92 LECTURES 



275 :) " Thus all our operations in longitude as well as latitude concur 

 in giving to the earth a figure elongated towards the pole." He adds : 

 " This discovery, so useful to the sciences and to navigation, and so 

 glorious to France, will be due to the Academy." 



7. The conflicting results thus obtained, taken in connexion with 

 the importance of the problem, determined the French Academy to 

 send out commissions, one to measure an arc of the meridian near the 

 equator, another in the most northern latitude accessible. 



This was in 1*735. The commission to the north was committed 

 chiefly to Maupertuis and Clairault, while that to the equator was 

 under the direction of Bouguer and Condamine. 



The place selected by Maupertuis and Clairault for the northern 

 line was at the northern extremity of the Gulf of Bothnia, com- 

 mencing at Tornea, on the gulf, and terminating at a place called 

 Kittis, in latitude 66° 48' 44". The work was accomplished amid 

 great difficulties, arising from the severities of the climate. The 

 commission returned after an absence of more than two years. An 

 account of it was published by Clairault in 1743. The length of a 

 degree was found, to be 61.195 toises. This result, by subsequent 

 measurement of Swanburg, was found to be slightly erroneous. 



The southern commission commenced their operations at Targui in 

 Peru, near the equator, and continued the line to Cotshequi, about 3° 

 south of it. This commission was absent nine years.* A detailed 

 account of the work was given by Bouguer in one volume, 8vo., pub- 

 lished 1749. The length of a degree was found to be 60.4G8 toises. 



The results of these measurements dissipated all doubts as to the 

 earth's figure. They showed an unquestionable lengthening of the 

 degrees as we go from the equator to the pole, and a consequent flat- 

 tening at the pole. 



8. In the mean time, while these important measurements were in 

 progress in Peru and Lapland, Cassini de Thury, third of the name 

 and grandson of Dominic, in connexion with Lacaille, in 1739, re- 

 measured the entire French arc from Perpignan to Dunkirk, with 

 every possible care which could insure the utmost accuracy in the 

 result. Several errors of former measurements were corrected. The 

 comparison of a degree at the northern and southern extremities of 

 the arc, of some 400 miles in extent left, no room for doubt as to the 

 lengthening of the degrees as we proceed to the north. These three 

 measurements removed all doubts which might have existed as to the 

 figure of the earth. Thus the mathematicians, who deduced the ob- 

 lateness from principles purely dynamical, had the satisfaction of 

 finding their conclusions confirmed by the most elaborate measure- 

 ments. 



The next object of interest was to determine the exact amount ; 

 that is, to determine the exact length of the two axes of the figure ; 

 in other words, the equatorial and polar diameters. 



9. To determine the exact amount of oblateness, additional mea- 

 surements in different latitudes and different portions of the earth were 

 necessary. 



♦Left France ia May, 1735, returned in 1744. 



