[     439     ] 
LY.  On  the  Mode  in  which  Stringed  Instruments  give  rise  to 
Sonorous  Undulations  in  the  surrounding  Atmosphere.  By 
Robert  Moon,  M.A.,  Honorary  Fellow  of  Queen's  College, 
Cambridge*. 
THAT  the  tones  of  a  stringed  instrument  are  due  to  the 
action  upon  the  air  of  the  sounding-board,  and  in  no  per- 
ceptible degree  proceed  from  the  direct  action  upon  the  air  of 
the  strings  themselves,  may  be  taken  to  be  one  of  the  earliest 
discovered  facts  in  acoustics,  since  it  is  clear  that  no  such  in- 
strument of  any  of  the  kinds  with  which  we  are  familiar  could 
have  been  constructed  in  ignorance  of  it.  But  the  mode  in 
which  the  sounding-board  acts  on  the  surrounding  atmosphere 
so  as  to  give  rise  to  sonorous  undulations  is  a  subject  which  pre- 
sents extraordinary  difficulties,  which,  so  far  as  I  am  aware,  have 
not  been  adverted  to. 
Consider  the  case  of  the  grand  pianoforte  with  the  lid  wholly 
removed. 
The  sounding-board  consists  of  a  single  plate,  which  is  shrunk 
into  a  frame  in  such  a  manner  as  to  present  a  surface  which  is 
convex  upwards. 
The  lower  surface,  which  is  exposed  to  the  air,  is  crossed  at 
intervals  by  narrow  bands,  which  increase  its  rigidity  and  con- 
sequently its  sonorous  power,  but  which  need  not  further  attract 
our  attention. 
The  strings,  through  the  medium  of  the  bridge  which  is  firmly 
fixed  to  the  sounding-board,  exert  a  downward  pressure  on  the 
latter,  and  thus  bring  it  into  a  state  of  constraint  f, 
When  a  note  is  sounded,  the  hammer  striking  the  wire  up- 
wards, the  downward  pressure  on  the  bridge  is  relieved,  and  the 
sounding-board  bounds  upwards.  Thus  a  wave  of  condensation 
will  be  propagated  vertically  upwards,  and  a  wave  of  rarefaction 
vertically  downwards. 
The  mode  in  which  the  vibrations  of  the  board  may  be  pro- 
pagated vertically  above  or  vertically  below  the  instrument  is 
thus  conceivable  enough ;  but  what  of  the  space  outside  of  a 
vertical  cylinder  having  the  sounding-board  for  one  of  its  sec- 
tions ?  and  how  are  these  two  diverse  disturbances  (the  one  a 
condensation,  the  other  a  rarefaction)  to  combine  themselves  into 
a  spherical  wave  wholly  of  condensation  or  wholly  of  rarefaction, 
or  compounded  of  condensation  and  rarefaction  in  immediate 
sequence,  such  as,  to  common  apprehension,  appears  the  alone 
sufficient  agent  for  the  diffusion  of  sound  ? 
*  Communicated  by  the  Author. 
T  For  the  above  details  I  am  indebted  to'the  kindness  of  Mr.  Bruzaud, 
of  the  firm  of  Messrs.  Erard. 
