1. The experiments described in the following paper form part of an investigation with which one of the present authors has been engaged for many years past. The object of this investigation is the direct determination, in absolute measure, of the loss of energy, from a heated body to cooler surroundings, under differing conditions as to (1) the dimensions of the cooling body; (2) the nature of the surfaces of the cooling body and of the enclosure; (3) the mean absolute temperature of the cooling body and the envelope; (4) the nature of the atmosphere surrounding the cooling body. Several papers have already been published on this subject in the ‘Philosophical Transactions of the Royal Society’ and in the ‘Proceedings,’ and have been communicated to the British Association and elsewhere. In all of these the lowest temperature available was the atmospheric temperature, or rather the temperature of the water supply of the laboratory; and the body from which radiation was to take place was heated to a temperature as much above the atmospheric temperature as the circumstances connected with the experiment would, from time to time, permit. Thus the upper and lower limits of these experiments have been something below 1000° C. as the highest temperature of the cooling body, and, say, 10° C. as the lowest temperature of the enclosure. 2. Some time ago, through the kindness of Lord Blythswood, F. R. S., an unlimited supply of liquid air was placed at our disposal, to be followed later by a supply of liquid hydrogen. It seemed therefore most desirable to extend the research in the direction indicated by the new facilities given to us, which both greatly extended the limits governing the enquiry, and also made it possible to obtain determinations, in absolute measure, of thermal radiation between bodies at extremely low temperatures. It seemed specially interesting, for example, to determine, in absolute measure, the radiation under given circumstances from a body at, say, ordinary atmospheric temperature, to an enclosure at a temperature which may perhaps approximate to that of space. With the exception of some preliminary results, which were communicated 18 months ago to the British Association, nothing of the kind has been published, so far as we are aware.