in Gases at Low Pressures. 801 



has shown that the carrier of the positive current in flames 

 above a certain critical temperature is independent of the 

 salt introduced into the flame and the flame-gases, and is of 

 the mass of a hydrogen atom, while below the critical 

 temperature the carrier is much more massive, and depends 

 on the salts used in the flame. 



Size of the Ion. — Langevin has deduced from the kinetic 

 theory of gases the formula for the mobility of an ion k = eX\mv. 

 It would be interesting to calculate the approximate values 

 of the masses of the ions in the various gases using this 

 expression, and to compare them with the masses of the 

 molecules. In the expression for the mobility A, and u 

 represent the mean free path and the velocity of thermal 

 agitation of the ion. The mean free path of a molecule in 

 a gas in which there are n 2 molecules per unit volume, each 

 having a diameter p 2 , is given by 



X 2 _1 = 7r/v? 2 \/2. 



The mean free path of an ion of mass m 1 in the gas whose 

 molecules have, say, mass m 2 , is given by 



2 V nio 



m 2 



where p Y is the diameter of the ion. Hence the ratio Xjo for 

 the molecule to that of the ion is 



"" 2 p 2 V lm x ' 



since m x Vi 2 = m 2 r 2 2 . The relations between the mass and 

 diameter for the ion and molecule are not known, so that a 

 deHnite value cannot be given to this ratio ; but the trial of 

 probable values will show that for an approximation no very 

 grave error will be committed in assuming it to be unity. 

 Jn the following table (p. 802) the mass of the ion has been 

 obtained from h — eXjmv, assuming the ratio Xjv to be the 

 same for the ion and molecule. 



Calculating m from the formula Jc = eX/mv, it appears 

 that the ion at ordinary pressures consists of a group of 

 several molecules round the positive charge, and at very low 

 pressures the group dissociates into a less complex group. 



In the cases of air, carbon dioxide, and trydrogen, the 

 experiments were carried out to as low a pressure as possible. 

 There is a suggestion of a flattening in the air-curve when 



