Terrestrial Heat—Radiation—Transmission—Melloni’s experiments—Heat in Solar Spectrum—Polarization of Heat—Nature of Heat—Absorptions—Dew—Rain—Combustion—Expansion—Compensation Pendulum—Transmission through Crystals—Propagation—Dynamic Theory of Heat—Mechanical equivalent of Heat—Latent Heat is the Force of Expansion—Steam—Work performed by Heat—Conservation of Force—Mechanical Power in the Tides—Dynamical Power of Light—Analogy between Light, Heat, and Sound.

That heat producing rays exist independently of those of light is a matter of constant experience in the abundant emission of them from boiling water. They dart in divergent straight lines from flame and from each point in the surfaces of hot bodies, in the same manner as diverging rays of light proceed from every point of those that are luminous. According to the experiments of Sir John Leslie, radiation proceeds not only from the surface of substances, but also from the particles at a minute depth below it. He found that the emission is most abundant in a direction perpendicular to the radiating surface, and that it is more rapid from a rough than from a polished surface: radiation, however, can only take place in air and in vacuo; it is altogether imperceptible when the hot body is enclosed in a solid or liquid. Heated substances, when exposed to the open air, continue to radiate heat till they become nearly of the temperature of the surrounding medium. The radiation is very rapid at first, but diminishes according to a known law with the temperature of the heated body. It appears, also, that the radiating power of a surface is inversely as its reflecting power; and bodies that are most impermeable to heat radiate least. Substances, however, have an elective power, only reflecting heat of a certain refrangibility. Mr. Grove gives paper, snow, and lime as instances, which, although all white, radiate heat of different refrangibilities, while metals, whatever their colour may be, radiate all kinds alike.

Rays of heat, whether they proceed from the sun, from flame, or other terrestrial sources, luminous or non-luminous, are instantaneously transmitted through solid and liquid substances, there being no appreciable difference in the time they take to pass through layers of any nature or thickness whatever. They pass also with the same facility whether the media be agitated or at rest; and in these respects the analogy between light and heat is perfect. Radiant heat passes through the gases with the same facility as light; but a remarkable difference obtains in the transmission of light and heat through most solid and liquid substances, the same body being often perfectly permeable to the luminous, and altogether impermeable to the calorific rays. For example, thin and perfectly transparent plates of alum and citric acid sensibly transmit all the rays of light from an argand lamp, but stop eight or nine tenths of the concomitant heat; whilst a large piece of brown rock-crystal gives a free passage to the radiant heat, but intercepts almost all the light. Alum united to green glass is also capable of transmitting the brightest light, but it gives not the slightest indication of heat; while rock-salt covered thickly over with soot, so as to be perfectly opaque to light, transmits a considerable quantity of heat. M. Melloni has established the general law in uncrystallized substances such as glass and liquids, that the property of instantaneously transmitting heat is in proportion to their refractive powers. The law, however, is entirely at fault in bodies of a crystalline texture. Carbonate of lead, for instance, which is colourless, and possesses a very high refractive power with regard to light, transmits less radiant heat than Iceland spar or rock-crystal, which are very inferior to it in the order of refrangibility; whilst rock-salt, which has the same transparency and refractive power with alum and citric acid, transmits six or eight times as much heat. This remarkable difference in the transmissive power of substances having the same appearance is attributed by M. Melloni to their crystalline form, and not to the chemical composition of their molecules, as the following experiments prove. A block of common salt cut into plates entirely excludes calorific radiation; yet, when dissolved in water, it increases the transmissive power of that liquid: moreover, the transmissive power of water is increased in nearly the same degree, whether salt or alum be dissolved in it; yet these two substances transmit very different quantities of heat in their solid state. Notwithstanding the influence of crystallization on the transmissive power of bodies, no relation has been traced between that power and the crystalline form.

