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venient diftance from the pole, fix your staff perpendicular in the ground, then move backwards or forwards, till you find the point C, whence you may view the top of your staff, E, in a line with A the top of the object, then say, as CD:DE::CB: BA the height of the object Fig. 67. plate 5.

EXAMPLE.

Let BC be 80 feet, CD 5, and DE 4, required AB.

5 4 80

4

5)320

65=AB.

PROBLEM IV.

To measure the height of an object from the length of its shadow.

Place any staff of a known length in the fame plane with the object; then say, as the length of the staff's shadow, is to the length of the staff; fo is the length of the object's shadow: to its height.

EXAMPLE.

Wanting to know the height of a steeple, whofe fhadow I found to be 200 feet, I fixed my staff perpendicular to the horizontal plane, the length of the staff, is 4 feet, and of the fhadow, 6 feet, required the height of the steeple.

64 200

4

800

100

6,900

Anf. 150 feet high.

PROBLEM V.

To measure the height of an object, by a plane mirror, or by a bucket full of water. See fig. 69

Place the mirror or bucket between you and the object. So that the top of the object may appear in the middle of the horizontal surface, then fay, As the distance between the object, fhadow, and your feet, is to the height of the eye; fo is the distance between the object's fhadow, and the object; to the height of the object.

PROBLEM VI.

Distances may also be measured by loud founds, fuch as, the firing of a cannon, the talling of a bell, thunder, &c.

It has been found, by many exact experiments, that the uniform velocity of found, is 1142 feet, per fecond of time. If, therefore, the feconds elapfed, be multiplied by 1142, the duct will be the anfwer in feet.

pro

EXAMPLE I.

After feeing a flash of lightning, it was 8 feconds before I heard the thunder, required the distance.

1142
8

5280)9136(1
5280

3)3856

1285 Anf. 1 mile 1285 yards.

EXAMPLE II.

After obferving the firing of a cannon, 24 feconds elapfed, before I heard the report, required the distance. Anf. 5 miles 336 yards.

EXAMPLE III.

After observing a man ftriking a bell with a hammer, 5 fé conds elapfed before I heard the found. What was the dif tance? Anf. I mile 430 feet.

PROBLEM VII.

To find the velocity of the wind.

Obferve the fhadow of a cloud at any particular place, then count the number of seconds elapfed, before it reach any other particular place; then say, As the number of feconds elapfed

is to one hour. So is the distance of the two places, to the distance the wind, will pafs over in one hour.

Note, By a fimilar experiment, the velocity of running waters may be computed.

PROBLEM VIII.

Heights or depths may be estimated from the velocities acquired by falling bodies, and the spaces fallen through in given times, or from the time of falling.

In fucceffive equal parts of time, fuch as 1, 2, 3, 4, &c., the spaces paffed over, are in the series of the odd numbers, 1, 3, 5, 7, 9, 11, &c., and the acquired velocities, as 1, 2, 3, 4, &c. Hence, it is plain, that the velocities are as the times, and the spaces paffed over, are as the fquare of the times of falling. Thus, in a quarter of a second, from the inftant of beginning to fall, a body will fall foot; in half a second, it will have fallen 4 feet, in three quarters, 9 feet, and in one fecond, 16 feet. In the next fecond, it will fall through 16x3=48, which added to the velocity at the end of the former fecond, will give 64, the whole space fallen through in two feconds. In the third second, the body will fall through 5×16=80, which being added to the laft fum, 64, will give 144, the fpace paffed over in 3 feconds, and fo on continually.

For the continued addition of the odd numbers, gives the fquares of all numbers from unity and upwards.

Thus, In 1 fecond, a body will fall 16 feet, which is 1' X 16.
In 2 feconds, 1+3=4=2'x16=64.

In 3 feconds,!+3+5=9=31 & 9X16=144 and fo on.

EXAMPLE I.

How far will a body fall in 6 feconds?

6

a

36 the fquare of the time.

16

216

36

576 feet.

EXAMPLE II.

In what time will a body defcend through11 664 feet? 16)11.664(729(27 feconds.

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Required the laft acquired velocity, when a body has fallen s

feconds of time.

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