28 



NATURAL PHILOSOPHY. 



[Lesson XII. 



his back (Fig. 1(5) he must bend lor ward ; 

 and if he carries a load in his left hand 



Fig. 18. Fig 



(Fig. 17), he must bend the upper part of 

 his body to the right. 



154. T. What do you mean by in- 

 different equilibrium ? 



P. When any body is balanced in all 

 positions it is in a state of indifferent 

 equilibrium. For example, when the wheel 

 of a carriage is raised from the ground to 

 wash it, we have a body in a state of in- 

 different equilibrium, upon a fixed axis. 

 The common balance is an excellent ex- 

 ample of this state, when both scale-pans 

 are of equal weight. 



]')">. T. We will try an experiment 

 [Experiment 21]. I have here a bullet 

 with a hole in it, through which a string 

 passes, and you will see that when the 

 bullet is drawn out of the perpendicular 

 and let go, that it will swing backwards 

 and forwards. [Performs the experiment.] 

 You observe that it swings or oscillates, as 

 it is termed, and in doing so describes 

 a segment of a circle, which is called its 

 arc. Can you tell me what is the cause 

 of this? 



P. Gravity, which causes bodies to fall. 



15(5. 7\ What is the name applied to a 

 rod of iron with a weight at the lower part, 

 like my bullet and string? 



P. A pendulum ; which hangs perpen- 

 dicularly when at rest. The uppermost 

 part is called the axis or point of suspen- 

 sion, and the part where the ball is placed 

 is called the point of rest 



157. T. You have not explained to \\\<* 

 how it is that the pendulum swings to and 

 fro. 



P. When the ball of the pendulum is 

 raised to a height upon one side am! 

 liberty, it has a tendency to fall to the 

 ground by the force of gravity, but being 

 confined by the rod it makes a sweep to 

 the point of rest, and having acquired a 

 certain degree of velocity it sweeps on 

 until it ascends on the other side to nearly 

 the same height as that from which it was 

 set free. Its weight again draws it down, 

 and its velocity raises it to nearly the 

 same height as the point from which it 

 originally fell, and thus it continues to 

 swing to and fro until the force of gravity 

 overcomes the propelling force, and it 

 ultimately settles in a state of rest in its 

 original position. 



158. T. Then it appears that each sweep 

 of the pendulum decreases the length of 

 the arc. What is the reason ? 



P. The resistance of the atmosphere, 

 and the friction at its axis or point of 

 suspension. 



159. T. What is the length of the arc 

 traversed by the fall of a pendulum ? 



P. It is impossible to fix any certain 

 length, because it will depend upon the 

 force exercised in setting the pendulum 

 free ; it may be made to traverse any 

 number of degrees under 180, which is 

 half a circle ; but generally the extent of 

 the arc is from ten to twenty degrees. 



160. T. Does the length of the rod by 

 which the weight is suspended make any 

 difference in the oscillations of the pen- 

 dulum ? 



P. Yes ; the one with a long rod 

 vibrates or oscillates slower than the one 

 with a short rod, and here we have a mo- 

 tion analogous to that of falling bodies? 



161. T. Why is the vibration analogous 

 to the falling of bodies ? 



P. Because we have learned (see Les- 

 son XI.) that the motion of falling bodies 

 is increased in regular arithmetical pro- 

 gression; and, in the case of the pendulum, 

 their lengths are as the squares of the 

 times of vibration. Thus, if the times 

 occupied by one vibration of two pendulums 

 be 2 and 3 respectively, their lengths will 

 be as 4 and 9. 



