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



manifest that the stress* of the gas sideways would be 



P y =&>W+ip'V", (5) 



while the stress along the tube would be 



V x = yio r2 + l P > ; w /r2 + p'u r2 + p' / u lf \ . . (6) 

 which accordingly exceeds the transverse stress by 



K^f/vP + pVyP* (7) 



This, therefore, would be the Crookes's stress in the case 

 supposed. It is a very large quantity, since u' and a" would 

 be large if the streams could penetrate one another without 

 obstruction. The flow of heat, which we will designate by 

 the symbol G, would also be very large in the case supposed. 

 An expression for it can be easily found, but is not required 

 for our present purpose. 



11. The other limit is one that really occurs. It arises 

 when the molecules coming up to either piston and those re- 

 tiring from it form complementary parts, such that their co- 

 existence in the same space constitutes stationary unpolarized 

 gas. This happens only when the two pistons are at the same 

 temperature. In this case it is manifest that no heat is con- 

 veyed by the gas, and that the gas exerts the same pressure 

 in all directions. In symbolical language, 



G=0, 



K = 0, 



G being, as before, the symbol for the flow of heat, and k for 

 the Crookes's stress. This case may be described as one in 

 which the streams described in the last section experience such 

 effectual opposition from each other that the speed with w r hich 

 they advance is zero. For it is evident that the gas at any 

 station within the tube may, without any change of its pro- 

 perties, be described as consisting of two equal portions of 

 stationary unpolarized gas coexisting in the same space. 



12. In all other cases the pistons that close the ends of the 

 unit tube are at different temperatures, and the gas between 

 any two cross sections of the tube is polarized. Let us con- 

 sider a slice between two such sections, which are sufficiently 

 close to entitle us to regard the included gas as being through- 

 out in nearly the same state. The actual condition of the gas 



* The term " stress'' is here applied to the pressure within the gas in 

 any direction, viewed in conjunction with the equal pressure in the opposite 

 direction. It is. what Clausius has called " the positive momentum," 

 meaning thereby the sum of the components of the momenta of the mole- 

 cules resolved in a given direction, and all estimated as positive, whether 

 of molecules that move forward or backward. 



