570 HEAT a metallic cubical vessel at a certain distance from the blackened bulb of a thermometer, and filling it successively with water at different temperatures, as for instance at 20, 30, and 40 ; the temperatures indicated by the ther- mometer will be in the same ratio as those of the vessel containing the water. The second law follows from the geometrical principle that the surface of a sphere increases as the square of its radius. Let c, fig. 2, be a centre of ra- diation ; it will emit a certain number of rays, all of which will fall upon the inner surface of the sphere a J, or in the absence of this, upon the inner surface of the sphere d e, which has a radius twice as great as a &. Therefore the same amount of heat will fall upon either of the spheres. But the outer sphere has a sur- face four times as great as the inner one ; there- fore it receives upon the same extent of sur- face only one fourth as much heat. The same law may be demonstrated experimentally, by a method invented by Tyndall. He placed a FIG. 3. Law of Inverse Squares. thermo-electric pile, S, fig. 3, in front of a rectangular vessel filled with hot water and having its face coated with lampblack. The pile is placed in the small end of a hollow cone, having its inner surface blackened, to prevent reflection. The distance of the pile from the vessel may be changed, but the quantity of heat received will be the same. If the distance at S' is twice that at S, the surface of the cir- cle A' B', whose rays fall upon the pile at S', will have twice the radius and four times the surface of the circle A B, whose rays fall upon the pile at S. The third law is demon- strated as follows : Place a cube, a, fig. 4, filled FIG. 4. with hot water, in front of a thermo-electric pile, P, and also place a screen, S S, with an opening, between the cube and the pile. If the cube is first placed with its face per- pendicular to the rays r, r, and is then turned upon its axis without changing the distance of the centre of its face, but giving it an ob- lique position, the amount of heat indicated by the pile will remain the same, although rays from a greater extent of surface on the cube will pass through the opening in the screen. All bodies are regarded as possessing a certain degree of that molecular motion which con- stitutes heat, and as always emitting rays of heat, no matter what their temperature may be. Every body is constantly receiving rays of heat from all other bodies within the limits of radiation, and is at the same time returning rays of heat to these bodies. But the hotter bodies emit rays of greater intensity than those which they receive, so that they all have a ten- dency to arrive at a condition of equilibrium. This is called the doctrine of exchanges, and was proposed by Prevost, a professor at Geneva about the year 1790, under the name of the " theory of mobile equilibrium of tempera- ture." If a body could be so placed that it should continue to radiate more heat than it absorbed, there would come a time when its vibrations would cease, and it would possess no heat whatever ; in other words, it would arrive at a state of absolute zero. Modern physicists have assumed such a theoretical zero, and have calculated it to be at 459-13 below the zero of Fahrenheit's scale, or 272'85 below that of the centigrade. Newton was the first to enunciate a law of cooling, which was that "the quantity of heat lost or gained by a body at each instant is proportional to the difference between its temperature and that of the surrounding medium ;" but it has been found not to be general, and only applies when the differences of temperature are not more than 15 or 20 C. ; beyond that the loss or gain is greater than the law requires. No definite results were obtained till Dulong and Petit made a series of elaborate investigations, in which they placed the thermometer both in vacua and in air. A large thermometer was used, containing about three pounds of mercu- ry, and was placed in the centre of a hollow globe of thin copper having its interior surface covered with lampblack, and kept at a uniform temperature by immersion in a vessel of water, the bulb of the thermometer being hotter than the globe. The following are the results ob- tained when the globe was at the temperature of melting ice : VELOCITY OF COOLING AT DIFFERENT TEMPERA- TURES. Excess of temperature, Velocity of cooling In degrees F. per minute. 10-69 896 . 8-S1 860 7-40 824 6'10 288 4-89 252 ... 8-88 216 8-02 180 . 2-80 144 .. . 1-74 It is thus shown that the velocity of cooling at 300 is more than three times as much as at
