On  a  sheet  of  paper  let  us  mark  down  by  a  point  (Fig.  68)
the  place  occupied  by  the  earth  in  relation  to  the  sun.t
From  this  point  o,  we  draw  a  right  line  terminating  at  a,  the
sun's  noon-day  position  (for  example,  on  the  ist  of  January) ;
the  succeeding  lines  shall  touch  upon  a  a",  which  the  sun
occupies  successively  after  the  same  interval  of  time  (twenty-four

*  The  reader  should  turn  to  Kepler's  immortal  work, "  De  Motibus  Stellse
Martis,"  for  the  manifold  attempts  of  the  astronomer  to  bring  calculation
into  agreement  with  observation.  In  every  page  is  revealed  what  has  been
finely  called  "the  passionate  patience  of  genius."

*h  There  is  certainly  no  exaggeration  in  comparing  the  earth  to  a  point,
since  the  diameter  of  the  sun  is  112  times  that  of  the  earth,  and  its  mean
distance  a  little  more  than  12,000  terrestrial  diameters:  the  earth  is  but
a  microscopical  point  in  space,  if  we  compare  it  to  the  place  occupied  by
the  central  luminary.
AN  ILL  USTRA TIVE  DIA GRAM.  305

hours,  or  the  exact  duration  of  the  earth's  rotation  on  its  axis);
— and  let  us  continue  after  this  mode  until  the  sun  has  accom-
plished, by  its  own  proper  movement  from  west  to  east,  the
whole  circuit  of  the  heavens,  traversing  360  degrees  in  the
space  of  a  year.  If  we  ascribe  to
the  radius  oa  a  certain  length,
corresponding  to  a  definite  solai
diameter,  the  lengths  of  all  the
others,  corresponding  to  the  va-
riations of  the  same  diameter,
will  depend  upon  that  of  the  first,
which,  for  facility  of  calculation,
we  suppose  to  be  divided  into

One  thousand  partS.  Fl(i-  68.— Diagram  for  Kepler's  Laws.
