ON THE CONDUCTION OF HEAT. 25 



leaving expense out of the question, the real practical obstacle is the presence 

 of the air. We have seen that the law of cooling into air is different from 

 that of radiation. Even supposing, therefore, -we were in possession of the 

 correct statement of that law, such would be the difficulty of obtaining for- 

 mulae from it, that to attempt to eliminate its effect, together with that of 

 radiation, is almost hopeless. If it can be done at all, it must be by means 

 of experiments carried on in air of different elasticities. It has been proved 

 by MM. Dulong and Petit, that " the velocity of cooling of a body due to 

 the sole contact in a gas, depends, for the same excess of temperature, on the 

 density and temperature of the gas ; but this dependence is such that the 

 velocity of cooling remains the same if the density and the temperature of 

 the gas change in such a way that the elasticity remains constant." The 

 effect, then, of the presence of the air is to introduce a term which involves 

 a power of the elasticity as one factor, and a function of the excess of tem- 

 perature as another. The latter function may be determined (perhaps) by 

 means of a number of experiments made at different elasticities. But we 

 should greatly prefer a set of experiments on radiation in vacuo. It appears 

 to us, that the difficulty in this case is very much the same as that against 

 which MM. Dulong and Petit had to contend in investigating the kindred 

 law of radiation ; and we should conceive that a similar contrivance to that 

 which they used might be adopted to overcome it. All that we require is, 

 that a certain portion of a bar heated at one extremity, radiate in vacuo, and 

 that the temperature at two of its points, the other extremity being one, be 

 capable of constant observation. MM. Dulong and Petit made use of a cop- 

 per balloon which could be exhausted of air, and by means of ice be kept 

 constantly to the freezing temperature, notwithstanding the radiation of the 

 heat from the body within it. A somewhat similar contrivance we conceive 

 would serve for the conduct of the experiment before us. The bar of metal 

 to be experimented on migiit pass through the balloon and be heated in air, 

 whilst the assumed point of heating might be marked by a thermometer in- 

 serted into a hole in the bar just within the balloon. We wish M. Biot had 

 marked his lowest point, not at the surface of the heated mercury, but at a 

 point a little above it ; it would have insured greater steadiness in the re- 

 sults. Should any one think of undertaking this experiment, we would 

 recommend that he extend his observations over a wider range of tempera- 

 tures than M. Biot has done. The thermometer which represents the heated 

 end of the bar should stand permanently at every 5°, from 0° to as high as 

 can be accomplished. It must be borne in mind, that two at least of the ob- 

 servations are requisite for the determination of the constants, except in the 

 case of formula li. The observations should likewise embrace a succession 

 of bars of different substances, iron, brass, lead, etc., all of the same dimen- 

 sions. Different series of observations should be made, in which the dimen- 

 sions of the bars have different constant magnitudes, and others in which they 

 have different lengths. All the substances might be coated with the same 

 varnish, so as to render their radiating powers the same. With such experi- 

 ments, we have no doubt that the law of conduction, although not like the 

 law of radiation, an inference from direct observation, might be readily esta- 

 blished, and the science of heat placed on the same footing with the other 

 mathematical sciences. We hope that the Association, in making known the 

 wants of this branch of philosophy, will induce some of the numerous distin- 

 guished experimental philosophers whose names appear on their list, to take 



an interest in this matter. „ ,^ 



r. Kelland. 



