  We give bounds on the first non-zero eigenvalue of the scalar Laplacian for
both the Page and the Chen-LeBrun-Weber Einstein metrics. One notable feature
is that these bounds are obtained without explicit knowledge of the metrics or
numerical approximation to them. Our method also allows the calculation of the
invariant part of the spectrum for both metrics. We go on to discuss an
application of these bounds to the linear stability of the metrics. We also
give numerical evidence to suggest that the bounds for both metrics are
extremely close to the actual eigenvalue.
