THE DYNAMICAL THEORY OP GASES. 55 



If we assume with Clausius that the ratio of the mean energy of internal 

 motion to that of agitation tends continually towards a definite value (ft I), 

 we may conclude that, except in very violent disturbances, this ratio is always 

 preserved, so that 



E = (p-l)(?+if + ?) ........................ (67). 



The total energy of the invisible agitation in unit of volume will then be 



WP + tf + P) ................................. (68), 



or fp ............................... '..; ......... (69). 



This energy being in the form of invisible agitation, may be called the 

 total heat in the unit of volume of the medium. 



(y) Transference of Energy across a Plane Conduction of Heat* 

 Putting C = i/8(p + V + p)Jf, and u = u' ........................ (70), 



we find for the quantity of heat carried over the unit of area by conduction 

 in unit of time 



where f , &c. indicate the mean values of *> &c> They are always small 

 quantities. 



On the Rate of Variation of Q in an Element of Volume, Q being any property 



of the Molecules in that Element. 



Let Q be the value of the quantity for any particular molecule, and Q 

 the mean value of Q for all the molecules of the same kind within the element. 



The quantity Q may vary from two causes. The molecules within the 

 element may by their mutual action or by the action of external forces produce 

 an alteration of Q, or molecules may pass into the element and out of it, and 

 so cause an increase or diminution of the value of Q within it. If we employ 

 the symbol 8 to denote the variation of Q due to actions of the first kind on 

 the individual molecules, and the symbol 3 to denote the actual variation of Q 

 in an element moving with the mean velocity of the system of molecules under 



