Mr. G. J. Stoney on Polarization Stress in Gases. 413 

 the following expression for the polarization stress, 



K<* P (wy, (8) 



where the symbol oc means approximately varies as. Moreover 

 it can be shown* from various considerations that the flow of 



heat 



G oc pVW, 



or, by a simple transformation, 



GocpT.SV, (9) 



T being the temperature measured from absolute zero. Hence 

 from the approximate equations (8) and (9) we obtain the 

 equation 



G 2 

 "<*-jfl2> ( A ) 



which contains only quantities of which we already know 

 enough to make use of them. Equation (A) may be thrown 

 into a still more convenient form by writing P for the tension 

 of the surrounding atmosphere of gas, which is nearly the 

 same as the stress which the gas at the station we are consi- 



* One of the ways in which this may be proved is the following : — 

 Clausius has shown (Phil. Mag. xxiii. p. 514) that 



whence 



G=i/3 P (rv' 3 -rv" 3 ), . 



where I' and V ' 3 are the average values of I and V 3 under the integral 

 for positive values of /x (i. e. for molecules traversing the section of the 

 tube towards the cooler), and I" and V" 3 are the corresponding averages 

 for negative values of fi, i. e. for molecules traversing the section of the 

 tube in the opposite direction. 



Now it is evident that these quantities are capable of expansion in the 

 following form : — 



I'-l+A SV + \ < SV ) 2 + 



= l+Bi*V + 



V"»=V»(l+D x *V + ...), 



in which V 3 is the average of the values of V 3 for all directions. Whence 



G=|/3 /J (A 1 -B 1 + C 1 -D 1 )VW 

 -f terms containing higher powers of SV. 



