figure ;j. Mi \si ki mi \ is "i nn ii.no in of a degree 

 of latitude which were completed in different parts 

 of France in 1669 and 1718 gave differing results 

 which suggested that the shape of the earth is not 

 a sphere but a prolate spheroid (1). But Richer's 

 pendulum observation of 1672, as explained by 

 Huygens and Newton, indicated that its shape is 

 that of an oblate spheroid (2). The disagreement 

 is reflected in this drawing. In the 1730's it 

 was resolved in favor of the latter view l>\ two 

 French geodetic expeditions for the measurement 

 of degrees of latitude in the equatorial and polar 

 regions (Ecuador — then part of Peru — and Lapland). 



of Giovanni-Domenico, added the arc to the north 

 of Paris. The project was completed in 1718. The 

 length of a degree of arc south of Paris was found to 

 be greater than the length north of Paris. From the 

 difference, 57,097 toises 7 minus 56,960 toises, it wis 

 concluded that the polar diameter of the earth is larger 

 than the equatorial diameter, i.e., that the earth is a 

 prolate spheroid (fig. 3). 



Meanwhile, Richer in 1672 had been sent to 

 Cayenne, French Guiana, to make astronomical 

 observations and to measure the length of the seconds 

 pendulum. s He took with him a pendulum clock 

 which had been adjusted to keep accurate time in 



7 The toisc as a unit of length was 6 Paris feet or about 1,949 

 millimeters. 



8 Jean Richer, Observations aslronomiques el physiques faites 

 en risle de Caienne (Paris, 1679). John W. Olmsted, "The 

 Expedition of Jean Richer to Cayenne 1672-1673," Jsis 

 (1942), vol. 34, pp. 117-128 



Paris. At Cayenne, however, Richer found that the 

 clock was retarded by 2 minutes and 28 seconds per 

 day (fig. 1). He also fitted up a "simple" pendulum to 

 vibrate in seconds and measured the length of this 

 seconds pendulum several tunc-, every week lor In 



months. Upon his return to Palis, he found that 

 the length of the "simple" pendulum which beal 

 seconds at Cayenne was r, Paris lines ' shorter than 

 the length of the seconds pendulum at Paris. Hu 

 explained the reduction in the length of the seconds 

 pendulum — and, therefore, the lesser intensity of 

 gravity at the equator with respect to the value at 

 Paris — in terms of his theory of centripetal force as 

 applied to the rotation of the earth and pendulum. 1 " 



A more complete theory was given by Newton in 

 the Principle 11 Newton showed that if the earth is 

 assumed to be a homogeneous, mutually gravitating 

 fluid globe, its rotation will result in a bulging at the 

 equator. The earth will then have the form of an 

 oblate spheroid, and the intensity of gravity as a 

 form of universal gravitation will vary with position 

 on the surface of the earth. Newton took into 

 account gravitational attraction and centrifugal ac- 

 tion, and he calculated the ratio of the axes of the 

 spheroid to be 230:229. He calculated and prepared 

 a table of the lengths of a degree of latitude and of 

 the seconds pendulum for every 5° of latitude from 

 the equator to the pole. A discrepancy between his 

 predicted length of the seconds pendulum at the 

 equator and Richer's measured length was explained 

 by Newton in terms of the expansion of the s, ,\i- 

 with higher temperatures near the equator. 



Newton's theory that the earth is an oblate spheroid 

 was confirmed by the measurements of Richer, but 

 was rejected by the Paris Academy of Sciences, for 

 it contradicted the results of the Cassinis, father and 

 son, whose measurements of arcs to the south and 

 north of Paris had led to the conclusion that the 

 earth is a prolate spheroid. Thus, a controversy 

 arose between the English scientists and the Paris 

 Academy. The conflict was finally resolved by the 

 results of expeditions sent by the Academy to Peru 

 and Sweden. The first expedition, under Bougucr, 

 La Condamine, and Godin in 1735, went to a region 



'The Paris foot was 1.066 English feet, and there were 12 

 lines to the inch. 



>° Christiaan Huyoens, "De la cause de la pesanteur," 

 Divers ouvrages de malhematiques el de physique par MM. ilt 

 I' Academic Royal des Sciences (Paris, 1693), p. 305. 



11 Isaac Newton, Philosophiae naturalis principia malhemalica 

 (London, 1687), vol. 3, propositions 18-20. 



PAPER 44: DEVELOPMENT OP GRAVITY PENDULUMS IN THE 19TII CENTURY 



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