100  Mr.  R.  Moon  on  a  Simple  Case  of  Resonance. 
closed  end  thereof,  and  will  be  on  the  point  of  emerging  from 
the  open  end  and  of  undergoing  reflection  at  the  disk,  at  the 
precise  moment  that  the  latter  is  going  to  give  birth  to,  and  to 
propagate  within  the  pipe,  a  rarefaction.  These  two  disturbances, 
therefore,  t.  e.  the  twice  reflected  original  condensation  and  the 
first  rarefaction,  will  enter  the  pipe  together,  and  will  mutu- 
ally destroy  each  other  by  interference.  So  far  is  it,  therefore, 
from  being  true  that,  under  the  circumstances  referred  to,  "  the 
motion  accumulates  in  the  "  pipe  so  as  to  produce  a  "  vast  aug- 
mentation of  sound,"  the  process  of  reasoning  which  has  been 
adopted  tends  to  show  the  exact  contrary,  viz.  that  there  would 
be  in  the  pipe  immediately  after  the  second  impulse  was  con- 
cluded no  motion  whatever,  and  that  the  sonorous  effect  of  the 
vibrating  disk,  so  far  from  being  enhanced,  would  be  positively 
destroyed  by  the  closure  of  the  pipe. 
There  will  be  no  difficulty,  however,  in  explaining  this  re- 
markable phenomenon  if  we  consider  carefully  the  mode  in  which 
aerial  waves  are  generated  by  the  vibrating  disk. 
Suppose  the  pipe  A  B  to  be  open  at  both  ends,  and  that  we 
have  placed  within  it  a  closely  fitting  disk,  represented  by  D  ~D', 
capable  of  sliding  within  the  pipe ;  and  let  us  consider  the  effect 
of  the  disk  being  removed  from  one  position  of  rest,  D  D!,  to  an- 
other, dd',  during  the  interval  tr 
1)'  d> 
A  D  d  C  B 
It  is  evident  that  at  any  instant  during  the  first  portion  of  tt 
we  shall  have  to  the  right  of  the  disk  a  disturbance  in  the  nature 
of  a  condensation,  in  which  the  velocity  and  condensation  respec- 
tively will  have  their  maximum  values  at  the  point  of  contact 
with  the  disk,  and  will  thence  gradually  diminish  as  we  recede 
to  the  right  till  they  simultaneously  vanish ;  while  at  the  same 
instant  we  shall  have  on  the  left  side  of  the  disk  a  disturbance 
in  the  nature  of  a  rarefaction,  in  which  the  velocity  and  rarefac- 
tion will  in  like  manner  be  at  a  maximum  at  the  point  of  contact 
with  the  disk,  and  will  thence  gradually  dimmish  as  we  recede 
to  the  left  till  they  simultaneously  vanish. 
The  state  of  things  just  described  will  continue  till  the  disk 
has  attained  its  maximum  velocity,  at  which  epoch  the  air  in  con- 
tact with  it  on  either  side  will  also  have  its  maximum  velocity ; 
the  air  to  the  right  in  contact  with  the  disk  having  at  the  same 
time  its  maximum  condensation,  while  that  to  the  left  has  its 
maximum  rarefaction*. 
Subsequent  to  this,  at  any  instant  during  the  remainder  of  tt, 
*  The  two  disturbances  will  be  symmetrical  with  respect  to  the  disk  in 