The transmission of radiant heat is analogous to that of light through coloured media. When common white light passes through a red liquid, almost all the more refrangible rays, and a few of the red, are intercepted by the first layer of the fluid; fewer are intercepted by the second, still less by the third, and so on: till at last the losses become very small and invariable, and those rays alone are transmitted which give the red colour to the liquid. In a similar manner, when plates of the same thickness of any substance, such as glass, are exposed to an argand lamp, a considerable portion of the radiant heat is arrested by the first plate, a less portion by the second, still less by the third, and so on, the quantity of lost heat decreasing till at last the loss becomes a constant quantity. The transmission of radiant heat through a solid mass follows the same law. The losses are very considerable on first entering it, but they rapidly diminish in proportion as the heat penetrates deeper, and become constant at a certain depth. Indeed, the only difference between the transmission of radiant heat through a solid mass, or through the same mass when cut into plates of equal thickness, arises from the small quantity of heat that is reflected at the surface of the plates. It is evident, therefore, that the heat gradually lost is not intercepted at the surface, but absorbed in the interior of the substance, and that heat which has passed through one stratum of air experiences a less absorption in each of the succeeding strata, and may therefore be propagated to a greater distance before it is extinguished. The experiments of M. de Laroche show that glass, however thin, totally intercepts the obscure rays of heat when they flow from a body whose temperature is lower than that of boiling water; that, as the temperature increases, the calorific rays are transmitted more and more abundantly; and, when the body becomes highly luminous, that they penetrate the glass with perfect ease. The extreme brilliancy of the sun is probably the reason why his heat, when brought to a focus by a lens, is more intense than any that has been produced artificially. It is owing to the same cause that glass screens, which entirely exclude the heat of a common fire, are permeable by the solar heat.

The results obtained by M. de Laroche have been confirmed by the experiments of M. Melloni on heat radiated from sources of different temperatures, whence it appears that the calorific rays pass less abundantly not only through glass, but through rock-crystal, Iceland spar, and other diaphanous bodies, both solid and liquid, according as the temperature of their origin is diminished, and that they are altogether intercepted when the temperature is about that of boiling water.

In fact, he has proved that the heat emanating from the sun or from a bright flame consists of rays which differ from each other as much as the coloured rays do which constitute white light. This explains the reason of the loss of heat as it penetrates deeper and deeper into a solid mass, or in passing through a series of plates; for, of the different kinds of rays which dart from a vivid flame, all are successively extinguished by the absorbing nature of the substance through which they pass, till those homogeneous rays alone remain which have the greatest facility in passing through that particular substance; exactly as in a red liquid the violet, blue, green, orange, and yellow rays are extinguished, and the red are transmitted.

M. Melloni employed four sources of heat, two of which were luminous and two obscure; namely, an oil-lamp without a glass, incandescent platina, copper heated to 696°, and a copper vessel filled with water at the temperature of 178¹/₂° of Fahrenheit. Rock-salt transmitted heat in the proportion of 92 rays out of 100 from each of these sources; but all other substances pervious to radiant heat, whether solid or liquid, transmitted more heat from sources of high temperature than from such as are low. For instance, limpid and colourless fluate of lime transmitted in the proportion of 78 rays out of 100 from the lamp, 69 from the platina, 42 from the copper, and 33 from the hot water; while transparent rock-crystal transmitted 38 rays in 100 from the lamp, 28 from the platina, 6 from the copper, and 9 from the hot water. Pure ice transmitted only in the proportion of 6 rays in the 100 from the lamp, and entirely excluded those from the other three sources. Out of 39 different substances, 34 were pervious to the calorific rays from hot water, 14 excluded those from the hot copper, and 4 did not transmit those from the platinum.

Thus it appears that heat proceeding from these four sources is of different kinds: this difference in the nature of the calorific rays is also proved by another experiment, which will be more easily understood from the analogy of light. Red light, emanating from red glass, will pass in abundance through another piece of red glass, but it will be absorbed by green glass; green rays will more readily pass through a green medium than through one of any other colour. This holds with regard to all colours; so in heat. Rays of heat of the same intensity, which have passed through different substances, are transmitted in different quantities by the same piece of alum, and are sometimes stopped altogether; showing that rays which emanate from different substances possess different qualities. It appears that a bright flame furnishes rays of heat of all kinds, in the same manner as it gives light of all colours; and, as coloured media transmit some coloured rays and absorb the rest, so bodies transmit some rays of heat and exclude the others. Rock-salt alone resembles colourless transparent media in transmitting all kinds of heat, even that of the hand, just as they transmit white light, consisting of rays of all colours. Radiant heat is unequally refracted by a prism of rock-salt like light, and the rays of heat thus dispersed are found to possess properties analogous to the rays of the coloured spectrum.

The property of transmitting the calorific rays diminishes to a certain degree with the thickness of the body they have to traverse, but not so much as might be expected. A piece of very transparent alum transmitted three or four times less radiant heat from the flame of a lamp than a piece of nearly opaque quartz about a hundred times as thick. However, the influence of thickness upon the phenomena of transmission increases with the decrease of temperature in the origin of the rays, and becomes very great when that temperature is low. This is a circumstance intimately connected with the law established by M. de Laroche; for M. Melloni observed that the difference between the quantities of heat transmitted by the same plate of glass, exposed successively to several sources of heat, diminished with the thinness of the plate, and vanished altogether at a certain limit; and that a film of mica transmitted the same quantity of heat, whether it was exposed to incandescent platinum or to a mass of iron heated to 360°.

