6 E. 1). Preston — Measurement of the Peruvian Arc. 



uncertainty of several inches. Therefore, asserting that the 

 base contained an exact number of toises within the thickness 

 of a line, goes for nothing. Moreover the subsequent reduc- 

 tion gave a correction, different from what they had applied, 

 so that the finally adopted length of the base was not 6274 

 toises, as they wished it to be, but four inches and one and one- 

 half lines more than this. 



The Jength of the straight line connecting the two extremi- 

 ties of the base was found by first comparing the actual meas- 

 ure with the line as traced on the ground, and then deducing 

 the quantity sought from this last line. An approximate value 

 for the base line substituted in the formula* 



■/- 



cdx 



yV + (b + xy 



gives the correction to reduce the actual measures to the 

 ground line, considering it sensibly straight for each of the 

 seven parts into which the whole base was divided. The abso- 

 lute and relative heights of the extremities and the interme- 

 diate points were determined, which furnished the data for 

 referring the ground line to the air line connecting the extrem- 

 ities. The result of the entire work was : 



Ground line longer than actual measure 1-52101 



Ground line longer than air line 0"23100 



Air line longer than actual measure 1*29301 



The correction for temperature applied to the Tarqui base 

 would indicate a coefficient of expansion of '000015 for the 

 wooden rods, which is between that of glass and brass but 

 somewhat nearer the latter. But then not' very much reliance 

 can be put on the temperatures. That of the base of verifica- 

 tion was only estimated, f and could not certainly have been 

 known within several degrees. But the accordance of the 

 results, errors of compensation being disregarded, would indi- 

 cate that the temperatures were correct to within one-fourth of 

 a degree. An examination of the record shows conclusively 

 that this could not have been the case. On the other hand 

 the Spanish officers correct the second base by about eight feet 

 which would require a coefficient of expansion, based On the 

 same difference of temperature, at least twice that given above.J 



* The earth's radius is c: x is the length of the line, and b an auxiliary con- 

 stant. 



f Mesure des trois premiers degres du Meridien, par M. de la Condamine, Paris, 

 1751, p. 83; see also in this connection "Zeitschrift fur Iustrumentenkunde," 

 August, 1885, p. 271, and " Resultate iiber die peruanische Gradmessung." 

 Monat. Corresp., 1887, p. 240. 



X Observaciones astronomicas y physicas hechas de orden de S. M. en los regnos 

 del Peru. Por Juan y Ulloa, Madrid, 1748, p. 166. 



