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, fhadow, and your feet, is to the height of the eye; so 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 tolling 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 product will be the anfwer in feet. EXAMPLE I. After seeing a flash of lightning, it was 8 feconds before I heard the thunder, required the distance. 1142 5280)9136(1 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 diftance. Anf. 5 miles 336 yards. EXAMPLE III. After observing a man striking 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 feconds elapfed, before it reach any other particular place; then fay, 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 fal ling 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 fecond, from the inftant of beginning to fall, a body will fall 1 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 space 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 12 X 16. In 2 feconds, 1+3=4=2'x16=64. In 3 feconds, 1+3+5=9=3' & 9×16=144 and so on. EXAMPLE I. How far will a body fall in 6 feconds? 6 6 36 the fquare of the time, 216 36 576 feet. EXAMPLE II. In what time will a body defcend through11 664 feet? 16)11.664(729(27 feconds. Required the laft acquired velocity, when a body has fallen s feconds of time. EXAMPLE IV. If a body move at the rate of 1360 feet per fecond, How far muft it fall to acquire that velocity? Note, The laft acquired velocity, divided by 16, will quot the fpaces in feet, through which the body falls in any fecond, and is always lefs by unity than double the time of falling. In the following Table, the column titled T denotes the feconds of time from 1" to 60"; S the fpaces paffed over in any fecond of time. The third column gives the heights from which a body would fall at the end of any given time, from " to 60", and column 4th denotes the laft acquired velocity at the end of any given time. Thus, at the end of 22 feconds, the body falls 43 feet; it has fallen from the height of 7744 feet, and moves with a velocity of 688 feet. per fecond.; TABLE |