338 Remarks on Bordas Geometrical Measurement 



that measurement carefully, as given by Baron Humboldt in 

 his Personal Narrative, translated by M. Williams. 



It is there concluded to be 1905 toises, or 11430 French 

 feet, which are equivalent to 1 2,182 English feet. I have also 

 examined all the calculations, so far as the data have enabled 

 me, and in every instance, except in some which appear to be 

 typographical errors, the results seem to be exact. It is to be 

 regretted, however, that the vertical angles are not recorded in 

 the document from which Baron Humboldt obtained his data, 

 and which he entitles Manuscrit du Depot But as all the other 

 results have been computed accurately, there is every reason to 

 believe that the heights of the summit of the Peak above each ex- 

 tremity of the extended base, derived by calculation from the 

 measured base, are also correct. The depressions of the sea from 

 the same points, allowing 008, or about ^■q\\\, of the intercept- 

 ed arc for the effect of refraction, conformable to the observa- 

 tions of Mudge, Colby, and Delambre, are also correct. The 

 effect of refraction upon the height of the Peak above the base, 

 amounting to about 14 French feet, is also applied. These 

 embrace all the corrections except one — the deviation of the cir- 

 cle of curvature from the tangent. Of this I can find no trace 

 in any part of the extract above quoted, and for that reason, I 

 am inclined to think it has been entirely omitted. It amounts 

 to QQ French feet from the one point of observation, and to 70 

 from the other. From the well-known ability of M. Borda, it 

 is difficult to suppose that he had neglected so important an ele- 

 ment ; but as no mention is made of it, and in his^r^^ measure- 

 ment a much greater error existed, from an angle being erro- 

 neously noted, there is some reason to fear that, through some 

 oversight, this correction has been neglected. At all events, 

 such omissions do sometimes occur, as I found in Captain Sa- 

 bine''s computation of the height of a hill in Spilzbergen, as re- 

 corded in the Philosophical Transactions for 1826. The height, 

 in this instance, was computed from two points, nearly equidis- 

 tant, and also from a third, about double the distance of these. 

 Now, as the deviation of the curve from the tangent increases 

 as the square of the distance, it would be about four times as 

 great at the latter point as it was at the two former, and, conse- 

 quently, without this correction, the height from the last place 

 was so much smaller than the other two, that it was rejected as 



