THE PROBLEMS OF SOLUTION 113 



each other, against the frictional resistance of the 

 liquid medium. A certain freedom of interchange, 

 at all events, is thus indicated between the ions, 

 and the freedom of interchange exists whether the 

 current passes or not. Such freedom, indeed, had 

 been inferred long ago from the phenomena of 

 double decomposition observed in the chemical 

 reactions between solutions of different salts. 



So far the conductivity relations indicate the 

 possibility of ionic interchange between the parts 

 of the dissolved molecules, though the conformity 

 of solutions with Ohm s law does not, of itself, 

 necessitate the idea of permanent ionic freedom. 

 But on any other view the possibility of inter- 

 change must be secured by collisions between the 

 dissolved molecules, and consequent interchanges 

 between their ions, which would thus work their 

 way through the solution by a series of such 

 collisions. The velocity with which this process is 

 effected must depend on the frequency of collision, 

 which would be proportional to the square of the 

 concentration. The ionic velocities, then, on this 

 supposition, would increase in proportion to the 

 square of the concentration of the solution, and the 

 conductivity, which depends on the product of the 

 ionic velocities and the concentration, would vary 

 as the cube or third power of the concentration. 



But the facts are quite inconsistent with this 

 hypothesis. The conductivity is proportional at 

 the most to the first power of the concentration ; 

 and the ionic velocities, instead of increasing as 

 the square, are, in dilute solution, independent 

 of the concentration, and in more concentrated 

 solutions decrease with increasing concentration. 

 Thus again we are driven to the belief that the 



