three distinct cases. Let F denote degrees of Fahrenheit's scale, C degrees of the Centigrade, and R degrees of Reaumur; then

CASE 1.-For all temperatures above the freezing point, F 32

= R.

=

=

C.

CASE 2.-For all temperatures between the freezing point and the zero of Fahrenheit's scale, 32- F = - C - 4 R.

CASE 3.-For all temperatures below the zero of Fahrenheit, - 3 C = — 4 R."]

- 32 F

In different countries other divisions are used, adjusted, however, by the same fixed points. The Centigrade thermometer has, for the melting of ice, 0, and for the boiling of water, 100°, with the intervening space divided in 100 equal degrees. In Reaumur's thermometer, the lower point is marked

0, and the upper 80°.

The philosophical fact upon which the construction of the thermometer reposes, is, that quicksilver expands by an increase of heat, and is contracted by a diminution of it; and further, that these expansions and contractions are in proportion to the changes of temperature.

But for particular purposes thermometers have been made of oil, of alcohol, and of a great many other liquid bodies, and give rise to the same general results. As a uniform law it may therefore be asserted that all liquids dilate as their temperature rises, and contract as it descends.

But heat determines the volume of gases as well as of liquids. If we take a tube, a, Fig. 297, with a bulb at its upper extremity, b, and having partly

filled the tube with a column of water, coloured, to make its movements visible, the lower end dipping loosely into some of the same coloured water, contained in a bottle, c; on touching the bulb, b, the coloured liquid in the tube is pressed down by the dilation of the air, and on cooling the bulb the liquid rises, because the air contracts. And were the bulb filled with any other gaseous substance, such as oxygen, hydrogen, &c., still the same thing would take place. So gases, like liquids, expand as their temperature rises, and contract as it descends.

Such an instrument as Fig. 297 passes under the name of an Air Thermometer. Its indications are not altogether reliable, as may be proved by putting it under an air-pump receiver, when Fig. 297. its column of liquid will instantly move as soon as the least change is made in the pressure of the air. It is affected, therefore, by changes of pressure as well as changes of temperature.

There is, however, a form of air thermometer which is free from this difficulty. It is the Differential Thermometer. This instrument consists of da tube, a b, Fig. 298, bent at right angles towards its ends, which terminate in two bulbs, c d. In the horizontal part of the tube is a little column of liquid marked by the black line, which serves as an index. If the bulb c is touched by the hand, its air dilates and presses the index column over the scale; if dis touched the same thing takes place, but the column moves the opposite way; if both bulbs are touched at once, then the column, pressed equally in opposite directions, does not move at all. Of course, a similar reasoning

Fig. 298.

applies to the cooling of the bulbs. The instrument is therefore called a differential thermometer, because it indicates the difference of temperature between its bulbs, but not the absolute temperature to which it is exposed. In the same manner that we have thermometers, in which the changes of volume of liquids and gases are employed, to indicate changes of temperature, so, too, we have others in which solids are used. These generally consist of a strip of metal which is connected with an arrangement of levers or wheels, by which any variations in its length may be multiplied. The disturbing agencies, thus introduced by this necessary mechanism, interfere very much with the exactness of these instruments. And hitherto they have not been employed, except for special purposes, and can never supplant the mercurial thermometer.

It being thus established that all substances, gases, liquids, and solids, expand as their temperature rises, and contract as it falls, it may next be remarked that great differences are detected when different bodies of the same form are compared. There are scarcely two solid substances which, for the same elevation of temperature, expand alike. All do expand; but some more and some less. In the case of crystalline bodies, even the same substance expands differently in different directions. Thus a crystal of Iceland spar dilates less in the direction of its longer than it does in the direction of its shorter axis. The same holds good for liquids. If a number of thermometers, b c, Fig. 299, of the same size be filled with different liquids, and all plunged in the same vessel of hot water, f, so as to be warmed alike, the expansion they exhibit will be very different. Until recently it was believed that all gases expand alike for the same changes of temperature; but it is now known that minute differences exist among them in this respect. For every degree of Fahrenheit's thermometer atmospheric air expands of its volume at 32°.

