THE LAWS OF CONDUCTION OF HEAT IN BARS. 95 



sensible irregularities, depending on the primitive distribution of heat in the bar, 

 and on the want of uniformity in the temperature of its transverse section. The 

 nearer that we approach to the ideal of an infinitely slender bar, the more shall 

 we escape those periodical irregularities (see Art. 25 of the former part of this 

 paper), arising from the primitive distribution of heat in its substance, which no 

 doubt gives rise to some of the peculiarities of the inflections in the curves 

 of " rates of cooling." In particular, we may naturally ascribe, in part at 

 least, to the fact that the bar is heated first of all to a uniform temperature 

 throughout in the fusible metal bath, the relatively diminished rate of cooling 

 observed at the highest temperatures. At the same time I would repeat the 

 caution, that the hypothetical or dotted portion of those curves cannot be relied 

 on as expressing an actual fact, at least to more than a little way beyond the 

 range of experiment. 



§ III. On the Proportion of Heat dissipated from the Bar by Radiation and Convection. 



91. Although not of direct importance to the determination of conducting 

 power, I will indicate shortly how the numbers in Table VII., may be used to 

 ascertain the relative amount of heat lost by radiation and convection at any or 

 all points of the surface of the bar in Cases I. and II. The method was originally 

 due to Sir John Leslie, but was stated more clearly by Dalton (System of 

 Chem. Philosophy, p. 115), and was happily applied by Dulong and Petit. 

 Suppose the total " rate of cooling" of the same bar to be ascertained in air, first. 

 when it is naked, and, secondly, when covered with paper, and let the ratio of 

 the first case to the second be as 1 : p. Next, by comparing after the manner of 

 Leslie's canister-experiments the " emissive power" of the same two surfaces, 

 iron and paper, let it be as 1 : q. Let the required ratio of the heat lost by con- 

 vection to that lost by radiation be as 1 : x in the first case ; then, of course, it 

 will be in the proportion of 1 : qx in the second. But as the heat dissipated in 

 each case is the sum of the effects due to convection (which is always = 1), and 

 that due to radiation, we have 



and 



1 : p — \ + x : 1 + qx 



p-1 



x = 



9—P 



92. I have given in Table VII. the ratios of cooling, at different temperatures, for 

 Cases I. and II. , that is, for the same bar covered with paper and naked iron ; 

 and though the ratios vary somewhat,* yet they agree pretty nearly within the 



* Since this was written, I have observed that a like diminution of the ratios of cooling from glass 

 and silver up to a certain point, and afterwards an increase, was noticed .by Dulong and Petit, in 

 their admirable Memoir on the Law of Cooling, page 102. — Mem. Acad. Sci. Par. 



