SECT. IV.] 



UNIFORM LINEAR MOVEMENT. 



decreases in arithmetic progression from the fixed temperature 

 of the lower plane to the fixed temperature of the upper plane. 



The final temperatures are those which would have to be 

 given to the solid in order that its state might be permanent ; 

 the variable state which precedes it may also be submitted to 

 analysis, as we shall see presently: but we are now considering 

 only the system of final and permanent temperatures. In the 

 last state, during each division of time, across a section parallel 

 to the base, or a definite portion of that section, a certain 

 quantity of heat flows, which is constant if the divisions of time 

 are equal. This uniform flow is the same for all the intermediate 

 sections ; it is equal to that which proceeds from the source, and 

 to that which is lost during the same time, at the upper surface 

 of the solid, by virtue of the cause which keeps the temperature 

 constant. 



67. The problem now is to measure that quantity of heat 

 which is propagated uniformly within the solid, during a given 

 time, across a definite part of a section parallel to the base : it 

 depends, as we shall see, on the two extreme temperatures a 

 and b, and on the distance e between the two sides of the solid ; 

 it would vary if any one of these elements began to change, the 

 other remaining the same. Suppose a second solid to be formed 

 of the same substance as the first, and enclosed between two 



I 



Fig. 2. 



infinite parallel planes, whose perpendicular distance is e (see 

 fig. 2) : the lower side is maintained at a fixed -temperature a , 

 and the upper side at the fixed temperature & ; both solids are 

 considered to be in that final and permanent state which has 

 the property of maintaining itself as soon as it has been formed. 



F. H. 4 



