  For a large class of systems of o.d.e.'s which have first integrals, the
method of arrays yields the following results:
  i) The first integrals $I$ can be found by solving systems of linear
equations.
  ii) How the first integral $I$ responds to changes in the system $S$.
  iii) An easy way for finding the first integral for a special class of first
integrals if they exist.
