THE LAWS OF CONDUCTION OF HEAT IN BARS. 



99 



100. The flux of heat is greatest in the hottest part of the bar, because the 

 temperature of the bar varies most rapidly there, and the heat is more rapidly 

 drawn towards the cold end. To give exact expression to the tendency of the 



heat to traverse the section of the bar at C, we will take Cc to represent the 

 thickness of a plate, bounded by imaginary parallel surfaces, situated transversely 

 within the bar through which the flow of heat is to be considered. This is to 

 be compared with the flow of heat across any other plate, Gg, of equal thickness, 

 in a different part of the bar. Then, according to Fourier, the flow of heat 

 across Cc will be proportional to the small decrement of temperature F$, by 

 which the side of the plate nearest to A is hotter than the farther side, and to 

 the Conductivity jointly. The value of this decrement, F$, is evidently nothing 



else than the differential coefficient -r-, which has been given in the last Table, as 



derived from the equations to the curve of statical temperature in Art. 71. 



101. Hence (in conformity with Arts. 7, 31, and 35 of the first part of this 

 paper), 



dv 



Flux of heat, or area CFE = — — x conductivity, 



dx 



or 



Conductivity 



Area CFE 



dv 



dx 



§ V. — The Method of this paper applied, under the usual assumptions made in the Theory 

 of Conduction, as a first approximation to the determination of Conductivity. 



102. The area of the statical curve of cooling to the right hand of any ordi- 

 nate is therefore to be found. It will be convenient, for this purpose, to show 

 what the nature of this curve would be were theusual assumptions of the mathe- 

 matical theory of Heat adopted. These assumptions are (1.) That the superficial 



