This paper presents a measurement of \mbox{$J/\psi$,$\psi'$}
differential cross
sections in $p\bar{p}$ collisions at $\sqrt{s} = 1.8~\mbox{TeV}$.  The
cross sections are measured above 4~\gevc\ in the central region
($|\eta| < 0.6$) using the dimuon decay channel.  The fraction of
events from $B$ decays is measured, and used to calculate $b$ quark
cross sections and direct \mbox{$J/\psi$,$\psi'$} cross sections.  The direct cross
sections are found to be more than an order of magnitude
 above theoretical expectations.