The  result  at  which  we  have  arrived  may  be  otherwise  stated
thus:*  If  Pi,  <?!  contain  any  new  variable  z  in  the  first  degree;
if  p2,  q2  contain  it  in  the  second  and  lower  degrees ;  if  pz,  q3  in
the  third,  and  so  on;  then  the  eliminant  will  in  general  contain
this  variable  in  the  mnm  degree.
It  is  evident  that  the  results  of  this  and  of  the  last  article  are
equally  true  if  the  equations  had  been  written  in  the  homo-
geneous form  aQxm  +  &c,  because  the  suffixes  in  the  two  forms
mutually  correspond.  And  again,  from  symmetry  it  follows  that
the  result  of  this  article  would  be  equally  true  if  the  equations
had  been  written  in  the  form  amxm  +  rna^x^y  4-  &c,  where  the
suffix  of  any  coefficient  corresponds  to  the  power  of  x  which
it  multiplies,  instead  of  to  the  power  of  y.
