102  Mr.  R.  Moon  on  a  Simple  Case  of  Resonance. 
1.  The  portion  of  rarefied  wave  which  the  retreat  of  the  disk 
towards  D  D'  will  have  created. 
2.  The  portion  of  the  condensed  wave  before  spoken  of,  which 
has  already  undergone  reflection  at  the  disk. 
3.  The  remainder  of  the  same  condensed  wave,  i.  e.  the  por- 
tion of  it  which  has  still  to  undergo  such  reflection. 
Of  these  three  superposed,  or  partially  superposed  disturb- 
ances— assuming  the  motion  of  the  disk  during  the  second  in- 
terval tt  to  be,  except  as  regards  direction,  the  same  as  in  the 
first — the  first  two  will  destroy  each  other  by  interference,  in 
the  manner  already  explained,  leaving  the  third  as  that  which 
alone  needs  to  be  regarded  in  estimating  the  pressure  exerted  on 
the  right  face  of  the  disk  during  the  second  interval  tr 
On  the  other  hand,  on  the  same  assumption  as  to  the  motion 
of  the  disk,  it  is  clear  that  the  pressure  on  the  left  side  of  the 
disk  at  any  instant  during  the  second  interval  ti  will  be  that  due 
to  a  condensation,  and  will  be  equal  to  the  pressure  at  the  same 
instant  on  the  opposite  side  of  the  disk  which  would  be  due  to 
the  reflected  portion  of  the  condensed  wave,  supposing  no  such 
interference  as  before  mentioned  to  have  taken  place — and 
therefore  equal  to  the  pressure  actually  exerted  on  the  disk  by 
the  unreflected  portion  of  the  condensed  wave,  since  the  pres- 
sures on  the  disk  of  these  two  portions  of  the  condensed  wave  are 
necessarily  equal. 
On  the  above  assumption,  therefore,  as  to  the  motion  of  the 
disk,  it  is  clear  that  the  pressures  on  the  two  sides  of  the  disk  at 
any  instant  during  the  second  interval  tt  would  be  equal  and  op- 
posite, so  that  there  would  be  an  entire  absence  of  any  such 
force  restraining  the  motion  of  the  disk  as,  if  the  tube  were  left 
open,  would  necessarily  exist. 
It  follows,  therefore,  that  during  the  second  interval  tt  the 
disk  will  move  through  a  longer  space  than  it  did  during  the 
first,  and  that  this  increased  amplitude  of  vibration  is  due  exclu- 
sively to  the  presence  of  the  stopper  at  C. 
During  the  next  vibration  of  the  disk  (i.  e.  in  its  motion  to  the 
right  during  a  third  interval  t,)  similar  effects  will  occur.  In 
this  case,  however,  the  argument  may  be  presented  more  simply 
in  a  somewhat  different  form. 
If  the  closure  of  the  tube  had  no  effect  in  accelerating  the 
motion  of  the  disk  during  the  second  interval  tj}  it  is  clear  that 
at  the  beginning  of  the  third  interval  tt  the  air  to  the  right  of  the 
disk  would  be  at  rest,  since  the  whole  of  the  original  condensed 
wave  would  then  have  undergone  reflection  at  the  disk  and  have 
been  destroyed  by  interference  in  the  manner  already  explained. 
But  by  reason  of  the  closure  of  the  tube  the  excursion  of  the 
disk  to  the  left  during  the  second  interval  tt  will,  as  already 
