CHAPTER IX. 



THEORY OF A NON-CONSERVATIVE GAS (CONTINUED). 



THE TRANSFER AND DISSIPATION OF ENERGY. 

 \/ The vibrations set up by collisions. 



236. WHEN a molecule is describing a free path, the changes in its 

 coordinates will of course be deducible from its own energy function. Let 

 us, on the grounds explained in the last chapter, suppose this energy function 

 to contain terms of the form 



'2L = a^ + a4? + (471), 



2F=6 1 < 1 2 4-M> 2 2 + (472), 



in which the a's and b's are constants, these terms representing the 

 isochronous internal vibrations of the molecules. The quantities Qnfa... 

 are principal coordinates of the system, and have the property that their 

 equations of motion are independent of one another and of the other 

 coordinates of the molecule. The variation of any coordinate $ is given by 

 an equation of the form 



a$ + &0 = (473). 



The solution of this equation is 



(f> =A cospt + Bsiupt (474), 



in which A , B are arbitrary constants, and p is given by 



ap*-b = Q (475). 



Let us suppose that at time t = the motion of this molecule is disturbed 

 by an encounter with a second molecule, this encounter lasting until time 

 t = r. The influence of this second molecule upon the first will be capable 

 of being expressed by a force function of the form 



U 1 S<f> 1 + U 2 S<j> 2 + (476), 



and from = to t=r the equation expressing the change of the coordinate </> 

 will no longer be equation (473), but will be (dropping suffixes throughout) 



>=U... (477). 



