere mit Hilfe verschiedener Apparate' had 'verschiedene.'

Page 328: 'between the yard and the meter.' closing quote mark deleted.

Page 334: 'Mendenhall apparatus were part of' 'was' changed to 'were.'

Page 342: 'of the Geodetic Institute at Potsdam' had 'Postdam.'

Page 345: 'The gravimetric methods of physical' had 'mtehods.'

Footnote 1 'Société française de Physique' had 'Française.'

Footnote 3 'Cogitata physico-mathematica' had 'physica.'

Footnote 10 'mathématiques et de physique par MM. de l'Académie Royale'
had 'mathematiques,' 'Royal.'

Footnote 12 'par ordre du Roy au Pérou, pour observer'
had 'Perou, pour observir.'

Footnote 19 'Opticam et Astronomiam' had 'Astronomian.'

Footnote 20 'connaître la longueur du pendule qui'
had 'connaitre la longuer.'

Footnote 21 'Abhandlungen der Königlichen Akademie' had 'Königliche.'

Footnote 25 'pour déterminer la longueur du pendule' had 'longeur.'

Footnote 41 'Survey of India (Calcutta, 1879)' had 'Surey.'

Footnotes 45 and 47 'Société de Physique et d'histoire'
had 'd'historire.'

Footnote 49 'Über die Grösse und Figur der Erde' had 'Grosse.'

Footnote 53 'Bestimmung der Länge' had 'Lange';
'Astronomisch-Geodätische Arbeiten' had 'Astronomische';
'Veröffentlichungen des Königlichen' had 'Königliche.'

Footnote 55 '(1768), vol. 58, pPage 3$1:-335.' had '329-235.'

Footnote 66 'Comptes-rendus de l'Académie' had 'L'Académie.'

Footnote 81 'Sur l'Intensité absolue' had 'l'Intensite.'

Footnote 89 'Sitzungsberichte der Königlicher' had 'Königliche.'

Footnote 100 'Veröffentlichungen des Königlichen'
had 'Veröffentlichungen Königliche.'

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.

* * * * *

_Index_

A

Adams, W. B., 252
Agricola, Georgius, 215, 216
Airy, G. B., 319, 324, 332
Albrecht, Karl Theodore, 322, 338
Aldini, Giovanni, 124
Al-Mamun, seventh calif of Bagdad, 306
Almansi, Emilio, 339
Ames Manufacturing Company, 5, 7
Ampère, André Marie, 127, 129
Anckerswärd, Col. Michael, 157
Angle, Edward H., 295
Arago, Dominique François Jean, 129
Aristarchus of Samos, 54
Aristotle, 179, 306
Astor, John Jacob, 141

B

Baeyer, Adolf, 193
Baeyer, J. J., 321, 322, 324-327, 338, 346
Baily, Francis, 317
Baldwin, Matthias William, 264
Baltimore, Lord. _See_ Calvert.
Barlow, Peter W., 221, 227
Bartlett, Charles A., 8
Basevi, James Palladio, 345
Battison, E. A., 18
Beach, Alfred Ely, 224, 227-229, 231, 237
Bechil, Achild, 179
Bemis, Will, 20-22, 27
Bennet, Abraham, 124
Bennett, Frank M., 139, 150, 165
Benz, Carl, 6, 7
Bergh, Christian, 145
Berroth, A., 342
Berthelot, Marcellin, 189
Bertolla, Alessandro, 65
Bertolla, Bartolomeo Antonio, 31, 34, 36-41, 47, 51, 52, 57-59, 62, 63
Berzelius, Jöns Jakob, 133, 182
Bessel, Friedrich Wilhelm, 313, 314, 319, 320, 324, 325, 338, 346
Besson, Jacques, 107
Bettany, G. T., 136
Beyer, Dr. Henry Gustav, 275, 276
Biddle, James, 141
Biot, Jean Baptiste, 135, 325, 329
Black, G. V., 295
Black and Bell, plant at Stratford, 182
Blake, John B., 290, 291
Bohnenberger, Johann Gottlieb Friedrich, 315
Bollman, W., and Company, 91, 92
Bollman, Wendel, 79, 80-83, 85, 88-92, 94-97
Borda, J. C., 311, 312, 315, 325, 329, 346
Borghesi, Father Francesco, 31-59, 70, 71
Boscovitch, Père R. J., 310, 311
Boston Locomotive Works, 260
Bouguer, Pierre, 307, 309-311, 327, 343, 345
Boussingault, Jean Baptiste, 185
Boyd, John C., 276
Boyle, Robert, 178, 179
Brackenridge, S. M., 145
Brahe, Tycho, 54, 306
Brand, H., 178, 179
Brewington, M. V., 155
Brown, Adam and Noah, 141, 142, 145
Brown, Alexander Crosby, 165
Brown, E. J., 334, 339
Brown, Noah, 141, 150, 151
Browne, Charles, 157
Browne, Henry, 304, 314
Browns' yard, 142, 144
Bruhns, C., 322, 324, 338
Brunel, I. K., 217, 218
Brunel, Marc Isambard (the elder), 204, 205, 217, 218, 221, 224, 229,
231, 236
Brunner Brothers (Paris), 329
Buchner, Hans, 197, 200
Burleigh, Charles, 212, 213
Burleigh Rock Drill Company, 212
Burr, S. D. V., 236
Butzjäger, Johann Georg, 36, 37

