132 



THEORY OF HEAT. 



[CHAP. III. 



lateral solids bounded, one by the plane C and the plane A 

 produced, the other by the plane B and the plane A pro- 



\c 



duced, have at all points the constant temperature 0, some 

 external cause maintaining them always at that temperature; 

 lastly, the molecules of the solid bounded by A, B and C have 

 the initial temperature 0. Heat will pass continually from the 

 source A into the solid BAG, and will be propagated there in 

 the longitudinal direction, which is infinite, and at the same 

 time will turn towards the cool masses B and C, which will ab 

 sorb great part of it. The temperatures of the solid BAG will 

 be raised gradually : but will not be able to surpass nor even 

 to attain a maximum of temperature, which is different for 

 different points of the mass. It is required to determine the 

 final and constant state to which the variable state continually 

 approaches. 



If this final state were known, and were then formed, it would 

 subsist of itself, and this is the property which distinguishes 

 it from all other states. Thus the actual problem consists in 

 determining the permanent temperatures of an infinite rect 

 angular solid, bounded by two masses of ice B and G, and a 

 mass of boiling water A ; the consideration of such simple and 

 primary problems is one of the surest modes of discovering the 

 laws of natural phenomena, and we see, by the history of the 

 sciences, that every theory has been formed in this manner. 



165. To express more briefly the same problem, suppose 

 a rectangular plate BA C, of infinite length, to be heated at its 

 base A, and to preserve at all points of the base a constant 



