^{page 12 note *} The idea of this experiment was derived from a remark of Professor Forbes, who suggested that several plates of rock-salt, the one behind the other, might be advantageously substituted for a thick plate of the same material, as giving the very same result.

^{page 13 note *} To take a numerical example, let us suppose the heat from a single plate of rock-salt to be = 1, then the heat from a plate four times the thickness, or (which is the same thing) the heat from four single plates, one behind another, should be nearly four times as much, or = 4 (if we suppose the heat from each of these four plates to be readily passed by the plates between it and the pile), but the heat from the fourfold plate, instead of being four times as much, is not double of the heat from the single plate; hence, the heat from any of the interior plates of the compound plate is passed with great loss, by the plates between it and the pile. Now, since the absorption of a plate equals its radiation, the reason why the fourfold plate scarcely radiates twice so much as the single one is, that it scarcely absorbs twice as much; and this again is due to the fact, that the heat after it has passed the first plate of the fourfold plate has become sifted, and passes with little diminution of intensity through the other three plates.

^{page 19 note *} This will be clearly seen if we consider only those rays that are radiated perpendicular to the surface in the case of two parallel plates of polished metal of the same description radiating to one another. For let r be the common radiation of the point C in direction CD, and of the point D in the direction DC, then since these radiations are bandied backwards and forwards in the directions CD, DC, until they are extinguished, we have the total quantity of heat falling on D in the direction CD (if ar denote the proportion of r reflected after one single reflection) expressed as follows:—

But 1 − a denotes the absorptive power of the metallic surface (all the heat not reflected being absorbed). Hence, since the radiative powers of bodies are proportional to their absorptive powers (Leslie's Inquiry), 1 being the absorptive power of lamp-black, the perpendicular radiation of a lamp-black point will be which is the very same expression we have obtained for the total heat radiated and reflected together, falling on D, in the same perpendicular direction from the metallic point C.