Coloured glasses transmit rays of light of certain degrees of refrangibility, and absorb those of other degrees. For example, red glass absorbs the more refrangible rays, and transmits the red, which are the least refrangible. On the contrary, violet glass absorbs the least refrangible, and transmits the violet, which are the most refrangible. Now M. Melloni has found, that, although the colouring matter of glass diminishes its power of transmitting heat, yet red, orange, yellow, blue, violet, and white glass transmit calorific rays of all degrees of refrangibility; whereas green glass possesses the peculiar property of transmitting the least refrangible calorific rays, and stopping those that are most refrangible. It has therefore the same elective action for heat that coloured glass has for light, and its action on heat is analogous to that of red glass on light. Alum and sulphate of lime are exactly opposed to green glass in their action on heat, by transmitting the most refrangible rays with the greatest facility.

The heat which has already passed through green or opaque black glass will not pass through alum, whilst that which has been transmitted through glasses of other colours traverses it readily.

By reversing the experiment, and exposing different substances to heat that had already passed through alum, M. Melloni found that the heat emerging from alum is almost totally intercepted by opaque substances, and is abundantly transmitted by all such as are transparent and colourless, and that it suffers no appreciable loss when the thickness of the plate is varied within certain limits. The properties of the heat therefore which issues from alum nearly approach to those of light and solar heat.

Radiant heat in traversing various media is not only rendered more or less capable of being transmitted a second time, but, according to the experiments of Professor Powell, it becomes more or less susceptible of being absorbed in different quantities by black or white surfaces.

M. Melloni has proved that solar heat contains rays which are affected by different substances in the same way as if the heat proceeded from a terrestrial source; whence he concludes that the difference observed between the transmission of terrestrial and solar heat arises from the circumstance of solar heat containing all kinds of heat, whilst in other sources some of the kinds are wanting.

Radiant heat, from sources of any temperature whatever, is subject to the same laws of reflection and refraction as rays of light. The index of refraction from a prism of rock-salt, determined experimentally, is nearly the same for light and heat.

Liquids, the various kinds of glass, and probably all substances, whether solid or liquid, that do not crystallize regularly, are more pervious to the calorific rays according as they possess a greater refractive power. For example, the chloride of sulphur, which has a high refractive power, transmits more of the calorific rays than the oils, which have a less refractive power: oils transmit more radiant heat than the acids; the acids more than aqueous solutions; and the latter more than pure water, which of all the series has the least refractive power, and is the least pervious to heat. M. Melloni observed also that each ray of the solar spectrum follows the same law of action with that of terrestrial rays having their origin in sources of different temperatures; so that the very refrangible rays may be compared to the heat emanating from a focus of high temperature, and the least refrangible to the heat which comes from a source of low temperature. Thus, if the calorific rays emerging from a prism be made to pass through a layer of water contained between two plates of glass, it will be found that these rays suffer a loss in passing through the liquid as much greater as their refrangibility is less. The rays of heat that are mixed with the blue or violet light pass in great abundance, while those in the obscure part which follows the red light are almost totally intercepted. The first, therefore, act like the heat of a lamp, and the last like that of boiling water.

These circumstances explain the phenomena observed by several philosophers with regard to the point of greatest heat in the solar spectrum, which varies with the substance of the prism. Sir William Herschel, who employed a prism of flint glass, found that point to be a little beyond the red extremity of the spectrum; but, according to M. Seebeck, it is found to be upon the yellow, upon the orange, on the red, or at the dark limit of the red, according as the prism consists of water, sulphuric acid, crown or flint glass. If it be recollected that, in the spectrum from crown glass, the maximum heat is in the red part, and that the solar rays, in traversing a mass of water, suffer losses inversely as their refrangibility, it will be easy to understand the reason of the phenomenon in question. The solar heat which comes to the anterior face of the prism of water consists of rays of all degrees of refrangibility. Now, the rays possessing the same index of refraction with the red light suffer a greater loss in passing through the prism than the rays possessing the refrangibility of the orange light, and the latter lose less in their passage than the heat of the yellow. Thus the losses, being inversely proportional to the degree of refrangibility of each ray, cause the point of maximum heat to tend from the red towards the violet, and therefore it rests upon the yellow part. The prism of sulphuric acid, acting similarly, but with less energy than that of water, throws the point of greatest heat on the orange; for the same reason, the crown and flint glass prisms transfer that point respectively to the red and to its limit. M. Melloni, observing that the maximum point of heat is transferred farther and farther towards the red end of the spectrum, according as the substance of the prism is more and more permeable to heat, inferred that a prism of rock-salt, which possesses a greater power of transmitting the calorific rays than any known body, ought to throw the point of greatest heat to a considerable distance beyond the visible part of the spectrum,—an anticipation which experiment fully confirmed, by placing it as much beyond the dark limits of the red rays as the red part is distant from the blueish green band of the spectrum.

