8
DOC.
1
MECHANICS LECTURE NOTES
~`~
-
d"dy
_
Left-hand
side
( )
=
_
Ix
-y
hence
_
(dy
tdt
xY
Analogous equations
hold for the
other
axes.
Free
Fall. Force of
Gravity
Practical
and
CGS-Unit of Mass
We
measure
time
in
average seconds,
1
of the
aver.
solar
day,
and
24.60.60
lengths
in
cm.
1 cm
is
the hundredth
part
of the
distance
between
two
marks
of
a
specific
meter-stick
kept
in Sevres
near
Paris.
Besides the
quantities that depend
only
on
length and time
I
`~
I
,
our equation
~dt2
)
of
motion
contains
two
additional
quantities,
namely m
and
X
..
It
suffices to establish
a
unit for
one
of these
quantities,
because the
equations
of
motion
make
it
possible
then
to establish
the
second
one.
[p. 12]
For
if
we
have
defined
a
unit for
m,
then
we can
define
mB
=K
as
the unit of
force
that
force which
imparts
to
the
unit
of
mass
the acceleration
1.
Conversely,
if
we
have
established
a
unit
for
the
force,
than
the unit
mass
is
that
mass
to which
the
force
1
imparts
the acceleration
1.
From the theoretical
point
of
view it
does
not matter for which
of the
quantities
we
will establish
a unit,
but from
a
pragmatic point
of
view it does.
Earlier
(before
Gauss) one
could[13]
A unit for the
force can
be defined
in
the
following way
in Paris
the earth
exerts
a quite
specific
force
on
1
cc
water at
4°.
I call
this
unit of
force
1
gram.
(In addition,
the
kg
is
also
used.)
This
definition
suffers
(for precise
investigations)
from
the
following
drawback.
If
people
who
are
not in Paris wish to
measure a
force
accurately,
they
must
compare
the
force
to
be measured
with
the force that terrestrial
gravitation
exerts
on
1
cc
water in
Paris.
To
this extent
the
application
of the definition
is
cumbersome.
[p. 13]
But the situation
is
different
if
the unit of
mass
(also
called
"gram")
as
the
mass
of
one cc
water at
4°.
In
this
definition,
which
now
in
physical
investigations
no
particular
location
on
the
earth
plays a
role. The
mass
1
gr can
be
realized at
once
at
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