  The recently developed weakly nonlinear theory of dynamic fracture predicts
$1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$
displacement-gradients, where $r$ is measured from the tip of a tensile crack.
We show that the $1/r$ singularity does not automatically conform with the
notion of autonomy (autonomy means that any crack tip nonlinear solution is
uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and
that it does not automatically satisfy the resultant Newton's equation in the
crack parallel direction. We show that these two properties are interrelated
and that by requiring that the resultant Newton's equation is satisfied,
autonomy of the $1/r$ singular solution is retained. We further show that the
resultant linear momentum carried by the $1/r$ singular fields vanishes
identically. Our results, which reveal the physical and mathematical nature of
the new solution, are in favorable agreement with recent near tip measurements.
