On the Height of Mountains, Headlands, fyc. 19 



31°, and the height of the barometer 29£ inches, at 26057 feet j 

 then the density at the surface, and one foot above it, will be 



a=0; d=26057. 

 A = l; D =26056. 

 That is, the pressure at the surface will be equal to a column of 

 air of uniform density of 26057 feet high ; and consequently, one 

 foot above the surface =26056 feet high, or a foot less. 

 Since the densities are as the pressures, we have 



A-a=l=#log. 

 and making 26057 =n, 



26057 

 26056 



J 



n 

 we have 1 =x log. 





n _/l 1 1 1 



Bat log-^Zl-M^+g^+g^+^+to, 



And when, as in the present case, n is a large number, all the 

 terms but the first may be neglected as unimportant ; also since 

 M =.43429448, the modulus of decimal or common logarithms, 



_ -43429 448 

 .\l_a?X 26057 ; 



26057 

 whence #= 43 400443 ^^Qfy vev Y near *y- 



The above formula is reduced to 



d 



A = 60000 log. g feet; 



or putting m and M the height of the mercury at the earth's sur- 

 face and at the altitude A, then the fraction 



d m 



D = M' 



Also since six feet are equal to one fathom, the simple multiplier 

 60000 for feet becomes 10000 for fathoms, which is more con- 



venient 



d 



Hence instead of A=60000 log. ^ feet, 



we have A =10000 log. ^ fathoms, 



which is the formula formerly used in measuring altitudes by the 

 barometer. 



With respect to the height taken for the homogeneous column 

 of air different writers vary, but this difference does not affect 



