636 Prof. Townsend and Mr. Kirkby on Conductivity produced 



The equation takes into account the fact that each negative 

 ion generated by collision produces a. ions per centimetre as 

 well as the original n ions. 



In our experiments the number n is easily found for the 

 larger pressures, being proportional to the smallest current 

 given in the tables. In these cases the force acting on the 

 gas is insufficient to cause new ions to be produced by 

 collisions, and is large enough to collect all the ions generated 

 "by the rays on the plates. This is obvious from the fact that 

 the current is practically constant for a large range of forces 

 of the order of 80 volts per centimetre. 



The ratio - for any other force X is the ratio of the 



n J 



current produced by X to the current obtained with the 

 smallest force given in the tables. These ratios can therefore 

 be obtained by experiment, and by means of equation (1) the 

 values of a corresponding to the different values of X and p 

 can be calculated. The values of a obtained by equation (1) 

 for a fixed pressure and force were the same for different 

 values of /. 



This point was examined very carefully with air ; and it will 

 be seen from the experiments given in the two previous papers, 

 that when a is constant the effects produced by changing the 

 distance / are in accordance with the formula. At lower 

 pressures, when new ions are generated with forces less than 

 80 volts per centimetre, the current corresponding to n Q was 

 found by an application of the theory to which we have 

 already alluded, and of which we shall give a simple expla- 

 nation. 



In section 5 of the paper in the Phil. Mag. to which we 

 have referred, it was shown that an ion travelling freely be- 

 tween two points differing in potential by 4 volts acquires a 

 velocity ten times as great as its mean velocity of agitation. 

 If we assume for the present that the mass of a negative ion 

 is smaller than the mass of a molecule of a gas, then the 

 velocities acquired by the negative ions under small electro- 

 motive forces will be so great in comparison with the velocities 

 of agitation of the molecules, that the latter may be considered, 

 to be at rest. 



In travelling under an electric force through the gas, an ion 

 makes a number of collisions with the molecules, the velocities 

 of impact depending upon the free paths. The circumstances 

 attending the collisions will vary in many ways, and the 

 impacts may be considered to be of various typos, On some 

 occasions, when the velocity of the colliding ion is sufficiently 

 great, the effect of the collision will be to produce two new 



