.*.  the  density  is  diminished  one-half  early  in  the  fourth  stroke.
7.  The  manometer  has  to  register  a  pressure  exceeding  that  of  the
r.tmosphere  by  three  times.
.*.  its  length  must  be  not  less  than  §-  x  30  =  45  inches.
[n'  -  n  =  2w%,  see  Art.  1 1 7.]

8.  Weight  of  water  discharged  per  minute
1     5    0    1000      50P0tt.
■TV


4    2  16  16


lbs.
EXAMPLES.  39

9.  Weight  of  water  discharged  per  minute

7T    3        1000     30007r„

since  the  effective  range  of  the  piston  is  only
33-3l£=f  feet.
10.  The  exhaustion  is  accompanied  by  cooling  which  is  sometimes
sufficient  to  cause  condensation  of  the  vapour

/4\5     1024

11.  The  density  has  become  (  -  J  =  — —  of  its  original  amount.
•  '•  oToi  =  '67232  of  the  air  has  been  pumped  out.
31^5

12.  The  increased  pressure,  due  to  the  escape  of  carbonic  acid  gas,
would  drive  out  some  of  the  water  and  .*.  the  displacement  being
increased  without  increase  of  weight,  the  tension  of  the  rope  would  be
diminished.
13.  Let  x  feet  be  occupied  by  air.
x        33


5~52+a7,
x2  +  52#- 165=0,
(x+55)(x-3)  =  0,
x=3  as  the  negative  root  cannot  apply  to  this  problem.
14.  The  float  rises  out  of  the  water  as  the  water  rise's  higher  in  the
bell,  owing  to  the  increase  of  density  of  the  air  displaced  by  the  upper
part  of  it.
Examples.
P-F

1.  Weight  of  water  displaced  =  — ^—  x  W=P  —  PfJ

.'.  the  bell  is  in  equilibrium,  and  as  in  Art.  184  this  equilibrium  is
unstable.
2.  After  three  strokes,  the  height  of  the  mercury

=  (-)  x  30  =  12 1  inches  nearly.
