434  Mr.  E.  F.  Burton  on  the  Properties  of 
of  solid  and  liquid,  and  /  is  a  linear  magnitude,  measuring. 
the  u  facility  of  slipping  "  and  equal  to  ~  ; 
m  being  the  coefficient  of  viscosity  of  the  liquid. 
/3  the  coefficient  of  sliding  friction  of  fluid  in  contact 
with  the  wall  of  the  tube. 
Lamb  gives  reasons  for  supposing  that  I  and  d  are  of  the 
same  order  of  magnitude  (that  of  10~8  cms.).  Of  course  if 
l  =  d.  HelmhohVs  formulae  remain  unchanged,  and  it  is  very 
probable  that  the  ratio  —,   differs  very  little  from  unity. 
Lamb  deduces  the  following  expression  for  the  velocity  (y) 
of  a  charged  particle  through  a  liquid  under  an  electric 
force,  when  the  motion  has  become  steady : — 
Xe=±7rcr  .  fju  .  v  .-    , (2) 
where     X  =  gradient  of  electric  potential  in  the  liquid. 
e  =  charge  on  the  particle. 
a  =  radius  of  the  particle, 
and  /L6  and  /  as  above. 
We  may  look  upon  the  particle  with  the  double  electric 
layer  as  a  small  condenser  of  two  concentric  spheres  whose 
distance  apart  (d,  same  as  before)  is  small  compared  with  a. 
The  capacity  of  such  a  condenser  would  then  be  given  by 
G=iK>    (8) 
where  K  =  s.i.c.  of  the  medium  between  the  layers. 
If  V  indicates  the  contact  difference  of  potential  between 
the  solid  and  the  liquid,  we  have 
«=?£.*; (4) 
substituting  this  value  of  e  in  equation  (2)  and  transposing 
we  get 
v-©=x-f' v 
all    electrical    measurements    being    made    in    electrostatic 
units. 
This  equation,  which  is  similar  to  one  given  by  Perrin*. 
*  Jour,  de  Chun.  Phys.  t.  xi.  no.  10,  p.  607  (1904). 
