790 GEOGRAPHICAL LATITUDE. 



this purpose they bad a bar of iron whereon was marked a toise. This 

 was kept in the shade in the guard teut, but no regard seems to have 

 been paid to the fact that the iron also was subject to constant changes 

 in length. In computing the final result an allowance was made for its 

 expansion by heat, probably for the average temperature of Peru above 

 that of Paris. This toise was afterward adopted as the standard of 

 measure under the name of toise of Peru, and with it all subsequent 

 surveys have been compared. All the angles of each triangle were 

 actually observed, many of them twice, with different instruments and 

 by different observers, and some of them even three times.' Experi- 

 ments were made to determine as nearly as possible the constant fail- 

 ure of the quadrants, which of course was taken into account in the 

 observations, besides which other corrections were made to reduce the 

 sum of all three angles to 180°, the amount of this last correction sel- 

 dom reaching 30 seconds.'' The first base line was measured by two 

 different parties starting at the opposite ends, and had an extent of 6,272 

 toises. The second line, for verification, was 5,259 toises long, which 

 according to Bouguer was within 3 to 4 feet, according to La Condamine, 

 withinone toise, of the trigonoraetrically calculated length. The entire 

 line had an amplitude of 3° 1' 3."3,^ crossed the equator, and measured 

 176,940 toises, according to Bouguer,* or 176,930,according to Condamine.^ 

 The operations were carried on at an altitude of more than 1,000 feet 

 above sea level, to which all measurements must be reduced. Accord- 

 ing to actual measurement the first degree from the equator is 56,767 

 toises long, from which 21f toises were subtracted to reduce to sea 

 level, and 6 to 7 toises added for expansion of the standard in the heat, 

 giving for the true value of a degree of latitude at the equator 56,753 

 toises.^ The entire operation was subjected to a searching criticism at 

 the beginning of the present century, in the light of more recent re- 

 searches, with the following result: " Wenn wir daher nach sorgfalti- 

 ger Erwiiguug aller vorher erorterten Umstande der Ungewissheit in 

 der Grosse eines Breiten-Grades am Jiiquator noch auf 80-100 Toisen 

 festsetzen, so glauben wir keine Ungerechtigkeit gegen die franzosi- 

 schen uud spanischen Messkilnstler zu begehen, deren Arbeiten keines- 

 wegs aus Mangel an Geschicklichkeit, sondern enizig wegen Unvol- 

 kommenheit der damaligen Instrumente nicht den Grad von Genauig- 

 keit haben konnteu, der zu einer Gradmessung erfordert wird."^ 



The next great survey was also the work of French savants, but was 

 undertaken for a different j)urpose. It was now admitted on all sides 

 that the earth is flattened at the poles; but there was in France at 



' Bouguer, Figure de la terre, 100, 101. 



^lUd., 104. 



3 According to Zach's calculations, 3° 6' 0."9. Mon. Cor,, Oct., 1807, p. 320. 



*nid.,lbZ. 



"Posch, 47. 



« Bouguer, 272. 



'Zach, Mon. Cor., Oct., 1807, p. 325. 



