  Using the approach of autonomous Hamiltonian dynamical system, we attempt to
estimate the as yet unknown upper limit on the size of the galactic halo
surrounding galaxies (lenses). The key to determine the size of the halo is to
determine the maximum radius up to which stable material circular orbits are
admissible. We shall illustrate the approach by considering a solution of the
Weyl gravity containing a halo parameter $\gamma$. The upper limit for several
observed lenses are calculated for a typical value of $gamma$ for definiteness,
with and without the cosmological constant $\Lambda $. These lenses (all having
Einstein radius $R_{\text{E}}\approx 10^{23}$ cm) consistently yield an upper
limit $R_{\text{max}}^{\text{stable}}$($\simeq 4.25\times 10^{27}$ cm) inside
the de Sitter radius only when $\gamma$ is \textit{negative}, while a positive
$\gamma$ yields $R_{\text{max}}^{\text{% stable}}$ always exceeding the de
Sitter radius.
