Mr. G. J. Stoney on Polarization Stress in Gases. 409 



above, with perfectly reflecting sides. Such a tube exerts no 

 friction on gas flowing along it, nor does it occasion any loss 

 of energy. Let it contain a large number of gaseous mole- 

 cules between pistons at temperatures T x and T 2 . And let us 

 further suppose that the molecules of the gas, as they leave 

 either piston, acquire the property of not interfering with 

 or being obstructed by the molecules that have last left the 

 other. This imaginary state of the gas would re suit in 

 two streams constantly travelling in opposite directions along 

 the tube. Let us follow one of these streams. It starts 

 from its piston with a mean of the squares of the veloci- 

 ties of its molecules v\ determined by the temperature of the 

 piston, and in numbers per unit of time represented by p'u f , 

 p' being the density of the stream and v! the average of the 

 normal components of the velocities at starting. Then, how- 

 ever the velocities and directions may have been distributed 

 at starting, the jostling of the molecules of this stream among 

 one another will reduce the stream as it advances to the condi- 

 tion of unpolarized gas travelling along the tube with the velo- 

 city u. The molecules are henceforward moving with veloci- 

 ties among themselves which, measured from their advancing 

 centre of mass, have an average square of the velocities w 

 which is given by the equation 



Pv*=u' 2 +I3w' 2 , (1) 



fi being the known numerical coefficient representing the 

 ratio of the total energy of the gas to its " energy of agita- 

 tion." This equation is only the symbolical expression of the 

 fact that no energy has entered or left the gas. The stream 

 moving in the opposite direction furnishes the similar equa- 

 tion 



#>f=t*" 2 + /3™" 2 (2) 



rs of molec 

 lal, we ha^ 



p'u' = p"u" (3) 



We have also 



P = P' + P" (4) 



Of the quantities which enter into these equations, p, 

 the density of the gas, is known, and v l} v 2 , u f , and zt" are 

 known functions of T t and T 2 , the temperatures of the pistons. 

 Hence these equations enable us to determine the remaining 

 quantities (/, p /f , w' ', and w" . 



Now, under the conditions that have been laid down, it is 



And since the numbers of molecules reaching and receding 

 from each piston are equal, we have the further equation 



