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This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system $\Omega \left(M_m^{\ell }\right)$ on the space of $(m,\ell )$-velocities of a smooth manifold $M$. Here we show that the characteristic system of $\Omega \left(M_m^{\ell }\right)$ agrees with the Lie algebra of $Aut\left({ℝ}_m^{\ell }\right)$, the structure group of the principal fibre bundle ${\check{M}}_m^{\ell }⟶J_m^{\ell }\left(M\right)$, hence it is projectable to an irreducible contact system on the space of $(m,\ell )$-jets ($=\ell$-th order contact elements of dimension $m$) of $M$. Furthermore, we translate to the language of Weil bundles the structure form...