Mr.  R.  Moon  on  a  Simple  Case  of  Resonance.  103 
shown,  have  been  increased;  and  the  rarefaction  which  it  leaves 
behind  it  will  be  increased  in  like  manner;  so  that  this  latter 
disturbance  (that  is  to  say,  the  rarefaction  to  the  right  of  the 
disk  which  its  motion  to  the  left  tends  to  create)  will  not  be  en- 
tirely destroyed  by  interference  with  the  original  condensed  wave; 
in  other  words,  we  shall  have  at  the  beginning  of  the  third  in- 
terval tt  a  rarefied  wave  in  position  and  circumstances  precisely 
similar  to  the  original  condensed  wave  at  the  beginning  of  the 
second  interval  tt;  i.  e.  by  reflection  at  C  it  will  have  become 
doubled  upon  itself  within  the  portion  C  D  of  the  pipe,  and  will 
be  on  the  point  of  undergoing  reflection  at  the  disk. 
The  reflection  of  this  rarefied  wave  at  the  disk  will  have  the 
effect  of  subjecting  the  latter  at  each  instant  of  the  third  inter- 
val t{  to  the  influence  of  two  rarefactions,  the  presence  of  each 
of  which  is  entirely  attributable  to  the  occurrence  of  the  stopper 
at  C ;  viz.  the  rarefaction  of  the  reflected  portion,  together  with 
that  also  of  the  unreflected  portion  of  the  last-mentioned  wave. 
The  tendency  of  these  will  manifestly  be  to  solicit  the  disk  in 
the  direction  in  which  it  is  moving,  and  a  further  increase  in  the 
amplitude  of  excursion  of  the  disk  wTill  necessarily  take  place. 
The  same  reasoning  will  apply  to  the  motion  of  the  disk  du- 
ring successive  intervals,  till  at  last,  supposing  the  impulses  to 
be  communicated  to  the  disk  by  means  of  a  tuning-fork,  the  in- 
creasing rigidity  of  the  fork  will  prevent  any  further  enlarge- 
ment of  its  excursions  -y  but  in  the  mean  time  such  an  increased 
amplitude  of  excursion  will  have  been  produced  as  fully  to  ac- 
count for  the  great  increase  of  tone  which  takes  place  under  the 
circumstances  which  we  have  been  considering. 
If  it  be  asked  why,  in  the  case  discussed  by  Sir  John  Her- 
schel,  the  tendency  to  accumulation  of  vibrations  in  the  closed 
tube  does  not  produce  the  effects  he  supposed  to  result  from  it, 
it  may  be  replied  that,  if  the  reasoning  which  I  have  applied  to 
Professor  Tyndall's  case  were  adapted  to  Sir  John  Herschel's 
case,  it  would  immediately  appear  that  the  stopper  at  C,  by  re- 
flecting a  wave  back  upon  the  disk,  would  have  the  effect  of  dimi- 
nisking  the  excursion  of  the  latter  and  the  consequent  loudness 
of  the  sound. 
I  may  also  observe  that,  if  in  Sir  John  HerscheFs  case  all  the 
accumulation  took  place  which  he  supposed  to  occur,  the  loud 
sound  spoken  of  could  only  be  intermittent,  prevailing  at  most 
during  very  brief  intervals  separated  by  much  longer  intervals  of 
almost  total  silence — a  variation  in  the  phenomenon  which,  so 
far  as  I  am  aware,  has  not  been  observed  to  occur. 
G  New  Square,  Lincoln's  Inn, 
January  ('),  1872. 
