G. Jonnstons Stonrty On Polarization Stress in Gases. A5 
the molecules of other gases are also quantities of this order. But it is not 
necessary for our present purpose to establish this. The only circumstance 
relating to these inner motions with which we are here directly concerned is 
that the energy which is transferred from molecule to molecule, is employed 
partly in altering the velocities with which the molecules travel about and partly 
in altering these internal motions and (perhaps) collocations; and that ' the 
proportion of the energy which is employed in the former way bears on the 
average a numerical ratio to the whole energy transferred, which can be 
determined experimentally (see Maxwell’s “ Theory of Heat,’ p. 299), and is 
denoted in the sequel by 7 | 
10. We may now proceed to determine limits between which the thermal and 
mechanical properties of the gas must lie. For this purpose let us imagine a tube 
of the kind described 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 molecules between pistons at temperatures 
T, & T,. And let us further suppose that the molecules of the gas, according 
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 result 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 velocities of its molecules v,’ determined 
by the temperature of the piston; and in numbers per unit of time represented 
by »’ w’, »' being the density of the stream and u/ the average of the normal 
components of the velocities at starting. Then, however 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 vt advances to the 
condition of unpolarized gas travelling along the tube with the velocitu uw. The 
molecules are henceforward moving with velocities among themselves which, 
measured from their advancing centre of mass, has an average square of the 
velocities w’* which is given by the equation 
Bots=u2+ Bw . 2 1. . (1) 
6 being the known numerical coefficient representing the ratio of the total energy 
of the gas to its “energy of agitation.” 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 equation 
Bui 1 Geri ween (2) 
And since the numbers of molecules reaching and receding from each piston are 
equal, we have the further equation. 
ou’ =u" eed titovor cs (3) 
We have also 
p=p' +p” eco e Ge o 8 (4) 
