From  hf  in  the  circle^
draw  h  k  parallel  to/6^
and  cutting  d  g  ia  k;
then  d  k  will  be  the
vertical  projection  of  a


Kg.  14.
radius  of  the  circle  perpendicular  to  e/.  Then  on  the  major  axis,
ef,  and  minor  semi-axis,  d  k,  describe  an  ellipse;  that  ellipse  will
be  the  required  vertical  projection  of  the  circle.
The  horizontal  projection  is  obtained  by  a  precisely  similar
process,  the  rule  of  Article  24  being  now  used  to  find  the  angle
which  the  given  plane  makes  with  the  horizontal  plane  of  pro-
jection.
The  two  ellipses  are  both  touched  by  a  pair  of  tangents,  M  i».
Digitized  by  VjOOQIC


16  GEOMETBY  OF  MACHINERY.
L  I,  perpendicular  to  X  X;  and  the  diameters,  Z  m,  L  M,  are  the
projections  of  one  diameter  of  the  circle^viz.,  that  diameter
in  which  the  plane  A  B  C  is  cut  at  right  angles  hy  a  plane  parallel
to  X  X.  Tine  perpendicular  distance,  N  n,  between  the  two
tangents  is  equal  to  the  diameter  of  the  circle  multiplied  by  the
cosine  of  the  angle  which  the  giT^n  plane  makes  with  X  X^  and
is  bisected  bj  the  line  D  d.
Digitized


by  Google


17


CHAPTER  IL

OF  THE  HOnOVS  OF  PRIMARY  MOVINO  PIECES  IK  ICACHIHES.
Section  L — General  Eooplanationa.
