The first part of this communication was devoted to a recapitulation of the advances in the Theory of Exchanges made by Stewart in 1858, and published in the Transactions of the Society for that year. Such a recapitulation it will be seen is necessary; as Stewart's papers seem either to have fallen into oblivion or to be deemed unworthy, of notice. It was pointed out that Stewart showed in these papers that the radiation within an impervious enclosure containing no source of heat must ultimately become, like the pressure of a non-gravitating fluid at rest, the same at all points and in all directions; but that this sameness is not, like that of fluid pressure, one of mere total amount; it extends to the quantity and quality of every one of the infinite series of wave-lengths involved. For, as one or more of the bodies may be black, the radiation is simply that of a black body at the temperature of the enclosure. Any new body, at the proper temperature, may be inserted in the enclosure without altering this state of things; and must therefore emit precisely the amount and quality which it absorbs. This remark contains all that is yet known on the subject. For we have only to assume for the purpose of reasoning, the existence of a substance partially, or wholly, opaque to one definite wave-length, and perfectly transparent to all others; or with any other limited properties we choose; and suppose it to be put (at the proper temperature) into the enclosure. If we next assume that its temperature when put in differs, from that of the enclosure, the experimental fact that, in time, equilibrium of temperature is arrived at, shows that the radiation of any particular wave-length by a body increases with rise of temperature. And so forth.