The extension of the conception of temperature to a single monochromatic ray, just discussed, implies that at the same point in a medium, through which any rays whatever pass, there exist in general an infinite number of temperatures, since every ray passing through the point has its separate temperature, and, moreover, even the rays of different color traveling in the same direction show temperatures that differ according to the spectral distribution of energy.
In addition to all these temperatures there is finally the temperature of the medium itself, which at the outset is entirely independent of the temperature of the radiation. This complicated method of consideration lies in the nature of the case and corresponds to the complexity of the physical processes in a medium through which radiation travels in such a way.
It is only in the case of stable thermodynamic equilibrium that there is but one temperature, which then is common to the medium itself and to all rays of whatever color crossing it in different directions.
In practical physics also the necessity of separating the conception of radiation temperature from that of body temperature has made itself felt to a continually increasing degree. Thus it has for some time past been found advantageous to speak, not only of the real temperature of the sun, but also of an "apparent" or "effective" temperature of the sun, i.e., that temperature which the sun would need to have in order to send to the earth the heat radiation actually observed, if it radiated like a black body. Now the apparent temperature of the sun is obviously nothing but the actual temperature of the solar rays,On the average, since the solar rays of different color do not have exactly the same temperature. depending entirely on the nature of the rays, and hence a property of the rays and not a property of the sun itself. Therefore it would be, not only more convenient, but also more correct, to apply this notation directly, instead of speaking of a fictitious temperature of the sun, which can be made to have a meaning only by the introduction of an assumption that does not hold in reality.
Measurements of the brightness of monochromatic light have recently led L. Holborn and F. KurlbaumL. Holborn und F. Kurlbaum, Annal. d. Physik 10, p. 229, 1903. to the introduction of the concept of "black" temperature of a radiating surface. The black temperature of a radiating surface is measured by the brightness of the rays which it emits. It is in general a separate one for each ray of definite color, direction, and polarization, which the surface emits, and, in fact, merely represents the temperature of such a ray. It is, according to equation [eqn:(136)] (136), determined by its brightness (specific intensity), , and its frequency, , without any reference to its origin and previous states. The definite numerical form of this equation will be given below in [sect:166.] Sec. 166. Since a black body has the maximum emissive power, the temperature of an emitted ray can never be higher than that of the emitting body.