Compendium of Natural and Experimental Philosophy 7




What is the Pendulum?

  1. REGULATORS OF MOTION. – THE PENDULUM. The Pendulum * consists of a weight or ball suspended by a rod, and made to swing backwards and forwards.


* The pendulum was invented by Galileo, a great astronomer of Florence, in the beginning of the seventeenth‘ century. Perceiving that the chandeliers suspended from the ceiling of a lofty church vibrated long and with great uniformity, as they were moved by the wind or by any accidental disturbance, he was led to inquire into the cause of their motion, and this inquiry led to the invention 6f the pendulum. From a like apparently insignificant circumstance arose the great discovery of the principle of gravitation. During the prevalence of the plague, in the year 1665, Sir Isaac Newton retired into the country to avoid the contagion. Sitting in his orchard, one day, he observed an apple fall from a tree. His inquisitive mind was immediately led to consider the cause which brought the apple to the ground, and the result of his inquiry was the discovery of that grand principle of gravitation which may be considered as the. first and most important law of material nature. Thus, out of what had been before the eyes of men, in one shape or another, from the creation of the world, did these philosophers bring the most important results.


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What are the motions of a pendulum called, and how are they caused?

  1. The motions of a pendulum are called its vibrations or oscillations, and they are caused by gravity.*

* When a pendulum is raised from a perpendicular position, its weight will cause it to fall, and, in the act of falling, it acquires a degree of motion which impels it to a height beyond the perpendicular almost as great as that to which it was raised. Its motion being thus spent, gravity again acts upon it to bring it to its original perpendicular position, and it again acquires an impetus in falling which carries it nearly as high on the opposite side. It thus continues to swing backwards and forwards, until the resistance of the air wholly arrests its motion.

It will be understood that gravity affects every part of the length of the pendulum. A ball or flattened weight is attached to the lower end of the pendulum to concentrate the effects of gravity in a single point.

In the construction of clocks, an apparatus connected with the weight or the spring is made to act on the pendulum with such a force as to enable it to overcome the resistance of the air, and keep up a continued motion.


What is the arc of a pendulum?

The part of a circle through which it moves is called its arc.

What difference is there in the time of vibrations of pendulums of equal length?

  1. The vibrations of pendulums of equal length are very nearly equal, whether they move through a greater or less part of their arcs. **

** It has already been stated that a body takes the same time in rising and falling when projected upwards. Gravity brings the pendulum down, and inertia causes it to continue its motion upwards.

Fig. 57.

  1. In Fig. 57 AB represents a pendulum, D F E C the arc in which it vibrates. If the pendulum be raised to E it will return to F, if it be raised to C it will return to D, in nearly the same length of time, because that, in proportion as the arc is more extended, the steeper will be its beginnings and endings, and, therefore, the more rapidly will it fall.***

***The length of the arc in which a pendulum oscillates is called its amplitude.


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On what does the time of the oscillations of a pendulum depend?

  1. The time occupied in the vibration of a pendulum depends upon its length. The longer the pendulum, the slower are its vibrations. *

* The weight of the ball at the end of a pendulum does not affect the duration of its oscillations.

What is the length of a pendulum that vibrates once every second of time?

  1. The length of a pendulum which vibrates sixty times in a minute (or, in other words, which vibrates seconds) is about thirty nine inches. But in different parts of the earth this length must be varied.

Which must be the longer, to vibrate seconds at the equator or one at the poles?

A pendulum to vibrate seconds seconds at the equator, must be shorter than one which vibrates seconds at the poles. **

** The equatorial diameter of the earth exceeds the polar diameter by about twenty-six miles; consequently the poles must be nearer to the centre of the earth’s attraction thin the equator, and gravity must also operate with greater force at the poles than at the equator. Hence, also, the length of a pendulum, to vibrate in any given time, must vary with the latitude of the place.


How is a clock regulated?

  1. A clock is regulated by lengthening or shortening the pendulum. By lengthening the pendulum, the clock is made to go slower; by shortening it, it will go faster. ***

*** The pendulum of a clock is made longer or shorter by means of a screw beneath the weight or ball of the pendulum. The clock itself is nothing more than a pendulum connected with wheel-work, so as to record the number of vibrations. A weight is attached in order to counteract the retarding effect of friction and the resistance of the air. The wheels show how many swings or beats of the pendulum have taken place in a given time, because at every beat the tooth of a wheel is allowed to pass. Now, if this wheel have sixty teeth, it will turn round once in sixty vibrations of the pendulum, or in sixty seconds; and a hand, fixed on the axis of the wheel projecting through the dial-plate, will be the second-hand of the clock. Other wheels are so connected with the first, and the number of teeth in them is so proportioned, that the second wheel turns sixty times slower than the first, and to this is attached the minute-hand; and the third wheel, moving twelve times slower than the second, carries the hour baud. On account of the expansion of the pendulum by heat, and its contraction by cold, clocks will go slower in summer than in winter, because the pendulum is thereby lengthened at that season.


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What proportion are the pendulums?

