178 Dr. 0. W. Richardson on the Structure of 



high the value of pv'/76, when X = l electrostatic unit of 

 potential per centimetre, was eqnal to 425 for positive and 

 505 for negative ions. At low pressures, however, the value 

 of the product for both kinds of ions increased, and this 

 increase commenced at a higher pressure with negative than 

 with positive ions. This increase can be accounted for by 

 supposing that the ions at high pressures consist of a primitive 

 ion combined with a number n of gas molecules. This com- 

 paratively complex ion dissociates as the pressure is reduced, 

 and we get a dynamic equilibrium between the two kinds of 

 ions and the neutral gas molecules. The observed conductivity 

 will thus be due to a mixture of two kinds of ions possessing 

 different ionic velocities. The equilibrium postulated by this 

 hypothesis will be attained long before the ions recombine 

 with those of opposite sign, owing to the fact that the number 

 of ions of either sign present vanishes in comparison with 

 the number of molecules. We shall confine our attention to 

 the case of the negative ions, as the data for the positive are 

 not sufficiently complete. 



Suppose that at any assigned pressure p the gas contains 

 two kinds of negative ions, viz., those which occur alone at 

 high pressures and for which pv/76 = 504, together with those 

 which occur alone at the very lowest pressures and for which 

 pv/76 has a considerably higher value (670). Let C, be the 

 concentration of, and [pv] x the value of pv for, the first kind 

 of ion, and C 2 and \_pv 2 ~] the corresponding quantities for the 

 second kind. The case is in all respects analogous to that of 

 chemical dissociation; and since the first kind give rise to the 

 second as the pressure is reduced, it is evident that the second 

 must be produced with increase of volume. We shall therefore 

 suppose that each ion of the first kind, when it dissociates, 

 gives rise to one ion of the second kind together with n 

 molecules of gas. Since the concentration of the gas is pro- 

 portional to its pressure, we have when equilibrium is attained, 



where k is a constant. 



Now the value of pv which is measured experimentally is 

 the average for the whole of the ions present, and is given by 



p c 1+ o 3 



_ [ pv]2+kp n [P V ]l 

 1 + kp n 



so that 



«._ r ,-,1 - l>1f-l>]i = A . 