C

Calvert, George, Lord Baltimore, 156
Calvin, Melvin, 200
Canning, Stratford, 139
Carlisle, Anthony, 124
Carrel, Alexis, 291
Casciarolo, Vicenzo, 179
Cassini, Giovanni-Domenico, 306, 307
Cassini, Jacques, 306
Cassini de Thury, J. D., 311, 312, 315, 325, 329, 346
Cavallo, Tiberio, 124
Cavendish, Henry, 123
Cellérier, Charles, 320, 321, 325, 326, 329, 336
Chapman, Fredrik Henrik af, 156, 166
Charles II of England, 152, 153
Charles VI, Emperor of Austria, 32
Chevreul, Michel, 189
Clairaut, Alexis Claude, 308, 309, 343, 345
Clark, J. S., 342
Clark, John, 91
Clarke, A. R., 345
Cles, Baron of, 57, 59
Coast and Harbor Defense Company, 141
Coast Defense Society, 141, 142
Cochrane, Sir Thomas, 231, 232
Colbert, Jean Baptiste, 306
Colburn, Zerah, 259
Colden, C. D., 149
Coleman, Laurence V., 290
Colgan, P., 10
Colton, Arthur, and Company, 278
Cook, A. H., 342
Cook, Guy S., 339, 342
Copernicus, 54
Copperthwaite, William Charles, 224
Cori, Carl F., 200
Cori, Gerti T., 200
Crookes, William, 192
Cummings, James, 125, 127-129, 133-136

D

Dagger, Benjamin M., 290
Danforth Cooke & Co., 252
Danish Greenland Company, 150
Danish Royal Archives, 139, 150
Davy, Sir Humphry, 185
Dearborn, Henry, 141, 142
Deats, William, 9
Decatur, Stephen, 141
Defforges, C., 314, 329, 346
De Freycinet, Louis Claude de Saulses, 317
De Hevesy, George, 198, 200
De la Hire, Gabriel Philippe, 306
De la Vega, Garcilaso, 185
De Prony, M. G., 314
Deptford Yard (England), 165
De Saussure, Théodore, 185
Di Noris, Cristoforo Sizzo, 59
Dixon, William S., 276
Doane, Thomas, 210, 212, 213, 215
Dodrill, Forest D., 290
Donner, Joseph, 277
Douglas, W. & B., Company, 113
Drake, Edwin L., 213
Drinker, Henry S., 224, 237
Drury, Gardner P., 260
Dryden, Hugh L., 342
Du Buat, L. G., 314
Duperry, Capt. Louis Isidore, 317
Duryea, Charles, 3-13, 15, 16, 19-21, 26, 27
Duryea, J. Frank, 3-7, 9-13, 15-23, 26, 27
Duryea Motor Corporation, 5
Duryea Motor Wagon Company, 3, 27
Duryea Power Company, 5

E

Eastwick, Andrew M., 259
Eckford, Henry, 142
Einthoven, Willem, 290
Emerson, John Haven, 285
Emmet, ----, 144
Eratosthenes, 306, 308, 342
Erman, Paul, 128, 129, 132, 133
Eudoxus of Cnidus, 306
Euler-Chelpin, Hans von, 197, 200
Evans, Samuel, 141, 145
Evelyn, John, 32

