  The formula existing in the literature for the ADM mass of 2D dilaton gravity
is incomplete. For example, in the case of an infalling matter shockwave this
formula fails to give a time-independent mass, unless a very special coordinate
system is chosen. We carefully carry out the canonical formulation of 2D
dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity
one must add a boundary term to the bulk Hamiltonian to obtain a well-defined
variational problem. This boundary term coincides with the numerical value of
the Hamiltonian and gives the correct mass which obviously is time-independent.
