318  Mr.  S.  A.  Shorter  on  the 
The  Mechanical  Properties  of  the  Surface  Layer. 
On  examining  the  surface  in  the  usual  way  by  means  of 
the  torsion-balance,  it  was  found  that  the  effect  of  the  surface 
on  the  motion  of  the  disk  depends  upon  the  dimensions  of 
the  various  parts  of  the  apparatus.  If  a  very  powerful  wire 
is  used,  twisting  the  torsion-head  sets  up  oscillations  which 
are  damped  by  the  surface.  If  a  very  weak  wire  is  used,  a 
large  rotation  is  required  to  set  up  visible  motion,  and  this 
motion  consists  of  a  simple  drift  towards  the  position  of 
equilibrium  of  the  wire.  With  wires  of  intermediate  strength 
it  is  possible  to  obtain  some  indication  of  a  temporary  position 
of  equilibrium.  The  disk  moves  rapidly  forward,  suddenly 
comes  to  rest  for  an  instant,  and  then  moves  forward  again. 
With  a  wire  of  suitable  torsional  moment  it  is  possible  to 
obtain  a  type  of  motion  which  clearly  demonstrates  the  elastic 
nature  of  the  forces  called  into  play  by  the  shearing  of  the 
surface.  On  twisting  the  torsion-head  the  disk  moves 
forward,  comes  to  rest,  and  then  moves  back  against  the 
torsional  couple  of  the  icire,  comes  to  rest,  moves  forward 
again,  and  so  on  :  in  this  way  executing  a  few  rapid  oscilla- 
tions before  settling  clown  to  a  simple  drift.  These  oscillations 
do  not  take  place  about  a  fixed  centre.  The  motion  is  a 
compound  of  clamped  oscillatory  motion  and  translational 
motion  in  the  direction  of  the  initial  twist  of  the  wire. 
It  is  difficult  to  obtain  these  oscillations  with  a  fresh  surface. 
Thev  are  more  readily  obtained  after  the  solution  has  been 
standing  for  some  time.  If,  however,  the  motion  is  started 
by  giving  the  vessel  containing  the  solution  a  small  rapid 
rotation,  oscillations  are  easily  obtained  provided  the  moment 
of  inertia  of  the  suspended  system  is  not  too  great.  If 
the  suspending  wire  has  a  very  small  torsional  moment, 
the  motion  set  up  is  damped  oscillatory  motion  without 
translation. 
It  is  clear  that  shear  in  g  of  the  surface  gives  rise  to  forces 
of  an  elastic  nature.  These  forces  are  not  permanent,  so  that 
the  surface  maybe  described  as  viscous-elastic.  We  will  next 
investigate  mathematically  the  effect  of  a  viscous-elastic 
medium  on  the  motion  of  the  disk. 
Mathematical  Tlieory  of  the  Motion. 
Suppose  a  circular  disk  of  radius  r±  and  moment  of  inertia  I 
to  be  suspended  by  a  wire  of  torsional  moment  e.  Let  the 
disk  touch  centrally  the  surface  of  a  saponine  solution  con- 
tained in  a  circular  vessel  of  radius  r2.  Let  6  be  the  angular 
displacement  of  the  disk  from  the  position  of  zero  torsion  of 
