physical geodesy by stating 113 that it alone can give: 



i . 1 he flattening of the reference ellipsoid. 



2. The undulations .Y of the geoid. 



3. The components of the deflection of the vertical £ 

 and 77 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 moun- 

 tainous 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 Veiling Meinesz state: 



It is the firm conviction of the authors that the gravi- 

 metric method is by far the best of the existing methods 

 for solving the main problems of geodesy, i.e., to deter- 

 mine 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 in- 

 tensity 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 de- 

 veloped by Huygens. Invariable compound pendu- 

 lums with single axes also have been used to deter- 

 mine relative values of gravity by comparative times 

 of swing. 



The history of gravity pendulums begins with tin- 

 ball or '■simple'' pendulum of Galileo as an approxi- 



13 Ibid., p. 309. 

 » [bid., p. 310. 



mation to the ideal simple pendulum. Determina- 

 tions of the length of the seconds pendulum by French 

 scientists culminated in a historic determination at 

 Paris by Borda and Cassini, from the corrected ob- 

 servations with a long ball pendulum. In the 19th 

 century, Bessel found the length of the seconds pen- 

 dulum at Konigsberg and Berlin by observations with 

 a ball pendulum and by original theoretical considera- 

 tions. During the century, however, the compound 

 pendulum came to be preferred for absolute and rela- 

 tive determinations. 



Capt. Henry Kater, at London, constructed the first 

 convertible compound for an absolute determination 

 of gravity, and then he designed an invariable com- 

 pound 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 Ham- 

 burg of a Repsold-Bessel pendulum for the U.S. Coast 

 Survey and observed with it in Geneva, Paris, Berlin, 

 and London. L'pon an initial stimulation from 

 Baeyer, founder of Die Europdische Gradmessung, 

 Peirce demonstrated by experiment and theory that 

 results previously obtained with the Repsold ap- 

 paratus 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 soke 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 



Mb 



BULLETIN 240: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY 



