  We derive analytic solutions for the potential and field in a one-dimensional
system of masses or charges with periodic boundary conditions, in other words
Ewald sums for one dimension. We also provide a set of tools for exploring the
system evolution and show that it's possible to construct an efficient
algorithm for carrying out simulations. In the cosmological setting we show
that two approaches for satisfying periodic boundary conditions, one overly
specified and the other completely general, provide a nearly identical
clustering evolution until the number of clusters becomes small, at which time
the influence of any size-dependent boundary cannot be ignored. Finally we
compare the results with other recent work with the hope of providing
clarification over differences these issues have induced. We explain that
modern formulations of physics require a well defined potential which is not
available if the forces are screened directly.
