214 PHENOMENA, ATOMS, AND MOLECULES 



By substituting (31) and (32) in (22), and solving for 6 we find 



.»= ' ''~^' . (35) 



. «lMl I «IM8 

 Vi Vt 



Tliese last three equations furnish a complete solution of our problem 

 in the case of the second hypothesis. 



COMPARISON WITH THE OLDER THEORY 



It will be interesting to compare the results obtained by each of the 

 above hypotheses, with those found by the theory developed in Part II 

 of this paper. The Equations 21 and 26, of Part II (page 427), correspond 

 to the Equations 17 and 33 derived above. However, since the nomencla- 

 ture previously used differs from that employed here it will be worth while 

 to go through the derivation of the older equation again by a method which 

 will bring out clearly the difference between the two viewpoints. 



It is assumed that out of all the atoms striking the surface, the fraction 

 tti is absorbed by the metal, whereas for the molecules the corresponding 

 fraction is 02. It is assumed further that the surface of the metal contains 

 hydrogen molecules and atoms in equilibrium with each other. Let Vi and 

 V2 be the rates at which atomic and molecular hydrogen, respectively, 

 escape from the surface. 



We may thus derive the equations 



20) = j^i — ami (36) 



w = a2)U2 — V2, (37) 



from which we obtain 



v\ = 2(1} -\- ami ■ v3o) 



Vi = OL^n^ — 0}. (39) 



It is assumed that the equilibrium inside the metal obeys the law of 

 mass action, so that the concentration of molecular hydrogen is propor- 

 tional to the square of the concentration of atomic hydrogen. It is further 

 assumed that the rates at which each of the gases escapes from the surface, 

 is proportional to the corresponding concentration in the metal. Thus, 

 V1-/V2 is a constant proportional to the equilibrium constant in the metal. 

 Let this constant be represented by A. Then we have by (38) and (39) 



A - ^"^^^ + ■ ^")' . (40) 



