On Kohlrausch's Theory of Ionic Velocity. 43 



molecules of the metals are similar dynamical systems, and 

 also that 



N \T) m 



This concludes the experimental inquiry as to rigidity. The 

 result shows that rigidity in its essence is a kinetic phenomenon 

 almost as simple in character as the elasticity of perfect 

 gases. 



[To be continued.] 



VI. Note on Kohlrausch's Theory of Ionic Velocity, By 

 W. C. Dampier Whetham, B.A., Coutts Trotter Student 

 of Trinity College, Cambridge *. 



KOHLRAUSCH calculates his numbers for the specific 

 velocities of different ions from measurements of the 

 conductivities of salt-solutions, and of their migration con- 

 stants, on the supposition that all the molecules of the salt 

 present in solution are actively concerned in conveying the 

 current. The values thus obtained were found to agree with 

 experiment in certain cases by Prof. Oliver Lodge, and an 

 investigation I am now engaged in carrying out seems also 

 to confirm them. It seems to be generally supposed that this 

 is inconsistent with any theory (such as that of dissociation) 

 which supposes only a certain part of the salt to be active (see 

 Lodge, B. A. Report, 1886, p. 391), though some such form of 

 theory seems to be required by the relations shown to exist by 

 Arrhenius, Yan't Hoff, Ostwald, and others. If we examine 

 the matter a little more closely, however, I think the two sup- 

 positions can be reconciled. Suppose that the ratio of the 

 numbers of the active and the inactive molecules (which is 

 generally supposed to measure the " dissociation ") represents in 

 reality the average ratio of the time during which each molecule 

 is active to the time during which it is inactive. Every mole- 

 cule is in turn active, but at any instant only a certain fraction 

 of the molecules are active. [In terms of the dissociation 

 hypothesis, the dissociation ratio measures the ratio of the 

 mean free time to the mean paired time of the ions.] This is, 

 of course, equivalent to supposing a certain fixed fraction of 

 the whole number of molecules to be active, as far as statical 

 effects, such as osmotic pressure, are concerned, but when we 

 consider the velocities of the ions the case is different. 



* Communicated by the Physical Society: read May 9, 1891. 



