[     99    ] 
XI.  On  a  Sh?iple  Case  of  Resonance.     By  Robert  Moon,  M.A., 
Honorary  Fellow  of  Queen's  College,  Cambridge*. 
I  DESIRE  to  direct  attention  to  a  very  simple  instance  of 
resonance,  in  the  attempts  to  explain  which  a  considerable 
amount  of  confusion  appears  to  have  arisen. 
The  case  to  which  I  refer  is  that  described  in  Nos.  185,  186 
of  the  article  on  Sound  in  the  Encyclopedia  Metropolitanaf. 
Suppose  that  a  pipe  closed  at  one  end  has  at  its  opposite  ex- 
tremity a  disk  so  placed  as  nearly  to  close  it;  and  suppose  that, 
by  means  of  a  tuning-fork  or  otherwise,  the  disk  is  made  to  vi- 
brate in  such  a  manner  "  that  the  performance  of  one  complete 
vibration,  going  and  returning,  shall  exactly  occupy  as  much 
time  as  a  sonorous  pulse  would  take  to  traverse"  a  space  equal 
to  double  the  length  of  the  pipe.  The  "first  impulse"  of  the 
disk  upon  "  the  air  will  be  propagated  along  the  pipe  and  re- 
flected at  the  stopped  end,  and  will  again  reach  the  disk  just  at 
the  moment  when  the  latter  is  commencing  its  second  impulse. 
But,  the  absolute  velocity  of  the  disk  in  its  vibrations  being  ex- 
cessively minute  compared  with  that  of  sound,  the  reflected  pulse 
will  undergo  a  second  reflection  at  the  disk  as  if  it  were  a  fixed 
stopper.  It  will,  therefore,  in  its  return  exactly  coincide  and 
conspire  with  the  second  original  impulse  of  the  disk ;  and  the 
same  process  being  repeated  on  every  impulse,  each  will  be  com- 
bined with  all  its  echoes,  and  a  musical  tone  will  be  drawn  forth 
from  the  pipe  vastly  superior  to  that  which  the  disk  vibrating 
alone  in  free  air  would  produce." 
Nothing  can  be  more  lucid,  or  apparently  more  convincing, 
than  this  explanation.  Unfortunately  the  facts  do  not  corre- 
spond with  the  conclusicn  to  which  the  argument  points. 
If  we  are  to  accept  the  very  precise  and  reiterated  statements 
upon  the  subject  of  Professor  Tyndall  (Tyndall  'On  Sound/  ubi 
svpra),  such  an  increase  of  tone  as  that  above  referred  to  occurs, 
not  when  the  length  of  the  pipe  is  half,  but  when  it  is  one 
quarter  of  the  length  of  a  wave  whose  period  of  vibration, 
"  going  and  returning,"  is  the  same  as  that  of  the  disk  ;  and  if 
the  above  process  of  reasoning  be  applied  to  this  altered  state  of 
circumstances,  it  will  be  found  to  lead  to  a  conclusion  precisely 
the  opposite  to  that  which  has  been  above  arrived  at. 
For,  supposing  the  "first  impulse"  propagated  by  the  disk 
into  the  pipe  to  consist  of  a  condensation  f,  such  condensation 
will  have  entered  the   pipe,   will  have  been  reflected  at  the 
*  Communicated  by  the  Author, 
t  See  also  Tyndall  '  On  Sound/  186/,  pp.  1/3-5. 
X  The  adoption  of  the  alternative  supposition  would  lead  to  the  same 
conclusion. 
H  2 
