t it ji ii which the ellipticity of the earth can be derived 

 from values of the intensity of gravity. 



Early in the T'tli century a systematic series ol 

 ciIim-i a atiuiis lieu. in to he ((indue lid in onlci 

 termine the intensity of gravity at stations .ill 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, 

 (ioldinghaiu. and other British pendulum swingers. 

 As has been noted previously, a Kater invariable 

 pendulum was used by Adni. Lutke of Russia on 

 a trip around the world. The French also sent 

 OUl expeditions to determine values ol gravity. 

 Alter several decades of relative inactivity, ( apt 

 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. |. I lersehel. 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, 



I in extensive sets of observations of gravity pro- 

 vided the basis of calculations of the elliptic itv <>l the 

 earth. Col. A. R. Clarke in his Geodesy (Lo 

 1880) calculated the ellipticity from the results of 



gravity surveys to be _ -■_• ('I interest is the 



calculation hv Charles S. Peirce, who used onl) 

 determinations made with Kater invariable pendu- 

 lums and corrected for elevation, atmospheric effect, 

 and expansion of the pendulum through tempera- 

 ture. 110 He calculated the ellipticity of the earth 



tobe 291.5±0.9 



The 19th century witnessed the culmination oi 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 gravit) formula 

 expresses the value of normal gravity at a point on 



">» Sec footnote 89. 



"" C. S. Peirce, "On the Deduction of the Ellipticity of the 

 Earth, from Pendulum Experiments," Report of the Superintendent 

 of the L'.S. Coast and Geodetic Survey for JS80-SI (Washington, 

 1883) app. no. 15, pp. 442-456. 



the ellipsoid as a function of gravity at sea level at 

 the equator, and of latitude. I !<• embly 



of the Internationa] I nion ol Geodes) and Geophys- 

 ics, which was founded after \\ orld War 1 to continue 



the wmk ul Die Internationale lixhnessung, adopted 



in 1924 an international reference ellipsoid 

 which the ellipticity, or flattening, is Hayford's 



value H _. In 1930, the genera] assembly adopted 



a correlated International Gravity Formula of the form 



y-~ y 1 i .-; sin o > sin 



where ■, is normal gravit) at latitude <;>. y a is the 

 value ol gravit) al sea level at the equator, |9 is a 

 eter which is computed on the basis of ( llairaut's 

 theorem from the flattening value of the meridian, 

 and t is a ((instant which is derived theoretically. 

 I he plumb line is perpendicular to the geoid, and 

 da components ol angle between the perpendiculars 

 oid and reference ellipsoid are deflections of 

 the vertical, ["he geoid is above die 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, 

 metric data are used for the determination of the 

 geoid and components ol deflections of the vertical. 

 Foi this purpose, one must reduce observed values 

 of gravity to sea level by various reductions, sin h as 

 free-air. Bouguer. isostatic reductions. Ug ' s obsei ved 

 gravity reduced to sea level a\m\ ; is normal gravity 

 obtained from the International Gravit) Formula, 

 then A«/=<7o — Y i s die gravity anomaly. "- 



In 1849, Stokes derived a theorem whereby the 

 distance \ of the geoid from the ellipsoid of reft 

 can be obtained from an integration of gravit) 

 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 astro- 

 nomical-geodetic methods, could give information 



only concerning the external form of the figure of 

 the earth. The gravimetric mtehods of physical 

 \. in conjunction with methods such as those 

 of seismology, enable scientists to test hypotheses 

 concerning the internal structure of the earth. 

 Hciskanen and Vening Meinesz summarize the 

 present-day achievements of the gravimetric method of 



1,1 Hi isk vm s vm> Yi ninq Meinesz, op. cit. (footnote 95), p. 

 74 

 112 Ibid., p. 76. 



PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN III! Till CENTURY 



345 



