  In calculations of the hyperfine splitting in charmonium, the contributions
of the disconnected diagrams is considered small and is typically ignored. We
aim to estimate nonperturbatively the size of the resulting error, which could
potentially affect the high precision calculations of the charmonium spectrum.
Following our work on the effects of the disconnected diagrams in unquenched
QCD presented at Lattice 2007, we study the same problem in the quenched case.
On dynamical ensembles the disconnected charmonium propagators contain light
modes which complicate the extraction of the signal at large distances. In the
fully quenched case, where there are no such light modes, the interpretation of
the signal is simplified. We present results from lattices with $a\approx 0.09$
fm and $a\approx 0.063$ fm.