In all these experiments M. Melloni employed a thermomultiplier,—an instrument that measures the intensity of the transmitted heat with an accuracy far beyond what any thermometer ever attained. It is a very elegant application of M. Seebeck’s discovery of thermo-electricity; but the description of this instrument is reserved for a future occasion, because the principle on which it is constructed has not yet been explained.

In the beginning of the present century, not long after M. Malus had discovered the polarization of light, he and M. Berard proved that the heat which accompanies the sun’s light is capable of being polarized; but their attempts totally failed with heat derived from terrestrial, and especially from non-luminous sources. M. Berard, indeed, imagined that he had succeeded; but, when his experiments were repeated by Mr. Lloyd and Professor Powell, no satisfactory result could be obtained. M. Melloni resumed the subject, and endeavoured to effect the polarization of heat by tourmaline, as in the case of light. It was already shown that two slices of tourmaline, cut parallel to the axis of the crystal, transmit a great portion of the incident light when looked through with their axes parallel, and almost entirely exclude it when they are perpendicular to one another. Should radiant heat be capable of polarization, the quantity transmitted by the slices of tourmaline in their former position ought greatly to exceed that which passes through them in the latter, yet M. Melloni found that the quantity of heat was the same in both cases: whence he inferred that heat from a terrestrial source is incapable of being polarized. Professor Forbes of Edinburgh, who prosecuted this subject with great acuteness and success, came to the same conclusion in the first instance; but it occurred to him, that, as the pieces of tourmaline became heated by being very near the lamp, the secondary radiation from them rendered the very small difference in the heat that was transmitted in the two positions of the pieces of tourmaline imperceptible. Nevertheless he succeeded in proving, by numerous observations, that heat from various sources is polarized by the tourmaline; but that the effect with non-luminous heat is very minute and difficult to perceive, on account of the secondary radiation. Though light is almost entirely excluded in one position of the pieces of tourmaline, and transmitted in the other, a vast quantity of radiant heat passes through them in all positions. Eighty-four per cent. of the heat from an argand lamp passed through them in the case where light was altogether stopped. It is only the difference in the quantity of transmitted heat that gives evidence of its polarization. The second slice of tourmaline, when perpendicular to the first, stops all the light, but transmits a great proportion of heat; alum, on the contrary, stops almost all the heat, and transmits the light; whence it may be concluded that heat, though intimately partaking the nature of light, and accompanying it under certain circumstances, as in reflection and refraction, is capable of almost complete separation from it under others. The separation has since been perfectly effected by M. Melloni, by passing a beam of light through a combination of water and green glass, coloured by the oxide of copper. Even when the transmitted light was concentrated by lenses, so as to render it almost as brilliant as the direct light of the sun, it showed no sensible heat.

Professor Forbes next employed two bundles of laminÆ of mica, placed at the polarizing angle, and so cut that the plane of incidence of the heat corresponded with one of the optic axes of this mineral. The heat transmitted through this apparatus was polarized from a source whose temperature was even as low as 200°; heat was also polarized by reflection; but the experiments, though perfectly successful, are more difficult to conduct.

It appears, from the various experiments of M. Melloni and Professor Forbes, that all the calorific rays emanating from the sun and terrestrial sources are equally capable of being polarized by reflection and by refraction, whether double or single, and that they are also capable of circular polarization by all the methods employed in the circular polarization of light. Plates of quartz cut at right angles to the axis of the prism possess the property of turning the calorific rays in one direction, while other plates of the same substance from a differently modified prism cause the rays to rotate in the contrary direction; and two plates combined, when of different affection, and of equal thickness, counteract each other’s effects as in the case of light. Tourmaline separates the heat into two parts, one of which it absorbs, while it transmits the other; in short, the transmission of radiant heat is precisely similar to that of light.

Since heat is polarized in the same manner as light, it may be expected that polarized heat transmitted through doubly refracting substances should be separated into two pencils, polarized in planes at right angles to each other; and that when received on an analyzing plate they should interfere and produce invisible phenomena, perfectly analogous to those described in Section XXII. with regard to light (N.221).

