

&< 



Figure 4. — The direct use of a clock to measure the force of gravity was found to be limited in accuracy 

 by the necessary mechanical connection of the pendulum to the clock, and by the unavoidable difference 

 between the characteristics of a clock pendulum and those of a theoretical (usually called "simple") pendu- 

 lum, in which the mass is concentrated in the bob, and the supporting rod is weightless. 



After 1735, tnc clock was used only to time the swing of a detached pendulum, by the method of "coinci- 

 dences." In this method, invented by J. J. Mairan, the length of the detached pendulum is first accurately 

 measured, and the clock is corrected by astronomical observation. The detached pendulum is then 

 swung before the clock pendulum as shown here. The two pendulums swing more or less out of phase, 

 coming into coincidence each time one has gained a vibration. By counting the number of coincidences 

 over several hours, the period of the detached pendulum can be very accurately determined. The length 

 and period of the detached pendulum are the data required for the calculation of the force of gravity. 



in Peru, and, with the help of the Spaniard Ullo, 

 measured a meridian arc of about 3°7' near Quito, 

 now in Ecuador.' 2 The second expedition, with 

 Maupertuis and Clairaut in 1736, went to Lapland 

 within the Arctic Circle and measured an arc of 

 about 1° in length. 1 ' The northern arc of 1° was 

 found to be longer than the Peruvian arc of 1°, and 



i' Pierre Bouguer, l.a figure de la terre, determinle pai lei 

 observations de Messieurs Bouguer el de La Condamine, envoyes 

 par ordre du Roy au Perou, pour observii au> environs de Vequateur 

 (Paris, 1749). 



,3 P. L. Moreau de Maupertuis, Lafigure de la terre d'eterminet 

 par Us observations de Messieurs de Maupertuis, Clairaut, Camus, he 

 Monnier, V Abbe Outhier et Celsius, faites par ordre du Roy au cercle 

 polaire (Paris, 1738). 



thus it was confirmed that the earth is an oblate 

 spheroid, that is, flattened at the poles, as predicted 

 by the theory of Newton. 



The period from Eratosthenes to Picard has been 

 called the spherical era of geodesy; the period from 

 Picard to the end of the 19th century has been called 

 the ellipsoidal period. During the latter period the 

 earth was conceived to be an ellipsoid, and the de- 

 termination of its ellipticity, that is, the difference of 

 equatorial radius and polar radius divided by the 

 equatorial radius, became an important geodetic 

 problem. A significant contribution to the solution 

 of this problem was made by determinations of 

 gravity by the pendulum. 



An epoch-making work during the ellipsoidal era 



308 



BULLETIN 240: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY 



