5:38 Prof. Clausius on the Conduction of Heat by Gases. 



For the sake of greater convenience we will still somewhat 

 alter the form of this equation. If we denote the velocity of the 

 molecules in the normal condition of the gas by u , and the ab- 

 solute temperature by T , we have 



*z 2 T 



and thence 





" = vT ^ T • ( 55 ) 



The foregoing equation thus becomes 



5 kmTS u*6 /YdT ._ 



*- 24— T^— Vp' ' • • (° 6 > 



If we assume the freezing-point as the temperature of the gas in 

 its normal condition, T ==273 nearly, and T = 273 + tf, where / 



following equation (he. cit. p. 23), 



E=-iA(mNwZ) (B) 



6 dx 



Then, in order to obtain the vis viva which traverses the plane instead of 

 the mass, he simply substitutes in this equation the vis viva of a molecule, 

 -\kmu 2 , for the mass of a molecule m, and so obtains equation (A). If we 

 now consider equation (B) more closely, and substitute there also its value 



■^ e for I, we get 



This equation proclaims that, if the temperature of the gas varies in the 



du 

 direction of x so that -r- has an appreciable value, a progressive move- 

 ment of the mass in the direction of x must take place, inasmuch as more 

 molecules pass through the plane in one direction than in the other. It is 

 therefore contradictory of the supposition which we must make when we 

 speak of the conduction of heat ; for we understand by conduction of heat 

 a progressive movement of the heat without a progressive movement of the 

 mass. 



Independently, therefore, of the question whether equation (B) is ad- 

 missible or not, we are forced to one of the following conclusions : in esta- 

 blishing his equations, Maxwell either had in view a state of things quite 

 different from what we presuppose in speaking of conduction of heat, 

 namely, such a state that the gas has a progressive movement in a parti- 

 cular direction, in which case his equation (A) does not express what we 

 understand by conduction of heat, and what is expressed by my equation 

 (XIII.), but a motion of heat accompanied, and partly occasioned, by a 

 motion of mass ; or else he really intended to represent the condition in 

 which a movement of heat takes place unaccompanied by a movement of 

 mass, in which case the equation (B) is wrong, and the equation (A) de- 

 duced from it is only approximately correct because two errors have par- 

 tially neutralized each other. 



