SECT. I.] INTRODUCTION. 19 



to the quantity of heat taken as unit. This ratio is not the same 

 for all sections : it is a function $ (#) of the distance r, at which 

 the section is situated. It is required to find an analytical expres 

 sion of the function &amp;lt;f&amp;gt; (#). 



11. The foregoing examples suffice to give an exact idea of 

 the different problems which we have discussed. 



The solution of these problems has made us understand that 

 the effects of the propagation of heat depend in the case of every 

 solid substance, on three elementary qualities, which are, its capa 

 city for heat, its own conducMity, and the exterior conducibility. 



It has been observed that if two bodies of the same volume 

 and of different nature have equal temperatures, and if the same 

 quantity of heat be added to them, the increments of temperature 

 are not the same; the ratio of these increments is the, ratio of 

 their capacities for heat. In this manner, the first of the three 

 specific elements which regulate the action of heat is exactly 

 defined, and physicists have for a long time known several methods 

 of determining its value. It is not the same with the two others ; 

 their effects have often been observed, but there is but one exact 

 theory which can fairly distinguish, define, and measure them 

 with precision. 



The proper or interior conducibility of a body expresses the 

 facility with which heat is propagated in passing from one internal 

 molecule to another. The external or relative conducibility of a 

 solid body depends on the facility with which heat penetrates the 

 surface, and passes from this body into a given medium, or passes 

 from the medium into the solid. The last property is modified by 

 the more or less polished state of the surface ; it varies also accord 

 ing to the medium in which the body is immersed ; but the 

 interior conducibility can change only with the nature of the 

 solid. 



These three elementary qualities are represented in our 

 formulae by constant numbers, and the theory itself indicates 

 experiments suitable for measuring their values. As soon as they 

 are determined, all the problems relating to the propagation of 

 heat depend only on numerical analysis. The knowledge of these 

 specific properties may be directly useful in several applications of 

 the physical sciences ; it is besides an element in the study and 



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