IG Dr. Arxott on the Measurements of Heights. 



H = (B - « (6I0-4938 + lO ' + n^^ (B - '0) = 



(B -6) (610-4933 + f (<^ lii5pA>) X.- 



and iu order to compare this with formula V, it may be exhibited thus: 



H = (B — &) (510-4933 + ^ (t + (B — i) Y. 



which is obtained directly from the formula U. In both cases we may 

 take 510J in place of 510-4933. By examining these two last formulas, 

 it is obvious that if in place of 500 or 700 feet of ascent for each centes- 

 imal degree, it were 100 X d, then the portion to be added to t wiU be 



^ — TT — I, so that any one may alter the formula to suit his own 



experience. For although I have, for convenience, used 275 feet of 

 ascent for each degree of Fahrenheit, or 500 for each centesimal degree, 

 (which coiTCsponds to about 290 for 1° Fahr.) being two degrees for each 

 degree of difference in the boiling points, or 700 feet for each centesimal 

 degree in the tropics, I have already said that the aveiage number of 

 feet, or the relation of the difference of temperature to that of the boUing 

 points, must be ascertained by observations on the spot. Besides, the 

 temperature of the atmosphere at different places is influenced by so many 

 accidental circumstances, that this mode of making the correction must be 

 regarded merely as an approximation, when actual observation at the 

 lower station cannot be obtained, and as preferable to making no correc- 

 tions at all on the approximate height. 



If our object is to calculate the height above the level of the sea in the 

 tropics, upon the understanding that water boils there at 212° Fahr., or 

 100° Cent., where the weather is steady, and the barometer stands at 30 

 inches ; then it will give a result not far from the truth, if we ascertain 

 what is the actual boiling point of the instrument at that pressure, either 

 by observation or calculation in the way already indicated, and substitute 

 this for B in the formula employed. Such cannot be strictly correct, 

 because the constants have been adapted to a thermometer which really 

 indicated 212° under the above pressure; but it must be obvious to any 

 one, that until the thermometer has been compared with the barometer, 

 and its boiling point at 30 inches of pressure ascertained, it is in vain 

 to look for even an approximation in this way, to the height of the station. 



In such a case, the preferable mode, perhaps, is to discover the co-effi- 

 cients suited to the instrument. From what has been said, it is obvious 

 that if the decrement of atmospheric temperature be uniform, while the 

 difference of elevation is so, we may represent the corrected height by 

 d (x + yt + zd) = hy when d is the difference between 212° (if on 

 Fahrenheit's scale,) and the observed boiling point, and t the observed 

 temperature of the air ; — at some other elevation, as little above the level 

 of the sea as convenient, let this be D (.-c -f 2/ T -h zD) = H ; and at 

 some intermediate height, I (x -\- y t Jf. zq) =: n. Now if d, t, and h, in 



