  We provide necessary and sufficient conditions on the derived type of a
vector field distribution $\Cal V$ in order that it be locally equivalent to a
partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first
order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$, $q\geq 1$. This result
fully generalises the classical Goursat normal form. Our proof is constructive:
it is proven that if $\Cal V$ is locally equivalent to a partial prolongation
of $\Cal C^{(1)}_q$ then the explicit construction of contact coordinates
algorithmically depends upon the integration of a sequence of geometrically
defined and algorithmically determined integrable Pfaffian systems on the
ambient manifold.