F

Faraday, Michael, 125
Faye, Hervé, 325-327, 336-338, 346, 347
Ferchl, Fritz, 285
Fernel, Jean, 306
Fernelius, Jean, 179
Feulgen, Robert, 193
Fink, Albert, 79, 91
Fischelis, Robert P., 287
Fischer, Emil, 193
Fleming, Sir Alexander, 290, 295
Flint, James Milton, 273-278
Fox, Josiah, 157
Francis I, Emperor of the Holy Roman Empire, 42, 44, 52, 58
Fulton, Robert, 139, 141, 142, 144, 147, 149, 150, 157, 159, 165
Furtwängler, P., 337-339

G

Gahn, Johann Gottlieb, 182
Galilei, Galileo, 304, 305, 346
Galvani, Luigi, 124
Garfield, James A., 272
Garrison, Fielding H., 277
Gauss, C. F., 320
Gautier, P., 339
Gay-Lussac, Joseph Louis, 125, 182
Gilbert, L. W., 127-129, 132
Gobley, Nicolas Théodore, 191
Godin, Louis, 307
Goldingham, John, 316, 345
Goode, G. Brown, 273
Graham, Thomas, 182, 183, 185
Gravatt, C. U., 276
Greathead, James Henry, 204, 218, 221, 224, 229, 231, 235-237
Greely, A. W., 329
Griffenhagen, George B., 290, 291
Grubenmann, Hans, 85
Grubenmann, Johann Ulrich, 85
Gulf Oil and Development Company, 338
Gurley, Ralph R. (USN), 150, 151
Gustav III of Sweden, 156, 157
Gwynn, Stuart, 210

H

Hahn, Father Philipp Matthäus, 33
Haid, M., 335
Hall, Basil, 316
Hammond, William Alexander, 273
Hankwitz, Gottfried, 180
Harden, Arthur, 197, 200
Harrington, Frank, 7
Harrison, Joseph, Jr., 259
Hartford Machine Screw Company, 6
Hartmann, Immanuel Peter, 181
Haskin, DeWitt C., 204, 232, 234-236
Haupt, Herman, 96, 204, 209, 210
Hawley, C. E., 6, 11
Hawthorn, Leslie, and Company (Scotland), 166
Heaviside, W. J., 321, 345
Heiskanen, W. A., 338, 345, 346
Hellot, Jean, 180
Helmert, F. R., 338, 339
Helmholtz, Hermann von, 326
Henderson, Alfred R., 291
Henkel, Silon, 290
Henry II, King of France, 179
Herschel, John, 319, 328, 345
Heyl, Paul R., 339, 342
Hindle, Charles F., 290
Hinkley, Holmes, 252, 260, 263
Hirsch, Adolph, 322, 324-326
Hittorf, Wilhelm, 181
Hobson, Joseph, 237
Hoefer, Ferdinand, 179
Holmberg, Wilhelm, 178
Holt, L. Emmett, 276
Hoppe-Seyler, Felix, 193
Howard, George W., & Company, 8
Hull, A. S., 251, 268
Humboldt, Alexander von, 185
Huygens, Christiaan, 179, 304, 305, 307, 314, 342, 346

I

Ibañez, Carlos, 325
Incas, 185

J

Jefferson, Thomas, 145
Jeffreys, Sir Harold, 342
Jones, Jacob, 141
Jones, Thomas, 318
Jones, William, 147

K

Kater, Henry, 304, 314-320, 325, 327, 329, 345, 346
Kells, Charles E., 295
Klein, Father ----, 33
Kletwich, Johann Christopher, 179
Knight, ----, 83
Koett, Albert B., 287
Koppe, Émile, 181
Kornberg, Arthur, 200
Kossel, Albrecht, 200
Kraft, Johann Daniel, 179
Kramer, Dr. ----, 181
Kühnen, F., 338, 339
Kunckel, Johann, 179

L

La Condamine, Charles Marie de, 307, 310, 311, 343
Lange, W., 199
Laplace, Marquis Pierre Simon de, 309, 313, 320
Latrobe, Benjamin H., 82, 83, 85, 87-91, 208, 209
Laurie, J., 157
Lavoisier, Antoine Laurent, 181, 185
Law, Henry, 218
LaWall, Charles H., 285
Laws, John Bennet, 186
Lederle Laboratories, 290
Leibnitz, Gottfried Wilhelm von, 179
Lennox, Charles, third Duke of Richmond, 185
Leonhardi, Johann Gottfried, 179
Levine, Phoebus Aaron Theodor, 193
Lewis, Jacob, 141
Lewis, Morgan, 141
Lewton, Frederick L., 277
Liebig, Justus, 183, 185, 186
Liebreich, Oscar, 191
Lilly, Eli, and Company, 283
Lindbergh, Charles A., 291
Lipmann, Fritz, 200
Lippi, Fra Lippo, 42
London, E. S., 193
Long, Crawford W., 294
Long, Stephen H., 85
Longomontanus, Christian Severin, 54
Lorenzoni, Giuseppe, 336, 339
Lütke, Count Feodor Petrovich, 316, 345