  1. The lengths of pendulums are to each lengths of other as the square of the time of their vibration.
  2. According to this law, a. pendulum, to vibrate once in two seconds, must be four times as long as one that vibrates once in one second; to vibrate once in three seconds, it must be nine times as long; to vibrate once in four seconds, it must be sixteen times as long‘; once in five seconds, twenty-five times as long, &c.

The seconds employed in the vibrations being

1, 2, 3, 4, 5, 6, 7, 8, 9,

the length of the pendulums would be as

1, 4,. 9, 16, 25, 36, 49, 64, 81.

A pendulum, therefore, to vibrate once in five seconds, must be over eighty feet in length.

  1. As the oscillations of a pendulum are dependent upon gravitation, the instrument becomes useful in ascertaining the force of gravity at different distances from the centre of, the earth.
  2. It has already been stated that the centrifugal force at the equator is greater than in those parts of the earth which are near the poles. As the centrifugal force operates in opposition to that of gravity, it follows that the pendulum must also be affected by it; and this affords additional reason why a pendulum, to vibrate seconds at the equator, must be shorter than one at the poles. It has been estimated that, if the revolution of the earth around its axis were seventeen times faster than it is, the centrifugal force at the equator would be equal to the force of gravity, and, consequently, neither could a pendulum vibrate, nor would bodies there have any weight.
  3. As every part of a pendulum-rod tends to vibrate in a different time, it is necessary that all pendulums should. have a weight attached to them, which, by its inertia, shall concentrate the attractive force of gravity.
  4. Pendulums are subject to variation in warm and cold weather, on account of the. dilatation and contraction of the materials of which the rod is composed, by heat and cold. For this reason, the same pendulum is always longer in summer than it is in winter; and a clock will, therefore, always be slower in summer than in winter, unless some means are employed by which the effects of heat and cold on the length of the pendulum can be counteracted. This is sometimes effected in what is called the gridiron pendulum by combining bars or rods of steel and brass, and in the mercurial pendulum by enclosing a quantity of quicksilver in a tube near the bottom of the pendulum.
  5. In order to secure a continuous motion to the pendulum (or, in other words, to keep a clock in motion), it is necessary that the pendulum should hang in a proper position. A practised ear can easily detect any error in this respect by the irregularity in the ticking, or (as it is called) by its being“ out of beat.“


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To remedy this fault, it is necessary either to incline the clock to the one side or the other, until the tickings are synchronous; or, in other words are made at equal intervals of time. It can sometimes be done without moving the clock, by slightly bending the upper appendage of the pendulum in such a manner that the two teeth, or projections, shall properly articulate with the escapement-wheel. [See

No. 303.]

  1. Table of the Lengths of Pendulums to vibrate Seconds in different latitudes.
Inches. Inches.
At the equator, 39. At the equator, 39.
Lat. 10~ North, 39.01 Lat. 10~ South, 39.02
20 „ 39.04 20 „ 39.04
30 „ 39.07 30 „ 39.07
40 „ 39.10 40 „ 39.10
50 „ 39.13 50 „ 39.13
60 „ 39.16 60 „


  1. The observations have been extended but little further, north or south of the equator. Different observers have arrived at different results; probably on account of their different positions in relation to the level of the sea in which the observations were made. In such a work as this, a table of this kind, without pretending to extreme accuracy, is useful, as showing that theory has been confirmed by observation.
  2. The moving power of a clock is a weight, which, being wound up, makes a constant effort to descend, and is prevented by a small appendage of the pendulum, furnished with two teeth, or projections, which the vibrations of the pendulum cause alternately to fall between the teeth of a wheel called the escapement-wheel.

The escapement-wheel is thus permitted to turn slowly, one tooth at a time, as the pendulum vibrates. If the pendulum with its appendage be removed from the clock, the weight will descend very rapidly, causing all the wheels to revolve with great velocity, and the clock becomes useless as a time-piece.

  1. The moving power of a watch * is a spring, called the mainspring, which being tightly wound around a central pin, or axis, its elasticity makes a constant effort to loosen.

*A watch differs from a clock in having a vibrating wheel, instead of a pendulum. This wheel is moved by a spring, called the hair-spring. The place of the weight is supplied by another larger spring, called the, mainspring.

This power is communicated to a balance-wheel, acted upon by a hair-spring, and having an escapement similar- to that of the clock.


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If the hair-spring, with the escapement, be removed, the main spring, being unrestrained will cause the wheels to revolve with great rapidity, ant the watch, also, becomes useless as a time-piece.*

* As a regulator of motion, the pendulum of the clock is to be lengthened or shortened, and the hair-spring of a watch is to be tightened or loosened. This is to be done in the former case in the manner already explained in the text; in the latter, by turning what is called the regulator, which tightens or loosens the hair-spring.

What is a Battering Ram?

  1. THE BATTERING RAM. The Battering Ram was a military engine of great power, used to beat down the walls of besieged places.

Fig. 58.

Explain Fig. 58.

