when  the  body  P  descends,  it  is  solely  by  the  action  of
gravity  upon  this  body  that  the  two  bodies  are  put  in
motion,  and  so  from  the  force  P  alone,  that  motion  is  ini-


parted  to  the  mass  —  -  .     In  these   conditions,  the  fall

g

will  take  place  with  a  uniformly  accelerated  motion,  but
evidently  less  rapid  than  when  the  body  P  is  entirely
free.  The  curve  traced  by  the  style  is  a  parabola,  more
open  than  in  the  case  of  a  free  fall,  and  serves  to  demon-
strate, as  we  have  before  observed,  the  velocity  Y  of  a
system,  at  the  end  of  any  time,  a  second,  for  example.
The  continuous  action  of  a  force  P  imparts,  then,  in  a

second,  to  the  mass  ---  |r  a  velocity  Y  measured  experi-

mentally.
P'-fl/

We  may  also  observe  the  velocity  V  of  a  mass  --  =-

j/

in  similar  circumstances,  by  substituting  a  weight  P'  for
the  weight  P,  and  for  the  body  drawn  a  weighty/  instead
of  p.
Now,   in  this    twofold    substitution   we    may  make
P'+2/,  in  which  case  the  mass  put  in  motion  in


P+z?  P'-h0'

both  cases  is  identical  :  --  —  being  equal  to  —  S-  ;   we

t/  </

thus  realize  the  circumstance,  that  two  motor  weights,
which  are  true  forces,  may  be  acting  the  same  time  upon

the  same  mass   —  -  ;  and  observing  the  acquired  veloci-

y

ties  Y  and  Y7  in  the  two  cases,  all  that  is  needed  to  estab-
lish the  principle  is  that  the  figures  give  the  proportion

Y  :  Y'  :  :  P  :  F,

which  is  an  interpretation  of  the  principle  of  the  propor-
tionality offerees  and  velocities  already  enunciated.
