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are very difficult to determine with exactness in a moveable 

 quadrant of a foot radius. According to the manuscript 

 kept in the Dep6t de la Marine, this verification of the verti- 

 cal angles did not take place j and the accordance of the two 

 altitudes of the Piton above the points d and e is a proof ra- 

 ther of the constancy of the error of collimation, than of the 

 precision of the absolute value of the angles. In order to 

 have obtained two comparative results, Mr. de Borda should 

 have taken seven zenith distances j that of the summit seen 

 at c and at d, that of the signal d seen at a and at e, that of 

 the signal c seen at a, and the depressions of the horizon of 

 the sea measured at d and at a. It is well known, that these 

 zenith distances are more difficult to obtain with exactness 

 than the oblique angles of position, especially when we can- 

 not make use of an astronomical circle of repetition. Far- 

 ther, in similar circumstances, a method is so much the more 

 disadvantageous, as the vertical angles are more numerous. 

 To solve the question, what is the number of toises by which 

 the height of the Peak may have been found too great, or too 

 little, I have supposed an error in the measure of the base, 

 in that of the vertical angle subtended by the mountain, and 

 in the terrestrial refractions. If the volcano be 1925 toises 

 of absolute height, instead of 1905 toises, the angle of P at 

 c would be, according to Mr. Oltmann's calculation and 

 mine, 10° 36' 34", instead of 11°29 / 18", found by Mr. 

 de Borda the bases c d and a b 3 would be 9258 and 1392 

 feet, instead of 9159 and 1278. But how can it be sup- 

 posed, that he was deceived 7' 16" in determining the error 

 of collimation of the quadrant, and fourteen feet in the double 

 measurement of a base of 229*5 toises ? We are ignorant 

 at how much Mr. de Borda estimated the effect of the terres- 



the height of the Sun above the horizon of the sea, and in an 

 artificial horizon, and reducing these heights to the same 

 instant. 