  1. Its construction, and the principle on which it was worked, may be understood by inspection of Fig 58, in which A B represents a large beam, heavily loaded, with a head of iron, A, resembling the head of a ram, from which it takes its name. The beam is accurately balanced, and suspended by a rope or chain C, hanging from another beam, supported by the frame D E F G. At the extreme end B, ropes or chains were attached, by which it could be drawn upwards through the arc of a circle, like a pendulum. The frame was sometimes mounted on wheels.
  2. Battering rams were frequently from fifty to a hundred feet in length, and, moving with a force compounded of their weight and velocity, were almost irresistible.**

** The ram used by Demetrius Poliorcetes at the siege of Rhodes was one hundred and six feet long. At the siege of Jerusalem Vespasian employed a ram fifty feet long, armed with an iron butt, with twenty-five projecting points, two feet apart, each as thick as the body of a man. The counter weight at the hindmost end amounted to 1075 cwt., and 1500 men were required to work the machine.


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  1. The force of a battering ram is estimated by its momentum, that is its weight multiplied by its velocity.
  2. Questions for Solution.

(1.) Suppose a battering ram weighing 5760 lbs., with a velocity of 11 feet in a second, could penetrate a wall, with what velocity must a cannon-ball weighing 24 lbs. move to do the same execution?  5760 X 11 = 63360 : 24 – 2640 feet, or one half of a mile in a second.

(2.) If a battering ram have a momentum of 58,000 and a velocity of 8, what is its weight 1 Ans. 7250

(3.) If a ran have a weight of 90,000 and a momentum 81,000, what is its velocity? Ans. 9

(4.) What is the weight of a ram with a velocity of 12 and a momentum 60,000? Ans. 5000.

(5.) Will a cannon-ball of 9 lbs. and a velocity of 3,000, or a ram with a weight of 15,000 and a velocity of 2, move with the greater force? Ans. The ram.

What is the Governor?

  1. THE GOVERNOR. The Governor is an ingenious piece of mechanism, constructed on the principle of the centrifugal force, by means of which the supply of power in machinery is regulated.*

* This very useful appendage to machinery, though long used in mills and other mechanical arrangements, owes its happy adaptation to the steam engine to the ingenuity of Mr. James Watt.

In manufactures, there is one certain and determinate velocity with which the machinery should be moved, and which, if increased or diminished, would render the machine unfit to perform the work it is designed to execute. Now, it frequently happens that the resistance is increased or diminished by some of the machines which are worked being stopped, or others put on. The moving power, having this alteration in the resistance, would impart a greater or less velocity to the machinery, were it not for the regulating power of the governor, which increases or diminishes the supply of water or of steam, which is the moving power.

But, besides the alteration in the resistance just noticed, there is, also, frequently, greater changes in the power. The heat by which steam is generated cannot always be perfectly regulated. At times it may afford an excess, and at other times too little expansive power to the steam. Water, also, is subject to change of level, and to consequent alteration as a moving power. The wind, too, which impels the sails of a wind-mill, is subject to great increase and diminution. To remedy all these inconveniences is the duty assigned to the governor.


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Fig. 59

Explain Fig. 59.

  1. Fig. 59 represents a governor. A B and A C are two levers, or arms, loaded with heavy balls at their extremities B and C, and suspended by a joint at A upon the extremity of a revolving shaft A D. A a is a collar, or sliding box, connected with the levers by the rods b a and c a, with joints at their extremities. When the shaft A D revolves rapidly, the centrifugal force of the balls B and C will cause them to diverge in their attempt to fly off, and thus raise the collar a, by means of the rods b a and c a. On the contrary, when the shaft A D revolves slowly, the weights B and C will fall by their own weight, and the rods b a and c a will cause the collar a to descend. The steam valve in a steam engine, or the sluice-gate of a water-wheel, being connected with the collar a, the supply of steam or water, which puts the works in motion, is thus regulated.

What is the Main-spring of a watch?

  1. The Main-spring of a watch consists of a long ribbon of steel, closely coiled, and contained in a round box. It is employed instead of a weight, to keep up the motion.
  2. As the spring, when closely coiled, exerts a stronger force than when it is partly loosened, in order to correct this inequality the chain through which it acts is wound upon an axis surrounded by a spiral groove (called a fusee), gradually increasing in diameter from the top to the bottom so that, in proportion as the strength of the spring is diminished, it may act on a larger lever, or a larger wheel and axle.

Fig. 60.

Explain Fig. 60.

  1. Fig. 60 represents a spring coiled in a round box. A B is the fusee, surrounded by a spiral groove, on which the chain C is wound. When the watch is recently wound, the spring is in the greatest state of tension, and will, therefore, turn the fusee by the smallest groove, on the principle of the wheel and axle.


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As the spring loses its force by being partly unwound, it acts upon the larger circles of the fusee; and the want of strength in the spring is compensated by the mechanical aid of a larger wheel and axle in the larger grooves. By this means the spring is made at all times to exert an equal power upon the fusee. The motion is communicated from the fusee by a cogged wheel, which turns with the fusee.