OF ARTS AND SCIENCES. 143 



XII. 



NOTE OX THE DETERMINATION OF THE LAW OF PROPA- 

 GATION OF HEAT IN THE INTERIOR OF A SOLID 

 BODY. 



By B. O. Peirce, Jr. 



Presented April 11th, 1877. 



Newton's experiments upon the amount of heat communicated from 

 a body ^ to a neighboring body B, at a lower temperature than 

 A, led him to think that this amount was directly proportional to the 

 difference of temperature between the two bodies. In 180o. Biot, 

 assuminof that Newton's results were reliable, conceived that the same 

 law must hold for the communication of heat between two neighboring 

 molecules in the interior of a solid body, and he compared the observed 

 temperatures at different points of a long bar heated at one end with 

 the temperatures calculated on the assumption that the flux of heat 

 in the direction x is represented by 



dv 

 dx 



where y. is constant for the same body and v is the temperature of the 

 point under consideration. Fourier — whose " Tlieorie de la Chaleur " 

 was written in 1811, but not published until 1822 — followed Biot 



in assuming 



dv 

 dx 



to represent the flux of heat in the inside of a body, and 



7 dv 

 dx 



the radiation at its surface, where x and h are different constants which 

 he calls respectively the " conducibilite propre " and '• condiicibilite 

 relative a I'air atmospherique." Just before Fourier's work was 

 publijjhed, MM. Dulong «nd Petit showed that the amount of heat 

 communicated from one body to another depends not only upon the 



