on the Formula for measuring Heights by the Barometer. £559 
but the distance of the points, at which they were taken 3 from 
the summit of the mountain, having been determined from the 
same data, they do not furnish the altitude, by means of distinct 
and independent measurements. As matters stand, these results 
differ from each other by 7 feet ; a difference which appears to 
be too great, when it is stated, that the base-line, which formed 
the ground-work of the calculation, was twice measured, and 
though 14,076 feet in length, the two measurements agreed with- 
in less than a foot. The theodolite, with which the angles were 
taken, is well known to be one of the finest instruments that have, 
at any time, been employed in geodesic operations. In these 
circumstances, there seems to be good reason for suspecting, ei- 
ther that the geometrical height, which General Roy assigns to 
Moel Rilio, is too small, or that some error had mingled with 
his barometrical observations. Of the two suppositions, the lat- 
ter is the more probable ; and yet a deviation of 7 feet in the 
altitude, would have required a difference of about 40" from the 
angles of elevation, as they are actually given, — an extent of er- 
ror, which could not be supposed to occur, with the most care- 
less use of the instrument. 
On the whole, it may be inferred, from the examples of baro- 
metrical measurement which have been examined, that, though 
the heights of places, deduced by the common formula, may de- 
viate considerably from the true altitudes* in extreme cases of 
atmospheric dryness or humidity, they approach to them so very 
closely, in the mean hygrometric condition of the air, over the 
temperate zones, that they may still be relied upon, for all the 
ordinary purposes to which barometrical measurements are ap- 
plied. At the same time, it appears to be equally certain, that 
none of the formulse, which have yet been proposed, will give 
results at all conformable to the truth, when they are used for 
the computation of heights, either within the Tropics, or beyond 
the Polar Circles. In the former case, they will give the heights 
too small ; while, in the latter, they will be found to err equally 
in excess. Mr Playfair, in his elaborate and elegant paper, u On 
the Causes which affect the Accuracy of Barometrical Measure- 
ments was duly aware of the influence which the varying hu- 
0 Transactions of the Royal Society of Edinburgh, vol. i. p. 127, 
R 2 