It was shown, in the same section, that if light polarized by reflection from a pane of glass be viewed through a plate of tourmaline, with its longitudinal section vertical, an obscure cloud, with its centre wholly dark, is seen on the glass. When, however, a plate of mica uniformly about the thirteenth of an inch in thickness is interposed between the tourmaline and the glass, the dark spot vanishes, and a succession of very splendid colours are seen; and, as the mica is turned round in a plane perpendicular to the polarized ray, the light is stopped when the plane containing the optic axis of the mica is parallel or perpendicular to the plane of polarization. Now, instead of light, if heat from a non-luminous source be polarized in the manner described, it ought to be transmitted and stopped by the interposed mica under the same circumstances under which polarized light would be transmitted or stopped. Professor Forbes found that this is really the case, whether he employed heat from luminous or non-luminous sources: and he had evidence, also, of circular and elliptical polarization of heat. It therefore follows, that if heat were visible, under similar circumstances we should see figures perfectly similar to those given in Note 213, and those following; and, as these figures are formed by the interference of undulations of light, it may be inferred that heat, like light, is propagated by undulations of the ethereal medium, which interfere under certain conditions, and produce figures analogous to those of light. It appears also, from Mr. Forbes’s experiments, that the undulations of heat are longer than the undulations of light; and it has already been mentioned that Professor Draper considers them to be normal, like those of sound.

That light and heat are both vibrations of the ethereal medium is not the less true on account of the rays of heat being unseen, for the condition of visibility or invisibility may only depend upon the construction of our eyes, and not upon the nature of the motion which produces these sensations in us. The sense of seeing may be confined within certain limits. The chemical rays beyond the violet end of the spectrum may be too rapid, or not sufficiently excursive, in their vibrations, to be visible to the human eye; and the calorific rays beyond the other end of the spectrum may not be sufficiently rapid, or too extensive, in their undulations, to affect our optic nerves, though both may be visible to certain animals or insects. We are altogether ignorant of the perceptions which direct the carrier-pigeon to his home, or of those in the antennÆ of insects which warn them of the approach of danger; nor can we understand the telescopic vision which directs the vulture to his prey before he himself is visible even as a speck in the heavens. So, likewise, beings may exist on earth, in the air, or in the waters, which hear sounds our ears are incapable of hearing, and which see rays of light and heat of which we are unconscious. Our perceptions and faculties are limited to a very small portion of that immense chain of existence which extends from the Creator to evanescence.

The identity of action under similar circumstances is one of the strongest arguments in favour of the common nature of the chemical, visible, and calorific rays. They are all capable of reflection from polished surfaces, of refraction through diaphanous substances, of polarization by reflection and by doubly refracting crystals; their velocity is prodigious; they may be concentrated and dispersed by convex and concave mirrors; they pass with equal facility through rock-salt and are capable of radiation; and they are subject to the same law of interference with those of light: hence there can be no doubt that the whole assemblage of rays visible and invisible which constitute a solar beam are propagated by the undulations of the ethereal medium, and consequently as motions they come under the same laws of analysis.

When radiant heat falls upon a surface, part of it is reflected and part of it is absorbed; consequently, the best reflectors possess the least absorbing powers. The temperature of very transparent fluids is not raised by the passage of the sun’s rays, because they do not absorb any of them; and, as his heat is very intense, transparent solids arrest a very small portion of it. The absorption of the sun’s rays is the cause both of the colour and temperature of solid bodies. A black substance absorbs all the rays of light, and reflects none; and since it absorbs, at the same time, all the calorific rays, it becomes sooner warm, and rises to a higher temperature, than bodies of any other colour. Blue bodies come next to black in their power of absorption. And, since substances of a blue tint absorb all the other colours of the spectrum, they absorb by far the greatest part of the calorific rays, and reflect the blue where they are least abundant. Next in order come the green, yellow, red, and, last of all, white bodies, which reflect nearly all the rays both of light and heat. However, there are certain limpid and colourless media, which in some cases intercept calorific radiations and become heated, while in other cases they transmit them and undergo no change of temperature.

