Mobility of the Positive Ion in Flames.' 787 



this becomes 



where /\ 2 ls the mean free path of a gas molecule, and 

 A," 1 = it . y/2 n 2 <r 2 . 



Also an assumption of equipartition of energy gives 



m 1 v i 2 = m 2 v 2 ~ 



w hence finally the mobility 



k 1== 2w 2 )'. X /ZI1 



m 2 v 2 \l+y/ V a?(l + #) 



= K 2 .^(i/).<f>U). 



In this result suffix 2 refers to the molecule, whilst the 

 two factors yfr(y) and cf>(x) give the corrections due to the 

 size and mass ot the ion being different to those of the molecule. 

 ]f we knew in general terms the relation between the size and 

 the mass of a molecule, we could solve this equation directly 

 and find the mass of an ion as soon as we knew its mobility. 

 In the absence of such knowledge we are driven to make 

 tentative solutions. As the flame gases are mostly air, w r e 

 shall assume the kinetic constants of air in our solutions. 

 Taking the result obtained at 1950°, viz. a mobility of 350, 

 such a high mobility suggests a very small ion, so we make a 

 tentative solution of the mobility of a charged atom of 

 hydrogen. The following data are used : — 



T at 1950° abs. 



© 



A-2 



v 2 —12 x 10 4 cm. /sec. 



e 3xl0 14 . „ c 

 — = — — — m .b.b. units. 

 m 2 29 



*=&; 00) =7-48. 



y=0-35; f(y) = 2-20. 



Whence the mobility 1x4 = 320 cm. a second. The expe- 

 rimental value obtained is so close to this that one concludes 

 that at 1950° the positive ion either is, or else has the same 

 mass as, an atom of hydrogen. Further, according to the 

 formula proposed, the mobility should vary as \/o, i. e. as 

 the square root of the temperature. A reference to the 

 results (Table II., columns V. and VI.) shows that this 

 relation actually does hold true very closely between 1950 J 



