Barometer applied to the Measurement of Heights. 363 



we shall be able to determine the height h in any part of the 

 earth, when z, a/, T, T', corresponding to the extreme points of h 

 are known; or we may retain the coefficient 10000 unaltered, 

 and apply the correction to the result, according to the follow- 

 ing table ; 



Latitude. Correction. 



. . -(- 3^2 f the approximate height. 



5 tf& + si* 



100 . + _i_ 



15 . - + T *t 



20 . . + T |o 

 25 . . + -gi-g 



30o .. -f- _i_ 

 35 . . + T '3o 



40 . . + rf Tr 

 45 . . + 



55 . yoV? 



60o .. T i_ 



65 . si? 



70o . . . T i 

 750 . . __ __ 



80 



85 . - 



90 . . 3!^ 



474. As the fraction - is always very small, we shall have 



R 



very nearly the value of A, independently of the term containing 

 this fraction ; by substituting the approximate value thus obtained 



for /i, in the fraction -, we shall have very nearly the correction 



due to the variation of gravity at different elevations in the same 

 latitude; and by substituting the value of h thus corrected in the 



fraction - we can approximate the true height still more nearly. 



R 



But this second substitution is altogether superfluous in the cases 

 which ordinarily occur. Indeed, except where h is very great, 



we may neglect- entirely, and the general formula then becomes 