All substances may be considered to radiate heat, whatever their temperature may be, though with different intensities, according to their nature, the state of their surfaces, and the temperature of the medium into which they are brought. But every surface absorbs as well as radiates heat; and the power of absorption is always equal to that of radiation; for, under the same circumstances, matter which becomes soon warm also cools rapidly. There is a constant tendency to an equal diffusion of heat, since every body in nature is giving and receiving it at the same instant; each will be of uniform temperature when the quantities of heat given and received during the same time are equal—that is, when a perfect compensation takes place between each and all the rest. Our sensations only measure comparative degrees of heat: when a body, such as ice, appears to be cold, it imparts fewer calorific rays than it receives; and when a substance seems to be warm—for example, a fire—it gives more heat than it takes. The phenomena of dew and hoar-frost are owing to this inequality of exchange; the heat radiated during the night by substances on the surface of the earth, into a clear expanse of sky, is lost to us, and no return is made from the blue vault, so that their temperature sinks below that of the air, whence they abstract a part of that heat which holds the atmospheric humidity in solution, and a deposition of dew takes place. If the radiation be great, the dew is frozen and becomes hoar-frost, which is the ice of dew. Cloudy weather is unfavourable to the formation of dew, by preventing the free radiation of heat; and actual contact is requisite for its deposition, since it is never suspended in the air like fog. Plants derive a great part of their nourishment from this source; and, as each possesses a power of radiation peculiar to itself, they are capable of procuring a sufficient supply for their wants. The action of the chemical rays imparts to all substances more or less the power of condensing vapour on those parts on which they fall, and must therefore have a considerable influence on the deposition of dew. There may be a low degree of humidity in the air which may yet contain a great quantity of aqueous vapour, for vapour while it exists as gas is dry. The temperature at which the atmosphere can contain no more vapour without precipitation is called the dew point, and is measured by the hygrometer. In foretelling the changes of weather it is scarcely inferior to the barometer.

Steam is formed throughout the whole mass of a boiling liquid, whereas evaporation takes place only at the free surface of liquids, and that under the ordinary temperature and pressure of the atmosphere. There is a constant evaporation from the land and water all over the earth. The rapidity of the formation does not depend altogether on the dryness of the air; according to Dr. Dalton’s experiments, it depends also on the difference between the tension of the vapour which is forming, and that which is already in the atmosphere. In calm weather vapour accumulates in the stratum of air immediately above the evaporating surface, and retards the formation of more; whereas a strong wind accelerates the process by carrying off the vapour as soon as it rises, and making way for a succeeding portion of dry air.

Rain is formed by the mixing of two masses of air of different temperatures; the colder part, by abstracting from the other the heat which holds it in solution, occasions the particles to approach each other and form drops of water, which, becoming too heavy to be sustained by the atmosphere, sink to the earth by gravitation in the form of rain. The contact of two strata of air of different temperatures, moving rapidly in opposite directions, occasions an abundant precipitation of rain. When the masses of air differ very much in temperature, and meet suddenly, hail is formed. This happens frequently in hot plains near a ridge of mountains, as in the south of France, from the sudden descent of an intensely cold current of wind into a mass of air nearly saturated with vapour. Such also is the cause of the severe hail-storms which occasionally take place on extensive plains within the tropics.

An accumulation of heat invariably produces light: with the exception of the gases, all bodies which can endure the requisite degree of heat without decomposition begin to emit light at the same temperature; but, when the quantity of heat is so great as to render the affinity of their component particles less than their affinity for the oxygen of the atmosphere, a chemical combination takes place with the oxygen, light and heat are evolved, and fire is produced. Combustion—so essential for our comfort, and even existence—takes place very easily from the small affinity between the component parts of atmospheric air, the oxygen being nearly in a free state; but, as the cohesive force of the particles of different substances is very variable, different degrees of heat are requisite to produce their combustion. The tendency of heat to a state of equal diffusion or equilibrium, either by radiation or contact, makes it necessary that the chemical combination which occasions combustion should take place instantaneously; for, if the heat were developed progressively, it would be dissipated by degrees, and would never accumulate sufficiently to produce a temperature high enough for the evolution of flame.

It is a general law that all bodies expand by heat and contract by cold. The expansive force of heat has a constant tendency to overcome the attraction of cohesion, and to separate the constituent particles of solids and fluids; by this separation the attraction of aggregation is more and more weakened, till at last it is entirely overcome, or even changed into repulsion. By the continual addition of heat, solids may be made to pass into liquids, and from liquids to the aËriform state, the dilatation increasing with the temperature; and every substance expands according to a law of its own. Gases expand more than liquids, and liquids more than solids. The expansion of air is more than eight times that of water, and the increase in the bulk of water is at least forty-five times greater than that of iron. Metals dilate uniformly from the freezing to the boiling points of the thermometer; the uniform expansion of the gases extends between still wider limits; but, as liquidity is a state of transition from the solid to the aËriform condition, the equable dilatation of liquids has not so extensive a range. This change of bulk, corresponding to the variation of heat, is one of the most important of its effects, since it furnishes the means of measuring relative temperature by the thermometer and pyrometer. The rate of expansion of solids varies at their transition to liquidity, and that of liquidity is no longer equable near their change to an aËriform state. There are exceptions, however, to the general laws of expansion; some liquids have a maximum density corresponding to a certain temperature, and dilate whether that temperature be increased or diminished. For example—water expands whether it be heated above or cooled below 40°. The solidification of some liquids, and especially their crystallization, is always accompanied by an increase of bulk. Water dilates rapidly when converted into ice, and with a force sufficient to split the hardest substances. The formation of ice is therefore a powerful agent in the disintegration and decomposition of rocks, operating as one of the most efficient causes of local changes in the structure of the crust of the earth; of which we have experience in the tremendous Éboulemens of mountains in Switzerland. But Professor W. Thomson has proved experimentally that it requires a lower temperature to freeze water under pressure than when free.

