46 G. JounstonE Stoney On Polarization Stress in Gases. 
Of the quantities which enter into these equations , the density of the gas is 
known, and 2, v,, u’, and wu”, are known functions of T, and T,, the temperatures 
of the pistons. Hence these equations enable us to determine the remaining quantities 
p, 9, w’, and w”. 
Now, under the conditions that have been laid down, it 1s manifest that the 
stress* of the gas sideways would be 
P30 04-50, Wil.) oie (ele eel ie) (5) 
while the stress along the tube would be 
P= 1'w'?-f49"w!-4 plu?tp/ul. . (6) 
which accordingly, exceeds the transverse stress by 
(ONY OHE 5 6 566.665 5100 6 (7) 
This, therefore, would be the Crookes’s stress in the case supposed. It is a very 
large quantity, since wu’ and w” 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 retiring from it form complementary parts 
such that their coexistence 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 conveyed by the gas, and that the gas exerts 
the same pressure in all directions. In symbolical language— ‘ 
G being, as before, the symbol for the flow of heat, and « 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 which they 
advance is reduced to zero. For it is evident that the gas at any station within 
the tube may, without any change of its properties, 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 consider a slice between two such sections, which are sufficiently 
close to entitle us to regard the included gas as being throughout in nearly the 
same state. The actual condition of the gas within the slice may evidently be con- 
ceived of as arising from the coexistence of two streams travelling in opposite 
directions along the tube, and each consisting of gas which is less polarized, 1.e., 
which deviates less from the condition of ordinary gas, than the gas that results 
* 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 molecules resolved in a 
given direction, and all estimated as positive, whether.of molecules that move forward or backward. 
