DOC.
71
PRINCETON LECTURES 279
PRE-RELATIVITY PHYSICS
ently,
from
a
right-handed
system
to
a
left-handed
system,
from the
Axv.
There
is a
gain
in
picturesqueness
in
regard-
ing
a
skew-symmetrical
tensor
of
rank
2
as a
vector
in
space
of three
dimensions,
but it
does
not represent
the
exact nature
of
the
corresponding quantity
so
well
as
considering
it
a
tensor.
We
consider
next
the
equations
of
motion
of
a con-
tinuous medium. Let
p
be
the
density,
u,
the
velocity
components
considered
as
functions
of
the co-ordinates and
the
time,
Xv
the volume
forces
per
unit
of
mass,
and
pvo
the
stresses
upon
a
surface
perpendicular to
the
tr-axis
in
the direction
of
increasing
xv.
Then
the
equations
of
motion
area,
by
Newton’s
law,
P
duv
dt
dp,c
dxo
+
pXv
in
which
duv/dt
is
the
acceleration
of
the
particle
which
at
time
t
has
the co-ordinates
xv.
If
we
express
this
accelera-
tion
by
partial
differential
coefficients,
we
obtain,
after
dividing
by
p,
(16)
du,
du,__1
dfK,
dt "*+
dx,
U'
p
dx,
^
'
We
must
show
that
this
equation
holds
independently
of the
special
choice of the Cartesian
system
of co-ordinates.
(uv)
is
a
vector,
and therefore
duv/dt
is
also
a
vector.
duv/dxo
is
a
tensor
of
rank
2,
duv/dxo
uT
is
a
tensor
of
rank
3.
The
second
term
on
the
left results from
contraction
in
the
indices
o,
T.
The
vector
character
of the second
term
on
the
right
is
obvious.
In
order that the
first
term
on
the
right may
[19]