We express the coverage (occupation fraction) theta in powers of time
t for four models of two-dimensional lattice random sequential adsorpt
ion (RSA) to very high orders by improving an algorithm developed by t
he present authors [J. Phys, A 29, L177 (1996)]. Each of these series
is,to the best of our knowledge, the longest at the present. We analyz
e the series and deduce accurate estimates for the jamming coverage of
the models. (C) 1998 American Institute of Physics.