784 Mr. S. G. Lusby on tie 



mobility tban tbose produced by the monovalent metals. At 

 1150° the ratio of the two mobilities is very closely 2 to 1. 

 This confirms a result obtained by H. A. Wilson quoted 

 before, viz. that in hot air at 1270° monovalent metals gave 

 an ion moving twice as quickly as that coming from divalent 

 metals. A fuller discussion of results is given in the next 

 two sections. 



(8) Structure of the Positive Ion Flame. 



In order to form some theory as to the nature of the ion 

 we require to know its mass, or else its " electric atomic 

 mass." This can be calculated approximately from the 

 mobility by using Langevin's simple formula for the mo- 

 bility k = \e/mv, where the quantities have their usual 

 significance. This formula involves the following assump- 

 tions : — (1) that the velocity of the ion due to the electric 

 field is negligible in comparison with its thermal velocity of 

 agitation ; (2) that the ion comes to rest after each collision; 

 and (3) that the charge of the ion does not affect its irean 

 free path (as deduced from the kinetic theory of gases). In 

 the present experiments the first assumption is amply justified. 

 The second cannot be absolutely true, but we can form a 

 rough idea as to the nature of the error involved. The 

 question of the " persistence " of velocity of uncharged 

 molecules after collision has been investigated by Jeans *, 

 who shows that, on the average, there is a tendency for a 

 molecule to persist in moving along its original path after 

 collision with 40 per cent, of its original velocity. If the 

 colliding body is much smaller than the molecule, the per- 

 sistence is only 33 per cent., if much larger 50 per cent. In 

 general, the effect of this persistence of velocity is to increase 

 the free path ; e. g. as regards calculation of viscosity, this 

 increase is 25 per cent. The order of this increase is much 

 the same in all kinetic theory calculations. Now, coming to 

 the third assumption, we find ourselves faced with corrections 

 of a different order and a more doubtful nature. It was first 

 shown by Langevinf that the effect of endowing a molecule 

 of a gas with a charge is to decrease its free path; this 

 decrease is due to the mutual induction between ion and 

 molecule. It can be shown that if A/ is the free path of a 

 charged molecule, and A that of an uncharged molecule, 



* .leans, ' Dynamical Theory of Gases,' p. 236. 



t Langeviu, Ann. de Chim. et Phys. vii. p. 28 (1903). 



