For  the  motion  in  the  direction  AC  can  neither  ac-
celerate nor  retard  the  approach  of  the  body  to  the  line
BD  which  is  parallel  to  AC,  (Art.  29.  Ex.  S.)  ;  hence,
the  body  will  arrive  at  BD,  in  the  same  time  that  it  would
have  done,  had  no  motion  been  communicated  to  it  in  the
direction  AC,  that  is  in  T''.  In  the  same  manner,  the
motion  in  the  direction  AB  can  neither  make  the  body


30


THE    COMPOSITION    AND


approach  to,  nor  recede  from,  CD;  therefore,  in  conse-
quence of  the  motion  in  the  direction  AC,  it  will  arrive
at  CD  in  the  same  time  that  it  would  have  done,  had
no  motion  been  communicated  in  the  direction  AB,  that  is
in  T".  Hence  it  follows  that,  in  consequence  of  the  two
motions,  the  body  will  be  found  both  in  BD  and  CD
at  the  end  of  T",  and  will  therefore  be  found  in  D,  the
point  of  their  intersection.
Also,  since  a  body  in  motion  continues  to  move  uni-
formly forward  in  a  right  line,  till  it  is  acted  upon  by
some  external  force  (Art.  27-)?  the  body  A  must  have
described  the  right  line  AD,  with  an  uniform  motion.
(39.)  To  illustrate  this  proposition,  suppose  a  plane
ABDC,  as  the  deck  of  a  ship,  to  be  carried  uniformly
forward,  and  let  the  point  A  describe  the  line  AC  in  T";
also,  let  a  body  move  uniformly  in  this  plane  from  A  to
B,  in  the  same  time.  Complete  the  parallelogram  BC,
and  draw  the  diagonal  AD.  Then  at  the  end  of  T"  the
body,  by  its  own  motion,  will  arrive  at  B;  also  by  the
motion  of  the  plane,  AB  will  be  brought  into  the  situation.
