786 Mr. S. G. Lusby on the 



fair in the case of many gases ; but an examination of the 

 law connecting mobility and temperature seems to decide in 

 favour of the cluster theory. If the ion is a single molecule, 

 then its mobility varies as \/v, i. e. as the square root of the 

 temperature ; this change will be slightly complicated by 

 the change in Mj/Mo, which, as is shown below, decreases 

 directly as the temperature. The general effect would be 

 that the mobility would increase at a rate somewhat quicker 

 than the square root of the temperature. The experiments 

 of Phillips *, however, show that between very wide limits 

 of temperature the mobility increases directly as the tem- 

 perature. These results help us to decide the ambiguity as 

 to the nature of the ion in favour of a cluster. 



At the temperature of flame experiments the effect of 

 electric induction is extremely small even for a single mo- 

 lecule ion. It is seen that Mj is independent, of temperature, 

 since (K — 1) and n vary in the same way; and as M 2 varies 

 directly as the temperature, therefore the ratio of Mi/Mj 

 decreases directly as the temperature increases. For air 

 at 0°, M 1 /M 2 = 3-3, for air at 2000°, M^M^O**; that is, the 

 free path of a molecule would be decreased about 40 per cent. 

 This effect would be annulled by that due to persistence of 

 velocity, which, as we have shown, makes the free path 

 increase about 25 per cent. 



To sum up our discussion as to the fundamental assumptions 

 involved in equating the mobility of an ion to \ejmv at 

 flame temperature, we conclude that the error is at the 

 most only about 25 per cent., and is most probably far 

 less. 



We have now to substitute in this formula the values of r 

 and v proper to a foreign body moving amongst the molecules 

 of a given gas. If the mass of the foreign body, i. e. the 

 ion, is »>!, the mass of a molecule m 2 , and the number of 

 molecules per c.c. is %, then the free path of the foreign 

 body (X 2 ) is given by 







A, l — irn" l - 



\ + o 



'A 2 





2 



) 



wker 



eo-,= 



<7 2 = 



diameter of the 



*1 5) 



ion, 

 mole 



cu. 



Pu 



tting 





and 



^1 

 cr 9 



)V 



m. 



Phillips, Proq. Roy, Soc. A. Ixxviii. (1906). 



