Dr. Arnott on the Measurements of Heiyhts. 15 



subject, as it may assist materially in making the correction on the heights 

 derived from the boiling point, particularly in such situations as Dr. T. 

 Thomson is now exploring. 



Let us assume that the boiling point, under a pressure of 30 inches, is 100" 

 Cent., then if Jf Cent, be the temperature of boiling water on a mountain, 

 and B that below, 1000 (B — 6) will represent the approximate height 

 at the temperature of 2^° by my formula ; or according to Leslie, at 5° or 

 5J°. If in the tropics it require 700 feet of ascent to show a decrease of 



one centesimal degree in the temperature of the aii*, then -s- (B — h) will 



will represent the difference between the observed temperatures of the air 

 (i) at the upper and lower stations, (whether the latter be or be not at 



the level of the sea,) which last will be i + — (B — h), and twice 



the sum of the temperatures is — — ~-^ — K But if we assume 



the constant multiplier to be 1000 for the temperature of 5°, we must 

 deduct 4 X 5 = 20 from the above, leaving ^8 < + 20 (B — h) — 140 ^ 



the correction to the approximate height is then (B — h) x 



/28 « + 20 (B — 6) — 140\ , . , n j . .u . u • u. • .i, 

 ( ^ ), which, added to that height, gives the 



trueheight = H = 1000(B-6)+(B-6) ( 28 ^ + 20 (B - 6) - 140 ^ 

 = 2 (B - ft) (490 + 2 « + 10 (B^-^)) 



But if it be found that 500 feet accords as well with the results for 

 each Centigrade degree, in the tropics as in Europe, the above formula 

 becomes — 

 2(B — &)(490 + 2« + 2(B — 6),or4(B — i)(245 + f + (B — 6))...S 



1 have mentioned already my reasons for thinking that 5° is too high, 

 and that a mean temperature of 2J is better suited to the constant 1000 ; 

 according to this view, the above two formulas become — 



2(B — 5) (495 + 2 ^ + ^^ ^^ ~ ^)) T 



2 (B — &) (495 + 2 < + 2 (B - 6)) U 



In reducing these last to Fahrenheit's scale, I shall take the constant 



550, which answers to a moan temperature of 32°, and as —- = 2, I 



shall assume that the tcmperatm-c of the air decreases 1° Fahr. for every 

 275 feet of ascent. The corrected height then becomes 



H =- (B — h) (510-889 + 1-222 (< + (B — h)) V. 



or in round numbers H = (B — 6) (511 + 1-2 (^ + (B — 6)) W. 



But if in the tropics it requires an ascent of 700 feet to give a decrease 

 of 1" Cent., or 390 feet for 1" Fahr., and we have to employ formula T, it, 

 when adapted to Fahrenheit's thermometer, becomes 



R 



