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the length is verified by causing pendulums, whose lengths are as the numbers 1, 4, 9, . . . . to oscillate simultaneously. The corresponding numbers of oscillations in a given time are then found to be proportional to the fractions 1,,, etc. . . . which shows that the times of oscillation increase as the numbers 1, 2, 3, . . . . . etc.

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By taking several pendulums of exactly equal length B, C, D (fig. 51) but with spheres of different substances, lead, copper, ivory, it is found that, neglecting the resistance of the air, these pendulums oscillate in equal times, thereby showing that the accelerating effect of gravity on all bodies is the same at the same place.

59. Measurement of the force of gravity. -The relation which the fourth law of the pendulum establishes between the number of oscillations in a given time, and the force of gravity, is used to determine the magnitude of this force at different places on the globe. By counting the number of oscillations which one and the same pendulum makes in a given time, a minute, for example, in proceeding from the equator towards the poles, it has been found that this number continually increases, proving, therefore, that the force of gravity increases from the equator towards the poles.

Fig. 52.

By means of the pendulum the velocity has been calculated which a body acquires in falling, in a second of time, in vacuo, that is to say, when it experiences no resistance from the air. At London this is 32.19 feet.

Since the velocity which a body imparts to a movable body in a given time is greater in proportion as this force is more intense, the force of gravity in different places is measured by the velocity which it imparts to a body falling freely in a vacuum: in London, for instance, its intensity is 32:19 feet, at the equator, 32'09, and at Spitzbergen, 32:25 feet.

60. Application of the pendulum to clocks.-The regulation of the motion of clocks is effected by means of pendulums, that of

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Application of the Pendulum to Clocks.

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watches by balance-springs. Pendulums were first applied to this purpose by Huyghens in 1658, and in the same year Hooke applied a spiral spring to the balance of a watch. The manner of employing the pendulum is shown in fig. 52. The pendulum rod passing between the prongs of a fork, a, communicates its motion to a rod, b, which oscillates on a horizontal axis, o. To this axis is fixed a piece, mn, called an escapement or crutch, terminated by two projections or pallets, which work alternately with the teeth of the escapement

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wheel, R. This wheel being acted on by the weight tends to move continuously, let us say, in the direction indicated by the arrowhead. Now if the pendulum is at rest, the wheel is held at rest by the pallet, m, and with it the whole of the clockwork and the weight. If, however, the pendulum moves and takes the position shown by the dotted line, m is raised, the wheel escapes from the confinement in which it was held by the pallet, the weight descends, and causes

the wheel to turn until its motion is arrested by the other pallet, ; which in consequence of the motion of the pendulum will be brought into contact with another tooth of the escapement wheel. In this manner the descent of the weight is alternately permitted and arrested—or, in a word, regulated—by the pendulum. By means of a proper train of wheelwork the motion of the escapement is communicated to the hands of the clock; and consequently their motion, too, is regulated by the pendulum.

Hence, to regulate a clock when it goes too slow or too fast, the length of the pendulum must be altered. If the clock goes too slow, it is because the pendulum oscillates too slowly, and it must therefore be shortened; if, on the contrary, it goes too fast, it must be lengthened. This shortening or lengthening is usually effected at the top of the pendulum by varying the length of the oscillating portion of the plate to which it is suspended. Clocks are provided with a simple arrangement for this purpose, which, however, is not represented in the figure.

61. Metronome.-This is another application of the isochronism of the oscillations of the pendulum, and is used to mark the time in practising music. As this time varies in different compositions, it is important to be able to vary the duration of the oscillations, which is effected as follows. The bob of the pendulum, B (fig. 53), is of lead, and it oscillates about an axis, o; the rod which is prolonged above this axis is provided with a weight, A, which slides on this axis and can be fixed in any position. This weight obviously acts in opposition to the oscillations of the bob, B, for when this tends to oscillate, for instance, from right to left, the weight tends to move the rod in the opposite direction, and this resistance which it affords to the motion is greater the longer the arm of the lever, A o, on which it acts. Hence the higher the weight, A, is raised, the slower are the oscillations. At the base of the instrument there is

a clockwork motion, which works an escapement with such force that, at each oscillation of the pendulum, a tooth strikes strongly against a palette fixed to the axis, o, thus producing a regular beat which gives the time. In front of the box which contains the mechanism is a scale with numbers, indicating the height at which the weight must be placed to obtain a given number of oscillations in a minute. In the drawing this weight is at the number 92, which indicates that the pendulum makes 92 oscillations in a minute.

