on the Formula for measuring Heights by the Barometer. 231 
explained, the formation of this coefficient requires very lit*, 
tie calculation *. 
The whole formula, with the corrections I have proposed, 
and demonstrated to be necessary, will assume a form which will 
not be greatly more complex than that which it formerly posses- 
sed, while it will certainly be better adapted to all the varying 
conditions of the atmosphere. If h represent, as before, the 
difference of elevation in fathoms, we have 
in which t is the temperature of the air at the lower station, i' 
that at the upper ; ftbo elastic force of vapour at the lower sta- 
tion, and f that at the upper ; b the height of the mercury, in 
inches, at the lower station, having the temperature T ; and p 
the corrected height of the mercury in the barometer, at the 
upper station, reduced from the temperature T' to the tempe- 
rature T, by multiplying it by the coefficient 1 -j- =000103 
(T — T). 
To bring the formula with these corrections to the test of 
experiment and observation, I made choice of a sloping hill, in 
the parish of Moulin, which rises, by an easy ascent, from a flat 
and extensive meadow, on the left bank of the river Tummel, 
to the height of about 1000 feet. The point which I usually 
employed as the lower station, was nearly 250 feet above the 
river ; and from that point to the summit, the profile of the hill, 
on the side by which I generally ascended, was composed of a 
* The physical principles on which this coefficient rests, furnish a satisfactory 
explanation of a fact, noticed in a contemporary Journal of Science, by Mr Bab- 
bage, namely, 44 That when the lower observation is made in a narrow or deep 
valley, situated at the foot of a mountain range, the upper observation being made 
on an exposed summit, the elevation of the mountain thus determined falls short 
of its true height.” In such a case it is evident, that the intermediate strata be- 
tween the two stations are placed in circumstances to be powerfully affected by 
humidity ; of course, the great dilatation which they suffer from the influence of 
aqueous vapour tends to increase the altitude of the mercury in the barometer at 
the upper station, and by thus bringing the ratio of the two pressures nearer to 
equality, diminishes, in a corresponding degree, the computed height by the com- 
mon formula. 
