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The size of the hole in the screen S, and its distance from the radiomicrometer, then give the apparent area of bright carbon as seen from the latter.

The screen S is made of copper, and is really a flat box (Fig. 2)

FIG. 2.

provided with an inlet and an outlet tube, so that a continual stream of water from the ordinary house supply could be kept running through it a precaution necessary from its proximity to the In the experiments, a plentiful stream was kept running through this box, and thence on to the water-jacket round the radiator, the supply being sufficient to prevent any perceptible heating of the screen.

arc.

A small hole cut in the side of the wooden box enabled us, with the aid of mirrors, to use a pencil of the light of the arc for reflection from the mirror of the radio-micrometer, thus obviating the necessity of a lime-light, or other bright source, while an incandescent lampfilament provided us with an extremely sharp band of light on the scale of the radiator. (A larger and better mirror had been affixed to this since its use in our work on the solar temperature, and this mirror, with an incandescent lamp, gives a band of light with edges so sharp on the "temperature scale," that it could, if necessary, be read to the tenth of a millimetre, which is beyond our ordinary requirements.)

The theory of the method is very simple; essentially it is the same as that which applies to the estimation of the effective temperature of the sun, without the complications arising from atmospheric absorption, &c.

In the case of the sun, we can only hope to find (at least at present) the effective temperature, as we know little of the radiating power of the photospheric substances, but in the case of the carbons of the arc,

we may assume that we are dealing with a "black" surface of approximately unit emissive power.

Let then

T1 = absolute temperature of bare platinum-strip at balancing point,

e = ratio of emissive power of a black surface to that of the bare metallic surface at this temperature,

A = ratio of the area subtended by the platinum to that subtended by the glowing carbon, at the receiving surface of the radio-micrometer,

and q = ƒ(T) be the "law of radiation" for a black surface, where q = quantity of radiation as a function of the absolute temperature T1 of the radiating surface.

Then the radiation from the carbon is A/e times the intensity of that from a black surface at a temperature T1.

If the radiation from the platinum at the temperature T1 be put

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whence T2 may be obtained, when we know (1) the law of radiation, (2) the ratio of the emissive powers of bare and blacked platinum. We go on to discuss these two points together, as the experiments on the first give us information on the second.

The Law of Radiation and the Ratio of the Emissive Powers.

In our paper already quoted we have given a series of experiments on the radiation from bare platinum at temperatures up to 1600° C. approximately, and we have shown that a simple fourth-power law expresses the results very closely, so that for these experiments the "law of radiation is q = a(TT), where T = absolute temperature of radiating surface, To temperature of surrounding medium, a = a constant, and q = radiation in arbitrary units. At high temperatures To becomes unimportant, and the expression simplifies still further to q = aT1.

Experiments on a blackened surface are difficult to carry out at

anything beyond moderately low temperatures; we therefore assumed in our former work that the form of the law was the same for a blackened as for a bright surface, there being good grounds, both theoretical and experimental, for such a belief. Further investigations, however, indicate that this assumption is not correct, as will be seen from the experiments detailed below.

A series of experiments on the radiation from bare platinum was made first, exactly in the same way as those described in our work of last year, that is to say, the radiation from the platinum at different temperatures was allowed to fall on a radio-micrometer of the ordinary form, the sensibility of which was reduced sufficiently to give a readable deflection at the highest temperature used, the deflection as given by the scale-readings being then taken as proportional to radiation. This proportionality has been shown before to be strictly true for deflections up to and greater than those obtained in these experiments.

The platinum-strip was next blackened on one side with black oxide of copper, which was ground very fine, mixed up with methylated spirit, and laid on with a camel's-hair brush; this, when the liquid had dried off, gave a very good, even, dead-black surface, the emissive power of which may be taken as approximately equal to that of an ideal black surface.

Lampblack, of course, is useless for these experiments, since it burns off at something under 500° C.; it could only be used if the radiator could be placed in a vacuum, or in an atmosphere having no action on the carbon, for which purpose we are having apparatus specially constructed.

At about 900° C. the black oxide of copper begins to suffer a change; its surface becomes somewhat shiny, and an alloy is formed with the platinum; this puts a limit to the temperature at which the radiation may be taken as that of a "black" surface. Our first strip was spoiled in discovering this limiting temperature; the second strip (after calibration, &c., and radiation experiments with the metal bare) was covered on both sides and examined during the progress of the experiments, which was stopped as soon as the black surface showed any signs of change of physical condition; these were not only apparent to the eye, but were also immediately indicated by a variability of temperature, due to the alteration of emissive power, as the reduction of the oxide crept over the surface of the strip.

Platinum-black would have no advantages in this connection over the copper-oxide, as it reverts to the metallic condition at very nearly the same temperature as that at which the oxide changes in the way mentioned above.

The two series of experiments gave the figures in the following tables :

:

The 1st column gives the absolute temperature of the platinum.

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The same results are shown graphically in fig. 3, in which the curve is drawn from the formula through points denoted thus O, while the experimental points are denoted thus .

The curve for bare platinum was taken first, and a simple fourthpower law tried on it; this was found to agree very closely with the observed results throughout the range of the experiments, except at

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FIG. 3.-Curve showing the relation of radiation to temperature in the case of (1) bare platinum, (2) blacked platinum.

the lowest temperatures, thus confirming our work of last year, but in the case of the blacked platinum the curve is much less steep than that given by a fourth-power law. In fact, after several trials it was found that the exponent 34, in the expression q = aT followed the curve fairly well, but that a formula of the form

q = a (T3—T3)+b(Ta—T,1),

would fit both curves, the values of a and b being obtained from the respective experiments in the two cases.

In this expression, as before, q represents quantity of radiation, T the absolute temperature of the radiating surface, To the

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