M

Macquer, Peter Joseph, 180
Marestier, Jean Baptiste, 147, 149, 159, 162
Marggraf, Andreas Sigismund, 180
Maria Theresa, Empress of Austria, 31, 41, 42, 44, 57, 58
Mariners' Museum, 165
Markham, Erwin F., 8, 9, 15, 16, 19-22, 27
Marmion, R. A., 276
Marsh, James, 145
Marshall, Charles, 11, 16
Maudslay, Henry, 106, 113
Maupertius, P. L. Moreau de, 308, 343
Maxwell, James Clerk, 324
May, Arthur J., 139
Mayer, Jo, 285
McMurtrie, Daniel, 276
Medi, Enrico, 342
Meigs, M. C., 96
Meineke, ----, 128
Mendenhall, Thomas Corwin, 319, 331, 332, 334, 347
Merrick, C. E., 10
Mersenne, P. Marin, 305
Meton, 48
Meyerhof, Otto, 194, 200
Miescher, Johann Friedrich, 192
Miller, Patrick, 156, 157
Mitchill, Samuel L., 141, 142
Monauni, Giovanni Battista, 40, 52
Monroe, James, 145
Montgéry, M., 147, 149-152, 159
Morgan, "Mr.", 144
Morris, Tasker and Company, 94
Morris, Thomas, 141, 142
Morton, Arthur O., 290
Morton, William, 294
Mount Clair shops, 83, 89, 92
Mowbray, George W., 213, 215
Muspratt, James, 186

N

Nagel, Oscar P., 295
Nason, Joseph, 114
National Maritime Museum (England), 147, 156, 165
Nelson, Robert J., 295
Nesbitt, Mr. and Mrs. D. H., 13
Newton, Sir Isaac, 303-305, 307, 308, 342, 343
Nicholson, William, 124
Nietzsche, Friedrich, 186, 187, 189
Nobel, Alfred B., 213
North, Simeon, arms factory, 114
Norwood, Richard, 306

O

Ochoa, Severo, 200
Oersted, Hans Christian, 125-130, 132-136
Ohm, Georg Simon, 123, 135
Oken, Lorenz, 132
Olson, Carl G., 118
Oppolzer, Theodor von, 322, 324-327
Owen, H. S., 5

P

Page, Irving, 4
Parke, Davis & Company, 273
Parmelee, L. J., 10
Patapsco Bridge and Iron Works, 92, 95
Patrick, Mr. and Mrs. ----, 13
Patterson, Carlile Pollock, 325, 326
Peirce, Charles Sanders, 314, 322-329, 332, 336-339, 342, 345-347
Pelouze, Théophile Juste, 189
Pepys, Samuel, 155
Perry, Oliver, 141
Peters, C. A. F., 322, 324
Petty, Sir William, 152, 153, 155, 166
Pfaff, Christian Heinrich, 132
Philolaus, 54
Phoenix Iron Works, 92
Physick, Philip Syng, 294
Picard, Abbé Jean, 306, 308-311, 342
Plantamour, E., 319-321, 324-326
Poggendorf, Johann Christian, 127-129, 132-134, 136
Poissant, A. A., 10
Pope Manufacturing Company, 6, 12
Porter, David, 144
Posidonius, 306
Pratt, Thomas W., 91
Preston, E. D., 328, 329
Ptolemy, 54
Purcell, William, 147
Putnam, G. R., 339
Putnam Machine Works, 212
Pythagoras, 54, 306

Q

Quare, Daniel, 32

R

Raschig, Christoph Eusebius, 129
Rasmussen, Kjeld, 150
Reed, D. A., 27
Reeves, Samuel J., 92, 95
Repsold, A., and Sons (Hamburg), 320, 322, 338, 339, 346
Richer, Jean, 307, 342
Richmond, Duke of. _See_ Lennox.
Riciolus, 54
Rigsarkivet (Denmark), 147
Ritter, Johann Wilhelm, 129
Roebling, John A., 83, 90
Roentgen, Wilhelm Konrad, 290, 294
Rouelle, Guillaume François, 181
Royal Society of London, 152
Russell, John W., & Sons Company, 9, 10, 18, 20
Russell, William J., 9, 10, 15, 18
Rutgers, Henry, 141, 142

