128  Lord  Kayleigh  on  an  Instrument 
the  direction  of  the  length  of  the  batten  produces  a  displace- 
ment proportional  to  the  force*.  The  tracing  point,  by 
which  the  movements  are  recorded,  is  at  the  other  end,  as 
nearly  as  possible  in  the  line  joining  the  two  points  of 
attachment  of  the  four  suspending  wires. 
The  longitudinal  forces  are  due  to  the  vibrations  of  pen- 
dulums hanging  from  horizontal  cross-pieces  attached  to  the 
batten  at  their  centres.  The  two  ends  of  a  wire  or  cord  are 
attached  to  the  extremities  of  a  cross-piece,  the  bob  of  the 
pendulum  being  a  mass  of  lead  (perhaps  half  a  pound)  carried 
at  the  middle  of  the  cord.  When  set  swinging  the  move- 
ments  of  the  pendulums  are  thus  parallel  to  the  batten  and 
tend  (o  displace  it  along  its  length.  In  my  apparatus  the 
length  of  the  longest  pendulum  is  3^  feet. 
Under  the  influence  of  one  pendulum  the  tracing  point 
describes  a  small  simple  harmonic  motion  along  the  length 
of  the  batten.  In  order  to  draw  a  curve  of  sines  the  smoked 
glass  destined  to  receive  the  record  should  move  vertically 
in  its  own  plane.  I  found  it  more  convenient  and  sufficient 
for  my  purpose  to  substitute  a  movement  of  rotation.  A  disk 
(like  the  face-plate  of  a  lathe)  revolves  freely  in  a  vertical 
plane  round  a  horizontal  axis.  To  this  disk  a  piece  of  smoked 
glass  is  cemented  and  the  tracing  is  taken  near  the  circum- 
ference, the  axis  of  rotation  being  at  the  same  level  as  the 
tracing  point,  so  that  the  movement  of  vibration  is  radial. 
The  disk  must  be  made  to  revolve  slowly  and  with  uniform 
angular  velocity.  To  effect  this  I  employed  a  sand-clock,  a 
device  which  works  better  than  would  be  expected  |-  The 
sand,  carefully  sifted  and  dried,  is  contained  in  a  vertical 
metal  tube  of  about  1  inch  diameter,  and  escapes  below  through 
a  small  aperture  of  size  to  be  determined  by  trial.  On  the 
sand  rests  a  weight,  of  such  diameter  as  to  fit  the  tube  ea-ily  ; 
and  this  in  its  descent  rotates  the  disk  by  means  of  a  thread, 
of  which  the  free  part  is  vertical  while  the  remainder  engages 
a  circumferential  groove.  The  descent  of  the  weight  is 
practically  independent  of  the  quantity  of  sand  remaining  at 
any  time  t.  It  is  scarcely  necessary  to  say  that  the  revolving 
parts  must  be  so  weighted  as  to  keep  the  thread  tight. 
The  advantages  cf  the  apparatus  depend  of  course  upon 
the   facility  with  which  a  number  of  vibratorv  movements 
*  la  strictness  this  presupposes  the  fulfilment  of  a  condition  involving 
the  period  of  the  force  and  that  of  free  vibration  under  the  influence  of 
the  spring,  which  it  is  scarcely  necessary  to  enter  upon. 
t  tt  was  used  hy  H.  Draper  to  drive  an  equatorialiy  mounted  telescope. 
}  See  Xote  at  end  of  paper, 
