Mr.  R.  Moon  on  a  Simple  Case  of  Resonance.  101 
the  disturbances  will  be  of  this  kind  :  viz.  to  the  right  the  velo- 
city and  condensation  will  increase  till  each  attains  its  maximum, 
and  will  thence  gradually  diminish  till  they  vanish  together; 
while  on  the  left  hand  the  disturbance  will  be,  mutatis  mutandis, 
of  precisely  similar  character. 
At  the  end  of  the  interval  tl  we  shall  have  on  either  side  of  the 
disk  a  complete  wave,  on  the  right  of  condensation,  on  the  left 
of  rarefaction,  each  capable  of  propagating  itself  without  the  aid 
of  the  disk,  whose  creative  function  with  regard  to  each  will  be 
then  finally  closed. 
It  results  from  what  has  preceded,  that  at  each  instant  of  the 
interval  t/  we  shall  have  on  the  right  of  the  disk,  and  acting  upon 
it,  a  condensation,  on  the  left  a  rarefaction — the  difference  of 
which  will  constitute  a  retarding  force,  which  must  have  the 
effect  of  reducing  the  amplitude  of  vibration  of  the  disk,  and  of 
reducing  consequently  the  loudness  of  any  sound  which  may  be 
due  to  such  vibration. 
I  now  proceed  to  show  that  in  the  experiment  before  us  the 
effect  of  closing  the  pipe  at  the  point  indicated  by  Professor 
Tyndall  is,  by  detaining  the  aerial  waves  and  returning  them 
successively  upon  the  disk  at  the  proper  moment,  to  destroy  or 
reduce  the  retarding  force  exerted  upon  the  disk  by  the  sur- 
rounding air,  so  that,  up  to  a  certain  limit,  the  amplitude  of 
vibration  of  the  disk,  and  with  it  the  intensity  of  the  sound 
resulting  from  its  motion,  will  be  increased  at  each  succeeding 
excursion. 
Let  us  now  suppose  the  pipe  to  be  closed  by  a  fixed  stopper 
at  C,  CD  being  equal  to  half  the  length  of  the  wave  of  conden- 
sation produced  by  the  motion  in  the  time  tt  of  the  disk  from 
D  J)'  to  d  d'}  or  equal  to  a  quarter  of  the  mixed  wave  of  conden- 
sation followed  by  rarefaction  which  would  be  produced  by  the 
vibration  of  the  disk  in  the  time  2tt  from  DD'  to  dd!  and  vice 
versa. 
The  motion  of  the  disk  from  D  D'  to  dd!  will' have  forced  into 
the  portion  of  the  pipe  to  the  right  a  condensed  wave,  which  will 
be  reflected  at  C,  and  at  the  end  of  the  time  t,  will  be  ready  for 
reflection  at  the  disk;  precisely  at  the  moment  when  the  latter, 
by  its  return  movement  from  d  d1  to  D  Df,  is  preparing  to  propa- 
gate into  the  portion  dC  of  the  pipe  a  rarefied  wave. 
Hence  at  any  instant  during  the  second  interval  tt  (in  which 
the  disk  moves  from  dd'  to  DD')  we  shall  have  the  following 
disturbances  to  the  right  of  the  disk,  viz. : — 
this  sense,  viz.  that  at  equal  distances  from  the  latter  the  excess  above  the 
mean  density  of  the  one  will  be  equal  to  the  defect  below  that  density  of 
the  other,  at  the  same  time  that  the  velocities  are  equal  and  in  the  same 
direction. 
