modifications-white malleable metal, and grey powder. The transition temperature is 20°, just a little above the average temperature of the air. The grey powder is the stable form below 20°. Hence it follows that all the malleable tin in the world, except on the hottest summer days, is in an unstable condition. It is only passive resistance of some kind which prevents all the tin vessels in the world slowly crumbling to powdered grey tin. § 6. Velocity of Transformation We have just seen that a crystal of sodium thiosulphate will make the unstable liquid thiosulphate pass into the stable form, so will the presence of a little grey tin facilitate the transformation of white into grey tin. This crumbling of tin to a grey powder is known as the tin pest. The disease is, therefore, infectious. The surface of a piece of diseased tin is shown in Fig. 3. The change is slow at ordinary temperatures. But articles of tin which have been buried a few hundred years are in almost every case in a more or less advanced state of disintegration. The comparative rigidity or immobility of the molecules of a solid offers a kind of frictional resistance to change, analogous to the action of a brake upon the wheels of a car. If it were not for passive resistance the speed of transformation from one allotropic form to another would be faster the more distant the temperature away from the transition-point. Experiment shows that the rate of transformation of white into grey tin increases as the temperature is reduced below the transition-point, 20°. At -50°, for instance, the transformation is very rapid. As a general rule, passive resistance increases as the temperature falls below the transition-point. The one effect works against the other. If be the prevailing temperature, we may write Velocity of change at 0° = transition temperature less è Or, if V denotes the velocity of transformation, R the magnitude of the passive resistance at 0°, and E the difference of the temperature between the transition point and 0°, we have— a result which bears a close formal analogy with Ohm's well-known law. It may be assumed that E also represents the amount of energy to be degraded in the process. This formula states in symbols the observed facts that the greater the value of E, the greater the velocity of transformation; and the greater the value of R, the less the velocity. These experiments teach us four important facts which must be clearly understood: (1) A substance may exist in two or more forms having different properties. (2) Only one of these forms is, in general, stable at any given temperature. (3) The transformation of a substance from its unstable to its stable form occupies time. (4) The transformation from the unstable to the stable form may be hindered or even arrested by passive resistance for an indefinite time. The phenomena are not always so obtrusive as the changes which take place with sulphur, tin, and mercury iodide. We naturally ask, how can we tell whether a substance is capable of existing in different allotropic forms? As a matter of fact, we select some physical property of the substance and measure it at different temperatures: if there is a sudden change in the physical property of the substance at any particular temperature, we infer that there is some drastic change going on in the internal structure of the substance. § 7. Cooling Curves Let the temperature of a cooling copper bar at 200° be measured every ten minutes. Let distances at right angles to the line 0°-200° (Fig. 4) represent 200 150 100% 50 20 40 60 Time FIG. 4.-Cooling Curve of Solid Copper. time, and vertical distances from the line 0-60, the corresponding temperatures of the bar. We thus obtain the series of points shown in Fig. 4. Draw a line so as to lie most evenly among the points. The result is a so-called cooling curve. The simple form of the cooling curve in Fig. 4 gives no evidence of any sudden change in the nature of the cooling copper. If a curve is drawn for water cooling down from |