Doppler's  principle  can  be  very  strikingly  observed  in  the
case  of  sound  waves,  because  of  the  slow  velocity  with  which
they  travel;  it  is  perfectly  easy  to  produce  experimentally
velocities  of  translation  of  the  sounding  body  or  the  observer
which  are  more  nearly  comparable  with  the  velocity  of  sound
than  we  can  in  the  case  of  light.     This  was  first  done  by


644  SPECTROSCOPY

Buys-Ballot,'  in  1845,  who  made  observations  with  locomotives
on  the  Netherlands  railway.  Probably  most  people  are  familiar
with  the  change  in  pitch  which  takes  place  in  the  whistle  of  an
engine  as  they  pass  in  a  fast  travelling  railway  train,  especially
if  when  in  a  fast  train  an  engine  is  passed  rnoving  in  the
opposite  direction  and  whose  whistle  is  sounding ;  the  same
may  be  noticed  in  the  flattening  of  the  pitch  of  a  bicycle  bell
as  it  passes  in  the  street.  Since  the  velocity  of  light  is  so
great  very  great  speeds  are  necessary  to  produce  a  measurable
change  in  the  oscillation  frequency  of  a  spectrum  line.  The
motion  necessary  to  produce  a  particular  change  in  the
frequency  may  be  found  from  the  equations  given  above.  In
Case  2,  of  observer  at  rest  and  source  in  motion,  we  have —

V

and  thus  \v  +  bk  =  v\',

v '
thence  b  =  -AX  —  A')  for  approach  when  A


is  less  than  A,


V ,


and  b  -  t-(A'  —  A)  for  recession  when  A

is  less  than  A',
Generally,  therefore,        +  b  =  -r— >

where  AA  is  the  change  in  wave-length  observed.
