  A description of the canonical formulation of lineal gravity minimally
coupled to N point particles in a circular topology is given. The Hamiltonian
is found to be equal to the time-rate of change of the extrinsic curvature
multiplied by the proper circumference of the circle. Exact solutions for pure
gravity and for gravity coupled to a single particle are obtained. The presence
of a single particle significantly modifies the spacetime evolution by either
slowing down or reversing the cosmological expansion of the circle, depending
upon the choice of parameters.
