and Tlco New Types of Viscosity. 3 



2. Tico New Types of Viscosity of Electric Origin, and 

 Fundamental for Uie Theory of Electrolytic Conduction. 



In the previous paper, the resistance to the motion of an 

 ion was written down simply as that calculated by Stokes 

 for the motion of a sphere through a viscous fluid. That 

 expression suffices for the electrically neutral molecule 

 diffusing in a non-electrolytic solution. But in an electro- 

 lytic solution the electric forces acting amongst the ions 

 introduce powerful stresses and in association with them 

 important viscosities of an interesting type. As the solvent 

 in ionizing the solute pulls the ions of the molecule asunder 

 against their strong electric attraction, we must suppose that 

 in general it keeps a positive ion as far as possible from its 

 nearest negative neighbours. Thus the positive and the 

 negative ions are uniformly distributed through the solvent, 

 which preserves the average uniformity in such a way that 

 each of 2q ions in a volume 1 is at the centre of a domain l/2q, 

 and the domains are arranged in regular order, those of 

 positive and negative ions occurring alternately. In this way 

 an ionized solution is the seat of a powerful distribution of 

 polarity similar to that which I have taken to be the basis of 

 rigidity (" The Electric Origin of Rigidity," Phil. Mag. [6] 

 vii. p. 417). On the sudden application of electric force to 

 an ionized solution the positive ions begin to move with the 

 force and the negative against it, straining the polarization 

 from its state of uniformity. There is an instantaneous 

 resistance due to the rigidity of the regularly distributed ions. 

 But the actions which produced the original uniformity tend 

 to restore it, so that the ions move so as to relax the strain. 

 The rate at which they yield is best specified by Maxwell's 

 time of relaxation (" The Dynamical Theory of Gases," Phil. 

 Mag. [4] xxxv. 1868). Maxwell's method of passing from 

 rigidity to viscosity, founded upon conceptions of the great 

 French school of elasticians, is the following : — 



In a piece of matter a strain is produced by displacement s 

 and the stress F is excited. Then by Hooke's law F = Es. 

 In a solid body free from viscosity E is a constant coefficient 

 of elasticity, and 



dF/dt = Eds/dt. 



But in a viscous body F is also a function of the time, and 

 tends to disappear at a rate depending on F and the nature 

 of the substance. Suppose this rate proportional to F, then 



OF/dt = Fds/dt -F/T, 



B2 



