of 100 yards, I found the

of elevation of the top of

the tower CBE to be 33° 45': what then is the height

11. Suppose a and c to be two stations on sloping ground, o an object on the top of a hill, and the s OCA, OAC, measured with a sextant, to be 79° 29′ and 63° 11′ respectively: also, suppose the 4 of elevation at A is 6° 36', and at c. 5° 22′; what are the horizontal distances and height of the object, Ac being 410 yards? Ans. AG 660.302, CB 600.728,

12. Wanting to know the distance between the inaccessible objects H, M, and also their heights, we measured a base AB of 670 yards, on ground nearly horizontal, and at the extremities A, B, took the following angles:

SBAM 40° 16′ ▼

АВН 42°22′

MAH57° 40′HBM71° 7′

MAR 3° 46′

HB P 3° 33′

From whence it is required to find the heights and di

stance. Ans. HM 1174 yds. MR 91.5, and HP 43.9.

13. Wanting to know the distances of an object at D from two others A, B, I set up a pole at c, in a right line with A, B, and took the angle ACD, 57°; I then measured CD 784.8 yards, and at D the angles CDA, ADB were 14° and 41° 30′; required A D, DB, and Ab. Ans. AD 696.1, DB 712.4, AB 499.3 yds.

B

14. In the year 1784, a base B c being measured on Blackheath, of a mile in length, the angles of elevation of Lunardi's balloon were taken, at the same time, by observers placed at its two extremities and in the middle; the one at в being 46° 10′, that at p 55°8′ and that at c 54° 30': required the height oA of the balloon. Ans. 2 miles.

P

B

15. Let BC be a measured base of 370 yards, on the plane ABC, and suppose marks are set up at the stations A, B, C, and the following angles, taken with a sextant, to the elevated object o;

SOAC 20° 50′S OBA 73° 44′

OCB 149° 10′ OAB 80° 18' OBC 16°4′OCA 140° 6'

Required the distance of the object o from the station c, and its height above the plane of the base B c.

Ans. OD 162.3, CD 367.5, co 401.75.

0

B

16. Supposing it were possible to see a light-house or other object A, in the horizon, at the distance of 154 miles, it is required to find its height AB, the diameter of the earth. B D being 7958 miles, and its circumference 25000 miles.

Ans. 3 miles nearly, being about the height of Chimborazo, the highest mountain of the Andes, and, probably, in the world.

D

17. Suppose OB to be an object standing on the horizontal plane ABC, and that AC is a measured base of 250 yards, at the extremities of which A, c, the following angles have been taken, OAC 56° 46', O CA 62° 54′, and the 4s of elevation O AB 6° 40′, and OC B 7° 6'; it is required to find its height OB, and the horizontal distances AB, CB.

Ans. AB 254.989, CB 238.814, and oв 29.745 yds.

18. At the top of a tower C D 150 feet high, I took the angle AC B, subtended by two distant objects A, B, 69° 27′, also the angles of depression C A D 1° 48′, and CBD 2° 20′, from which it is required to find the distances A B, BD, DA.

Ans. BD 3681.2, DA 4773, AB 4900.9.

B

19. At a point c in the horizontal plane ABC, I took the angle ECD 59° 20′ subtended by the tops of two towers, whose heights DA, E B, were known to be 167 and 205 feet respectively, and also the angles

of elevation DCA 3° 15', and ECB 4° 25'; from which it is required to find the distances CA, CB, and A B. Ans. CA 2940.9, CB 2654.1, AB 2786.3.

20. Observing an object o A at a distance, I took its angle of elevation OBA at the place where I stood, and found it to be 50° 23′. I then measured a distance Þ3 of 60 yards, in the most convenient direction the ground afforded, and at this station found its elevation OPA to be 40° 33'. After which I measured on, in the same line, 50 yards further to c, and at this place found its elevation o CA to be 30° 40′; from whence it is required to determine the height of the object, and its distance from each of the three stations B, P, C. Ans. AB 65.4173, AP 92.36787, Ac 132.5726, and height oa 79.02912.

A

21. Observing three objects A, B, C, whose distances asunder are known to be as follows: A B 8 miles, BC 12 miles, and a c 7+ miles, I took their angles of po.