Prof. Clausius on the Conduction of Heat by Gases. 531 



employing in the above formula, which is deduced without con- 

 sidering the accidental variations, a mean value for the velocity 

 which is easily arrived at, and which, though not strictly accu- 

 rate, may still be regarded as sufficiently so, considering the 

 uncertainty which still prevails in regard to the value of e. 



§ 27. We will employ that mean value of u which gives the 

 same vis viva as the velocities which actually occur. This value 

 may be obtained by taking the arithmetical mean of the squares 

 of the velocities, and extracting therefrom the square root. 



In this case the product ^klS mu 2 has a simple meaning. It 

 represents, namely, the vis viva, or, in other words, the quan- 

 tity of heat contained in a unit of volume of the gas in its nor- 

 mal condition. If 7 stands for the specific heat of a unit of 

 volume of the gas, the volume being kept constant, 7T will 

 represent this quantity of heat ; or if the freezing-point be 

 taken as the normal temperature T , it will be represented 

 approximately by y . 273 ; whereby equation (XV.) becomes 



K= T Vw; ( 57 ) 



and if 7 be expressed in common heat-units, the conduction of 

 heat is also expressed in common heat-units by employing this 

 formula. The magnitude u may be deduced as follows from 

 the formula which I formerly* established for the moving velo- 

 city of the molecules, 



485 " /rax 



Wo=-7-> ( 58 ) 



where or denotes the specific gravity of the gas in question com- 

 pared with atmospheric air. The foregoing equation is thus 

 transformed into 



K = 202-l-^e (XVII.) 



For the simple permanent gases, and such compound gases 

 as suffer no contraction on the combination of their elements, 

 the specific heat 7 is the same as for atmospheric air ; and if a 

 cubic metre, which contains 1 *2932 kilog. atmospheric air in the 

 normal condition, be taken as our unit of volume, 



7 = 0-1686. l-2932 = O21803. . . . (59) 

 By employing this value, we get for the gases mentioned 



K=^- 6 e (XVIII.) 



Hence for the three simple permanent gases and for atmospheric 

 air, which must be treated as a simple gas in relation to the 



* Phil. Mag. S. 4. vol. xvii. p. 124. 

 2 N 2 



