and Two New Types of Viscosity. 5 



that the solvent is exercising forces upon the ions tending to 

 bring them back to uniform distribution. This is the same 

 force which produces ionization. Let us denote it by I, some 

 of whose properties we shall obtain in Section 5 ; then we 

 write T proportional to l/qil\ , equal say to C/^IXq where C 

 is a constant, l/q t being introduced because each ion controls 

 stress over area 1/^. Thus for this new viscosity of the ions 

 as an electrically polarized medium, which we shall denote 

 by f, we have 



f=27rC^3/3KIX (4) 



But we must consider another similar type of viscosity. 

 The charges of the ions throw the molecules of the solvent 

 into a state of polarization. We may call this the induced 

 polarization. A charge e at the centre of an ion of radius a 

 causes — e to be induced in the solvent immediately around 

 it over a spherical surface of radius rather larger than a. 

 This e measures the whole electric "displacement" through 

 larger and larger spheres, so that we have an intensity of 

 polarization varying inversely as the square of the distance 

 from the central ion causing it. In my paper on rigidity it 

 is shown that rigidity is equal to the electrostatic energy per 

 unit volume. Hence on account of induced polarity we have 

 an induced rigidity varying inversely as the fourth power of 

 the distance from the ion producing it. If strain associated 

 with this rigidity is relaxed through relative motion of the 

 ion and the rest of the solution, then there is a second type 

 of viscosity of electric origin called into play. On account 

 of the inverse fourth power law, the effects of this are most 

 important quite close to the ion. We can express the polarity 

 caused by the charge e of an ion of radius a by means of a 

 distribution of electricity of surface-density — e/4z7r(a + l) 2 

 over the spherical surface of the solution of radius a + 1 round 

 the ion. As I is the small average gap between ion and 

 solution, we shall neglect it and assume a surface-density 

 — e'4:7ra 2 over the sphere of radius a. The mutual energy of 

 this surface-charge and the central e is e 2 /Iva, where K is the 

 dielectric capacity of the stuff of the ion. This energy we 

 may locate in the volume AiraH between ion and solution. 

 The energy per unit volume is e 2 /47rKa 3 Z, which is the induced 

 rigidity round the ion. For the time of relaxation we may 

 assume that it is inversely proportional to the velocity A of 

 the ion, not the velocity A at zero concentration, because in 

 the previous case we considered all the ions as one medium 

 interspersed through the solvent as another, but in the 

 present case we are considering each ion and its induced 



