Gases by the Motion of Negatively charged Ions. 217 



latter were at rest. The mean free path of a molecule 

 travelling in an atmosphere in which the molecules are at 

 rest would he greater in the ratio v /2 = l*41 than the free 

 path when all the molecules are moving with their velocities 

 of agitation *. We therefore conclude that a molecule of air 

 moving with a great velocity through a centimetre of air at 

 1 millimetre pressure would make 90*7 collisions. 



An ion under similar circumstances makes 21 collisions. 

 Hence the ratio of the free paths is 4'3 : 1. This bears out 

 the conclusion to which we were led from other considera- 

 tions, that the negative ion is small compared with a 

 molecule. If we disregard the charge on the ion and con- 

 sider that it is a material particle whose dimensions are 

 small compared with those of a molecule, its free path would 

 be four times the free path of a molecule. The ratio which 

 we have obtained 4*3 : 1 shows that the number of collisions 

 made by an ion, estimated according to the theory of vis- 

 cosity of gases, would be 7 per cent, greater than the 

 number of collisions in which it is possible for new ions to 

 be formed. 



Let 2S be the distance between the centres of two mole- 

 cules of air when a collision occurs, and let d be the dis- 

 tance between the centre of a molecule and the centre of an 

 ion when new ions are formed. 



Then 4S^ _ 4^5 



<P ' 1 * 



Hence d = -96 S. 



It is usual to assume that S is the radius of the sphere of 

 action which surrounds a molecule, and that the radius of 

 the molecule is much smaller. If we adopt this view, it will 

 be found difficult to explain the results at which we have 

 arrived. It would appear from the above value of d that new 

 ions are made when the original ion comes inside the sphere 

 of action of a molecule, provided that the velocity of the ion 

 is sufficiently great. The effect of a collision under these 

 circumstances ought to diminish as the velocity of the ion is 

 increased ; the experiments, on the contrary, show that the 

 production of ions increases as the velocity is increased. 



It therefore appears from the results of the present 

 experiments that some part of the molecule itself must 

 extend to a distance S from the centre, in order that an ion 

 should produce two new ions when c Z = * 9 (3 S. 

 * Maxwell, Phil. Mag. xix. (1863). 

 Phil. Mag. S. G. Vol. 1. No, 2. Feb. 1901. Q 



