  Using the FOCUS spectrometer with photon beam energies between 20 and 160
\gev, we confirm the existence of a diffractively photoproduced enhancement in
$K^+K^-$ at 1750 \mevcc with nearly 100 times the statistics of previous
experiments. Assuming this enhancement to be a single resonance with a
Breit-Wigner mass shape, we determine its mass to be $1753.5\pm 1.5\pm 2.3$
\mevcc and its width to be $122.2\pm 6.2\pm 8.0$ \mevcc. We find no
corresponding enhancement at 1750 \mevcc in $K^*K$, and again neglecting any
possible interference effects we place limits on the ratio $\Gamma (X(1750) \to
K^*K)/\Gamma (X(1750) \to K^+K^-)$. Our results are consistent with previous
photoproduction experiments, but, because of the much greater statistics,
challenge the common interpretation of this enhancement as the $\phi (1680)$
seen in $e^+e^-$ annihilation experiments.
