172 PHENOMENA, ATOMS, AND MOLECULES 



On the other hand, if we place ou = o in (21), we obtain the condition 

 for equihbrium. In this case (21) becomes 



A = («;/«,) • {my/m\ (24) 



and by combining this with (23) we find the desired relation between A 

 andK 



K = VJ^rRTz Wo;) A. (25) 



If we now substitute in (21) the values of m\ and m2 from Equation 5 

 and then combine with (25), we obtain 



p2 W V 2 irRTa/a2 V 2 



Here To is the temperature of the gas around the wire at a distance X 

 from it (corresponding to circle C of Fig. i). When (0 = and T^ = T2 

 this equation reduces to the ordinary form of the law of mass action. 

 The "drop in concentration" corresponding to the drop in temperature 

 previously considered is equivalent to 0)V2JrRTa/ai.^^ 



In the above equation pi and p2 are the partial pressures of hydrogen 

 atoms and molecules at a distance X from the wire. 



Let us substitute the numerical values of the constants involved in 

 (26). If we express p in mm. of mercury, then the factor V^^iR is 17.15- 

 If we place d = 0.00706 cm. (the diameter of the wire) in (17) we find 

 CO = 10.8 Wd/Qi- Substituting these in (26), we obtain 



^2 — 131 Wz,VTa/«2?l ^ ^^ 



Here p is expressed in mm., Wjj in watts per cm., and qi in calories per 

 gram. 



DIFFUSION OF ATOAIIC HYDROGEN AWAY FROM THE WIRE 



In the calculation of the temperature drop around a wire in hydrogen, 

 we used two methods which led to Equations 11 and 12, respectively. 

 Similarly, in the calculation of the concentration drop, two methods 

 may be used. The method adopted above in obtaining Equation 27 is 

 analogous to that used in deriving (11), whereas the following method 

 corresponds to that employed in obtaining (12). 



In the "paper of 191 2" it was shown that 



Wd = SDgiCi (3) 



^° Expressed as partial pressure instead of concentration. 



