272 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 



vapours, there is little difference in value between the positive and negative 

 mobilities. The greatest differences are found for the elementary gases : air, oxygen, 

 hydrogen, and helium. There are several instances, including most of the ethyl 

 compounds, in which the positive ion has a greater mobility than the negative; 

 hitherto, only one gas, viz., acetylene,* was known in which this was the case. 



9. Theoretical Considerations. 



The Law of Mobility of the Ions formed in Gaseous Media. In the following 

 treatment, which is based on the kinetic theory of gases, an attempt is made to obtain 

 a theoretical expression for the velocity with which a charged body of dimensions 

 comparable with those of a molecule would move in the gas under the action of an 

 electric field of given intensity. It is necessary at the outset to fix our ideas of a 

 molecule and an ion ; for this purpose the following conceptions are introduced : 



A molecule is regarded as a nucleus surrounded by a sphere of force of radius ^s. 

 The spheres of force are supposed mutually impenetrable. 



An ion is regarded as involving two distinct elements : 



(i) A mass (independent of the charge). Considering this element alone, let us 

 represent the ion as a nucleus surrounded by a sphere of force of radius ^s'. 



(ii) A charge e (electrostatic units). During motion of the ion through the gas 

 the effect of this charge is equivalent (as will be shown) to an increase in the volume 

 of the force sphere (i) of the ion, the mass remaining unaltered. 



A collision occurs between two molecules when the distance between their centres 

 is equal to the sum of the radii of their force spheres. 



LANGEVINJ has shown that the velocity of an ion under unit electrostatic intensity 



is given by 



k = eL/MV, 



where M denotes the mass of the ion, L its mean free path through the gas, and V its 

 mean velocity of thermal agitation. As the ion moves through the gas the charge 

 associated with it attracts the neutral molecules ; there results an increase in the 

 mean collision frequency of the ion and consequently a diminution in its mean 

 free path. 



Expression for the Mean Free Path of the Ion. Consider the motion of an ion and 

 a molecule regarded in the light of two interacting free particles. Let E, denote the 

 potential due to the polarisation of the molecule by the charge on the ion,! so that the 



* ZELENY, 'Phil. Mag.,' vol. 46, p. 132, 1898. 

 t 'Ann. de Chim. et de Phys.,' vii., 28, p. 335, 1903. 



I The polarisation of the molecule by the electric field is regarded as negligible in comparison with that 

 due to the ionic charge. 



