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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 elapsed, 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.
12851 Anf. i mile 12855 yards.
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 conds elapsed before I heard the found. What was the diftance ? 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 feconds 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* *16=64.
In what time will a body descend throuç h11 664 feet?
seconds of time.
15*16=240, the last acquired velocity.
If a body move at the rate of 1376 feet per second, How far muft it fall to acquire that velocity?
In the following Table, the column titled T denotes the seconds of time from 1" to 60"; S the spaces passed over in any second of time. The third column gives the heights from which a body would fall at the end of any given time, from j" to 60"; and column 4th denotes the last acquired velocity at the end of any given time. Thus, at the end of 22 seconds, the body has fallen from the height of 7744 feet, and moves with a velocity of 704 feet per second,