Surface  Elasticity  of  Saponine  Solutions.  321 
the  motion  becomes  aperiodic  (Curve  V.).  On  further  stand- 
ing, the  motion  changes  to  oscillatory  motion  of  the  second 
type.  The  transition  is  first  indicated  by  a  momentary 
retardation  after  the  rapid  initial  motion  (Curve  IV.).  This 
becomes  more  and  more  marked  till  it  amounts  to  an  actual 
stoppage  (Curve  III.).  After  this  a  slight  backward  motion 
can  be  detected.  This  increases  (Curve  II.) ,  and  soon  it 
becomes  possible  to  obtain  two  oscillations,  then  three,  and  so 
on ;  till  on  twisting  the  torsion-head  we  obtain  several,  as  in 
Curve  I. 
A  study  of  the  above  curves  will  show  that  it  is  quite 
useless  to  attempt  to  measure  the  surface-rigidity  statically 
by  means  of  the  torsion-balance.  The  temporary  position  of 
equilibrium  indicated  by  a  stoppage  or  a  backward  movement 
of  the  disk  does  not  afford  any  measure  of  the  ratio  between 
the  torsional  moments  of  the  wire  and  the  surface.  In  the 
following  investigation,  the  elasticity  has  been  measured 
dynamically.     If  the  torsional   moment  of  the  wire  is  very 
small,  we  have 
6  =  A  +  Be' 
provided  that 
Hence 
4^T2>I. 
__  (4tt2  +  X2)I 
*+c 
). 
where  T  is  the  period  and  X  the  logarithmic  decrement  of  the 
oscillations  set  up  by  giving  the  vessel  an  initial  rotation. 
Measurement  of  the  Surface  Rigidity. — Fresh  Surfaces. 
Apparatus. — The  disk  was  made  of  brass  and  had  a  diameter 
of  7 '10  cms.  The  upper  end  of  the  suspending  wire  was 
clamped  to  a  bracket  firmly  fixed  to  the  wall.  The  lower 
end  of  the  wire  was  clamped  centrally  to  a  short  piece  of 
brass  rod  whose  lower  end  could  be  screwed  into  the  centre 
of  the  disk.  A  small  mirror  was  fixed  to  the  rod  so  as  to 
enable  the  motion  of  the  disk  to  be  observed  by  means  of 
a  distant  telescope  and  scale.  The  moment  of  inertia  of  the 
suspended  system  was  2050  grm.cm.2  In  all  the  experiments, 
the  period  of  oscillation  under  the  action  of  the  wire  was 
very  large  compared  with  the  period  under  the  action  of 
the  surface,  so  that  the  torsional  moment  of  the  wire  was 
negligible.     The  vessel  for  holding  the  solution  was  made  of 
Phil.  May.  S.  6.  Vol.  11.  No,  62.  Feb.  1906.  Y 
