=97. Experimental Study of Falling Bodies.=--To study falling bodies experimentally by observing the fall of unobstructed bodies is a difficult matter. Many devices have been used to reduce the motion so that the action of a falling body may be observed within the limits of a laboratory or lecture room. The simplest of these, and in some respects the most satisfactory, was used by Galileo. It consists of an inclined plane which reduces the effective component of the force of gravity so that the motion of a body rolling down the plane may be observed for several seconds. For illustrating this principle a steel piano wire has been selected as being the simplest and the most easily understood. This wire is stretched taut across a room by a turn-buckle so that its slope is about one in sixteen. (See Fig. 80.) Down this wire a weighted pulley is allowed to run and the distance it travels in 1, 2, 3, and 4 seconds is observed. From these observations we can compute the distance covered each second and the velocity at the end of each second. [Illustration: FIG. 80.--Apparatus to illustrate uniformly accelerated motion.] In Fig. 63, if _OG_ represents the weight of the body or the pull of gravity, then the line _OR_ will represent the effective component along the wire, and _OS_ the non-effective component against the wire. Since the ratio of the height of the plane to its length is as one to sixteen, then the motion along the wire in Fig. 80 will be one-sixteenth that of a falling body. =98. Summary of Results.=--The following table gives the results that have been obtained with an apparatus arranged as shown above. In this table, column 2 is the one which contains the results directly observed by the use of the apparatus. Columns, 3, 4, and 5 are computed from preceding columns. (1) (2) (3) (4) (5) No. of Total Distance Velocity at Acceleration seconds distance each second end of second each second moved Per second Per second 1 30 cm. 30 cm. 60 cm. 60 cm. 2 120 cm. 90 cm. 120 cm. 60 cm. 3 270 cm. 150 cm. 180 cm. 60 cm. 4 480 cm. 210 cm. 240 cm. 60 cm. Column 5 shows that the acceleration is uniform, or the same each second. Column 4 shows that the velocity increases with the number of seconds or that _V_ = _at_. Column 3 shows that the increase in motion from 1 second to the next is just equal to the acceleration or 60 cm. This is represented by the following formula: _s_ = 1/2 _a_(2_t_ - 1). The results of the second column, it may be seen, increase as 1:4:9:16, while the number of seconds vary as 1:2:3:4. That is, _the total distance covered is proportional to the square of the number of seconds_. This fact expressed as a formula gives: _S_ = 1/2_at_².