.      ^  The  other,  more  real  and  more  difficult  case,  is  that

Motions  of  a  sys-  j-  ^^  --j  j  /.it  •  _

tern.  of  the  motion  of  a  system  of  bodies  m  any  way  con-

nected, whose  proper  motions  are  altered  by  the  conditions  of  their
connection.  There  is  a  new  elementary  conception  about  the
measurement  of  forces  which  some  geometers  declare  to  be  logi-
cally deducible  from  antecedent  considerations,  and  to  which  they
would  assign  the  place  and  title  of  a  fourth  law  of  motion.  For
the  sake  of  convenience,  we  may  make  it  into  a  fourth  law  of  mo-
tion ;  but  such  is  not  its  philosophical  character.  The  idea  is,  that
forces  which  impress  the  same  velocity  on  different  masses  are  to
each  other  exactly  as  those  masses ;  or,  in  other  words,  that  the
forces  are  proportional  to  the  masses,  as  we  have  seen  them,  under
the  third  law  of  motion,  to  be  proportional  to  the  velocities.  All
phenomena,  such  as  the  communication  of  motion  by  collision,  or
in  any  other  way,  have  tended  to  confirm  the  supposition  of  this
new  kind  of  proportion.  It  evidently  results  from  this,  that  when
we  have  to  compare  forces  which  impress  different  velocities  on
unequal  masses,  each  must  be  measured  according  to  the  product
of  the  mass  upon  which  it  acts  by  the  corresponding  velocity.
This  product  is  called  by  geometers  quantity  of  motion ;  and  it  de-
termines the  percussion  of  a  body,  and  also  the  pressure  that  a
body  may  exercise  against  any  fixed  obstacle  to  its  motion.
