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venient distance 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.
Let BC be 80 feet, CD 5, and DE 4, required AB.
5:4: : 80
To measure the height of an object from the length of its fbadow.
Place any staff of a known length in the same 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.
Wanting to know the height of a steeple, whose shadow I found to be 200 feet, I fixed my staff perpendicular to the horizontal plane, the length of the staff, is 41 feet, and of the thadow, 6 feet, required the height of the steeple.
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 say, As the distance between the object, shadow, and your feet, is to the height of the eye ; so is the distance between the object's shadow, and the object; to the height of the object.
Distances may also be menfured by loud sounds, fich as, the firing
of a cannon, the telling of a bell, thunder, &c.
It has been found, by many exact experiments, that the uniform velocity of sound, is 1142 feet, per second of time. If, therefore, the seconds elapfed, be multiplied by 1142, the product will be the answer in feet.
After seeing a flash of lightning, it was 8 seconds before I heard the thunder, required the distance.
After obferving the firing of a cannon, 24 seconds elapsed, before I heard the report, required the distance. Ans. 5 miles 336 yards.
After observing a man striking a bell with a hammer, 5
fe. conds elapsed before I heard the sound. What was the distance ? Anf. i mile 430 feet.
To find the velocity of the wind.
Observe the shadow of a cloud at any particular place, then count the number of seconds elapsed, before it reach any other particular place ; then fay, As the number of seconds elapsed
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 similar experiment, the velocity of running waters
may be computed.
Heights or depths may be estimated from the velocities acquired by fal,
ling bodies, and the spaces fallen through in given times, or from the time of falling.
In successive equal parts of time, such as 1, 2, 3, 4, &c., the spaces passed 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 passed over, are as the square of the times of falling. Thus, in a quarter of a second, from the instant 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 second, 16 feet. In the next second, it will fall through 16X3=48, which added to the velocity at the end of the former second, will give 64, the whole space fallen through in two seconds. In the third second, the body will fall through 5*16=80, which being added to the last sum, 64, will give 144, the space passed over in 3 seconds, and so on continually.
For the continued addition of the odd numbers, gives the squares of all numbers from unity and upwards.
Thus, In 1 second, a body will fall 16 feet, which is 1° *16.
In 2 seconds, i+3=4=2' x16=64.