2S± Mr. C. D. Child on Ionization in the 



molecules by their impact ; the two may combine, forming 

 molecular negative ions ; or the two may separate without 

 any permanent effect upon either. 



The second of these effects would not change the total 

 number of ions, but it would change the number of electrons, 

 and the electrons are the principal carriers of the current. 

 We may find an expression for the number of electrons 

 which combine with molecules, as follows. The total number 

 of collisions between electrons and molecules is hn^. The 



number resulting in ionization is bnhe x. Hence, the 



cS 



number which do not ionize is bnS(l — e~xj. If we use 

 k to express the ratio between the number combining and 

 the total number of collisions which do not produce ionization, 



CO 



the number which combine is kon^l — e x ). This is the 

 same quantity as that indicated by ftn^ in a preceding 

 paragraph. 



It would be reasonable to assume that k is a function of 

 the electric force, but it will be shown in a followino- 

 paragraph that the data on the unstriated discharge agree 

 better with the assumption that k is a constant. Therefore, 

 for the present we shall make such an assumption. 



With a steady condition of the current and a constant 

 electric force along the length of the discharge, the number 

 of electrons formed per second must equal the number 

 combining with the positive electrons plus those combining 

 with the molecules, or 



_cj _cS 



on-fie Xz=cc 1 n 1 m-\-khn i S(l — e x). 

 This can best be tested by expressing X in terms of 3 

 and m. 8 is the density and m, the number of positive ions, 

 increases as the current increases. By the following trans- 

 formations it is possible to express X in this way. 



■-H+^)+<i+*>. 



cB 



(5) 



X= — j-4 = s-^ r- (6) 



