TRACT 26.

MEAN DENSITY OP THE EARTH.

17

These few numbers are the results of the calculation of severalhundreds of triangles, conceived in a vertical position, theirbases being either the horizontal lines above-mentioned, orother lines drawn as diagonals between many distant pointsin the survey, according to the number of vertical angleswhich had been observed ; and of these bases, whether realor imaginary, each generally afforded two vertical triangles,as the angles of elevation and depression were taken alter-nately at both ends of the lines. It is scarcely necessary toremark, that all these triangles are right-angled, the commonbase being one of the sides about the right angle, and theother the difference in altitude between the two given pointsor extremes of the base; and this difference in altitude isfound from the application of this proportion, as radius is tothe tangent of the angle of elevation or depression, so is thegiven base, to the altitudinal difference between the two givenpoints, exclusive of the height of the theodolite or other in-strument, which was afterwards allowed for. From the reso-lution of all these triangles, and taking the means of the manycorresponding results, were obtained the following numbers,which show how many feet the points denoted by the lettersstanding against them, are below the level of the point n, orthe Western cairn, on the ridge of the hill. They are all re-ferred to this point n, at the Western extremity of the ridgeof the hill, because it is the most elevated point in the wholesurvey.

o 1184

y 2898

H 2143

u 1613

e 2145

p 1457

A 1303

w 2024

x 1996

M 1958

K 480

B 1313

L 2006

s 1964

m' 322

R 1948

c 1384

Y 2335

a 1012

f' 2246

B"1920

D 1445

V 2119

b 823

t' 2815

« 2898

F 1904

T 2114

c 1364

k 2835

(8 2901

G 1935

Z 1815

d 1539

S' 172

These depressions, and those of several other principalpoints, were first carefully computed by means of variousdifferent bases, as so many places from which the sectionswere to commence.

VOL. II.

c