258 ON THE HEIGHT OF THE 



But from Major Lambton's obfervations in the peninfulaof India, ter- 

 redrial refra&ion was found to vary from ^th to -Vth*, or on a medium 

 •|th of the contained arc. As this mean refraction may bethought 

 more applicable to the north of India, than that deduced from the 

 trials made in the climate of Great Britain, I fhall compute from al- 

 titudes reduced by this as well as the preceding correction for refrac- 

 tion, and contrail the re'fults with limilar calculations in which the re- 

 fraction fhall be taken at the utmoft quantity which any pall experience 

 could juftify, viz. |d of the arc. 



To compute from the data, we have, in an oblique plane triangle s 

 the angle ( B ) at the bafe of the mountain, which exceeds a right angle 

 by half the contained arc ; or (which is she fame thing) by half the 

 angle at the earth's centre fubtended by that arc; the angle (S) at the 

 ftation of obfervation, which is the fum of the obferved altitude 

 ( corrected for refraclion ) and half the contained are ; and one fide 

 (A), which is the chord of the contained arc, or diftance between 

 the bafe of the mountain and ftation of obfervation, differing 

 but a few feet, in the cafes before us, from the circular arc 

 itfelf. The angles and one fide of the triangle being thus known, the 

 other two fides may be found j one of which, fubtending the angle 

 S, is the height of the mountain, or perpendicular from its fummit to 

 the middle of its bafe. The obfervations at Pilibhit and JU'hpur, cal- 

 culated upon this principle, and with an allowance of v Vth for refraction, 

 give 22436 and 22-146, for the elevation of the peak obferved from 

 thofe flations ; or on a mean 22291 feet above the level of the plains of 

 Rohilkhand ; or about 22800 feet above the level of the Tea. 



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