HYDROGEN INTO ATOMS 163 



These considerations lead us to conclude that the effects of convection 

 currents can he neglected even at pressures as high as 200 mm. We shall 

 see that the decrease in the values of S at the lower pressures is due to a 

 temperature discontinuity at the surface of the wire. 



THE TEMPERATURE-DROP AT THE SURFACE OF THE WIRE 



Kundt and Warburg,'* in a study of the viscosity of gases at low 

 pressures, showed, both experimentally and theoretically, that there is 

 a certain apparent slipping of the gas along the surface. In gases at 

 atmospheric pressure this effect is very small, but it varies inversely pro- 

 portional to the pressure and thus becomes very important at low pressures. 

 The thickness of the layer in which this slipping occurs is approximately 

 equal to the mean free path of the gas molecules. Kundt and Warburg 

 predicted, from the analogy between viscosity and heat conduction, that a 

 corresponding discontinuity in temperature at the surface of a solid body 

 would be observed in the case of heat conduction through gases at low 

 pressure. 



Over twenty years later Smoluchowski ^ actually observed and studied 

 this temperature drop and developed the theory of it. The temperature 

 drop occurred within a layer about equal in thickness to the free path of 

 the molecules. Smoluchowski found that in some gases, particularly hy- 

 drogen, the amount of heat given up to the gas by a solid body was only 

 a fraction of that which should be delivered if each molecule striking the 

 surface reached thermal equilibrium with the solid before leaving it. 



Smoluchowski developed the theory of this effect along the lines of two 

 alternative hypotheses, which he denotes by A and B. 



Hypothesis A is equivalent to that made more recently by Knudsen.® 

 It assumes, when molecules of a temperature Ti strike a surface at a higher 

 temperature To, that the molecules leaving the surface have a temperature 

 T which is intermediate between T2 and Ti and that the relation holds 



T-Ti = a(T2-Ti) (8) 



where a is a number less than unity and is called by Knudsen the "accom- 

 modation coefficient." 



Hypothesis B is similar to that originally used by Maxwell "^ in dealing 

 with the slip of gases. It assumes that, of all the molecules striking the 

 surface, a fraction, /, reaches thermal equilibrium with it, while the fraction 

 I — / is reflected without change of temperature (or rather velocity). 



'^ Pogg. Ann., 156, 177 (1875). 



^ Wicd. Ann., 64, loi (1898) ; IVicn. Sitciinysbcr., 108, 5 (1899) ; Phil. Mag., 46, 

 192 (1898). 



'^ Ann. Phys., 34, 593 (1911)- 

 "^ Phil Trans, 170, 231 (1879) 



