$$ \frac{d \phi}{ds} = \frac{\partial \phi}{\partial x_{\mu}}
\frac{\partial x_{\mu}}{\partial s} $$
so that
$$ \psi = \frac{\partial \phi}{\partial x_{\mu}} \frac{dx_{\mu}}{ds} $$
is also an invariant for all curves which go out from a point in the
continuum, _i.e._, for any choice of the vector _dx__{μ}. From which
follows immediately that