SECT. II.] RECIPROCAL CONDUCIBILITY. 227 



248. If \ve attributed a greater value to the volume w, which 

 serves, it may be said, to draw heat from one of the bodies 

 for the purpose of carrying it to the other, the transfer would 

 be quicker ; in order to express this condition it would be 

 necessary to increase in the same ratio the quantity k which 

 enters into the equations. We might also retain the value 

 of G) and suppose the layer to accomplish in a given time a 

 greater number of oscillations, which again would be indicated 

 by a greater value of k. Hence this coefficient represents in some 

 respects the velocity of transmission, or the facility with which 

 heat passes from one of the bodies into the other, that is to say, 

 their reciprocal conducibility. 



249. Adding the two preceding equations, we have 



dz + d/3 = 0, 



and if we subtract one of the equations from the other, we have 

 d*-d/3+2 (a-/3) - rft = 0, and, making a - = ;/, 



7)1 



Integrating and determining the constant by the condition that 



_1M 



the initial value is a - b, we have y = (a b) e m . The differ 

 ence y of the temperatures diminishes as the ordinate of a loga 



rithmic curve, or as the successive powers of the fraction e~m 

 As the values of a. and /?, we have 



1 1 _?? 1 1 -*** 



a =-(a + l) ---(a-b} e , ft = - (a + b) + ^ ( - b} e m . 



250. In the preceding case, we suppose the infinitely small 

 mass &&amp;gt;, by means of which the transfer is effected, to be always 

 the same part of the unit of mass, or, which is the same thing, 

 we suppose the coefficient k which measures the reciprocal con 

 ducibility to be a constant quantity. To render the investigation 

 in question more general, the constant k must be considered 

 as a function of the two actual temperatures a. and ft. We should 



then have the two equations dx. = - (a - ft) dt, and 



152 