Fig. 299.

a

Gases, liquids, and solids compared together, for the same change of temperature, exhibit very different changes of volume; gases being the most dilatable, liquids next, and solids least of all. This probably arises from the fact that the cohesive force, which is the antagonist of heat, is most efficient in solids, less so in liquids, and still less in gases.

CHAPTER LXIX.

OF RADIANT HEAT.

Path of Radiant Heat-Velocity of Radiant Heat-Effects of SurfaceLaw of Reflection-Reflection by Spherical Mirrors-Theory of Exchanges of Heat-Diathermanous and Athermanous Bodies-Properties of Rock Salt-Imaginary Colouration.

EXPERIENCE shows that whenever a hot body is freely exposed its temperature descends, until eventually it comes down to that of the surrounding bodies. There are two causes which tend to produce this result. They are radiation and conduction.

All bodies, whatever their temperature may be, radiate heat from their surfaces. It passes forth in straight lines, and may be reflected, refracted, and polarised like light.

The rate at which radiant heat moves is the same, in all probability, as the rate for light. It has been asserted that its velocity is only four-fifths that of light; but this seems not to rest upon any certain foundation.

As respects the rapidity or facility with which radiation takes place, much depends on the nature of the surface. The experiments of Leslie show

M

that, at equal temperatures, such as are smooth are far less effective than such as are rough. This result he established by taking a cubical metallic vessel, c, filled with hot water, the four vertical sides being in different physical conditions-one being polished, a second slightly roughened, a third still more so, and the fourth roughened and blackened. Under these circumstances, the rays of heat escaping from each surface, as it was turned in succession toward a metallic reflector, M, raised a thermometer, d, placed in the focus, to very different degrees, the polished one producing the least effect.

Fig. 300.

Just as light is reflected, so, too, is heat. If we take a plate of bright tin, and hold it in such a position as to reflect the light of a clear fire into the face, as soon as we see the light we also feel the impression of the heat. The law for the one is also the law for the other "the angle of reflection is equal to the angle of incidence"-and consequently mirrors with curved

e

surfaces act precisely in one case as they do in the other. We have already shown, Chapter XXXVI., how rays diverging from the focus of a mirror are reflected parallel, and how parallel rays falling on a mirror are converged. And it is upon that principle that we account for the following striking experiment. In the focus of a concave metallic mirror let there be placed a red-hot ball, a, Fig. 301; the rays of heat diverging from it in right lines, a c, a d, a e, a f, will be reflected parallel in the lines c g, d h, e i, f k, and, striking upon the opposite mirror, will all converge to b, in its focus. If, therefore, at this point any small combustible body, as a piece of phosphorus, be placed, it will instantly take fire, though a distance of twenty or fifty feet may intervene between the mirrors. Or, if the bulb of an air thermometer be used instead of the phosphorus, it will give at once the indication of a rapid elevation of temperature.

Fig. 301.

But this is not all; for if, still retaining the thermometer in its place, we remove away the red-hot ball and replace it by a mass of ice, the thermometer instantly indicates a descent of temperature-the production of cold. At one time it was supposed that this was due to cold rays which escaped from the ice, after the same manner as rays of heat; but it is now admitted that the effect arises from the circumstance that the thermometer

bulb, being warmer than the ice, radiates its heat to the ice, the temperature of which ascends precisely in the same manner as that in the former experiment; the red-hot ball, being the warmer body, radiated its heat to the thermometer.

In fact, these experiments are nothing more than illustrations of a theory which passes under the name of "The Theory of the Exchanges of Heat." This assumes that all bodies are at all times radiating heat to one another; but the speed with which they do this depends upon their temperature, a hot body giving out heat much faster than one the temperature of which is lower. Thus, if we have a red-hot ball and a thermometer bulb in presence of one another, the ball, by reason of its high temperature, will give more heat to the bulb than it receives in return; its temperature will therefore descend while that of the bulb rises. But if the same bulb be placed in presence of a mass of ice, the ice will receive more heat than it gives, because it is the colder body of the two, and the temperature of the thermometer therefore declines.

All bodies are at all times radiating heat, their power of radiation depending on their temperature, increasing as it increases, and diminishing as it diminishes.

