SECT. IV.] UNIFORM LINEAR MOVEMENT. 



51 



We may now imagine many other systems of two molecules, 

 the first of which sends to the second across the plane L, a certain 

 quantity of heat, and each of these systems, chosen in the first 

 solid, may be compared with a homologous system situated in the 

 second, and whose action is exerted across the section L ; we 

 can then apply again the previous reasoning to prove that the 



a ~ b a ~~ 



ratio of the two actions is always that of - - to 



e e 



Now, the whole quantity of heat which, during one instant, 

 crosses the section Z, results from the simultaneous action of a 

 multitude of systems each of which is formed of two points; 

 hence this quantity of heat and that which, in the second solid, 

 crosses during the same instant the section L , are also to each 



other in the ratio of ^ to a ~ _ 

 e e 



It is easy then to compare with each other the intensities of 

 the constant flows of heat which are propagated uniformly in the 

 two solids, that is to say, the quantities of heat which, during 

 unit of time, &quot;cross unit of surface of each of these bodies. The 



ratio of these intensities is that of the two quotients a ^~ and 



a -b 



~i If the two quotients are equal, the flows are the same, 



whatever in other respects the values a, b } e, a, U, e, may be ; 

 in general, denoting the first flow by F and the second by F t 



we shall have == = ^~ -r- a ~ . 



68. Suppose that in the second solid, the permanent tempera 

 ture a of the lower plane is that of boiling water, 1 ; that the 

 temperature e of the upper plane is that of melting ice, 0; that 

 the distance e of the two planes is the unit of measure (a 

 metre); let us denote by K the constant flow of heat which, 

 during unit of time (a minute) would cross unit of surface in . 

 this last solid, if it were formed of a given substance ; K ex- ( 

 pressing a certain number of units of heat, that~is to say a certain 

 number of times the heat necessary to convert a kilogramme 

 of ice into water : we shall have, in general, to determine the 



42 