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^[13] 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 32°. 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 140° 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 of electricity discharged, and is due to its excessive velocity and the violent compression of the air in its transit through the atmosphere. Prodigious quantities of heat are constantly absorbed or disengaged by the changes to which substances are liable in passing from the solid to the liquid and from the liquid to the gaseous form and the contrary, causing endless vicissitudes of temperature over the globe, and endless expansions and contractions, which are correlative terms for heat and cold, while radiation of heat is merely a transfer of motion from the particles on the surface of bodies to the adjacent particles of the atmosphere.

By the continual application of heat, that is of the expansive force, liquids are converted into steam or vapour, which is invisible and highly elastic. Under the mean pressure of the atmosphere, that is when the barometer stands at 30 inches, water in a boiler absorbs heat continually till it attains the temperature of the boiling point, which is 212° Fahrenheit. After that it ceases to show any increase of sensible heat; but when it has absorbed an additional 1000° of heat or expansive energy, that energy converts it into steam, and a condensing force equivalent to 1000° of heat reduces it again to water. Water boils at different temperatures under different degrees of pressure. It boils at a lower temperature on the top of a mountain than on the plain below, because the weight of the atmosphere is less at the higher station. There is no limit to the temperature to which water might be raised: it might even be made red hot, could a vessel be found strong enough to resist the pressure, for the intensity of the expansive force prevented from having effect by the extreme pressure of the boiler would be converted into sensible heat which might eventually render the water red hot. Thus, since the force of steam is in proportion to the temperature at which the water boils, or to the pressure, it is under control, and, perhaps with the exception of electricity, it is the greatest power that has been made subservient to the wants of man.

It is found that the absolute quantity of heat consumed in the process of converting water into steam is the same at whatever temperature water may boil, but that the absolute heat of the steam is greater exactly in proportion as its sensible heat is less. Thus, steam raised at 212° Fahrenheit under the mean pressure of the atmosphere, and steam raised at 180° under half the pressure, contain the same quantity of heat, with this difference, that the one has more absorbed heat and less sensible heat than the other. It is evident that, as the same quantity of heat is requisite for converting a given weight of water into steam, at whatever temperature or under whatever pressure the water may be boiled, therefore, in the steam engine, equal weights of steam at a high pressure and a low pressure are produced by the same quantity of fuel; and whatever the pressure of the steam may be, the consumption of fuel is proportional to the quantity of water converted into vapour. Steam of whatever tension expands on being set free, but the expansion of high pressure steam at the expense of its sensible heat is so great, that the hand may be plunged into it without injury the instant it issues from the orifice of a boiler. The steam becomes hotter by friction in issuing through the orifice which maintains it in its dry form, for there is no doubt that high-pressure steam is dry.

The elasticity or tension of steam, like that of common air, varies inversely as its volume—that is, when the space it occupies is doubled, its elastic force is reduced to one half. The expansion of steam is indefinite; the smallest quantity of water expanded into vapour will occupy many millions of cubic feet; a wonderful illustration of the minuteness of the ultimate particles of matter.

The force of steam, tremendous as the lightning itself when uncontrolled, is merely the result of chemical affinity: it is the chemical attraction between the particles of carbon, of coal or wood, and the oxygen of the atmosphere. Mr. Joule has ascertained that a pound of the best coal when burnt gives sufficient heat to raise the temperature of 8086 pounds of water one degree of the Centigrade thermometer, whence it has been computed by M. Helmholtz that the chemical force arising from the combustion of that pound of coal is capable of lifting a body of one hundred pounds weight to the height of twenty miles. That is the work performed by the heat arising from the combustion of a pound of coal. In all cases where work is produced by heat, a quantity of heat proportional to the work done is expended; and conversely, by the expenditure of a like quantity of work, the same amount of heat may be produced. The equivalence of heat and work is a law of nature. The mechanical force exerted by the steam engine for example is exactly proportional to the consumption of heat, nor more nor less; if we could produce a greater quantity than its equivalent we should have perpetual motion, which is impossible. Mechanical engines generate no force. We cannot create force; we can only avail ourselves of the inexhaustible stores of nature, the lightning, fire, water, wind, chemical action, &c. The quantity of mechanical power in nature is ever the same; it is never increased, it is never diminished, throughout the whole circuit of natural powers. The conservation of force is as permanent and unchangeable as matter. It may be dormant for a time, but it ever exists. We are unconscious of the enormous dynamic power that is either active or latent throughout the globe, because we do not attend to it. By the ebb and flow of the tide alone a power is exerted by which 25,000 cubic miles of water is moved over a quarter of the globe every twelve hours; and Professor W. Thomson has computed, by means of Pouillet’s data of solar radiation and Mr. Joule’s mechanical equivalent of heat, that the mechanical value of the whole energy active and potential of the disturbances kept up in the ethereal medium by the vibrations of the solar light within a cubic mile of our atmosphere is equal to 12,050 times the unit of mechanical force, that is to say, 12,050 times the force that would raise a pound of matter to the height of one foot, whence some idea may be formed of the vast amount of force exerted by the sun’s light within the limits of the whole terrestrial atmosphere. (N.223.)

