ON THK CONDUCTION OF HEAT. 5 



ing experiments on vacuums of different degrees of imperfection, and tlience 

 computing the amount of error introduced by the action of a known quantity 

 of air. 



The result to which our authors arrived is expressed by the following law. 

 " When a body cools in vacuo, surrounded by a medium whose temperature 

 is constant, the velocity of cooling for excesses of temperature in arithmetical 

 progression increases as the terms of a geometrical progression, diminished 

 by a constant quantity." The formula which expresses the velocity of cool- 

 ing is ma {a — l), where a is the same for all bodies, viz. 1*0077 or 

 ^°/ri65, denotes the temperature (marked by the air-thermometer and 

 measured on the centigrade scale) of the vacuum in which the cooling body 

 is placed, and I the excess of the temperature of the body above 9. 



On cooling in air or in gases. — The hypothesis on which was computed 

 the velocity of cooling in air or any other gas, was, that the velocity might 

 be divided into two parts ; — the one, that due to direct radiation in vacuo ; 

 the other, that due to the actual presence of the gas. The gas was supposed 

 not to influence directly the process of radiation, but to act in aid of it by 

 conduction or convection, or a combination of both. Proceeding thus, MM. 

 Dulong and Petit first verified the observation of Leslie, " that the loss of 

 heat owing to the contact of a gas is independent of the state of the surface 

 of the body which cools." They showed next, " that the velocity of cooling 

 of a body, owing to the sole contact of 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 so long as the elasticity is 

 unaltered" They found also, "that the cooling power of a gas is, cceteris pa- 

 ribus, proportional to a certain power of its elasticity, but that the index of 

 the power varies for different gases;" and moreover, "that the velocities of 

 cooling due to a gas increase in geometrical progression as the excesses of 

 temperature increase in geometrical progression." 



We shall best understand the whole law of cooling by exhibiting it in the 

 shape of a single formula. It is as follows : 



Y -m.. 1-0077^ (1-0077^ - 1) -{- n eP h^'^^^, where m depends on the 

 nature of the surface, and n and p on the nature of the gas. is, as before, 

 the temperature of the gas, and + S that of the cooling body ; e, the elas- 

 ticity of the gas. 



If this be the law of nature, we can hardly term by the same word radiation 

 the loss of heat in vacuo, and the loss due to the action of the surrounding 

 air. We must therefore, for the present, confine our signification of this 

 term to the former, and admit that results deduced from the hypothesis of 

 radiation apply only to experiments carried on in a space free from air. 



b. Conduction. Ordinary experience teaches us that the power of con- 

 duction differs in different substances ; and it is natural to suppose, and has, 

 in fact, been universally admitted, that this difference is a difference in in- 

 tensity only. It is assumed that one and the same law holds good for all 

 bodies, but that a certain factor, on which the absolute amount of conduction 

 depends, differs accoi'ding to the nature of the substance. But to define the 

 law of conduction, which is the same for all substances, considerable diffi- 

 culty has been experienced. Lambert*, and the other early writers on the 

 subject, regarded the flow of heat as the flow of a fluid. But when we treat 

 the subject mathematically, and regard the flow of heat as the flow of an 



* Act. Helvet., vol. ii. p. 172. 



