To find how high a person at Philadelphia, must be raised into the atmosphere, and how far the sight must extend, to see London; the distance being 51 Degrees, on the Rotundity of the Earth, and the Diameter of the Earth 7964 Miles.

RULE.

From right to left, draw a line, to represent the earth's diameter, on which describe a circle with the chord of 60°; from the centre, raise a perpendicular, and where it cuts the circle, will represent Philadelphia, as at A, from which lay off 51 degrees, to represent London, as at B; from the centre, draw a line to B, and on the point B,

in the right angled triangle CBV, the angle VCB 51°, and base CB 3982 miles, are given to find the hypothenuse CV, from which, take the earth's semidiameter, leaves AV 2345 miles, the height required; and VB, 4917 miles, is the distance the sight must extend, to see London.

Note. The operations the same as Case 1, Right Angled Trigonometry.

V

Philadelphia..

A

C

London.

OF

DISTANCES.

PROBLEM I.

LET A and B be two houses on one side of a river, 293 perches asunder; and a tower at C, on the opposite side of the river, which makes an angle at A, with the line AB cf 53° 20′; and at B, with the line BA of 66° 20′. Required, the distance from the tower to each house?

Let B and C be two houses, and' an observer at A 252 perches from B, and 230 from C, finds that they make an angle at A of 70°. The distance between the houses is required?

Note. This is performed by Case 4 and 5, Oblique
Angled Trigonometry.

B

A

PROBLEM III.

Let D and C be two trees in a bog, and an observer at A and B 113 perches asunder, finds, that when at A, the tree at D makes an angle with the line AB of 100°; and that at C, makes an angle with the line AB, of 36° 30′; and when at B, the tree at D makes an angle with the line BA of 49°, and that at C of 121°. Required the distance these trees are asunder?

Answer 232.5 perches.

Note. By Case 1, Oblique Angled Trigonometry, find the distance from either station to each tree, as from B to D 216 perches; and to C 175.6 perches; then, by Case 4 and 5, find their distance apart."

To find the Content of a Square Piece of Land.

RULE.

Multiply the base into the perpendicular, and if they be in chains, divide the product by 10, for acres; and multiply the remainder by, for roods, and by 40 for perches; But if in perches, divide by 40 and by 4, for acres, roods and perches, as in the subsequent example.

EXAMPLE.

Let ABCDA be a square field, and each side 7 chains 29 links. Required the content, and to lay down a map by a scale of ten perches to an inch.