366  Prof.  A.  Cayley  on  a  Bicyclic  Chuck, 
which  is  the  centre  of  the  block  (3) ;  and  D  rotates  about  the 
point  A,  which  is  the  centre  of  the  segments  (4),  each  hole  being 
capable  of  describing  a  complete  circle ;  and  the  distances  A  B, 
BC,  CD,  and  DA  are  (within  limits)  adjustable  to  any  given 
values :  the  distance  of  the  holes  C,  D  is  made  equal  to  that  of 
the  two  pegs  next  referred  to. 
Connected  herewith  by  means  of  cylindrical  pegs  working  in 
the  holes  C,  D  respectively,  we  have  a  carrying-frame ;  viz.  the 
fourth  plane  contains  two  sides  (13)  of  this  carrying-frame, 
and  two  moveable  bars  (14),  attached  to  the  remaining  two  sides 
(15)  of  the  carrying-frame,  and  having  on  their  lower  surfaces 
the  pegs  which  work  in  the  holes  C  and  D  respectively— each 
bar  being  free  to  rotate  about  one  extremity,  and  being  clamp- 
able  at  the  other  extremity  so  as  to  allow  the  two  pegs  to  ber  ad- 
justed at  a  given  distance  from  each  other.  And  then  in  the  fifth 
plane  we  have  the  remaining  two  sides  (15)  of  the  carrying-frame. 
Rigidly  connected  with  the  carrying-frame  we  have  the  draw- 
ing-board ;  or,  to  make  the  whole  more  complete,  this  should  be 
adjustable  to  any  given  position  in  regard  to  the  carrying-frame 
by  giving  it  two  sliding  motions  crosswise,  and  a  rotating  motion, 
in  the  manner  of  an  eccentric  chuck. 
To  convert  the  apparatus  into  an  oval  chuck,  we  remove  alto- 
gether the  carrying-frame ;  and  in  the  third  plane  we  fix  to  the 
sides  (8)  of  the  handle-frame  two  bars  at  right  angles  to  these 
sides,  by  means  of  pegs  on  the  lower  surfaces  of  these  bars 
fitting  tightly  into  holes  on  the  sides  (8)  (which  holes  and  the 
ends  of  the  bars  are  shown  in  the  figure),  in  such  wise  that  these 
bars  include  between  them  the  piece  (9),  which  is  thereby 
kept  in  a  direction  at  right  angles  to  the  sides  (8),  and  thus 
slides  between  the  two  bars.  There  are  thus  in  the  handle-frame 
two  lines  at  right  angles  to  each  other,  which  pass  through  the 
fixed  points  A  and  B  respectively ;  so  that,  now  connecting  the 
drawing-board  directly  with  the  handle-frame,  the  apparatus 
has  become  an  oval  chuck,  viz.  the  curve  traced  out  on  the 
drawing-board  will  be  an  ellipse.  The  drawing-board  should 
be  adjustable  to  any  given  position  in  regard  to  the  handle- 
frame,  in  like  manner  as  it  was  to  any  given  position  in  regard 
to  the  carrying-frame ;  it  is  easy  to  arrange  as  to  this. 
It  is  hardly  necessary  to  remark  that  the  pencil  should  have 
two  sliding  motions  crosswise,  so  as  to  allow  it  to  be  adjusted  to 
any  given  position ;  and  a  small  up-and-down  motion,  so  that  it 
may  be  loaded  to  press  with  the  proper  force  upon  the  drawing- 
board. 
The  variety  of  forms,  even  with  a  fixed  adjustment  of  the 
chuck,  only  the  position  of  the  pencil  being  altered,  is  very  con- 
siderable: among  them  we  have  bent  ovals  and  pear-shapes, 
passing  through  cuspidal  forms  into  bent  figures-of-eight. 
