on  the  Translation  of  a  Vibrating  Body.  281 
Quantitative  Relations  in  the  experiments  and  analogical  facts  in 
the  phenomena  of  Light. 
The  UT3  No.  1  fork  makes  256  complete  vibrations  in  one 
second,  while  fork  No.  3  makes  254,  giving  for  the  respective 
wave-lengths  of  these  vibrations  4*367  and  4-401  feet,  which  we 
will  designate  in  order  as  X  and  X1 :  we  will  take  1118  feet  per 
second  as  the  velocity  of  sound  at  60°  Fahr. 
Now 
256  vibrations  in  1118  feet  make     ....     X=4*367feet, 
and 
254  vibrations  in  1118-2X  (  =  1109*266)  make  \= 4*367  feet. 
As  the  velocity  of  propagation  of  the  vibrations  and  X  are  the 
same  in  both  cases,  it  follows  that  (n=  —  V  the  number  of  vi- 
brations in  a  second  reaching  a  distant  point,  is  the  same,  and 
therefore  256  vibrations  from  a  body  at  rest  will  produce  the 
same  effect  on  a  distant  surface  as  254  vibrations  emanating 
from  a  body  which  moves  towards  that  surface  with  a  velocity  of 
2X  or  of  8*734  feet  per  second  ;  and  this  is  the  velocity  we  gave 
the  forks  in  exps.  6  to  9. 
We  will  now  examine  analogical  phenomena  in  the  case  of 
light.  Fork  1  giving  256  vibrations  a  second,  let  these  represent 
595  million  million  vibrations  a  second,  which  we  will  take  as  the 
number  of  vibrations  made  by  the  ray  Dj  of  the  spectrum.  Then 
fork  No.  3  will  represent  590  million  million  vibrations  per  se- 
cond, which  give  a  wave-length  '0000042  millimetre  longer  than 
that  of  Dp  and  near)y0correspond  with  an  iron  line  situate  *42 
division  below  D2  on  Angstrom's  chart.  We  saw  that  fork 
No.  3,  giving  254  vibrations  a  second,  had  to  move  towards  the 
ear  with  a  velocity  of  8*734  feet  to  give  the  note  produced  by 
256  vibrations  a  second  emanating  from  a  fixed  point ;  so  a 
star  sending  forth  the  ray  which  vibrates  590  million  million 
times  a  second,  will  have  to  move  towards  the  eye  with  a  velocity 
of  28,740  miles  per  second  to  give  the  colour  produced  when 
ray  T>1  emanates  from  a  stationary  flame. 
February  8,  1872. 
