on the Formula for measuring Heights hy the Barometer. 249 
the- common formulae which are now employed for the purpose 
could be relied upon, in all the varying conditions of the atmo- 
sphere, that mode of finding the difference of elevation between 
places, either remote from each other, or so situate as not to ad- 
mit, without great difficulty, of the application of geometrical 
measurement, would frequently, in these instances, be attended 
with the most obvious advantages. The geometrical methods of 
determining heights require, even where a good base-line can be 
obtained, a degree of accuracy in procuring the other necessary 
data of the problem, of which few, who do not possess a practical 
knowledge of the subject, are at all aware ; and of which still 
fewer can form any idea, who are ignorant of the refinements of 
which geodesic measurements are susceptible, when the most 
rigid exactness is aimed at. In such cases, not only must the 
base-line itself be repeatedly measured with the most scrupulous 
care, but, in taking the various angles which connect its extre- 
mities with the vertical line to be determined, the instrument 
with which the angles are observed, must be placed, at each sta- 
tion, so that its centre may be exactly in the angular point ; and 
such is the degree of adjustment necessary for the purpose, that 
the slighterst deviation from the proper position would lead to 
very considerable errors in the calculation of the ultimate result. 
Again, admitting that the angles have been duly measured, the 
corrections to be made upon each of them for atmospheric re- 
fraction, varying with the temperature and humidity of the air, 
and depending partly upon the height of the object, the very 
quantity to be determined, all conspire to throw a shade of un- 
certainty over the whole operation, which nothing can remove 
but a repetition of the measurements, under different circum- 
stances, conjoined with a sameness of result. Lastly, the height 
thus obtained must be corrected for the curvature of the earth ; 
and though the allowance thus rendered necessary, is but small 
when the object is near, as it yet increases with the square of the 
distance, it becomes too considerable to be neglected when the 
object is pretty remote. 
The measurement of heights by levelling is free from many 
of the difficulties which are inseparable from the geometrical 
methods, but it is liable to others of a nature no less objection- 
able, and equally unavoidable. The multiplicity of observations 
