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The dilatation of substances by heat, and their contraction by cold, occasion such irregularities in the rate of clocks and watches as would render them unfit for astronomical or nautical purposes, were it not for a very beautiful application of the laws of unequal expansion. The oscillations of a pendulum are the same as if its whole mass were united in one dense particle, in a certain point of its length, called the centre of oscillation. If the distance of this point from the point by which the pendulum is suspended were invariable, the rate of the clock would be invariable also. The difficulty is to neutralize the effects of temperature, which is perpetually increasing or diminishing its length. Among many contrivances, Graham's compensation pendulum is the most simple. He employed a glass tube containing mercury. When the tube expands from the effects of heat, the mercury expands much more; so that its surface rises a little more than the end of the pendulum is depressed, and the centre of oscillation remains stationary. Harrison invented a pendulum which consists of seven bars of steel and of brass, joined in the shape of a gridiron, in such a manner that, if by change of temperature the bars of brass raise the weight at the end of the pendulum, the bars of steel depress it as much. In general, only five bars are used; three being of steel, and two a mixture of silver and zinc. The effects of temperature are neutralized in chronometers upon the same principle; and to such perfection are they brought, that the loss or gain of one second in twenty-four hours for two days running would render one unfit for use. Accuracy in surveying depends upon the compensation rods employed in measuring bases. Thus, the laws of the unequal expansion of matter judiciously applied have an immediate influence upon our estimation of time ; of the motions of bodies in the heavens, and of their fall upon the earth ; on our determination of the figure of the globe, and on our system of weights and measures; on our commerce abroad, and the mensuration of our lands at home.

The expansion of the crystalline substances takes place under very different circumstances from the dilatation of such as are not crystallized. The latter become both longer and thicker by an accession of heat, whereas M. Mitscherlich has found that the former expand differently in different directions; and, in a particular instance, extension in one direction is accompanied by contraction in another : for example, Iceland spar is dilated in the direction of its axis of double refraction (N. 205), but at right angles to that axis it is contracted, which brings the crystal nearer to the form of the cube and diminishes its double refractive power. When heat is applied to crystals of sulphate of lime, the two optical axes (N. 207) gradually approach, and at last coincide; when the heat is increased, the axes open again, but in a direction at right angles to their former position. By experiment M. Senarmont has concluded, that in media constituted like crystals of the rhomboidal (N. 169) system the conducting power varies in such a manner, that, supposing a centre of heat to exist within them, and the medium to be indefinitely extended in all directions, the isothermal surfaces are concentric ellipsoids of revolution round the axes of symmetry, or at least surfaces differing but little from them. The internal structure of crystallized matter must be very peculiar thus to modify the expansive power of heat.

Heat applied to the surface of a fluid is propagated downwards very slowly, the warmer, and consequently lighter strata, always remaining at the top. This is the reason why the water at the bottom of lakes fed from Alpine chains is so cold ; for the heat of the sun is transfused but a little way below the surface. When the heat is applied below a liquid, the particles continually rise as they become specifically lighter, and diffuse the heat through the mass, their place being perpetually supplied by those that are more dense. The power of conducting heat varies materially in different liquids. Mercury conducts twice as fast as an equal bulk of water, and therefore it appears to be very cold. A hot body diffuses its heat in the air by a double process : the air in contact with it becoming lighter ascends and scatters its heat by transmission, while at the same time another portion is discharged in straight lines by the radiating power of the surface. Hence a substance cools more rapidly in air than in vacuo, because in the latter case the process is carried on by radiation alone. It is probable that the earth having been originally of very high temperature has become cooler by radiation alone, the ethereal medium being too rare to carry off much heat by contact.

Heat is propagated with more or less rapidity through all bodies ; air is the worst conductor, and consequently mitigates the severity of cold climates by preserving the heat imparted

to the earth by the sun. On the contrary, dense bodies, especially metals, possess the power of conduction in the greatest degree, but the transmission requires time. If a bar of iron twenty inches long be heated at one extremity, the heat takes four minutes in passing to the other. The particle of the metal that is first heated communicates the heat to the second, and the second to the third : so that the temperature of the intermediate molecule at any instant is increased by the excess of the temperature of the first above its own, and diminished by the excess of its own temperature above that of the third. That however will not be the temperature indicated by the thermometer, because as soon as the particle is more heated than the surrounding atmosphere it loses its heat by radiation, in proportion to the excess of its actual temperature above that of the air. The velocity of the discharge is directly proportional to the temperature, and inversely as the length of the bar. As there are perpetual variations in the temperature of all terrestrial substances, and of the atmosphere, from the rotation of the earth, and its revolution round the sun, from combustion, friction, fermentation, electricity, and an infinity of other causes, the tendency to restore the equability of temperature by the transmission of heat must maintain all the particles of matter in a state of perpetual oscillation, which will be more or less rapid according to the conducting powers of the substances. From the motion of the heavenly bodies about their axes, and also round the sun, exposing them to perpetual changes of temperature, it may be inferred that similar causes will produce like effects in them too. The revolutions of the double stars show that they are not at rest; and although we are totally ignorant of the changes that may be going on in the nebulæ and millions of other remote bodies, it is hardly possible that they should be in absolute repose ; so that, as far as our knowledge extends, motion is a law of the universe and the immediate cause of heat, as in the sunbeam so also in all terrestrial phenomena

