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Results are presented from a partial wave analysis of a sample of centrally produced mesons in the reaction $\mathrm{pp}\ensuremath{\rightarrow}{p}_{\mathrm{slow}}({K}_{S}{K}_{S}){p}_{\mathrm{fast}}$, with 800 GeV/c protons incident on a liquid hydrogen target. The meson system is found to be predominantly $S$ wave in the mass range between ${K}_{S}{K}_{S}$ threshold and $1.55\mathrm{GeV}{/c}^{2}$. The ${f}_{0}(1500)$ is observed in this region. Above $1.55\mathrm{GeV}{/c}^{2}$ two solutions are possible, one with mainly $S$ wave and another with mainly $D$ wave. This ambiguity prevents a unique determination of the spin of the ${f}_{J}(1710)$ meson.