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are corrections to be applied for absorption and reflection by parts of the apparatus, and by the medium through which the radiation. has passed. Before we can take up the study of the temperature of the sun, we must also consider what is called the Theory of Exchanges. Enunciated by Prevost towards the end of the eighteenth century and later elaborated by Balfour Stewart and Kirchhoff, the theory tells us (1) that any thermal equilibrium of an isolated body simply means equal giving and taking going on at the same time, (2) that good absorbers are good radiators, and so on. One branch of the theory deals with constant temperature enclosures. A body placed in a constant temperature enclosure acquires the temperature of the enclosure. The radiation in the enclosure has its energy distributed amongst the different waves in a certain definite way, dependent only on the temperature and independent of the nature of the enclosure. Such a stream of radiation is said to be 'full' radiation. It is identical in nature with the radiation from a heated lampblack surface at the same. temperature, and hence was at one time called 'black body' radiation. Bodies differ much in their radiating power; thus a polished platinum surface emits much less radiation than lampblack surface at the same temperature, but if a constant temperature enclosure were made of platinum or any other body and a narrow tunnel were made through the walls to let some of the radiation out, that radiation would be practically 'black body' or 'full' radiation and would equal that from a lampblack surface of the same size as the tunnel and raised to the same temperature. Much work has been done with black bodies of this construction to see how the intensity of full radiation depends upon the temperature of the radiator. A body placed in a constant temperature enclosure not only acquires the same temperature as the enclosure, but also absorbs and emits radiation in such a way that the quality of the radiation in all parts of the enclosure is kept absolutely uniform, and the amount per unit volume the same all over the enclosed space, this amount depending only on the temperature of the enclosure; and sometimes we even speak of the temperature of full radiation meaning the temperature of the lampblacked surface or of the

constant temperature enclosure which would supply exactly that same quality of radiation.

We have now to enquire into the relation between the amount of radiation from a surface and the temperature of that surface. The first law is due to Newton, who found out that the intensity of the stream of radiation from a hot body was proportional to the difference between the temperatures of the body and the surroundings; but it was soon found that this law was only approximately true. Dulong and Petit showed that a higher power of the temperature than the first was essential. Rosetti used nearly the third power, and in 1879 Stefan, working on some observational results of Tyndall's, showed that the radiation from a surface can be expressed by the formula

S = a T',

where T is the absolute temperature and a is a factor depending on the surface and the temperature. This law is known as the Law of Radiation or the Fourth Power Law. If the radiation is black-body radiation, a is a constant, and this constant has been evaluated most carefully by a large number of most refined experiments. Its value is 5.3 x 10 erg per sq. cm. per second per (degree). In the case of a platinum surface, the a is much smaller than the a of the lampblack surface, but if the temperature of the platinum is greatly increased the a of the platinum increases. and at very high temperatures, say, nearly two or three thousand degrees Centigrade, the a of the platinum approaches the black body a. In other words, all bodies tend to become 'full radiators' at high temperatures, a proceeding which is of great value in practical work on the measurement of the temperature of very hot bodies.


The radiating stream from a black body being given as aT', the absorption of the black body from its surroundings is given by aT ̧1, where T, is the temperature of the surroundings. The rate of cooling of the body is therefore given by a(TT). In the case of bodies of very high temperature, T1 is much greater than T., so that the formula aT can be used indiscriminately for the total stream and the balance of the output.

This fourth power law has been applied to the measurement of temperature by the aid of a simple radiation measurer known as Fery's Radiation Pyrometer. The stream of radiation from the black body, or from a tunnel dug into the mass of any body, is focussed by a gold-plated concave mirror upon a little thin blackened copper disc. The disc is warmed. Its temperature is measured by a delicate thermocouple, soldered to the back of the disc, and if readings are taken with two bodies at temperatures T, and 72, then obviously the galvanometers' readings C, and C, are in the ratio


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hence, if T, is known, T. can be found. The galvanometer scale can even be graduated to read 'black body' temperatures directly. In another form of the instrument, the copper disc is replaced by a spiral of compounded gold and silver strips, and the heating of the strips causes the spiral to wind or unwind, and the motion of a pointer fastened to the free end of the spiral indicates temperatures on a previously constructed scale. In both forms the instrument can be used by an ordinary workman, and one advantage that it has is, that its indications are independent, within wide limits, of the distance the pyrometer is away from the source of radiaion, as long as the image of the radiating source focussed by the mirror is larger than that of the copper disc or spiral upon which it falls. Thus the temperature of the sun may be taken by simply directing the instrument at the sun. At the same time, it may be necessary to introduce sector-diaphragms to cut down the amount of the radiation received, so that the pointer does not fly off the scales.

The distribution of the energy of a very hot body at some one temperature is shown in Fig. 1, and that through the spectrum of an incandescent gas in Fig. 2.

Lummer and Pringsheim investigated the energy distribution in the spectrum of a black body at different temperatures. The area under the intensity curve (Fig. 1) is a measure of the total

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energy output, and they showed that this area was proportional to the fourth power of the absolute temperature, thus confirming Stefan's Law. If we draw the tallest ordinate in Fig. 1, the corresponding abscissa gives us the wave-length of the particular waves which carry the maximum amount of energy. This wave


length is called Am When they investigated the energy distribution for black bodies of different temperatures they got curves like Fig. 3. Here each curve of a higher temperature lies wholly above the curve of a lower temperature. The areas under the curves are proportional to T1, and the next fact deduced was that

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as the temperature went up the wave-length of maximum energy decreased and decreased in such a way that the product, absolute temperature, was constant and equal to 2910, if Am is in microns and T in absolute degrees Centigrade. This law is known as the displacement law. It is important, for it affords a means of finding the temperature of the black body. For if in the energy distribution of any black body we find by some means the Am, we can get at once the temperature of the body by simple division.

We will now take up what is called the solar constant. The solar constant is the amount of energy which the sun sends per

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