As is the case. with light, so, too, with heat; there are substances which transmit its rays with readiness, and others which are opaque. We therefore speak of diathermanous bodies, which are analogous to the transparent, and athermanous, which are like the opaque. Among the former, a vacuum

and most gaseous bodies may be numbered; but it is remarkable that substances which are perfectly transparent to light are not necessarily so to heat. Glass, which transmits, with but little loss, much of the light which falls on it, obstructs much of the heat; and, conversely, smoky quartz and brown mica, which are almost opaque to light, transmit heat readily. But of all solid substances, that which is most transparent to heat, or most diathermanous, is rock salt; it has therefore been designated as the glass of radiant heat. If a prism be cut from this substance, and a beam of radiant heat allowed to fall upon it, it undergoes refraction and dispersion precisely as we have already described as occurring under similar circumstances with a glass prism for light in Chapter XXXIX. And if convex lenses be made of rock salt they converge the rays of heat to foci, at which the elevation of temperature may be detected by the thermometer. Heat, therefore, can be refracted and dispersed as easily as it can be reflected.

If we take a convex lens of glass and one of rock salt, and cause them to form the image of a burning candle in their foci, it will be found on examination that the image through the rock salt is hot, but that through the glass can scarcely affect a delicate thermometer. This experiment sets in a clear light the difference in the relations between glass and salt, the former permitting the light to pass, but not the heat, the latter transmitting both together.

When light is dispersed by a prism, the splendid phenomenon of the spectrum is seen. But, in the case of heat, our organs of sight are constituted so that we cannot discover its presence, and therefore fail to see the corresponding result. But it is now established beyond all doubt, that in the same manner that there are modifications of light giving rise to the various coloured rays, so, too, there are corresponding qualities of radiant heat. Moreover, it has been fully proved that, as stained glass and coloured

solutions exert an effect on white light, absorbing some rays and letting others pass, the same takes place also for heat. In the case we have already considered-of the imperfect diathermancy of glass-the true cause of the phenomenon is the colouration which the glass possesses as respects the rays of heat, and inasmuch as a substance may be perfectly transparent to one of these agents and not so to the other, so, also, a body may stop or absorb a given ray for the one, and a totally different one for the other. Glass allows all the rays of light to pass almost equally well, but it obstructs almost completely the blue rays of heat. The colouration of bodies, which has already been described as arising from absorption, may, therefore, be wholly different in the two cases; and as our organs do not permit us to see what it is in the case of heat, and we have to rely on indirect evidence, we speak of the imaginary or ideal colouration of bodies.

If heat, like light (as there are reasons for believing), arises in vibratory movements which are propagated through the ether, all the various phenomena here described can be readily accounted for. The undulations of heat must be reflected, refracted, inflected, undergo interference, polarisation, &c., as do the undulations of light, the mechanism being the same in both

cases.

CHAPTER L.

CONDUCTION AND EXPANSION.

Good and Bad Conductors of Heat-Differences among the Metals-Conduction and Circulation in Liquids-Point of Application of Heat-Case of Gases Expansion of Gases, Liquids, and Solids-Irregularity of Expansion in Liquids and Solids-Regularity of Gases.

WHEN one end of a metallic bar is placed in the fire, after a certain time the other has its temperature elevated, and the heat is said to be conducted. It finds its way from particle to particle,—from those that are hot to those that are cold.

But if a piece of wood or of earthenware be submitted to the same trial, a very different result is obtained. The further end never becomes hot; proving, therefore, that some bodies are good and others bad conductors of heat.

The rapidity with which this conduction from particle to particle takes place, depends, among other things, upon their difference of temperature. Thus, when the bulb of a thermometer is plunged in a cup of hot water, for the first few moments its column runs up with rapidity; but as the thermometer comes nearer to the temperature of the water, the heat is transmitted to it more slowly.

Of the three classes of bodies, solids are the best conductors, liquids next, and gases worst of all. Of solids, the metals are the best, and among the metals may be mentioned gold, silver, copper. Among bad solid conductors we have charcoal, ashes, fibrous bodies-as cotton, silk wool, &c.