5565. MOUNTAINS, Trigonometrical measurement.—
I thank you for * * * the corrections of Colonel Williams's altitudes
of the mountains of Virginia, * * * and
especially for the very able extract on barometrical
measures. The precision of the calculations,
and soundness of the principles on
which they are founded, furnish, I am satisfied,
a great approximation towards truth, and raise
that method of estimating heights to a considerable
degree of rivalship with the trigonometrical.
The last is not without some sources of
inaccuracy. The admeasurement of the base
is liable to errors which can be rendered insensible
only by such degrees of care as have
been exhibited by the mathematicians who have
been employed in measuring degrees on the
surface of the earth. * * * No two men
can differ on a principle of trigonometry. Not
so on the theories of barometrical mensuration.
On these have been great differences of
opinion, and among characters of just celebrity.
* * * In 1776, I observed the height of the
mercury at the base and summit of the mountain
I live on, and by Nettleton's tables, estimated
the height at 512.17 feet, and called it
about 500 feet in the Notes on Virginia. But
calculating it since on the same observations,
according to Bongour's method with De Luc's
improvements, the result was 579.5 feet; and
lately I measured the same height trigonometrically,
with the aid of a base line of 1,175 feet
in a vertical plane with the summit, and at the
distance of about 1500 yards from the axis of
the mountain, and made it 599.35 feet. I consider
this as testing the advance of the barometrical
process towards truth by the adoption of
the logarithmic ratio of heights and densities;
and continued observations and experiments
will continue to advance it still more. But the
first character of a common measure of things
being that of invariability, I can never suppose
that a substance so heterogeneous and variable
as the atmospheric fluid, changing daily and
hourly its weight and dimensions to the amount,
sometimes, of one-tenth of the whole, can be
applied as a standard of measure to anything,
with as much mathematical exactness, as a trigonometrical
process. It is still, however, a
resource of great value for these purposes, because
its use is so easy, in comparison with the
other, and especially where the grounds are
unfavorable for a base; and its results are so
near the truth as to answer all the common
purposes of information. Indeed, I should in
all cases, prefer the use of both, to warn us
against gross error, and to put us, when that
is suspected on a repetition of our process.
[347]
—
To Capt. A. Partridge. Washington ed. vi, 510.
(M.
1816)
