48 Emission and Transmission of Heat 



ity of the material, that is to say the value of M for / /'=i and 



This formula has been verified by experiment. 



We will first examine the conductivity of bodies which trans- 

 mit heat well, that is to say the metals, and then the conductivity 

 of bodies which transmit heat poorly. 



CONDUCTIVITY OF METALS 



827. When one end of a bar of metal is maintained at a con- 

 stant temperature, heat is transmitted along the bar and is dissi- 

 pated from its surface. If we suppose the bar to be so long that 

 the heat does not reach its farther extremity, and its section to be 

 so small that all the points of the same section have sensibly the 

 same temperature, we may readily find by calculation, for the 

 excess of temperature^ of any section above that of the air, at a 

 distance x from the extremity, the relation, 



\~Ph~' 



y=Ae 



in which A represents the constant excess of temperature of the 

 heated extremity over that of the air, 5" the section of the bar, P 

 its circumference, h its coefficient of cooling, and C the conduc- 

 tivity of the bar. 



828. In i8i6M. Biot verified the truth of this formula by 

 numerous experiments (Traite de Physique, 1816). Later in 

 1836 M. Despretz made further experiments which confirmed those 

 of M. Biot and which permitted him to determine the relative con- 

 ductivity of the metals, given in the following table:* 



Silver . . . 1000 Iron 119 



Copper . . . 736 Steel 116 



Gold . . . 532 Lead 85 



Tin .... 145 Plantinum ... 84 



829. These numbers cannot however be considered very ex- 

 act since to begin with, Newton's Law on which the formula 

 (827) depends, departs too far from the truth when the excesses of 

 temperature are considerable, and further because in measuring 

 the temperatures of the various sections of the bar holes were 



* The table given here is from more recent experiments of Frantz and Wiedermann 

 inwhich the errors due to boring holes in the bars were avoided by the use of thermo- 

 piles. 