S

Sabine, Capt. Edward, 315, 325, 329, 345
San Cajetano, Brother David à, 33
San Daniele, Father Aurelianus à, 33
Savage Factory, 88
Savart, Felix, 135
Sawitsch, A., 321, 322
Scheele, Karl W., 182
Schieffelin and Company, 273
Schmiedeberg, Oswald, 193
Schrader, Gerhard, 199
Schrötter, Anton, 181
Schumacher, H. C., 320
Schumann, R., 335, 336
Schweigger, Johann Salomo Christoph, 127-130, 132-134, 136
Seebeck, T., 128, 135
Shanley, Walter, 212
Shanley Bros., 215
Shea, T., 10
Smith, ---- (Captain, USN), 144
Smith, Alba F., 244, 246, 247, 259
Smith, Sir Sidney (RN), 155
Smith Carriage Company, 8
Snell, Willebrord, 306
Snow, ----, 8
Soemmering, S. T., 125
Sommeiller, Germain, 210
Sonnedecker, Glenn, 296
Speter, M., 127, 128
Squibb, E. R., and Sons, 285, 286
Statens Sjöhistoriska Museum (Sweden), 147
Stephenson, Robert, 90
Stephenson, Robert, & Hawthorns, Ltd., 253
Sterneck, Robert von, 331, 332, 335, 338, 346
Stevens, J., Arms and Tool Company, 4
Stevens-Duryea Company, 4
Stewart, Charles, 145
Stiles, George, 144
Stokes, George Gabriel, 324, 328, 329, 345, 346
Stoklasa, Julius, 186
Storrow, Charles S., 210
Stoudinger, Charles, 144
Strecker, Adolf Friedrich, 191
Stuart, Charles B., 139, 150
Stuart, J. E. B., 249
Sully, Henry, 32
Swaine, Jack, 26
Symington, William, 157

T

Tanner, Paul H., 295
Taunton Locomotive Works, 247
Taylor, Frank A., 292
Tegmeyer, John H., 91
Thames Iron-works Company (England), 165
Thenard, Louis Jacques, 125
Thomas, George S., 287
Thudichum, Ludwig, 192
Todd, Lord Alexander, 200
Tompion, Thomas, 32
Toner, Joseph Meredith, 271
Tovazzi, Giangrisostomo, 57, 58
Town, Ithiel, 85
Tromsdorff, Johann Bartholomacus, 125
Tweed, William Marcy (Boss), 229
Tyler, Daniel, 244, 253
Tyler, David B., 139

U

Ulloa, Antonio de, 308
Union Works, 260
Uppercu, Inglis M., 27

V

Vander Woerd, Charles, 116, 117
Van Marum, Martin, 123
Vening Meinesz, F. A., 337, 338, 345-347
Volet, Charles, 342
Volta, Alessandro, 123, 124, 127
Vulcan Foundry, 252

W

Wallace Brothers, 273
Ward, Frederick A., 120
Warrington, Samuel, 141
Warwick, George, 18
Watts, Frederick, 249
Weale, John, 218
Wernwag, Lewis, 89
Westhaeffer, Paul, 251
Wetmore, Dr. Alexander, 287
Wetschgi, Emanuel, 108
Wetschgi, Manuel, 108, 111
Whipple, Squire, 79, 83, 87, 91, 95
Whistler, George W., 83
White, C. H., 276
Whitebread, Charles, 277, 278, 281, 283, 285, 287
Whitney arms factory, 114
Wilkes, Charles, 317, 318
Wilkinson, David, 113
Williamson, Dowe, 32
Williamson, Joseph, 32
Willm, Edmond, 182
Willstätter, Richard, 191
Wilmarth, Seth, 244, 246, 247, 249, 260
Wilson, Frank E., 290
Wilstack, Paul, 155
Winans, Ross, 83
Winters, Joseph, 244
Winters, Father S. X., S. J., 42
Winz, Johann Christian, 36, 37
Wisshofer, Peter, 36, 37
Wolcott, Oliver, 141, 142
Wollaston, W. H., 125
Wright, Benjamin, 83
Wurtz, Adolphe, 185, 191

Y

Youle, John, foundry, 142

Z

Zamboni, Giuseppe, 132

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Transcriber's Notes (Index)

"Emmet, ----, 144" (was Emmett).

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