792 GEOGRAPHICAL LATITUDE. 



the results agreeing to the sixth of a second.^ This was to establish 

 the exact position of one point in the middle of the surveyed line; and 

 similar observations were necessary at both ends of the same. Two 

 base lines were measured, 6,075,90 and 6,006,25 toises long, respect- 

 ively. In fixing the permanent ends thereof and in the work of 

 placing the rules in the true direction, etc., this survey furnished the 

 model for the future ; and though more recent experts have changed 

 details of practice, they have offered nothing new in i>rinciple. In 

 reducing the length actually measured to the true basis of the survey, 

 certain slight alterations were necessary, which were made with the 

 greatest nicety. For instance, the line of Melun was not perfectly 

 straight, but was broken at one point by an angle of 179° 10' 49".09, 

 which necessitated calculations to give the length of the corresponding 

 straight line ; even the thickness of the cord bearing the plummet was 

 subtracted, and corrections for temperature, for inevitable errors in 

 tracing the line, and for the thickness of the rules, were added.^ When 

 all this was done it remained to reduce this to the arc of a circle and 

 then to sea level. Delambre says that the greatest error to be feared is 

 that of the '' vernier des languettes," or slides for measuring the inter- 

 vals between the rules, which error will not surpass one inch in 6,000 

 toises, 4 3 2V0 of the whole length.^ Work of such nicety is necessarily 

 slow, and it need not surprise one to learn that it took forty-one days of 

 actual work from 9 o'clock A. m. to sun-down to measure one line, and 

 that the greatest attainable speed was to place in a day ninety rules 

 end to end, or in other words — measure 360 meters.* 



Equal care was taken in locating the triangles, as witness a search 

 of six days for a place from which at one time three important points 

 might be seen or the measuring an angle 170 times (!), because of 

 the peculiar efiect of the sun's light at different times of the day on 

 a belvedere, which formed the point of a neighboring angle.' With 

 Borda's circle was observed not only the angle between the two lines 

 of the triangle, but also the zenith distance of each point. The size 

 of the angle was determined by the use of a series of twenty angles in 

 favorable cases, and of repeating doubtful cases at different hours of 

 the day.^ The result of the survey was to give to the forty-fifth degree 

 of latitude the value of 67,027 toises. 



Thus the eighteenth century proved conclusively what the genius of 

 the seventeeuth had only made probable on theoretical grounds, 

 namely, the flattening of the earth at the poles. It remained for the 

 nineteenth not only to determine exactly the quantity thereof, but to 

 bring to light another fact not dreamed of heretofore, i. e., that the 

 earth, even in its geodetic lines, has no regular geometrical figure 

 whatever. This was the finishing touch to the dream of the Pytha- 



i Base du syst^me I, 94. * Ibid., 85, 86. 



«/6td., II, 41-45. 6/6id.,i, 75. 



'/tid., m, 165. * Ibid., I, 117, 



