440     Mr.  R.  Moon  on  the  mode  in  which  Stringed  Instruments 
We  can  conceive  the  condensed  wave  extending  itself  horizon- 
tally beyond  the  limits  of  the  cylinder  of  which  we  have  spoken, 
and  then  descending  outside  the  cylinder  below  the  level  of  the 
sounding-board  ;  but  we  shall  have  contemporaneously  a  corre- 
sponding horizontal  extension  of  the  rarefied  wave,  which  must 
have  the  same  faculty  of  extending  itself  upwards  that  the  con- 
densed wave  has  of  extending  downwards. 
What  will  ensue  upon  the  meeting  of  these  two  opposite  dis- 
turbances ? 
One  consequence  of  their  meeting  clearly  will  be  that  the 
density  in  the  plane  of  the  sounding-board  will  be  that  of  equi- 
librium ;  so  that  in  every  direction  in  this  plane  we  shall  have 
an  entire  absence  of  that  alteration  of  density  which,  according  to 
the  received  theory  of  sound,  is  the  sole  agent  in  the  creation 
and  transmission  of  aerial  vibrations*.  Hence,  on  the  principles 
of  that  theory,  the  tones  of  the  instrument  might  be  expected  to 
be  inaudible  at  all  points  in  the  plane  of  the  sounding-board — 
a  phenomenon,  it  may  be  remarked,  which  has  not  hitherto 
been  observed  to  occur. 
But  the  subject  admits  of  being  considered  in  a  different 
manner. 
The  amplitude  of  vibration  of  the  sounding-board  will  be  very 
minute,  at  the  same  time  that  the  agitation  of  the  air  above  it 
occasioned  by  a  single  bound  upwards  of  the  board  will  extend 
over  a  very  considerable  space.  It  is  evident,  therefore,  that  the 
condensation  of  the  air  vertically  above  the  sounding-board  will 
be  extremely  small ;  and  it  is  quite  conceivable  that  the  principal 
influence  of  the  air  within  the  cylinder  in  moving  the  air  without 
the  cylinder  may  not  be  of  the  nature  already  described,  but  may 
be  due  to  lateral  adhesion. 
Assuming  this  to  be  the  case,  it  is  clear  that  the  particles  of 
air  around  the  instrument,  whether  within  or  without  the  cylin- 
der above  spoken  of,  and  whether  above  or  below  the  plane  of 
the  sounding-board,  will  have  this  feature  in  common,  viz.  a  ve- 
locity vertically  upwards.  Hence  it  is  easy  to  see  how  the  air 
in  every  direction,  upwards,  downwards,  and  laterally,  at  any 
given  instant  may  have  a  spherical  arrangement  of  this  kind,  viz. 
that  the  particles  in  each  spherical  shell,  described  about  the 
centre  of  vibration  of  the  sounding-board  as  a  centre,  have  the 
same  absolute  velocity  in  a  direction  vertically  upwards. 
*  It  is  curious  to  note  that  although  in  the  plane  of  the  sounding-board 
the  condensation  and  rarefaction  will  mutually  destroy  each  other,  this 
will  not  be  the  case  with  the  velocities  of  the  two  waves ;  so  that  the  par- 
ticles in  that  plane  will  have  a  vertical  motion.  I  apprehend,  however, 
that  few  will  attempt  to  account  for  the  transmission  of  sound  along  this 
plane  on  the  principles  of  transversal  vibration ! 
