for  Compounding  Vibrations.  129 
can  be  combined  *.  It  is  as  easy  to  record  the  effect  of  a 
number  of  pendulums  as  of  a  single  one,  the  contribution  in 
each  case  being  proportional  to  the  amplitude  of  vibration. 
In  my  instrument  there  are  six  pendulums,  the  shortest  of 
such  length  as  to  vibrate  about  twice  as  quickly  as  the 
longest.  The  frequencies  are  in  fact  somewhat  as  the  numbers 
5,  6,  7,  8,  9,  10.  No  precise  adjustment  was  attempted, 
the  object  being  in  fact  rather  to  avoid  anything  specially 
simple. 
The  lengths  of  the  pendulums  were  chosen  so  as  to  afford 
an  illustration  of  the  vibrations  constituting  white  light.  Of 
course  a  complete  physical  representation  of  light  from  the 
sun  or  from  the  electric  arc  would  need  a  much  larger  range 
of  frequency.  But  we  may  suppose  this  light  filtered  through 
media  capable  of  sensibly  absorbing  the  ultra- red  and  ultra- 
violet, while  still  remaining  white  so  far  as  the  eye  could  tell, 
even  with  the  aid  of  a  prism.  The  range  of  an  octave,  for 
which  provision  is  made,  then  amply  suffices. 
The  number  of  pendulums  may  seem,  and  perhaps  is,  rather 
small.  The  frequency,  e.  g.  7,  given  by  one  of  the  pendulums 
must  be  taken  to  represent  a  range  from  6J  to  7 -J,  with  an 
error  therefore  up  to  1  in  14.  Such  an  error  will  be  serious 
after  7  vibrations,  but  not  so  for  3  or  4  vibrations.  Hence  if 
we  limit  ourselves  to  sequences  of  3  or  4  waves,  the  repre- 
sentation is  about  good  enough. 
Connected  with  the  above  is  the  question  what  amplitudes 
of  vibration  are  to  be  assigned  to  the  various  pendulums.  It 
would  not  be  difficult  to  give  effect  to  an  assigned  law  of 
spectrum  intensity  whether  suggested  by  theory  or  found  in 
observation.  It  is  to  be  remembered,  however,  that  such 
laws  relate  to  averages,  and  do  not  give  the  relative  ampli- 
tudes at  any  particular  time,  which  will  indeed  vary  fortuitously 
over  a  rather  large  range.  I  thought  it  therefore  unnecessary 
to  be  very  particular  in  this  respect.  The  vibrations  of  the 
shorter  pendulums  die  down  more  rapidly  than  the  slower 
ones.  By  giving  the  former  an  advantage  at  starting  a  some- 
what wide  range  is  covered. 
The  tracings  presented  no  general  features  that  might  not 
have  been  anticipated.  A  few  specimens  are  reproduced — 
one  showing  the  operation  of  the  longest  and  shortest  pen- 
dulums alone,  the  others  the  effect  of  all  the  pendulums. 
*  The  principle  of  mechanical  addition  is  employed  in  an  instrument 
devised  by  Michelson. 
Phil.  Mag.  S.  6.  Vol.  11.  No.  61.  Jan.  190G.  K 
