450 Dr. W. F. G. Swann on the Expression for 



velocities lie between c and r + dc is Sji — Sj 2 . Writing 8$ 

 for this we have 



*. 2AX<? 2 \ . . , 



q/= — ^ e- hmc -cdc; 



dm 



.*. ,7 = —^ e- hmc -cdc. . . . (19) 



6m J 



On replacing A and Jim by the values given above and 

 writing u for the square root of the mean square velocity,. 

 we obtain 



-\/l-^ w 



which happens to be the same result as that obtained by 

 Lorentz by a different method. 



The Thermal Conductivity. 



r The determination of the thermal conductivity for a gas 

 when the molecules obey Maxwell's law is a well-known 

 problem. We shall, however, briefly survey the steps for the 

 purpose of applying it to the present problem. 



If in (10) we put X=0, and replace n by Ae- hmc2 c 2 dc, 

 v by c, and \ by X; where X c is the free path for velocity c, and 

 where the values refer to the plane PM, we shall obtain the 

 number of electrons which reach E per square centimetre- 

 per second, which have come from the ring of volume 

 27rR 2 sin ty dyjr dH, and whose velocities are contained within 

 the limits c and c + dc. 



We have for the number 



__ e - w 6 .3 dc u e ~ R ^R s i n ^ cog ^ df. 



" c 



Remembering that a.6 is the mean kinetic energy of an 

 electron at a temperature #, we have for the transference of 

 energy Q ll per square centimetre per second across the plane 

 PM at E, the result 



Q 1= = ~\ ~r— edc J sin -\jr cos yjr d\jr I e R/Ac ] ccO — a — . R cos <*jr \ dR. 



The corresponding quantity representing the flow from 

 right to left is obtained by replacing -p by , t , and the 

 resultant thermal current density is obtained by subtracting 