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Molecular Attraction.

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CHAPTER VI.

MOLECULAR ATTRACTION,

62. Cohesion and chemical affinity.—After having described, under the name of universal gravitation, the attraction which exists between the stars; and under that of gravity, the attraction which the earth exerts upon all bodies in making them fall towards it, we have to investigate the attractions which hold together the ultimate molecules of a body. These are-cohesion, affinity, and adhesion.

Cohesion is the force which unites two molecules of the same nature; for example, two molecules of water, or two molecules of iron. Cohesion is strongly exerted in solids, less strongly in liquids, and scarcely at all in gases. Its intensity decreases as the temperature increases, because then the repulsive force due to heat increases. Hence it is, that when solid bodies are heated they first liquefy, and are ultimately converted into the gaseous state, provided that heat produces in them no chemical change.

Cohesion varies not only with the nature of bodies, but also with the arrangement of their molecules; for example, the difference between tempered and untempered steel is due to a difference in the molecular arrangement produced by tempering. It is to the modifications which this force undergoes that many of the properties of bodies are due, such as tenacity, hardness, and ductility.

In large masses of liquids, the force of gravity overcomes that of cohesion. Hence liquids acted upon by the former force have no special shape; they take that of the vessel in which they are contained. But in smaller masses cohesion gets the upper hand, and liquids present then the spheroidal form. This is seen in the drops of dew on the leaves of plants; it is also seen when a liquid is placed on a solid which it does not moisten; as, for example, mercury upon wood. The experiment may also be made with water, by sprinkling upon the surface of the wood some light powder such as lycopodium or lampblack, and then dropping some water on it.

Chemical affinity is the force which is exerted between molecules not of the same kind. Thus, in water, which is composed of

oxygen and hydrogen, it is affinity which unites these elements, but it is cohesion which binds together two molecules of water. In compound bodies cohesion and affinity operate simultaneously, while in simple bodies cohesion has alone to be considered.

To affinity are due all the phenomena of combustion; when carbon burns it is affinity which causes this body to combine with the oxygen of the air to form the gas known as carbonic acid. It determines the combination of the elements, so that with a small number of them are formed the immense number of organic and mineral substances which serve for our daily uses.

The causes which tend to weaken cohesion are most favourable to affinity; for instance, the action of affinity between substances is facilitated by their division, and still more by reducing them to a liquid or gaseous state. It is most powerfully exerted by a body in its nascent state, that is, the state in which the body exists at the moment it is disengaged from a compound; the body is then free, and ready to obey the feeblest affinity. An increase of temperature modifies affinity differently under different circumstances. In some cases, by diminishing cohesion, and increasing the distance between the molecules, heat promotes combination. Sulphur and oxygen, which at the ordinary temperature are without action on each other, combine to form sulphurous acid when the temperature is raised. In other cases heat tends to decompose compounds by imparting to their elements an unequal expansibility; thus many metallic oxides, as for example those of silver and mercury, are decomposed, by the action of heat, into gas and metal.

63. Adhesion.-Adhesion is the name given to the attraction manifested by two bodies when their surfaces are placed in contact.

If two leaden bullets are cut with a penknife so as to form two equal and brightly polished surfaces, and the two faces are turned against each other until they are in the closest contact, they adhere so strongly as to require a force of more than 3 or 4 ounces to separate them. The same experiment may be made with two equal pieces of glass, which are polished and made perfectly plane. When they are pressed one against the other, the adhesion is so powerful that they cannot be separated without breaking. As the experiment succeeds in vacuo, it cannot be due to atmospheric pressure, but must be attributed to a reciprocal action between the two surfaces. The attraction also increases as the contact is prolonged, and is greater in proportion as the contact is closer.

To adhesion is due the resistance experienced in raising a plank

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