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euted by Mr. de Borda was a trigonometrical operation pre- 

 cisely similar to those, by which, in the measurement of a 

 meridian, the heights of signals, or of mountains near those 

 signals, above the level of the sea, is determined. It cannot 

 be denied, that the simplicity of a method, and the small 

 number of the elements entering into the calculation of the 

 altitude, offer peculiar advantages j but it would be unjust 

 to condemn more complicated operations, if we could be as- 

 sured, that the observers had taken the greatest care in the 

 resolution of each triangle. 



Mr. de Borda could not directly measure the great base of 

 1526 toises, at the extremities of which he determined the 

 oblique angles of position, and the vertical angles that sub- 

 tend the height of the volcano. The length of this base was 

 found by the resolution of two small triangles $ and this de- 

 termination deserves so much the more confidence, as all the 

 angles were directly measured, as the result obtained by 

 a small quadrant of Ramsden was verified by a reflect- 

 ing circle, as the errors of each angle do not appear to 

 have exceeded eight or ten seconds, and as the first base of 

 213 toises was measured twice, without finding more than 

 two inches and a half difference. I do not believe, that this 

 part of Mr. de Borda's measurement can have been deficient 

 in accuracy j and it must be hoped, that the same precision 

 was attained in the vertical angles, three of which were in- 

 dispensable for the measure of the Peak ; namely the sum- 

 mit of the Piton seen at d, the signal d seen at a, and the 

 depression of the horizon of the sea. It might have been 

 wished, that the observer had determined these angles by 

 means of his reflecting circle, employing as an artificial ho- 

 rizon a plane glass, or mercury* • for the error of the line 

 of collimation and the horizontal position of the instrument 



* I have shown in another place, that, on the seashore, 

 we can measure with great exactness the depression of the 

 horizon with a reflecting instrument, by taking alternately 



