the ISGMR measurements to longer isotopic chains. This provides strong motivation for measuring the ISGMR strength in unstable nuclei, a focus of current investigations at the new rare isotope beam facilities at RIKEN, GANIL, GSI, and NSCL [93–96]. Combined with the value of K$_{∞}$ = 240 ± 10 MeV obtained from the ISGMR and IS- GDR data [31, 65, 73, 97], we now have “experimental” values of both K$_{∞}$ and K$_{τ}$ which, together, can provide a means of selecting the most appropriate of the interactions used in EOS calculations. For example, this combination of “experimental” values for K$_{∞}$ and K$_{τ}$ essentially rules out a vast majority of the Skyrme-type interactions currently in use in nuclear structure calculations [90, 98]. Similar conclusions were reached for EOS equations in Refs. [99, 100]. We have measured the strength distributions of the isoscalar giant resonances (ISGMR, ISGDR, ISGQR, and HEOR) in the even-A 112 − $^{124}$Sn isotopes via inelastic scattering of 386-MeV α particles at extremely forward angles, including 0 $^{◦}$. The extracted parameters for these resonances are in good agreement with previously-obtained values where available. The ISGMR centroid energies are significantly lower than those predicted for these isotopes by recent calculations and point to the need for further theoretical exploration of applicable nuclear structure effects, especially the role of pairing in ISGMR strength calculations in the open-shell nuclei. The asymmetry-term, K$_{τ}$ , in the expression for the nuclear incompress- ibility has been determined to be − 550 ± 100 MeV from the ISGMR data in Sn isotopes and is found to be consistent with a number of indirectly extracted values for this parameter. We wish to thank the RCNP staff for providing high-quality α beams required for these measurements. This work has been supported in part by the US-Japan Cooperative Science Program of the JSPS, and by the National Science Foundation (Grants No. INT03-42942, VI. ACKNOWLEDGMENTS V. SUMMARY 24