1818.] On the Height of the Himalaya Mountains. 51 



of which, in feet, is 471,758. The altitude observed being 

 2° 48', and the refraction being taken at -^ of the intercepted 

 arc, the angles are S = 3° 20' 26" 15"' and P = 86° 0' 38" 15"', 

 with the side SB = 471,758 ; whence we have the side B P, or 

 height of the mountain = 27,558 feet. 



By a similar calculation of the altitude of the same mountain, 

 observed from the stations C and D, viz. 2° 19' and 1° 22% or, 

 corrected for refraction, 2° IP 32" and 1° 12' 6", with the dis- 

 tances above found, which in parts of a circle are 1° 29' 36" 36"' 

 and P58'48", and, reduced to the chords of the arcs in feet, 

 543,031 and 719,893, the height comes out 27,900 and 27,573 ; 

 or, on a mean of the three, 27,677 feet above the' plains of 

 Gorak'hpur ; and reckoning these to be 400 feet above the mouth 

 of the Ganges, as may be inferred from the descent of the stream 

 of rivers, the whole height is more than 28,000 feet above the 

 level of the sea. 



The following table exhibits a comparison of this result with 

 other computations made on different rates of refraction : 



Sta- Distance Intferc. arc Alt. by ] He j ht > allowing for refraction. 



tion. in miles, in deg. observ. t "8 g" TT TIT T7 TT 



A 89-35 1°17'51" 2°48' 24875 26663 27110 27476 27558 27626 27855 

 C 102-85 1 29 36 6'" 2 19 24348 26716 27308 27792 27900 27991 28294 

 D 136-35 1 58 48 1 22 21338 25494 26554 27384 97573 27773 28286 



Mean 23520 26091 26784 27551 27677 27797 28145 

 Extreme difference 3537 1222 774 408 342 365 439 



It is apparent, from inspection, that the observations at the 

 stations A and D agree best ; and, if that computation be 

 nearest the truth wherein the extreme differences are the least, 

 the conclusion will be that the height is about 27,550 feet ; such 

 being the elevation deduced from the mean of observations cal- 

 culated according to middle refraction. 



The limit of error arising from refraction must be taken at less 

 than 850 feet, as the observations at A and C coincide for the 

 height of 26,690 feet, ■£ of the contained arc being allowed for 

 refraction, and those at C and D for an elevation of 28,290 feet, 

 T ' T being allowed ; while those at A and D do so for the mean 

 altitude of 27,565 feet, refraction being taken at the middle rate 

 of -J- ; and a larger allowance than ■£- of the intercepted arc 

 (which would exceed mean celestial refraction for like altitudes) 

 cannot be requisite without very wide disagreements in observa- 

 tions made on different days, which would mark extraordinary 

 refraction; but this is not the case with those in question. 



The limits of error in respect of the observations themselves - , 

 whether for the distance or for the altitude, are more confined, 

 since the uncertainty in the distance, amounting to \ of a mile 

 in one instance, and -£■ a mile in the rest, induces uncertainty in 

 the computed elevation to no greater extent than 76 or 99 feet 

 for the nearer stations, and 180 feet for the most remote. An 



d 2 



