CHAPTER II 

 Transmission of Heat through Solid Bodies. 



When a solid body is limited by two parallel surfaces, main- 

 tained at temperatures constant but different, it is traversed by a 

 constant flow of heat proportional to the distance between these 

 two surfaces. This law may be deduced from the very nature it- 

 self of the movement of heat. Consider a homogeneous plate, 

 of thickness <?, of unit superficial area, and of which the surfaces 

 are maintained at the constant temperatures / and /, imagine the 

 thickness of the plate to be divided into a very great number of 

 extremely thin layers. The entire thickness of the plate being 

 obviously traversed simultaneously by a quantity of heat equal to 

 that which traverses any part whatsoever of its thickness, an 

 equal quantity of heat must pass simultaneously through each of 

 the elementary layers in question, then, since for any particular 

 body the quantity of heat transmitted can only depend on the 

 thickness, and on the difference of temperature, and since the 

 thicknesses are the same, it follows necessarily that the differences 

 of temperature of the surfaces of the elementary layers are the 

 same, and in consequence, that throughout the thickness of the 

 plate the temperature varies uniformly from / to /. As the quan- 

 tity of heat which traverses any layer is the same as that which 

 traverses any number whatsoever of layers, and since the differ- 

 ence of temperature of the outer surfaces is proportional to the 

 number of layers, and as the thickness is also proportional to the 

 number of layers, the equality in question can only exist as long 

 as the flow of heat is proportional to the total thickness, and we 

 have 



M= 



In this expression M represents the quantity of heat trans- 

 mitted by unit surface in unit time, /and/' the temperatures of 

 the two surfaces, e the thickness of the plate and Cthe conductiv- 



47 



