Hyperscaling in the Ising model on the simple cubic lattice

High-temperature series for the second spherical moment $M_2=\Sigma {\overrightarrow{\mathrm{x}}}^{}{x}^2〈{\sigma }_0{\sigma }_{\overrightarrow{\mathrm{x}}}〉$ are presented to 15 terms for the spin-$\frac{1}{2}$ Ising model, on both the simple cubic and body-centered-cubic lattices. These results are combined with previously known series to study hyperscaling to 15 terms on the simple cubic lattice. Some of the evidence suggests a violation of hyperscaling.