This is by no means hypothetical, but founded upon fact and experiment. Heat is produced by motion and is equivalent to it, for we measure heat by motion in the thermometer. The heat evolved by percussion is proportional to the force of the blow : by repeated blows iron becomes red hot; and the quantity of



heat produced by friction, whether the matter be solid or fluid, is always in proportion to the force employed : in cold weather we rub our hands to make them warm, and the harder we rub the warmer they become. The warmth of the sea after a storm is in proportion to the force of the wind; and in Sir Humphry Davy's experiment of melting ice by friction in the receiver of an air-pump kept at the freezing point, the heat which melted the ice was exactly proportional to the force of friction. This experiment proves the immateriality of heat, since the capacity of ice for heat is less than that of water. Thus mechanical action and heat are equivalent to one another. Mr. Joule of Manchester * has proved that the quantity of heat requisite to raise the temperature of a pound of water one degree of Fahrenheit's thermometer, is equivalent to the mechanical force developed by the fall of a body weighing 772:69 pounds through the perpendicular height of one foot. This quantity is the mechanical equivalent of heat. Thus heat is motion, and it is measured by force. In fact, for every unit of force expended in friction or percussion, a definite quantity of heat is generated ; and conversely, when work is performed by the consumption of heat, for each unit of force gained, a unit of heat disappears. For since heat is a dynamical force of mechanical effect, there must be an equivalent between mechanical work and heat as between cause and effect. (N. 222.)

Besides the temperature indicated by the thermometer, bodies absorb heat, and their capacity for heat is so various that very different quantities of heat are required to raise different substances to the same sensible temperature. It is evident, therefore, that much of the heat is absorbed and becomes insensible to the thermometer. That portion of heat requisite to raise a body to a given temperature is its specific heat, but the latent or absorbed heat is an expansive force or energy, which, acting upon the ether surrounding the ultimate particles of bodies, changes them from solid to liquid, and from liquid to vapour or gas. According to the law of absorption, the transfer of heat from a warm body to one that is cold is a mere transfer of force, in which the force of compression is exactly proportional to the force of expansion. Ice remains at the temperature of 32° Fahrenheit till it has absorbed 140° of heat, and then it melts, but without raising the temperature of the water above 32o. On the contrary, when a liquid is converted into a solid, a quantity of heat leaves it without any diminution of temperature. Thus water at 32° must part with 1400 of heat before it freezes. The slowness with which water freezes or ice thaws, is a consequence of the time required for the ethereal atmospheres round the particles of the water to contract or expand with a force equivalent to 140° of heat. A considerable degree of cold is felt during a thaw, because the ice in its transition from a solid to a liquid state absorbs sensible heat from the atmosphere and surrounding objects. The heat absorbed and evolved by the rarefaction and condensation of air is exactly proportional to the force evolved and absorbed in these operations. In fact, the changes of temperature produced by these rarefactions and condensations of air show that the heat of elastic fluids is the mechanical force possessed by them; and since the temperature of a gas determines its elastic force, it follows that the elastic force or pressure must be the effect of the motion of the constituent particles in any gas. Sir Humphry Davy, who first demonstrated the immateriality of heat, assumed the hypothesis that the motion we call heat is a rotation or vibration among the particles of the fluid, which, according to Mr. Joule, agrees perfectly with the observed phenomena, but he prefers the more simple view of Mr. Herapath, that the elastic force or pressure is due to the impact of the particles against any surface presented to them. Absorbed or latent heat may be regarded as a quiescent energy ready to be restored to the form of sensible heat when called forth: its vibrations as heat are extinguished for the time by being transferred to the internal expansive force, and are restored by compression. The absorbed heat of air and all elastic fluids may be forced out by sudden compression like squeezing water out of a sponge. The quantity of heat brought into action in this way is well illustrated by the experiment of igniting tinder by the sudden compression of air by a piston thrust into, a cylinder closed at one end. The development of heat on a stupendous scale is exhibited in lightning: it is proportional to the square of the quantity

*. This theory of heat and motion originated with Mr. Joule, of Manchester, who has maintained it with the greatest talent, both by experiment and analysis; and it has had an able advocate in Professor W. Thomson, of Glasgow.

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