106 THE ROYAL SOCIETY OF CANADA 



in the liquid, "e" the effective charge on the particle and mg the 

 gravitational pull on the particle in the water. The difference be- 

 tween the up and down motion will then be due to the settling caused 

 by gravity and to this motion Stokes' Law can be applied. 



The objection suggests itself that we are taking account of the 

 action of the weight of the particle although when the solution is not 

 acted upon by the electric field there is no settling noticeable. When 

 there is any appreciable settling the particle must attain a limiting 

 velocity, v, corresponding to the Stokes' formula, 



Weight = mg = ôtt n a v 



This requires a certain interval of time, for the particle begins to move 

 from rest and is accelerated under the force of gravity; the smaller 

 the particle the less the limiting velocity. At the same time the 

 smaller the particle, the greater the influence of the Brownian move- 

 ment caused by molecular shocks. Particles which do not show any 

 settling are those for which the Brownian movement is so large, that* 

 is, those for which the molecular shocks in random directions are so 

 potent, that the particles do not get a chance to attain the limiting 

 velocity in a downward direction due to gravitation. However, when 

 a vertical electrical fiteld is applied, which gives a motion to the par- 

 ticle greatly in excess of either the gravitational or Brownian move- 

 ment, the particles are dragged up or down through the liquid; under 

 such conditions, the comparatively insignificant gravitational force 

 will be added to the electrical for downward motion and subtracted 

 for upward motion. 



If V = limiting velocity due to electrical field, 

 and V = limiting velocity due to gravitation 



Xe+mg = 67r n a (V-|-v) (4a) 



Xe-mg=67: n a (V-v) (46) 



Subtracting these we have 



2 mg— 12k n a v 

 from which by equation (1) 



^2 = 9 n V 



2 ' {p-p')ë 

 In the table above for colloidal silver particles we have a motion 

 of 1 mm. in 20 minutes recorded. This gives for "v" in the above 

 formula 8-3X10"^ cm. per sec. Putting n equal to the viscosity of 

 water at 11°C. viz. 0-012 and p for silver equal to 10-5, we have 



a = 2-2XlO-^ cm. 



