The experimental work described in the present paper suggested itself to the writer in connection with an earlier investigation on the law governing the temperature variation of the complete photo-electric emission from a hot body, i. e. the photo-electric emission from a body in equilibrium with the full (black body) radiation corresponding to its temperature. By making use of hypotheses contained in the quantum theory, the writer obtained the following expression for the current per unit area C = AT (1+2kT/Ф+2k2T2/Ф2)e-Ф/kt, where Ф is the work done in removing an electron from the hot body, and is equal to hv, v being the lowest frequency of the radiation capable of producing a photo-electric emission, and h being Planck’s constant. The quantity k is the "gas constant” reckoned for one molecule, and A is a quantity independent of T, and characteristic of the substance. As the expression inside the brackets in the above formula does not differ appreciably from unity, the latter is substantially of the same type as Richardson’s equation C = ATλe-Ф/kT, (1) for the thermionic emission. Richardson* has also shown that it follows, from thermodynamic considerations, that this law governs the complete photo-electric emission. There is reason to believe that the thermionic emission is not wholly photo-electric in origin, but it is clear that some portion of it is the complete auto-photo-electric emission of the substance concerned, and that the law governing its temperature variation should be the same as that for the whole thermionic emission. We are thus led to expect that, when a body is exposed to an external source of full radiation, the same law will govern the variation of its complete photo-electric emission with the temperature of the source of the radiation. This expectation has been confirmed by experiments on the alloy of sodium and potassium, the description of which constitutes the subject of the present paper.