On the other hand, if a lamp-black surface be placed in the above position, since the stream of heat which flows from it is entirely independent of the reflection due to neighbouring bodies, the heat which it radiates when brought for a moment into an enclosure of lower temperature than itself will truly represent the stream of radiant heat due to the temperature of the lamp-black. 228. Suppose now that we have a thermometer with a blackened bulb, and that this is placed in a blackened enclosure of a lower temperature than itself, the heat which it radiates will represent the total radiation due to the temperature of the bulb, while that which it receives will represent the total radiation due to the temperature of the enclosure, and the difference between these two will thus be represented by the loss of heat experienced by the ther mometer. Thus, if be the temperature of the enclosure, and + 0 that of the bulb, then, since the stream of radiant heat (Art. 204) is a function of the temperature only, we shall have this stream represented by F (t + 0) and F (0) for these two temperatures, and the rate at which the thermometer loses heat will be denoted by F(+0) - F (0). This is the rate at which the instrument loses radiant heat, and it will also represent the rate at which it loses temperature, or the velocity of cooling, as this is termed, if we suppose that the specific heat (or heat required to produce a change of 1°) of the mercury of the thermometer remains the same for all the temperatures of the experiment. This, though not precisely, is very nearly the case, and hence the velocity of cooling of a thermometer placed in these circumstances may be regarded as representing with great accuracy the intensity of radiation. With these remarks we shall now discuss the experiments that have been made on velocity of cooling. VELOCITY OF COOLING; VARIATION WITH TEMPERATURE OF QUANTITY OF RADIATION. 229. Newton was the first to enunciate his views on the cooling of bodies. He supposed that a heated body exposed to a certain cooling cause would lose at each instant a quantity of heat proportional to the excess of its temperature above that of the surrounding air. It was, however, soon found that this law was not exactly followed, and several philosophers made experiments on the subject with more or less success, until the time of MM. Dulong and Petit, who made a very complete and successful investigation of the velocity of cooling of a thermometer both in vacuo and in air. It is with their experiments in vacuo that we have now to do. 230. The apparatus used by these experimentalists consisted of a hollow globe of thin copper with the interior blackened, which could be immersed in a vessel of water of known temperature. Through an orifice in this globe a thermometer could be inserted, so as to have its bulb in the centre of the globe. The temperature of this thermometer was always higher than that of the globe, and the number of degrees that the mercury would sink in a minute, supposing the cooling to be uniform during that time, was taken to denote the velocity of cooling. A preliminary set of experiments was first made, from which it appeared that the law of cooling of a liquid mass is independent of the nature of the liquid and of the form and size of the vessel which contains it. Having determined this, MM. Dulong and Petit proceeded to make their final experiments with a thermometer containing about 3 lbs. of mercury. In the first instance this thermometer preserved its natural vitreous surface, but since glass is exceedingly opaque towards the heat radiated at all the temperatures of the experiment, the results may be regarded as being nearly identical with those which a thermometer with a blackened bulb would have given. The following were the results obtained where the temperature of the enclosure was that of melting ice. We see at once from this table that the law of Newton does not hold, for according to it the velocity of cooling for an excess of 200° should be precisely double of that for an excess of 100°: now we find that it is more than three times as much. 231. In Dulong and Petit's experiments both the excess of temperature of the thermometer and also the absolute temperature of the enclosure were made to vary, that is to say, both and varied; and they obtained the following results. Now if we divide the numbers of the third column by the corresponding numbers of the second-for instance, 12.40 by 10.69—we find the quotient to be 1.16; and continuing the process for the other numbers in these columns, we find : 3rd column. 2nd column gives as quotients, 1.16, 1.18, 1.16, 1.15, 1.16, 1.17, 1.17, 1.18, 1.15. In like manner 4th column 3rd column gives as quotients, 1.16, 1.15, 1.16, 1.16, 1.17, 1.16, 1.17, 1.15, 1.16, 1.16. 5th column 4th column gives as quotients, 1.15, 1.16, 1.16, 1.15, 1.17, 1.16, 1.18, 1.16. 6th column 5th column gives as quotients, 1.15, 1.15, 1.16, 1.17, 1.16, 1.17, 1.17, 1.15. These numbers are all nearly the same, and their mean is 1.165. Hence we see that corresponding numbers in the various columns form a geometrical progression, so that if we denote a number in the second column by unity we shall have 1, 1.165, (1.165)2, (1.165)3, (1.165)*, as representing the velocities of cooling for the same excess of temperature for the cases where the temperature of the enclosure is denoted by 0°, 20°, 40°, 60°, and 80°. We are thus entitled to say that the velocity of cooling of a thermometer in vacuo for a constant excess of temperature increases in a geometrical progression when the temperature of the surrounding medium increases in an arithmetical progression, and the ratio of this progression is the same whatever be the excess of temperature. P 232. MM. Dulong and Petit soon saw that this remark would enable them to find the law of cooling. In the first place, it ought to be observed that the results already given are in accordance with the theory of exchanges, and that they form an additional proof of the truth of that theory. The theory of exchanges asserts that the loss of heat experienced by a thermometer cooling in vacuo is represented by the difference between the radiation due to the temperature of the thermometer and that due to the temperature of the enclosure. Hence, according to this theory, if A, B, C denote the absolute radiation at the temperatures a, b, c, of which a is the highest and c the lowest, then A-B will represent the rate of cooling of a ther mometer of temperature a in an enclosure of temperature b: B-C will represent the rate of cooling of a ther- A-C, or (A–B)+(B–C), that is to say, the sum the velocity of cooling is found to be 1.40. 2.171.40 = 3.57. Once more if a = 140° and c = 20° (t = 120°, 0 = 20°), we find from the same table that the velocity of cooling is 3.56. Now this is as nearly as possible equal to the sum of the two preceding rates, which was 3.57; so that the |