in Gases hy the Motion of Negatively Charged Ions. 639 



per centimetre in carbonic acid gas at the same pressure. The 

 mean free paths at that pressure are therefore the reciprocals 

 of these numbers. 



The mean free paths of molecules of gases at 760 mm, 

 pressure and 0° centigrade, as deduced from experiments on 

 viscosity, are * 1*78 xlO -5 centimetre for hydrogen and 

 *65 x 10 ~ 5 for carbonic acid gas. 



At one millimetre pressure and 12° centigrade the mean 

 free paths would be "0141 and '0051 for the two gases 

 respectively. (The temperature at wbich our experiments 

 were made was about 12° centigrade.) The number of 

 collisions per centimetre would consequently be 78 for 

 hydrogen and 196 for carbonic acid. gas. 



The collisions of a single molecule A with other molecules 

 of the gas arise partly from the motion of the molecule in 

 question, and partly from the general motion of the gas, If 

 the molecule were travelling so fast that the motion of trans- 

 lation of the rest of the gas was inappreciable in comparison 

 with it, the number of collisions per centimetre would be less 

 than the numbers given above in the ratio of 1 to 1*41. (See 

 Maxwell, Pbil. Mag. xix. 1860.) We therefore see that a 

 molecule of hydrogen travelling very fast through the other 

 hydrogen molecules would make 55 collisions per centimetre, 

 and a molecule of carbonic acid would make 138 collisions 

 per centimetre in an atmosphere of carbonic acid gas. The 

 corresponding number for air is 91. 



From these numbers we find that the mean free path of an 

 ion is longer than the mean free path of a molecule in the 

 following ratios : — 



4'8 : 1 in hydrogen, 



4*6 : 1 in carbonic acid gas, 



4*3 : 1 in air. 



If we suppose that the material of a molecule extends to a 

 distance R from the centre, then according to our theory 

 new ions are generated when the colliding ion, moving with 

 a sufficient velocity, comes within a distance R of the centre 

 of the molecule. If the linear dimensions of a negative ion 

 are small compared with those of a molecule, we see from the 

 above ratios that the centres of molecules are about 2R apart 

 when collisions occur. If the above ratios were exactly 4 : 1, 

 we should have concluded that molecules actually touch on 

 collision. 



We hope to obtain more accurate determinations of the 

 mean free path of ions by means of other experiments. In 



* Meyer, ' Kinetic Theory of Gases.' 



