280 Mr. 0. D. Child on Ionization in the 



average mass of the negative ions is much less than that of 

 molecules. That is, a large part of the negative ions must 

 be electrons, and therefore n^ is not excessively small when 

 compared with n 2 or m, and equation (2) is approximately 

 correct. 



But the principal reason for assuming that this equation 

 is correct is that such an assumption enables us to explain 

 the difficulties which are otherwise met, for this equation 

 leads to the conclusion that the rate at which ions recombine 

 does not vary as the square of the current, but approximately 

 as the first power of the current. In order to show this, one 

 must remember that there is not only the recombination of 

 positive and negative ions to form uncharged molecules, but 

 that there is also the change of the negative ions from 

 electronic to molecular size. 



There are, in fact, three kinds of recombinations. First, 

 the electrons may combine directly with positive ions and 

 form uncharged molecules; secondly, the electrons may 

 unite with uncharged molecules and form negative ions of 

 molecular size which we shall call molecular negative ions ; 

 and thirdly, these molecular negative ions may unite with 

 positive ionSj forming uncharged molecules. The rate of the 

 first of these recombinations is proportional to the number 

 of electrons times the number of positive ions, and may be 

 expressed by a^m. The second rate of recombination is 

 proportional to the number of electrons times the number of 

 molecules, and since the number of molecules is proportional 

 to the density of the gas, this may be expressed by f3n8, 

 where 8 is the density of the gas. The third rate is pro- 

 portional to the number of molecular negative ions times the 

 number of positive ions, and may be expressed by a 2 n 2 m. 

 In these expressions a l5 a 2j and (3 are constants depending 

 on the nature of the gas. Molecules are formed from the 

 ions by the recombination of electrons with positive ions, 

 and by the recombination of molecular negative ions with 

 positive ions. Hence for the total rate at which ions re- 

 combine we may write 



^\z=a 1 n 1 m-\-a 2 n 2 ?n ; (3) 



but the rate at which the molecular negative ions recombine 

 must equal the rate at which they are formed. Therefore, 

 ci 2 n. 2 m = (3nih and N = a 1 rc 1 m+/3tt 1 S. 



The chance of an electron combining with a positive ion 

 is under all conditions much less than that of its combining 

 with an uncharged molecule, because of the far greater 

 number of the molecules*. Therefore, we need consider 



* Thomsons ' Conduction of Electricity through Gases," 2nded. p. 26. 



