10 



MECHANICS. 



These examples appear to contradict 

 the conclusion to which our reasoning 

 has conducted us, but they only appear 

 to do so. It is perfectly true, that 

 gravity, as far as its attraction is con- 

 cerned, accelerates the descent of all 

 bodies equally; but when bodies fall 

 under ordinary circumstances, another 

 force opposed to gravity is produced, 

 which is the resistance of the air on the 

 surface of the descending body. Now 

 this resistance, unlike the force of gra- 

 vity, is not proportional to the weight or 

 quantity of matter in the body, but de- 

 pends on the surface which the body 

 happens to oppose to the air. A feather 

 exposes, in proportion to its weight, a 

 much greater surface to the air than a 

 piece of gold does, and therefore suffers 

 a much greater resistance to its descent. 

 That it is the weight of the air prevents 

 the descent, and causes the ascent of 

 the balloon, will be seen by reference to 

 the sixth chapter of our treatise on 

 Pneumatics, art, (51.) 



(28.) It may, however, be satisfactory 

 to establish, by immediate experiment, 

 the theorem that gravity, acting inde- 

 pendently of other forces, causes all 

 bodies to descend with the same velocity. 

 7. On the plate E 

 (fig. 7.) of the air 

 pump, place a tall 

 glass receiver R, 

 open at the top. 

 On the top place a 

 brass cover, fitting it 

 air-tight. Through 

 this cover let a wire 

 pass, air-tight also, 

 and bearing a small 

 stage, on which a fea- 

 ther and a piece of 

 metal are placed, the 

 stage being so con- 

 trived as to fall when 

 the wire is turned by 

 the hand at H. This 

 being arranged, let 

 the receiver be ex- 

 hausted bythe pump, 

 which having been 

 effected, turn the 

 wire at H, so as to let 

 the stage, on which 

 the feather and metal are placed, fall. It 

 will be found that the feather and 

 metal strike the pump plate E at the 

 same instant.* If we could construct 



* This experiment is called the " guinea and 

 feather experiment," a guinea having been commonly 

 used for the piece of metal. 



a small balloon of materials strong 

 enough to resist the elastic force of the 

 gas, which would tend to burst it when 

 placed in the exhausted receiver, we 

 should find not only that it would not 

 remain at the top, but that it would fall 

 as rapidly as a piece of lead. 



(29.) Having shown that the velocity 

 acquired by a falling body is propor- 

 tional to the time, it is natural to inquire 

 whether any rule can be obtained by 

 which we may compute the spaces 

 through which a body will fall in any 

 given time. Such a rule may be easily 

 derived by mathematical reasoning from 

 the rule already given for the velocity, 

 but the reasoning cannot be properly 

 introduced here.* The rule itself, how- 

 ever, is easily understood. If a falling 

 body descend through a certain space 

 in the first second of its fall, it will de- 

 scend through four times that space in 

 the first two seconds, nine times that 

 space in the first three seconds, sixteen 

 times that space in the first four seconds ; 

 arid in general, to find the space it will 

 fall through in any given number of 

 seconds, multiply the space through 

 which it falls in one second by the 

 squaret of the number of seconds in the 

 time of the fall. 



Thus if m be the space through which 

 a body would fall in one second, m T 2 

 is the space through which it will fall in 

 the number of seconds expressed byT; 

 and if S be this space, we have S = m T 2 . 

 We, therefore, commonly say, that the 

 spaces through which a body falls, are 

 as the squares of the times from the 

 beginning of its fall. 



(30.) We shall find the space through 

 which a body falls in the second second 

 of its descent, by subtracting the space 

 fallen through in the first second from 

 that fallen through in the first two 

 seconds. The former being expressed 

 by m, the latter is 4m and the difference 

 is 3 m. Again, the space it falls through 

 in the third second will be found by sub- 

 tracting the space described in the first 

 two seconds which is 4 m, from that 

 described in the first three seconds 

 which is 9 m, and the difference 5 m is 

 the space described in the third second. 

 In the same way we shall find that 7 m, 

 9m, II m, &c. are the spaces which it 



* Let S be the space described by the falling body. 

 V = j| =g T. Hence, d S=g T d T, which being 

 integrated gives S=J g. T 2 . 



t The square of a number is the number found by 

 multiplying the proposed number by itself, thus 

 2 X 2 or 4 is the square of 2, 3 X 3 or 9 is the square 

 of three, and so on. 



