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one-half but one-quarter. If the distance be three yards the quantity of heat is one-ninth, and so forth.

199. Interchange of heat among all bodies.-Owing to the radiation which is continually taking place in all directions round a body, there is a continual interchange of heat. If the bodies are all at the same temperature, each one sends to the surrounding ones a quantity equal to that which it receives, and their temperatures remain stationary. But if their temperatures are unequal, as the hot bodies emit more heat than they receive, they therefore sink in temperature; while, as the bodies of lower temperatures receive more heat than they emit, their temperature rises ; thus the temperatures are all ultimately equal. The radiation does not stop ; it goes on, but without loss or gain from each body, and this condition is accordingly known as the mobile equilibrium of temperature.

From what has been said it will be understood, that bodies, placed in our rooms, all tend to assume a uniform temperature ; generally speaking this is not the case, for many causes concur in cooling one set, and in heating the others. Thus bodies, placed near a wall, cooled by the exterior atmosphere, find a cause for cooling. Those, on the contrary, which are at the top, tend to acquire a higher temperature; for, as the air is always tending to rise as being less dense, the layers nearest the ceiling are always hotter than the lower ones.

From this continual interchange of heat, there is necessarily a limit to the cooling of bodies, for they always tend to resume, on the one hand, what they lose on the other. To have an indefinite cooling, a body should be suspended in space, not receiving heat from any body. As it then loses heat without acquiring any, there is no telling to what extent its temperature would sink.




200. Law of the reflection of heat.-- When the heat rays emitted by a source of heat fall upon the surface of a body, they are divided generally into two parts; one, which passes into the mass of a body and raises the temperature; the other, which darts


Reflection of Heat.


off from the surface like an elastic ball striking against a hard body; this is expressed by saying that these rays are reflected. Thus let A be a source of heat, a cubical box filled with hot water (fig. 170), and near it a screen which does not allow heat to pass, but near the bottom of which is an aperture. If behind this screen a polished surface be placed on which the rays emitted by the cube impinge, and beyond this again a differential thermometer, the latter indicates an increase of temperature when one of its bulbs is so placed that it receives the rays reflected by the polished body. In this experiment, rays like AB which fall on the reflecting surface are called

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Fig. 170. ncident rays, from a Latin word which signifies to fall; and the angle of incidence is not the angle which they make with the reflecting surface, but the angle, ABC, which they make with a right line, BC, perpendicular to this surface. In like manner the angle, CBD, which the reflected rays make with the same straight line, is called the angle of reflection.

The reflection of heat is always subject to the law, that the angle of reflection is equal to the angle of incidence. We shall subsequently see that the reflection of light is governed by the same law.

201. Reflection of heat from concave mirrors.—The effects of the reflection of heat may be very powerful when it takes place from the surface of concave mirrors, which are spherical surfaces of glass or of metal. These mirrors may be regarded as being made up of an infinite number of extremely small planes inclined towards each other in such a manner as to determine the curvature. From the symmetrical grouping of these small facets, it follows that when a group of rays fall upon a concave mirror, these rays, in obedience

to the laws of reflection coincide in a single point, to which the name focus is applied, to express the great quantity of heat which is concentrated there.

In treating of light we shall discuss in detail the properties of the focus in concave mirrors; for the present it will be sufficient to describe experiments which demonstrate the great intensity which radiant heat may acquire when concentrated in these points. Fig. 171 represents an experiment which is frequently made in physical lectures. Two reflectors, A and B (fig. 171), are arranged at a distance of 4 to 5 yards, and so that their axes coincide. In the focus of one of them, A, is placed a small basket, n, containing a red-hot


Fig. 171. iron ball. In the focus of the other, B, is placed an imflammable body, such as gun-cotton or phosphorus. The rays emitted from the focus, n, are first reflected from the mirror, A, in a direction parallel to the axis ; and impinging on the other mirror, B, are reflected so that they coincide in the focus m. That this is so, is proved by the fact that the inflammable substance placed in this point takes fire, which is not the case if it is above or below it.

The same effect may be produced by the sun's rays. For this purpose a concave reflector is so placed that the sun'srays strike directly against it (fig. 172), and if then a combustible substance, such as paper, wood, cork, etc., be held by means of a pincette in the focus, these bodies are seen to take fire. The effect produced depends on

-202] Reflecting Power of Substances. 197 the magnitude of the mirrors. With a mirror having an aperture of 6 feet, that is, the distance from one edge to the other, copper and silver are melted in a few minutes ; and silicious stones and flints are softened and even melted.

In consequence of the high temperature produced in the foci of concave mirrors and of the facility with which combustibles may be ignited, they have been called burning mirrors. It is stated that Archimedes burnt the Roman vessels before Syracuse by means of such mirrors. Buffon constructed burning mirrors of

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such power as to prove that the feat attributed to Archimedes was possible. The mirrors were made of a number of silvered plane mirrors about 8 inches long by 5 broad. They could be turned independently of each other in such a manner that the rays reflected from each coincided in the same point. With 128 mirrors and a hot summer's sun Buffon ignited a plank of tarred wood at a distance of 70 yards.

202. Reflecting power of various substances. It has been seen that heat which falls upon a body is always divided into two parts, one which is reflected on the surface, and the other which passes into the mass of the body, and raises its temperature. The quantities of heat thus absorbed, or reflected, vary in different substances; one set reflects much and the other little, which is expressed by saying that they have a great reflecting power ; others, on the contrary, reflect very little heat, but absorb a great deal, and are therefore spoken of as having great absorbing power. It is clear that these properties are the inverse of each other, for every body which absorbs much heat can reflect but little, and conversely.

In order to compare the reflecting powers of various substances, Leslie took as a source of heat a tin plate cube full of boiling water, which he placed in front of a concave mirror (fig. 173). The rays emitted from this towards the reflector tended after reflection to

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become concentrated on the focus F. In front of this were placed successively small square plates of paper, glass, metal, in short, of all the substances whose reflecting power was to be examined. As shown in the drawing, these rays, after a first reflection from the mirror, were reflected a second time from these plates, and finally impinged against the bulb of a differential thermometer. Now, as in this experiment the source of heat was the same, as was also the distance from the reflector, yet the thermometer indicated very various degrees of heat according to the material of which the small plates were formed. The temperature was highest when the

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