Page:The American Cyclopædia (1879) Volume XI.djvu/332

 320 MECHANICS expressed by the letter g. The following tahle embraces the facts contained in these laws : TABLE SHOWING LAWS OF FALLING BODIES. TIME IX SECONDS. 1 .. Velocities acquired In valnes otg. Sp.ce. fallen through in values of*7. Total height fallen through In valuei of J. ff = 82-16 ft. 20= 64-32" 80= 96-49 " 4(7=128-64 " 50=160-80 " 60=192-96 " 1= 16-08 ft. 8= 48-24 u 5= 80-40 " 7=112-56" 9=144-72 " 11=176-88 " 1= 16-08 ft. 4= 64-82 " 9=144-72 " 16=257-28 " 25=402 00 " 86=578-88 " 8 4 ... 5 c These laws may be experimentally verified with considerable accuracy, but in order to do so it is necessary to reduce the velocity of the falling body, because a body dense enough not to be much affected by the resistance of the air soon acquires so great a velocity that it cannot be estimated with accuracy ; and if the body is light, it soon meets with so much resistance that the motion becomes uniform. The most ancient method for diminishing the velocity was with the inclined plane, by Gali- leo. By referring to that part of this article which treats of the inclined plane, it will be seen that the force with which a body tends to move down such a plane is to the force with which it would fall freely as the height of the plane is to its length. If its height is 1 ft. and its length 16 ft., it will move down the plane 1 ft. during the first second, 3 ft. during the sec- ond second, and so on ; and therefore through PIG. 4. the 1 6 ft. during four seconds. But the results are not as accurate as with the employment of Atwood's machine, a simplified form of which, 'to facilitate explanation, is shown in fig. 4. Two equal weights, a and J, are suspended over a friction wheel placed at the top of a graduated post 9 or 10 ft. high. A platform, p, having a joint by means of which it may be suddenly dropped at any desired moment by connection with clockwork, is placed just below the wheel. The weight a is placed upon this platform and loaded with a metallic bar, whose gravity is used as the accelerating force. At a chosen moment the platform falls and the weight be- gins to descend with accelerated velocity. A ring, c, placed at any desired distance below the platform, takes off the accelerating bar, after which the weight descends with uniform motion, only imperceptibly retarded by the air and an exceedingly small amount of friction. If the sum of the weights a and b is 99 ounces and the accelerating bar weighs one ounce, gravity acts practically on only one ounce, but it has to give motion to 100 ounces ; therefore the velocity of descent will be ^ as great as that of a weight falling freely ; so that during the first second it will fall only 1-93 in., during the fourth second only 13*51 in., and during four seconds only 61-75 in. It will be observed that the velocity may be varied by changing the weight of the accelerating bar. By chang- ing the position of the ring c from one point to another, the rate of acceleration may be de- termined, and the velocity of motion attained at any point of time or space fallen through may be ascertained by measuring the uniform motion of the weights after the removal of the accelerating bar. The principal advantage of this machine is the facility it affords for estimating the relations between the accelera- ting force and the space described in a given time. Atwood's machine has been modified by Bourbouze so as to act somewhat on the principle of Morin's apparatus next described. The weights are set in motion by means of temporary magnets, and upon a cylinder cov- ered with smoked paper curves are traced by a vibrating style, which is also moved by a tem- porary magnet. Morin's apparatus is auto- graphic, and in some respects, especially in its great accuracy and facility in verifying the law of acceleration, is preferable to Atwood's ma- chine. Its essential parts are shown in fig. 5. A frame 8 or 10 ft. high holds the parts in position, which consist of a light wooden cylin- der, M, about one third of the length of which is shown in the figure. It is turned by a weight, Q, suspended by a cord passing around a drum, G, which carries a cog wheel c that plays into the endless screw a. At first the motion is accelerated, but after a short time, on account of the resistance of the air en- countered by the revolving fan which is turned by the endless screw d, uniform motion is at- tained. Then, by pulling a cord, K, a lever, A, displaces a catch, C, which liberates a weight, P, which then begins to fall with ac- celerated velocity between two vertical gui- ding wires. The weight is provided with a pen- cil, I, which describes a line in descending upon