The dynamic energy of the undulations of the solar light gives the leaves of plants the power of decomposing carbonic acid, and of separating the particles of carbon and hydrogen from the oxygen for which they have so strong an affinity. In this operation the undulations of the sunbeam are extinguished as light and heat, and Professor W. Thomson has proved that the quantity of these undulations thus extinguished is precisely equal to the potential or quiescent energy thus created, and that precisely that very quantity of light and heat is restored when the plants are burned, whatever state they may be in; and that thus, as Mr. George Stephenson^[14] has truly and beautifully observed, our coal fires and gas lamps restore to our use the light and heat of the sun of the early geological epochs which have rested as dormant powers under the seas and mountains for unnumbered ages. The sun is therefore the source of the mechanical energy of all the heat and motion of inanimate things, of all the motions of the heat and light of fires and artificial flames, and of the heat of all living creatures. For animal heat, and weights raised or resistance overcome, are mechanical effects of the chemical combination of food with oxygen; and food is either directly or indirectly vegetable, consequently dependent upon the sun.

Professor Helmholtz of Bonn has put in a strong point of view the enormous store of force possessed by our system by comparing it with its equivalent of heat. The force with which the earth moves in its orbit is such, that if brought to rest by a sudden shock, a quantity of heat would be generated by the blow equal to that produced by the combustion of fourteen such earths of solid coal; and supposing the capacity of the earth for heat as low as that of water, the globe would be heated to 11,200° Cent. It would be quite fused and for the most part reduced to vapour. If it should fall to the sun, which it would certainly do, the quantity of heat developed by the shock would be four hundred times as great.

The application of heat to the various branches of the mechanical and chemical arts has within the present century effected a greater change in the condition of man than had been accomplished in any equal period of his existence. Armed by the expansion and condensation of fluids with a power equal to that of the lightning itself, conquering time and space, he flies over plains, and travels on paths cut by human industry even through mountains with a velocity and smoothness more like planetary than terrestrial motion; he crosses the deep in opposition to wind and tide; by releasing the strain on the cable, he rides at anchor fearless of the storm; he makes the lightning his messenger; and like a magician he raises from the gloomy abyss of the mine the sunbeam of former ages to dispel the midnight darkness.

The principal phenomena of heat may be illustrated by a comparison with those of sound. Their excitation is not only similar but identical, as in friction and percussion; they are both communicated by contact and radiation; and Dr. Young observes that the effect of radiant heat in raising the temperature of a body upon which it falls, resembles the sympathetic agitation of a string when the sound of another string which is in unison with it is transmitted through the air. Light, heat, sound, and the waves of fluids are all subject to the same laws; their undulatory theories are perfectly similar: hence the interference of two hot rays must produce cold, that is, they must extinguish one another: darkness results from the interference of two undulations of light, silence ensues from the interference of two undulations of sound, and still water or no tide is the consequence of the interference of two tides. The propagation of sound, however, requires a much denser medium than that of light and heat; its intensity diminishes as the rarity of the air increases: so that, at a very small height above the surface of the earth, the noise of the tempest ceases, and the thunder is heard no more in those boundless regions where the heavenly bodies accomplish their periods in eternal and sublime silence.

A consciousness of the fallacy of our senses is one of the most important consequences of the study of nature. This study teaches us that no object is seen by us in its true place, owing to aberration; that the colours of substances are solely the effects of the action of matter upon light; and that light itself as well as heat and sound are not real beings, but mere motions communicated to our perceptions by the nerves. The human frame may therefore be regarded as an elastic system, the different parts of which are capable of receiving the tremors of elastic media, and of vibrating in unison with any number of superimposed undulations, all of which have their perfect and independent effect. Here our knowledge ends: the mysterious influence of matter on mind will in all probability be for ever hid from man.