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



molecules as it travels forward, while the reverse effect is pro- 

 duced upon the stream making its way in the opposite direc- 

 tion. On both accounts there will be gradients of density 

 and temperature along the tube between the heater and cooler. 

 Again, every encounter between molecules of the two streams 

 diminishes the momentum of one or both streams ; but, as we 

 have seen, the effect so produced does not go the length of 

 reducing the streams to rest. 



14. Hence we must bear in mind the gradients of tempera- 

 ture and density along the two streams, and the continual 

 fluctuation of the molecules that are to be referred to them, if 

 we want to regard the condition of the gas throughout the 

 whole length of the tube as arising out of the coexistence of 

 two streams of gas less polarized than itself. But with these 

 precautions the hypothesis maybe made; and accordingly the 

 condition of the gas at every cross section of the tube is inter- 

 mediate between a structure represented by the coexistence of the 

 two streams of unpolarized gas travelling simultaneously in op- 

 posite directions, which the encounters within each stream tend 

 to develop, and the condition of stationary unpolarized gas, 

 towards which the mutual interference of the two streams mo- 

 difies the structure. Hence there is some polarization stress 

 and some flow of heat all along the tube, though of less amount 

 than in the case considered in section 10. We may still em- 

 ploy equation (7) as the expression for the polarization stress, 

 if we use for p' and p" the densities of the streams at some 

 particular cross section of the tube, and if u' and u" are modi- 

 fied into what they become as the interference of the two 

 streams with one another is increased. It is not necessary 

 to ascertain what this modification will be : it is enough for 

 our purpose to know that u' and u" will be some functions of 

 V — Y" (where V /3 and V //3 are the averages of the cubes of 

 the velocities of the molecules that pass forwards and back- 

 wards respectively through the cross section), and that they 

 will be proportional to this quantity when all three are small. 



15. We may base upon this circumstance an investigation 

 into the laws of the phenomenon when the difference between 

 the temperatures of the heater and cooler is small compared 

 with their absolute temperatures. This case is of importance 

 because it is that which most frequently occurs, and is the 

 only one in reference to which accurate experiments have 

 been made. In this case p' and p" will each be nearly \p, 

 using p for the density of the gas at the position in the tube 

 which we are considering ; and V / — V", being small, may be 

 appropriately represented by SV. Then, remembering that u' 

 and u" are proportional to 8V, we obtain from equation (7) 



