Surface  Elasticity  of  Saponine  Solutions.  31^ 
the   wire,  and  let   L  be  the    moment  of  the  viscous- elastic 
forces  acting  on  the  disk. 
Neglecting  the  inertia  and  ordinary  viscosity  of  the  liquid, 
the  equation  of  motion  of  the  disk  will  be 
(ll- 
We  will  assume  that  the  quantity  L  obeys  the  equation 
dh  _    iie  _  l 
dtZ^dt       t' 
where  \x  is  related  to  the  absolute  coefficient  of  surface- 
rigidity  by  the  equation 
47r  v  i\2  r22 
The  dimensions  of  n  (which  we  need  not  formally  define) 
are  of  course  those  of  an  ordinary  coefficient  of  rigidity 
multiplied  by  a  length. 
Eliminating  L  between  the  first  two  equations,  we  have 
I  +  T#  +  TS+hH 
the  solution  of  which  takes  one  of  the  form? 
or 
0  =  Ae-"t  +  Be-&  cos(7/  +  C). 
according  as 
io 
4  (e  +  nf  t-(h2  +  20  e  fji  —  Se2)  I  t-  +  4e  I2  JO. 
There  are  three  possible  types  of  motion  :  (1)  when  r  is- 
so  small  that  the  above  expression  is  positive  ;  (2)  when  the 
expression  is  negative  ;  (3)  when  r  is  so  large  that  the 
expression  is  positive.  For  convenience  we  shall  refer  to 
these  as  (1)  oscillatory  motion  of  the  first  type  ;  (2)  aperiodic 
motion ;  (3)  oscillatory  motion  of  the  second  type.  The  two 
types  of  oscillatory  motion  are  quite  distinct.  When  t  is 
very  small  the  disk  oscillates  under  the  action  of  the  wire  and 
the  surface  exercises  a  damping  effect  on  the  motion.  When 
t  is  very  large  the  disk  oscillates  under  the  combined  action 
of  the  elastic  forces  of  the  disk  and  surface. 
Motion  according  to  the  equation 
flsAtJ-^  +  B*-^  cos(7*  +  C) 
is  not  necessarily  oscillatory  in   the  ordinary  sense  of  the 
