(70a) α = κM/4π
where M denotes the mass generating the field. It is easy to verify that
this solution satisfies approximately the field-equation outside the
mass M.
Let us now investigate the influences which the field of mass M will
have upon the metrical properties of the field. Between the lengths and
times measured locally on the one hand, and the differences in
co-ordinates _dx__{ν} on the other, we have the relation
_ds²_ = _g__{μν} _dx__{μ} _dx__{ν}.
For a unit measuring rod, for example, placed parallel to the _x_ axis,
we have to put
_ds²_ = -1, _dx₂_ = _dx₃_ = _dx₄_ = 0
then -1 = _g_₁₁_dx₁²_.
If the unit measuring rod lies on the _x_ axis, the first of the
equations (70) gives
_g₁₁_ = -(1 + α/_r_).