Ions and Electrons through Gases. 61 



mean free path. In the present experiments the positive 

 ions are shown to have a normal mobility for values of X/p 

 as great as 11, even if we take for X only the small values 

 of the critical field from which the mobility was estimated. 

 The normal character of the complete curves which were 

 obtained in the process of determining the critical potentials 

 indicates that neither the positive nor the negative ion is 

 appreciably altered in nature for much greater values of X/»„ 

 It should be remembered, however, that at the lowest pres- 

 sures employed we are nearing the conditions for which the 

 mobility law would be no longer valid even for an unchanging 

 ion. A simple calculation gives that in air ior p = '05 mm. 

 and with 1 volt fall of potential, the positive ion makes 

 about 330 collisions in traversing the distance of 2 cm. 

 between the electrodes. It is surprising that the mobility 

 law should be so nearly valid at this stage : the explanation 

 is probably that the velocity (3*3 x 10 4 cm./sec.) acquired by 

 the ion after describing freely a distance equal to the mean 

 free path is still smaller than the mean velocity of thermal 

 agitation of the molecules (4*6 X 10 4 ). If we suppose that 

 the mobility law is valid as long as the mean velocity of 

 agitation predominates, we find by calculation that in air the 

 law should hold for values of X/p up to 20. Loeb * has 

 recently made a series of determinations of the mobilities of 

 the ions in air under high electric fields, and has shown that 

 the mobilities remain normal at atmospheric pressure for 

 field strengths up to 12,450 volts per cm. ; the l&wpk = const, 

 was verified for values of X/p up to about 20. 



The preceding considerations indicate that the notion of an 

 ion as a cluster is unnecessary; the cluster theory must 

 depend for its continued existence on arguments essentially 

 different from those which have hitherto been advanced. 

 Moreover, it should be stated that evidence of a more direct 

 nature in favour of the single molecule theory has of late 

 years been forthcoming. Ohattock and Tyndallf in their 

 experiments on the point-discharge showed that the absorption 

 of positive ions of hydrogen by a metal corresponded to a 

 withdrawal of two atoms of hydrogen from the gas. Eriksont 



* Loeb, Proc. Nat. Ac. Sc. vol. ii. No. 7, p. 345 (1916) ; also Phys. 

 Rev. vol. viii. p. 633 (1916). Loeb has misunderstood me when he states 

 that I verified the law pk=const. for the ions in air up to values of X/p 

 as high as 34*5 ; as a matter of fact I maintained merely that the 

 negative ions were still in evidence for this value, whereas Townsend's 

 theorv would necessitate their complete disappearance for a value of X/« 

 equal to 0-2. (E. M. W.) IP 



+ Chattock and Tyndall, Phil. Mag. xvi. p. 24 (1908); also loc. cit. p 60 

 + Erikson, Phys. Rev. vol. vi. p. 345 (1915). r ' 



