338 DOC.
71
PRINCETON LECTURES
THE
GENERAL
THEORY
generalization
of
the
straight
line
of the Euclidean
geom-
etry.
For
such
a
line,
we
have
•(*)
=
-
TuaB
dxa/ds
dxB.
The left-hand
side is
to
be
replaced
by
d2xu/ds2,*
so
that
we
have
(90)
d2x"
ds2
+
r
*
dxa
dxa
_ *
ds ds =
U
We
get
the
same
line
if
we
find
the line which
gives
a
stationary
value
to
the
integral
ƒ
ds
or ƒ
y/g"jlxßdx,
[96]
between
two points
(geodesic
line).
*The
direction
vector at
a
neighbouring
point
of the
curve
results,
by a
parallel displacement along
the
line element
(dxB),
from the direction
vector
of each
point
considered.
[78]