  We show how a formula concerning ``vicious walkers'' (which basically are
nonintersecting lattice paths) on the cylinder given by P.J. Forrester can be
proved and generalized by using the Lindstr\"om--Gessel--Viennot method, after
having things set up in the right way. We apply the corresponding results to
the (thermodynamic limit of the) free energy of the ``lock step model of
vicious walkers'', thus completing (and in one instance correcting) the work of
Forrester . Moreover, we also show how a related formula given by I. Gessel and
C. Krattenthaler can be obtained from the same ``point of view''.
